A Trackless Auxiliary Transportation Robot System for Unmanned Material Distribution of Underground Coal Mine

A Trackless Auxiliary Transportation Robot System for Unmanned Material Distribution of Underground Coal Mine | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article A Trackless Auxiliary Transportation Robot System for Unmanned Material Distribution of Underground Coal Mine Mingrui Hao, Xiaoming Yuan, Jie Ren, Yueqi Bi, Xiaodong Ji, Sihai Zhao, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4955671/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Response to the current situation of backward automation level, heavy labor intensity and high accident rate in underground coal mine auxiliary transportation system, the trackless auxiliary transportation robot system (MTATBOTS) is presented in the paper. The robot is specially designed for long-range, space-constrained and explosion-proof underground coal mine environment. With onboard perception and autopilot system, the robot can perform automated and unmanned subterranean material transportation. The paper proposes an integrated-odometry-based method to improve position estimation and mitigate location ambiguities for simultaneous localization and mapping (SLAM) in large-scale, GNSS-denied and perceptually-degraded subterranean transport roadway scenario. Additionally, the paper analyzes the robot dynamic model and presents the nonlinear control strategy for the robot to autonomously tack a planned trajectory based on the path-following error dynamic model. Finally, the proposed algorithm and control strategy are tested and validated in a virtual underground transport roadway environment relying on the simulation model of the robot system. The test result indicates that the proposed algorithm can obtain more accurate and robust robot odometry and better underground roadway mapping result compared with other SLAM solutions. Physical sciences/Engineering/Electrical and electronic engineering Physical sciences/Engineering/Mechanical engineering Physical sciences/Energy science and technology/Fossil fuels/Coal underground coal mine auxiliary transportation robot SLAM explosion-proof autonomous driving Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 1. Introduction Coal mine intellectualization is the core technical support for the high-quality development of coal industry. Especially for the underground coal mine, the hash working condition, heavy labor intensity and frequent mining accidents make it increasingly difficult for enterprises to recruit employees engaged in subterranean environment works. Hereby, the construction of production automation, equipment robotization and unmanned operation based on the application of artificial intelligence, robot technology, industrial Internet, cloud platform and other labor-saving technologies in the whole underground mining process has become the main development goal of coal industry in the future[ 1 , 2 ]. Compared to the main transportation system which is responsible for the coal transportation, the auxiliary transportation system of underground coal mine is in charge of the transport of production consumables, working equipment and subterranean personnel. Because of the diverse transport objects, complex driving environments and heavy transport tasks, the auxiliary transportation system has become one of the most labor-intensive and accident-prone parts in the whole underground mining process. Therefore, an intelligent and unmanned auxiliary transportation system can effectively reduce the subterranean labors, increase the mining efficiency and lower the mining accident rate. Correspondingly, in the intelligent development plan for coal mines proposed by the Chinese government, the intelligent underground auxiliary transportation development goal with features of standardized loading, intelligent distribution, automatic transfer and unmanned transportation is proposed to promote the development of coal industry[ 3 ]. However, the current auxiliary transportation of underground coal mine mainly uses manually driven vehicles to perform transport tasks. Depending on different transportation conditions, auxiliary transport equipment can be broadly classified into two categories: railed locomotives and trackless vehicles. Compared with railed locomotives, the trackless auxiliary vehicles can perform transport task from point to point, avoiding transshipment process, which is more efficient, flexible and labor-saving. Currently, trackless auxiliary transportation mainly depends on explosion-proof rubber wheeled vehicles. However, these vehicles are mainly driven by explosion-proof diesel engines, depending on hydraulic or mechanical transmission, relying on human operation, which are hard to achieve automatic control and unmanned transportation. In addition, the existing trackless auxiliary transport system adopts different types of vehicles for diverse transport objects, resulting in a wide variety of transport equipment and heavy maintenance work. In short, relying on the existing equipment base, it is difficult to support the standardization and automation of underground transportation. In response to above problems, in this paper, a trackless auxiliary transportation robot system (MTATBOTS) used for material and consumables distribution in the underground coal mine is introduced, which is powered by explosion-proof lithium batteries and equipped with explosion-proof wired control system. The robot can be controlled by remote operation platform or onboard autopilot system to execute unmanned underground transportation. The paper describes the system composition and functional implementation of MTATBOTS, aiming at providing an intelligent transport terminal and feasible solution for intelligent auxiliary transportation of underground coal mine. The remainder of the paper is organized as follows: Section 2 presents an overview of the related unmanned technology and equipment development of intelligent mining; The general structure of MTATBOTS is shown in Section 3; Section 4 describes the autopilot system design of the robot; The robot dynamic model and control strategy are presented in Section 5; In Section 6, the simulation test results of the robot virtual model are presented; The paper ends with a conclusion in section 7. 2. Prior Works and Technical Challenges In order to improve transportation efficiency and reduce labor intensity, various types of automated and unmanned transport equipment are gradually put into the mining process of both coal mine and other mines. Generally speaking, the mining area is considered to be an ideal experimental site and technology landing scenario for some advanced technologies, such as autonomous driving. Because it can provide a specific enclosed area with no legal barriers and a regular route for vehicles driving at a low speed. In recent years, the autonomous driving has made big progress in some mining and machinery companies, especially in some open-pit mines. The productivity benefits of the autonomous open-pit mining truck fleet have helped reduced costs by around 20 per cent, and the autonomous trucks effectively shield employees from dangerous situations[ 2 ]. In the open-pit mining area, benefiting from the advantages of global navigation satellite system (GNSS), the autonomous driving system can more easily get the accurate location information of mining trucks, which is the premise and basis of automatic and unmanned transportation. In addition, the transport objects of open-pit mines are relatively fixed, mainly focusing on coal or other ores, which makes it easier to achieve standardized and automated transport process. However, considering that GNSS signals cannot spread in subterranean environment, precise localization of autonomous driving vehicles in underground terrain must be solved in other solutions. Additionally, the special features of underground coal mine environment pose challenges to the autonomous driving vehicle, including limited line-of-sight, large variations in illumination, obscurants (e.g., dust, fog, and moisture), restricted working space, self-similarity long-narrow roadways, degraded perception and sensing, constrained communication, radio frequency propagation challenges, explosion-proof requirements of electric components, increasingly complicated environment with the mining operations. And most challenging of all, however is the combination of all the above features. Thus, researchers have done much work to promote the application of relative technologies. Dong et al. proposed analytical and iterative velocity-free localization methods in complex and dynamic mining conditions[ 4 ]. Through the utilization of active sources, laser rangefinders, proximity sensor, in conjunction with the localization method, realize the accurate localization of autonomous rock drilling jumbo and explosive charging vehicle in deep underground mine. But the method relies on the sensor network deployed in advance, which will increase economic cost and infrastructure investment when used in large-scale underground coal mine roadways. Ebadi et al. presented a large-scale autonomous mapping and positioning method for exploration of perceptually-degraded subterranean environments based on the technology of simultaneous localization and mapping SLAM[ 5 – 7 ]. Depending on the centralized multi-robot SLAM system, robust estimate of the trajectories of multiple robots in large-scale, unknown, and complex subterranean environment can be obtained. Another algorithm named range-aided pose-graph-based SLAM was introduced by Funabiki et al. to execute position estimate in subterranean perceptual degraded environment under the help of sparsely deployed ranging beacons[ 8 ]. Kim et al. developed an autonomous driving robot that drives and returns along a planned route in an underground mine tunnel through a machine-vision-based road sign recognition algorithm[ 9 ]. Stefaniak et al . integrated the inertial measurement unit IMU and dynamic time warping DTW algorithms to locate the underground mine LHD and obtained robust performance[ 10 , 11 ]. A search-and-rescue robot system with explosion-proof and waterproof function used for remote sensing of the underground coal mine environment was introduced by Zhao et al. [ 12 ]. In addition, the ultra-wide band UWB technology is increasingly being used to locate personnel and equipment in underground coal mines[ 13 ], and it is also considered to be helpful for underground driverless vehicle. However, limited by the features of underground coal mine roadway, the construction of UWB positioning network covering the entire auxiliary transportation roadways is hard to implement and high cost. And considering the relative high speed and high safety requirements of underground transport vehicles, the dynamic positioning accuracy and signal stability of UWB in the underground environment need to be further testified and improved. Briefly, the above state-of-art solutions provide useful and positive references for intelligent unmanned auxiliary transportation of underground coal mine. Moreover, in recent years, several kinds of autonomous driving technology validation models of underground coal mine transport vehicles have been developed by equipment manufacturers and research institutions in China, as shown in Fig. 1 . These models are mainly converted from the existing explosion-proof trackless rubber wheeled vehicles by adding environmental sensors, such as Lidar, camera and millimeter wave radar. Some autonomous driving algorithms for underground coal mine environment were developed and testified depending on these prototypes. However, the automatic driving modification of existing explosion-proof trackless vehicles can hardly meet the standardized, continuous and unmanned requirements of intelligent auxiliary transport systems. MTATBOTS introduced in the paper is a new type of robotized coal mine auxiliary transport system, which is specially designed for the unmanned material distribution of underground coal mine. In the following article, the structural composition and functional design of the robot system will be described in details. (a) shows the traditional explosion-proof rubber wheeled vehicle for material transport; (b) shows the autonomous driving prototype of underground coal mine transport vehicle 3. General Structure of MTATBOTS MTATBOTS is designed for automated and unmanned transportation in underground coal mine. With modular structural design, MTATBOTS breaks through the conventional structure of explosion-proof trackless vehicles and divides the transport operations into different functional units. For different transport objects, the required functional units can be combined into a suitable transport vehicle, thus reducing the variety of vehicle types and facilitating standardized transportation. As shown in Fig. 2 , MTATBOTS consists of three main parts, including: Remote Monitoring Platform, Explosion-proof Wheeled Transport Robot and Multi-type Material Containers. 3.1 Remote Monitoring Platform Remote monitoring platform is the command and dispatch center of MTATBOTS. The platform can be independently arranged in the ground control center or integrated into the comprehensive dispatching system of coal mine. Remote monitoring platform has three main functions. First, it’s in charge of processing task information of required material type, underground destination and location of available wheeled transport robot. The robot can perform the transport task will be identified based on the information. Secondly, the remote monitoring platform is also responsible for calculating the global planning path of the robot from its current location to the required destination based on real-time underground traffic condition. The generated global planning path is then released to the identified robot as the task navigation information via the wireless communication network of coal mine. Third, the platform can monitor the robot’s operational status and execute remote takeover as needed to ensure transportation safety. 3.2 Explosion-proof Wheeled Transport Robot An explosion-proof wheeled transport robot (EWTBOT) used as automated-guided-vehicle is the transport actuator of MTATBOTS. EWTBOT is designed for the complex operating environment and special working conditions of underground coal mine, which equipped with the autopilot system as its control center and the explosion-proof wheeled electric chassis as its walking device. The configuration structure and chief components of the explosion-proof wheeled electric chassis are shown in Fig. 3 . The chassis is designed with a front-to-back symmetrical structure to achieve good maneuverability and bi-directional travel capability. Meanwhile, considering the limited underground working space, the chassis adopts a low-profile design with the dimensions of length 4500 mm, width 2000 mm, height 1000 mm. The chassis is powered by batteries and has zero emissions. Two blocks of explosion-proof lithium batteries are mounted in the middle of chassis, providing 64 kWh energy. The onboard energy system gives the robot a maximum driving range of 80 km to meet the demand of at least one round trip of material transportation in a large-scale underground coal mine. Furthermore, in order to solve the problems of driving range anxiety and excessive charging time faced by current explosion-proof electric vehicles, the chassis has battery quick-change function that allows it replace battery packs in ten minutes. In addition, the robot is equipped with a four-wheeled independent suspension system to achieve good driving stability when travelling in underground complicated road conditions. Hydraulic system of the chassis is powered by an explosion-proof oil pump motor to perform the braking function of the robot. The autopilot system of EWTBOT mainly includes environment perception system and decision control system. Two explosion-proof electric control boxes are symmetrically placed at the front and rear ends of the chassis to host onboard electric components and computing units. Four explosion-proof electric control boxes are arranged separately at the corners of the chassis, in which the sensors required for the environment perception system are placed. Powertrain system arrangement of EWTBOT is shown in Fig. 4 . The robot is equipped with two sets of driving units, each consisting of a 46 kW explosion-proof permanent magnet motor and a reducer with differential function. The power system enables the robot reach a maximum travel speed of 40 km/h and a maximum climbing capacity of 14°. Meanwhile, in order to obtain good passing ability in the underground limited space, the robot is equipped with two set of Ackerman steering mechanisms to perform four-wheel steering function and small turning radius. Moreover, each tire of the robot is equipped with a wheel-side enclosed wet brake. Considering the safety of braking, the brake adopts a safety type operating mode of spring-applied and hydraulically released that will be automatically locked when the robot loses power. In addition, the robot is equipped with polyurethane filled tires, increasing its adaptability to complex subterranean road conditions. The main characterized parameters of EWTBOT are listed in Table 1 . Table 1 Technical specifications of Explosion-proof Wheeled Transport Robot Items Parameters Robot Mass 5000 kg Maximum Load Capacity 5000 kg Robot Body Sizes 4500×2000×1000 mm Maximum Speed 40 km/h Climbing Capacity 14° Turning Radius ≤ 5400(outer) / ≥2800(inner) mm Maximum Driving Range 80 km Battery Capacity 64 kWh Installed Power 2×46 kW Perception Range 360° Perception Distance ≥ 20 m ①Explosion-proof electric steering gear; ②Steering swing arm; ③Steering tie rod; ④Wheel-side enclosed wet brake; ⑤Drive axle shaft; ⑥Reducer and differential gear; ⑦Explosion-proof permanent magnet motor. 3.3 Multi-type Material Containers Muti-type material containers is a series of removable top loading devices which could be quickly changed and installed on EWTBOT. As shown in Fig. 5 , several kinds of material containers are designed to meet the transportation needs of various materials during underground production in coal mines, such as anchor rods, anchor cables, building materials, pipes, meals and other spare parts or consumables. The volume and shape of the containers can be customized according to different mines’ demands. All kinds of loading containers are equipped with a unified installation interface and easy to be installed on the robot. After receiving the transportation order from the remote monitoring platform, EWTBOT selects a suitable container according to the task requirement, and then executes the material delivery task. Therefore, the robot system is conductive to the standardization and centralization of coalmine materials management and effective reduction of transport vehicle types. What’s more, the material containers can be replaced with other operating agency, such as robotic arms, lifting platforms and cable reels, to make the robot become a mobile operating platform. 4. Autopilot System of MTATBOTS 4.1 Autopilot System Configuration MTATBOTS has two working modes: the remote-control mode and the autopilot mode. When it’s in the autopilot mode, the robot can automatically perform underground transportation. The autopilot system configuration of MTATBOTS is shown in Fig. 6 , including remote monitoring platform, autopilot software platform, reference hardware platform and explosion-proof wheeled electric chassis. Except for remote monitoring platform, all the other systems are arranged on EWTBOT. Reference hardware platform mainly consists of sensing devices, positioning modules and computing unit. Autopilot software platform can be further divided into three parts: real time operating system, runtime framework and functional modules. The real time operating system adopts Ubuntu embedded operating system based on Linux core, using as interaction interface between software system and hardware platform. The runtime framework adopts robot operating system (ROS) that can provide complete development toolkit, flexible computing scheduling model and rich debugging tools. The functional modules include a series of software packages that are mainly used to implement application-level algorithms and procedures for autopilot functions, such as perception, localization, path planning and motion control. Explosion-proof wheeled electric chassis is the actuator of the autopilot system, which adopts explosion proof wire control technology to realize the horizontal and vertical motion of the robot. Compared to the variable ground transportation environment, the transport path of underground coal mine is relatively fixed. When MTATBOTS receives the transport task and destination information, its remote monitoring platform will calculate the global planning path based on the information of current underground traffic condition and available EWTBOT’s location. After receiving the start command, the identified EWTBOT will perform transport task along the global planning path. At the same time, considering that the underground coal mine roadway is an environment shared by equipment and personnel, the actual trajectory of the robot must take into account the changes of ahead obstacle information. Therefore, the implementation of MTATBOTS autopilot mode mainly depends on the EWTBOT autopilot system. The autopilot system equipped on EWTBOT adopts a four-level functional architecture, including the sensing layer, the perception layer, the decision layer and the execution layer. The sensing layer mainly consists of several kinds of sensors such as Lidar, Radar, RGB-D camera and IMU, providing the information of obstacles distribution and robot posture parameters. The perception layer calculates and fuses the collected information to estimate the robot’s location and obstacle distance. The decision layer determines the obstacle avoidance strategy and calculates the certain future period trajectory of the robot based on the above information. The execution layer is in charge of controlling the robot to travel along the local planning path provided by decision layer. 4.2 Environment Perception System of EWTBOT Accurate and fast environment perception is the premise and foundation for the safe and autonomous driving of EWTBOT in underground coal mine. Unfortunately, the auxiliary transportation roadway environment EWTBOT worked is often perceptual degradation, such as low or zero illumination, self-similar visual and geometric environment, and sometimes obscurants (fog, dust), as shown in Fig. 7 . Meanwhile, considering the large scale of underground coal mine auxiliary transportation roadways (some of roadways are dozens of kilometers long), these conditions make it difficult to achieve desired perception results through traditional methods. Furthermore, due to the explosion-proof requirement of underground coal mine, the commonly used detection sensors, such as Lidar and camera, can’t be directly applied in EWTBOT. The environment perception system of EWTBOT is specially designed for the conditions of underground transportation roadways. In order to get good perception performance in the underground perceptual degradation roadways, the combination of multi-type sensors, including Lidar, RGB-D Camera, Radar and IMU, is applied in EWTBOT’s environment perception system. In addition, all the sensors are specially explosion-proof designed for the underground coal mine environment. As shown in Fig. 8 , all the optical sensors have been enclosed in explosion-proof electric boxes on EWTBOT. Under the help of specially designed explosion-proof glasses, the sensors can work normally in underground roadways of wet, dusty and explosive-risk atmosphere. (a) shows the main explosion-proof electric box; (b) shows the corner explosion-proof electric box. The arrangement and detection range of perception sensors applied on EWTBOT are depicted in Fig. 9 . EWTBOT equips with two Lidar at the front and rear, each with a field of detection horizon of 270 degrees, thus achieving full coverage of the robot's surrounding environment detection. Meanwhile, two millimeter-wave radars are installed separately in the front and rear of EWTBOT, mainly for the detection and tracking of moving objects in the forward direction of the robot. Additionally, a total of 10 RGB-D cameras are arranged around the vehicle to achieve video coverage in the main directions of the robot. Additionally, several laser distance sensors are arranged on both sides of the robot, which can quickly obtain the real-time distance information between the body and both sidewalls of the roadways, using for the judgement of the robot’s lateral position in the tunnel. 4.3 Localization strategy of EWTBOT Accurate estimation of self-localization in underground coal mine transport roadways is another challenge for autopilot system of EWTBOT. Because GNSS-based localization is not applicable in subterranean environment, simultaneous localization and mapping based on the information collected by environment perception system is essential for the robot localization. However, the perceptual degradation of underground roadway environment is typically challenging for no matter Lidar-based or visual-based SLAM. In order to increase the localization accuracy, our approach is to use Lidar-centric SLAM solution fused by visual, IMU and wheel rotation information, which can obtain more accurate and robust robot odometry. Moreover, in order to mitigate the inevitable accumulation of global drift over large-scale underground roadways when using SLAM to position the robot, auxiliary localization methods are simultaneously introduced into the strategy. It is important to note that when the robot travels in underground coal mine, its driving range is strictly limited between the sidewalls of the roadway. Compared with the length along the roadway direction, the roadway width (generally no more than 6 m ) is almost negligible. Therefore, the localization of EWTBOT mainly depends on its accurate odometry along the subterranean roadway direction. For above reason, our localization strategy is to use multi-modal information to obtain the accurate robot odometry, and then utilize effective auxiliary positioning methods to correct and optimize the robot trajectory and posture, aiming at achieving accurate vehicle position coordinates and heading angles to conduct the robot’s automatic motion control. Figure 10 shows the overview of EWTBOT’s localization system architecture. As shown in the diagram, EWTBOT localization system mainly consists of two parts: onboard localization system and auxiliary localization system. A. Onboard Localization Solution Depending on EWTBOT’s onboard hardware platform, onboard localization solution is implemented through a complementary muti-modal SLAM system which includes two main components: the front-end and the back-end. 1 Front-end: Integrated Odometry. The front-end of onboard SLAM system is in charge of abstracting the saw sensor data into the robot odometry. With the different type of data collected by relevant sensors, three components of the robot’s odometry information can be obtained separately, including Lidar-inertial odometry, wheel odometry and visual-inertial odometry. The Lidar-inertial odometry component can fuse the Lidar point cloud matching results with the IMU data to derive the robot position and trajectory[ 14 , 15 ]. Our solution develops on top of an existing open-source implementation LIO-SAM[ 16 ]. This tightly-coupled Lidar inertial odometry framework can achieve accurate, real-time mobile robot trajectory estimation and map-building. In addition, the framework is suitable for multi-sensor fusion by formulating odometry atop a factor graph, thus additional sensor measurements, such as wheel odometry and UWB position information, can be incorporated into the framework as new factors to eliminate the sensor drift, which has significant importance especially in the large-scale underground roadway environment[ 17 ]. The visual-inertial odometry component fuses the matching result of sparse ORB features[ 18 ] between consecutive images filmed by RGB-D camera and the IMU data to estimate the robot odometry while reconstructing the environment[ 19 , 20 ]. Our solution builds upon the existing open-source implementation ORB-SLAM3[ 21 ], which is state-of-the-art visual odometry framework can perform visual SLAM with RGB-D camera. But considering that the visual odometry is not reliable in the low-texture underground roadway environment and is susceptible to illumination, the visual odometry component plays an auxiliary and complementary role in our strategy. The wheel odometry component can figure out the robot driving range based on the robot speed and heading angle gathered by motor encoder and IMU. However, affected by perceptually-degraded subterranean environment and poor road surface condition, each kind of odometry information can be biased or even missing when the robot travelling along the roadway. For examples: Long-range, corridor-like subterranean roadways and similar-structure intersections make Lidar-based odometry prone to drift; Uneven and slippery roadway surface make the wheel odometry inaccurate; Poor and drastic change illumination, dust, water puddles and non-Lambertian surfaces render visual odometry unreliable[ 22 ]. Above all, it is hard to obtain accurate and robust localization result depends on single source odometry information. Therefore, Kalman Filter is introduced in our strategy to consider all the three odometry components simultaneously and the integrated odometry information of the robot which is more reliable and robust can be figured out accordingly. 2. Back-end: Localization Optimization. The back-end of onboard SLAM system is in charge of optimizing robot trajectory and global map estimates by fusing the key frame information of integrated odometry from the front-end and the landmark position information from the priori roadway map via a nonlinear estimator approach named as pose graph optimization (PGO)[ 23 ]. The priori map of underground roadways can be obtained from the geographic information system (GIS) of coal mine or mapped from the onboard SLAM system. Position information of significant landmarks, such as underground traffic signs and signals, key intersections, artificial markings, can be marked in the map as the priori localization markers. When the robot travels along subterranean roadways, these markers can be captured by onboard RGB-D cameras under the help of YOLO[ 24 ]. YOLO produces a 2D bounding box around the detected marker, and then the position of the marker can be estimated according to the range of the bounding box center measured by the depth channel of RGB-D camera. The pose graph of EWTBOT is depicted in Fig. 11 . When the back-end receives the front-end odometry information, a serial of key frames is periodically instantiated in every 1 m displacement and the corresponding poses and odometry edges are added to the robot’s pose graph. When the back-end receives the landmark measurements, a landmark point whose position can be obtained from the priori roadway map is instantiated in the pose graph and an edge is added between the landmark and the corresponding observation pose. Based on the landmark position, the robot’s trajectory can be optimized accordingly and spurious loop closure that occurred frequently in perceptually-degraded subterranean roadways can be mitigated effectively. Therefore, the problem of the optimization of the robot’s odometry and trajectory can be formulated as pose graph optimization by integrating the priori landmarks position constrains. And the problem is implemented in our strategy based on GTSAM[ 25 ] framework and use the Levenberg-Marquardt algorithm to solve the nonlinear least squares problem. 5. Auxiliary Localization Solution In order to increase the robustness and the accuracy of EWTBOT localization, more auxiliary positioning solutions should be added besides the priori subterranean roadway information. In the absence of sufficient landmarks information provided for the robot odometry optimization, the arrangement of radio beacons which can publish position information to the robot is an effective and economic way to realize localization optimization, because its omnidirectional observability, ease of deployment, and robustness to the perceptually degraded subterranean environment[ 8 ]. In our strategy, UWB devices are adopted as radio beacons to provide the global positioning information for EWTBOT. Typically, positioning method that use radio beacons require a dense distribution of beacons. However, considering that deployment of enough radio beacons for large-scale underground roadways will significantly increase economic cost and the effective radio-ranging of each beacon is also severely limited by subterranean roadway geography, a limited number of explosive-proof UWB ranging beacons are sparsely deployed in the roadways, mainly in sharp turns and roadway intersections. These ranging beacons can provide global position information for the robot to eliminate accumulated errors. As shown in Fig. 10 , when the robot travels into the UWB beacon operation area, a beacon range edge will be added in pose graph between the beacon and the corresponding observation pose as a global constrain to correct the odometry and optimize the robot trajectory. In addition, all the UWB beacons are uniquely identified so that the robot can quickly locate itself when passing by, effectively reducing the computational burden and avoiding spurious loop closure. Furthermore, the remote monitor platform of MTATBOTS can also interact with the robot trajectory through manually transmit position information to the robot in cases that the operator identifies a loop closure which has not been detected by the onboard SLAM system or correct the spurious loop closure. 5. Motion Control of EWTBOT Driving stabilization and collision avoidance are two of the most crucial concerns when EWTBOT works in the underground roadways of limited space and multiple traffic participants[ 26 ]. The motion control strategy of the robot adopts a hierarchical control architecture consisting of decision-making layer and motion execution layer. In decision-making layer, a smooth and collision-free driving trajectory that meets kinematic and dynamic constraints of the robot is calculated based on the changing environmental information. In motion execution layer, the robot motion is decoupled into the lateral and longitudinal motion under Frenet coordinate system[ 27 ] with the planned driving path as the coordinate axis. The lateral motion controller manipulates the steering system according to the deviation between the robot actual position and the planned trajectory. The longitudinal controller controls the traction motor and the brake system to track the position and speed of the planned trajectory. In this section, the motion model of EWTBOT is described based on dynamics analysis, and then the motion control scheme of the robot is presented. 5.1 Motion forms of EWTBOT EWTBOT is equipped with two sets of Ackerman steering mechanisms at the front and rear respectively, which can realize a variety of motion forms to improve its maneuverability. Three motions forms of the robot are shown in Fig. 12, including front/rear wheel steering, four-wheel steering and crab walking. Compared with front wheel steering or rear-wheel steering, four-wheel steering can effectively reduce the turning radius of the robot. Crab walking make the robot travel diagonally, i.e., the driving direction is deflected by an angle between the longitudinal axis of the vehicle. In the crab walking mode, the robot can easily perform obstacle avoidance maneuvers in subterranean roadways of limited space. Moreover, the two steering systems serve as a backup for each other. If one of the steering system fails, the robot can still complete the steering maneuver. Front/Rear wheel steering (b) Four-wheel steering (c) Crab walking Figure 12. Multi-type motion forms of the explosion-proof wheeled transport robot. G is the robot CoG, positioned at X h and Y h in the global Cartesian coordinate system XOY . xGy is the robot body coordinate system with the robot’ longitudinal axis as x -axis and its lateral direction as y -axis. L is the robot axis distance. D is the robot wheel distance. P is the instantaneous center of steering of the robot. \(\:\varphi\:\) is the yaw angle of the robot. R min is the robot minimum turning radius. R max is the robot maximum turning radius. 5.2 Dynamic Model of EWTBOT The effectiveness of motion control of EWTBOT should be based on correct and reliable vehicle model[ 28 , 29 ]. A feasible local path planning trajectory generated by the decision-making layer needs to satisfy the kinematic and dynamic constraints of the robot[ 30 , 31 ]. In order to develop a reasonable control scheme and mitigate the computational burden, a planar 2-DoF bicycle model[ 32 ] is employed to represent the robot, depicted in Fig. 13(a), which utilizes small angle assumptions and the approximation that the tires on each axle can be lumped together. G is the center of gravity of the robot, which positioned at X h and Y h in the global Cartesian coordinate system XOY . And \(\:\varphi\:\) is the robot yaw angle between the earth coordinate system X -axis and the robot longitudinal x -axis. Thus, the robot position and posture in the earth fixed coordinate system can be defined by the vector \(\:[\begin{array}{ccc}{X}_{h}&\:{Y}_{h}&\:\varphi\:\end{array}{]}^{T}\) . Assuming that the robot drives at a constant speed v x in the direction of the robot’s longitudinal x -axis, the bicycle model consisting of the lateral and yaw dynamics in the robot body coordinate system xGy , the force and the torque equilibrium of the 2-DOF bicycle model in lateral direction can be derived as follows according to geometric relationships and dynamic analysis: $$\:\sum\:{F}_{y}=m({\dot{v}}_{y}+{v}_{x}\cdot\:\dot{\varphi\:})={F}_{yf}{cos}{\delta\:}_{f}+{F}_{yr}{cos}{\delta\:}_{r}\approx\:{C}_{\alpha\:f}\cdot\:{\alpha\:}_{f}+{C}_{\alpha\:r}\cdot\:{\alpha\:}_{r}$$ 1 $$\:\sum\:M={I}_{z}\ddot{\varphi\:}=a\cdot\:{F}_{yf}{cos}{\delta\:}_{f}-b\cdot\:{F}_{yr}{cos}{\delta\:}_{r}\approx\:a\cdot\:{C}_{\alpha\:f}\cdot\:{\alpha\:}_{f}-b\cdot\:{C}_{\alpha\:r}\cdot\:{\alpha\:}_{r}$$ 2 where F y is the force of the model in the direction of the robot lateral y -axis; M is the turning torque about the z -axis; m is the robot mass; I z is the moment of inertia about the z -axis; \(\:\varphi\:\) is yaw angle; v x and v y are the components of the velocity vector in the center of gravity along the x -axis and the lateral y -axis of the robot body coordinate system; β is the sideslip angle of the robot in the center of gravity. F yf and F yr are the lateral tire forces, perpendicular to the rolling direction of the tire, and proportional to the slip angle, α , between the local velocity vector and its forward direction; α f and α r respectively denote the front and rear tire slip angles; a and b are the distances from the center of gravity of the vehicle to the front and rear axles; δ f and δ r are the steering angles of the front and rear wheels with respect to the robot, which assumed to be small angles; C αf and C αr are the tire stiffness of the front and the rear tire pairs, respectively. Based on the velocity vectors’ geometric relationships of the robot’s center of gravity, the front and rear tire, depicted in Fig. 13(b), the slip angles can be obtained in the following equations: $$\:{\alpha\:}_{f}=-\left({\delta\:}_{f}-{\theta\:}_{f}\right)=\frac{\dot{\varphi\:}\cdot\:a+{v}_{y}}{{v}_{x}}-{\delta\:}_{f}\approx\:\beta\:+\frac{\dot{\varphi\:}\cdot\:a}{{v}_{x}}-{\delta\:}_{f}$$ 3 $$\:{\alpha\:}_{r}=-\left(\frac{\dot{\varphi\:}\cdot\:b-{v}_{y}}{{v}_{x}}-{\delta\:}_{r}\right)\approx\:\beta\:+{\delta\:}_{r}-\frac{\dot{\varphi\:}\cdot\:b}{{v}_{x}}$$ 4 where \(\:{v}_{y}/{v}_{x}={tan}\beta\:\approx\:\beta\:\) . Dynamic analysis of the 2-DOF model. Velocity vectors geometrical relationship of the model Figure 13. Two-degree-of-freedom model of the explosion-proof wheeled transport robot. G is the robot CoG; P is the instantaneous center of steering of the robot; F yf and F yr are the lateral tire forces of the front and rear axle; F xf and F xr are the components of force provided by the front and rear tires, respectively, in their direction of rolling; V is the robot velocity vector in the center of gravity, which has a longitudinal component v x and a lateral component v y , which identify the sideslip angle β ; V f is the front tire velocity vector; V r is the rear tire velocity vector. Furthermore, in order to meet the needs of the robot multiple motion forms, the control of the steering angles of the front and rear tire follows the following rule: $$\:{\delta\:}_{r}=\xi\:\cdot\:{\delta\:}_{f}$$ 5 where \(\:\xi\:\in\:\) [-1,1], \(\:\xi\:\) is the control scale factor. Next, by bringing Equations ( 3 ), ( 4 ) and (5) into Equations ( 1 ) and ( 2 ), the parametric 2-DOF vehicle model and the expression for the lateral position of the robot can be written as follows: $$\:\left\{\begin{array}{c}\ddot{y}=\left(\frac{{C}_{\alpha\:f}+{C}_{\alpha\:r}}{m{v}_{x}}\right)\dot{y}+\left(\frac{{C}_{\alpha\:f}\cdot\:a-{C}_{\alpha\:r}\cdot\:b}{m{v}_{x}}-{v}_{x}\right)\dot{\varphi\:}+\left(\frac{-{C}_{\alpha\:f}+\xi\:\cdot\:{C}_{\alpha\:r}}{m}\right){\delta\:}_{f}\\\:\ddot{\varphi\:}=\left(\frac{a\cdot\:{C}_{\alpha\:f}-b\cdot\:{C}_{\alpha\:r}}{{I}_{z}{v}_{x}}\right)\dot{y}+\left(\frac{{a}^{2}\cdot\:{C}_{\alpha\:f}+{b}^{2}\cdot\:{C}_{\alpha\:r}}{{I}_{z}{v}_{x}}\right)\dot{\varphi\:}+\left(\frac{-a\cdot\:{C}_{\alpha\:f}-\xi\:\cdot\:b\cdot\:{C}_{\alpha\:r}}{{I}_{z}}\right){\delta\:}_{f}\end{array}\right.$$ (6) Where y is the robot lateral displacement; \(\:\varphi\:\) is the yaw angle; δ f is the steering angle of the front wheel. By defining \(\:X=[\begin{array}{cc}\dot{y}&\:\dot{\varphi\:}\end{array}{]}^{T}\) as the state vector and \(\:U=\left[{\delta\:}_{f}\right]\) as the control vector, the robot model described in Eq. (6) can be converted into the state equation as: $$\:\dot{X}=AX+BU$$ 7 where $$\:A=\left[\begin{array}{cc}\frac{{C}_{\alpha\:f}+{C}_{\alpha\:r}}{m{v}_{x}}&\:\frac{{C}_{\alpha\:f}\cdot\:a-{C}_{\alpha\:r}\cdot\:b}{m{v}_{x}}-{v}_{x}\\\:\frac{a\cdot\:{C}_{\alpha\:f}-b\cdot\:{C}_{\alpha\:r}}{{I}_{z}{v}_{x}}&\:\frac{{a}^{2}\cdot\:{C}_{\alpha\:f}+{b}^{2}\cdot\:{C}_{\alpha\:r}}{{I}_{z}{v}_{x}}\end{array}\right],\:B=\left[\begin{array}{c}\frac{-{C}_{\alpha\:f}+\xi\:\cdot\:{C}_{\alpha\:r}}{m}\\\:\frac{-a\cdot\:{C}_{\alpha\:f}-\xi\:\cdot\:b\cdot\:{C}_{\alpha\:r}}{{I}_{z}}\end{array}\right]$$ 5.3 Path-following error dynamic model The control objective of EWTBOT is to make the position and the heading angle of the robot track the planned reference path. Using the desired path as the reference line, the robot movement can be decoupled separately as the lateral and longitudinal motion based on Frenet coordinate system. In the coordinate system, the direction along the desired path is taken as the longitudinal axis, and the direction perpendicular to the reference path is taken as the lateral axis[ 33 ]. As shown in Fig. 14 , the reference desired path of EWTBOT, on which the robot is supposed to drive, is depicted as the curve s . In addition, d represents the distance from the center of gravity of the robot to the closest point Q on the desired path, i.e., the orthogonal projection point of G on the reference path. Robot position under the Frenet coordinate system can be depicted as the longitudinal displacement s and the lateral displacement d . Thus, \(\:\dot{\varvec{s}}\) is the robot’s desired velocity at its projection point Q , along the tangential direction of the desired path. Under the global Cartesian coordinate system XOY , the actual position and the desired position on the reference path of the robot can be represented separately in position vectors of \(\:\overrightarrow{x}\) and \(\:{\overrightarrow{x}}_{r}\) . \(\:\theta\:\) and \(\:{\theta\:}_{r}\) respectively represent the robot’s actual heading angle and the desired heading angle on the reference trajectory. And then, defining d as the lateral position error and \(\:\left(\theta\:-{\theta\:}_{r}\right)\) as the heading error of the robot, the objective of the robot’s later control is to globally asymptotically minimize the two kinds of path-following errors. Besides, defining \(\:\left(\left|\overrightarrow{v}\right|-\left|\dot{s}\right|\right)\) as the robot’s velocity magnitude error, the objective of the robot’s longitudinal control is to minimize the longitudinal position error and the velocity error. In addition, assuming that \(\:\overrightarrow{\tau\:},\overrightarrow{n}\) are orthogonal unit vectors at point G , \(\:{\overrightarrow{\tau\:}}_{r},{\overrightarrow{n}}_{r}\) are orthogonal unit vectors at point Q , and the directions of \(\:\overrightarrow{n}\) and \(\:{\overrightarrow{n}}_{r}\) are consistent with the vectors of the actual velocity and the desired velocity of the robot, the lateral displacement d and the lateral velocity \(\:\dot{d}\) can be attained as follows: $$\:{\overrightarrow{x}}_{r}+d{\overrightarrow{n}}_{r}=\overrightarrow{x}\Rightarrow\:d=\left(\overrightarrow{x}-{\overrightarrow{x}}_{r}\right)\cdot\:{\overrightarrow{n}}_{r}$$ 8 $$\:\dot{d}=\left(\dot{\overrightarrow{x}}-{\dot{\overrightarrow{x}}}_{r}\right)\cdot\:{\overrightarrow{n}}_{r}+\left(\overrightarrow{x}-{\overrightarrow{x}}_{r}\right)\cdot\:{\dot{\overrightarrow{n}}}_{r}=\left|\overrightarrow{v}\right|{cos}⟨\overrightarrow{\tau\:},{\overrightarrow{n}}_{r}⟩=\left|\overrightarrow{v}\right|{sin}\left(\theta\:-{\theta\:}_{r}\right)$$ 9 Where \(\:\dot{\overrightarrow{x}}=\left|\overrightarrow{v}\right|\overrightarrow{\tau\:}\) ; \(\:{\dot{\overrightarrow{x}}}_{r}=\dot{s}{\overrightarrow{\tau\:}}_{r}\) ; \(\:{\dot{\overrightarrow{n}}}_{r}=-\kappa\:{\overrightarrow{\tau\:}}_{r}\dot{s}\) ; \(\:\kappa\:\:\) represents the curvature of the desired path. And the robot desired velocity can be calculated in the following equation: $$\:\dot{s}=\frac{\left|\overrightarrow{v}\right|\text{cos}\left(\theta\:-{\theta\:}_{r}\right)}{1-\kappa\:\cdot\:d}$$ 10 Considering that \(\:\theta\:=\varphi\:+\beta\:\) and \(\:{v}_{x}=\left|\overrightarrow{v}\right|{cos}\beta\:，{v}_{y}=\left|\overrightarrow{v}\right|{sin}\beta\:\) , the equations ( 9 ) and ( 10 ) can be written as follows: $$\:\dot{d}={v}_{y}\text{cos}\left(\varphi\:-{\theta\:}_{r}\right)+{v}_{x}{sin}\left(\varphi\:-{\theta\:}_{r}\right)\approx\:{v}_{y}+{v}_{x}\left(\varphi\:-{\theta\:}_{r}\right)$$ $$\:\dot{s}=\frac{{v}_{x}\text{cos}\left(\varphi\:-{\theta\:}_{r}\right)-{v}_{y}{sin}\left(\varphi\:-{\theta\:}_{r}\right)}{1-\kappa\:\cdot\:d}\approx\:\frac{{v}_{x}-{v}_{y}\left(\varphi\:-{\theta\:}_{r}\right)}{1-\kappa\:\cdot\:d}$$ 11 $$\:\left\{\begin{array}{c}\dot{d}={v}_{y}\text{c}\text{o}\text{s}\left(\varphi\:-{\theta\:}_{r}\right)+{v}_{x}{sin}\left(\varphi\:-{\theta\:}_{r}\right)\approx\:{v}_{y}+{v}_{x}\left(\varphi\:-{\theta\:}_{r}\right)\\\:\dot{s}=\frac{{v}_{x}\text{cos}\left(\varphi\:-{\theta\:}_{r}\right)-{v}_{y}{sin}\left(\varphi\:-{\theta\:}_{r}\right)}{1-\kappa\:\cdot\:d}\approx\:\frac{{v}_{x}-{v}_{y}\left(\varphi\:-{\theta\:}_{r}\right)}{1-\kappa\:\cdot\:d}\end{array}\right.$$ where \(\:\left(\varphi\:-{\theta\:}_{r}\right)\) is assumed as a small angle. Defining that \(\:{e}_{d}=d\) is the lateral error and \(\:{e}_{\varphi\:}=\varphi\:-{\theta\:}_{r}\) is the heading error, the following equations can be attained: $$\:{v}_{y}={\dot{e}}_{d}-{v}_{x}{e}_{\varphi\:}$$ $$\:{\dot{v}}_{y}={\ddot{e}}_{d}-{v}_{x}{\dot{e}}_{\varphi\:}$$ $$\:\dot{\varphi\:}={\dot{e}}_{\varphi\:}+{\dot{\theta\:}}_{r}$$ $$\:\ddot{\varphi\:}={\ddot{e}}_{\varphi\:}+{\ddot{\theta\:}}_{r}\approx\:{\ddot{e}}_{\varphi\:}$$ 12 $$\:\left\{\begin{array}{c}{v}_{y}={\dot{e}}_{d}-{v}_{x}{e}_{\varphi\:}\\\:{\dot{v}}_{y}={\ddot{e}}_{d}-{v}_{x}{\dot{e}}_{\varphi\:}\\\:\dot{\varphi\:}={\dot{e}}_{\varphi\:}+{\dot{\theta\:}}_{r}\\\:\ddot{\varphi\:}={\ddot{e}}_{\varphi\:}+{\ddot{\theta\:}}_{r}\approx\:{\ddot{e}}_{\varphi\:}\end{array}\right.$$ Next, by bringing Equations ( 12 ) into Equations (6), the path-following error dynamics model of EWTBOT can be written as follows: $$\:{\ddot{e}}_{d}-{v}_{x}{\dot{e}}_{\varphi\:}=\left(\frac{{C}_{\alpha\:f}+{C}_{\alpha\:r}}{m{v}_{x}}\right)\left({\dot{e}}_{d}-{v}_{x}{e}_{\varphi\:}\right)+\left(\frac{{C}_{\alpha\:f}\cdot\:a-{C}_{\alpha\:r}\cdot\:b}{m{v}_{x}}-{v}_{x}\right)\left({\dot{e}}_{\varphi\:}+{\dot{\theta\:}}_{r}\right)+\left(\frac{-{C}_{\alpha\:f}+\xi\:\cdot\:{C}_{\alpha\:r}}{m}\right){\delta\:}_{f}$$ $$\:{\ddot{e}}_{\varphi\:}=\left(\frac{a\cdot\:{C}_{\alpha\:f}-b\cdot\:{C}_{\alpha\:r}}{{I}_{z}{v}_{x}}\right)\left({\dot{e}}_{d}-{v}_{x}{e}_{\varphi\:}\right)+\left(\frac{{a}^{2}\cdot\:{C}_{\alpha\:f}+{b}^{2}\cdot\:{C}_{\alpha\:r}}{{I}_{z}{v}_{x}}\right)\left({\dot{e}}_{\varphi\:}+{\dot{\theta\:}}_{r}\right)+\left(\frac{-a\cdot\:{C}_{\alpha\:f}-\xi\:\cdot\:b\cdot\:{C}_{\alpha\:r}}{{I}_{z}}\right){\delta\:}_{f}$$ 13 $$\:\left\{\begin{array}{c}{\ddot{e}}_{d}-{v}_{x}{\dot{e}}_{\varphi\:}=\left(\frac{{C}_{\alpha\:f}+{C}_{\alpha\:r}}{m{v}_{x}}\right)\left({\dot{e}}_{d}-{v}_{x}{e}_{\varphi\:}\right)+\left(\frac{{C}_{\alpha\:f}\cdot\:a-{C}_{\alpha\:r}\cdot\:b}{m{v}_{x}}-{v}_{x}\right)\left({\dot{e}}_{\varphi\:}+{\dot{\theta\:}}_{r}\right)+\left(\frac{-{C}_{\alpha\:f}+\xi\:\cdot\:{C}_{\alpha\:r}}{m}\right){\delta\:}_{f}\\\:{\ddot{e}}_{\varphi\:}=\left(\frac{a\cdot\:{C}_{\alpha\:f}-b\cdot\:{C}_{\alpha\:r}}{{I}_{z}{v}_{x}}\right)\left({\dot{e}}_{d}-{v}_{x}{e}_{\varphi\:}\right)+\left(\frac{{a}^{2}\cdot\:{C}_{\alpha\:f}+{b}^{2}\cdot\:{C}_{\alpha\:r}}{{I}_{z}{v}_{x}}\right)\left({\dot{e}}_{\varphi\:}+{\dot{\theta\:}}_{r}\right)+\left(\frac{-a\cdot\:{C}_{\alpha\:f}-\xi\:\cdot\:b\cdot\:{C}_{\alpha\:r}}{{I}_{z}}\right){\delta\:}_{f}\end{array}\right.$$ By defining \(\:{E}_{rr}={\left[\begin{array}{cccc}{e}_{d}&\:{\dot{e}}_{d}&\:{e}_{\varphi\:}&\:{\dot{e}}_{\varphi\:}\end{array}\right]}^{T}\) as the state vector, the path-following error dynamics model described in Eq. ( 13 ) can be converted into the state equation as: $$\:{\dot{E}}_{rr}=\stackrel{\sim}{A}{E}_{rr}+\stackrel{\sim}{B}U+\stackrel{\sim}{C}{\dot{\theta\:}}_{r}$$ 14 where $$\:\stackrel{\sim}{A}=\left(\begin{array}{cccc}0&\:1&\:0&\:0\\\:0&\:\frac{{C}_{f}+{C}_{r}}{m{v}_{x}}&\:-\frac{{C}_{f}+{C}_{r}}{m}&\:\frac{a{C}_{f}-b{C}_{r}}{m{v}_{x}}\\\:0&\:0&\:0&\:1\\\:0&\:\frac{a{C}_{f}-b{C}_{r}}{{I}_{z}{v}_{x}}&\:-\frac{a{C}_{f}-b{C}_{r}}{{I}_{z}}&\:\frac{{a}^{2}{C}_{f}+{b}^{2}{C}_{r}}{{I}_{z}{v}_{x}}\end{array}\right),\stackrel{\sim}{B}=\left(\begin{array}{c}0\\\:\frac{-{C}_{f}+\xi\:{C}_{r}}{m}\\\:0\\\:\frac{-\xi\:b{C}_{r}-a{C}_{f}}{{I}_{z}}\end{array}\right),\stackrel{\sim}{C}=\left(\begin{array}{c}0\\\:\frac{a{C}_{f}-b{C}_{r}}{m{v}_{x}}-{v}_{x}\\\:0\\\:\frac{{a}^{2}{C}_{f}+{b}^{2}{C}_{r}}{{I}_{z}{v}_{x}}\end{array}\right)$$ Furthermore, by using Euler’s approximation, Eq. ( 14 ) can be discretised at sample time t s , and the discrete-time state equation can be obtained as: $$\:{E}_{rr}\left(k+1\right)={\stackrel{\sim}{A}}_{d}{E}_{rr}\left(k\right)+{\stackrel{\sim}{B}}_{d}U\left(k\right)+{\stackrel{\sim}{C}}_{d}{\dot{\theta\:}}_{r}\left(k\right)$$ 15 where \(\:{\stackrel{\sim}{A}}_{d}={\left(I-\frac{\stackrel{\sim}{A}{t}_{s}}{2}\right)}^{-1}\left(I+\frac{\stackrel{\sim}{A}{t}_{s}}{2}\right)\) , \(\:{\stackrel{\sim}{B}}_{d}={\left(I-\frac{\stackrel{\sim}{A}{t}_{s}}{2}\right)}^{-1}\stackrel{\sim}{B}{t}_{s}\) , \(\:{\stackrel{\sim}{C}}_{d}={\left(I-\frac{\stackrel{\sim}{A}{t}_{s}}{2}\right)}^{-1}\stackrel{\sim}{C}{t}_{s}\) , and I denotes the identity matrix. 5.4 Motion Control Scheme Depending on the path-following error dynamics model, the control strategy of EWTBOT is developed as shown in Fig. 15 . When EWTBOT receives the global planning path from Remote Monitoring Platform, the onboard decision-making layer of motion control system will generate a collision-free local planning path based on the global path. The local planning path is generated according to the distribution information of surrounding obstacles provided by the robot’s environment perception system. And the path consists of a series of adjacent discrete trajectory points, each of which contains the desired position coordinates and heading angle of the robot in certain planning moment, along with the information of the robot’s desired velocity and acceleration. Meanwhile, the current position and the heading angle of the robot can be acquired through the robot localization system. The above information, as well as the robot attribute parameters, will be passed into the path-following error dynamic model of EWTBOT as input data. The motion execution layer is responsible for manipulating the explosion-proof wire-controlled system to walk along the local planning path. In our strategy, the robot motion is decoupled into the lateral and longitudinal motion under Frenet coordinate frame. The lateral motion control of the robot can be figured out by minimizing the errors of the lateral displacement and the heading angle between the robot current state and the reference trajectory point. Accordingly, the robot lateral control output will be published to the corresponding steering motor, in terms of the front-wheel and rear-wheel turning angles. In the other hand, the longitudinal motion controller is in charge of tracking the desired velocity and acceleration of the reference trajectory point based on the robot’s actual speed and acceleration. Hereby, the robot longitudinal control outputs will be published in terms of throttle and brake pressure to the traction motors and the electro-hydraulic brake system separately. 6. Simulation Testing A simulated model of EWTBOT based on ROS and a virtual scenario of underground coal mine auxiliary transport roadways are established to facilitate the simulation testing of MTATBOTS, as shown in Fig. 16 . The virtual model of EWTBOT is build according to its real size and system configuration, which equipped with simulated environment perception system and motion control system. Under the control of the path-following algorithm based on the proposed motion control strategy, the virtual robot can travel along the desired trajectory in the simulated underground roadways. Meanwhile, with the help of SLAM algorithm, the environment perception system can estimate the motion state and position of the robot based on the acquired environment information and onboard sensor data. Accordingly, the robot trajectory and the roadway map can be obtained simultaneously. In order to testify the effectiveness of localization and control strategy of EWTBOT in the virtual underground scene, several kinds of SLAM solutions are implemented relying on the simulation model to estimate the robot odometry and build the scenario map. And the algorithms are tested separately by running at the same travelling route, hereby the robot odometry figured out through different localization solutions can be compared on the basis of actual robot trajectory. Left: Virtual auxiliary transport roadway scenario of underground coal mine; Right: Simulated model of EWTBOT. Figure 17 . shows the mapping results of the virtual underground roadways obtained through four different SLAM solutions. In the simulated underground roadway scenario, the vision-based SLAM can hardly execute the localization and mapping task independently, as shown in Fig. 17 (a), because of the featureless environment and varying illumination. As for the Lidar-based SLAM, it significantly underestimates the robot motion in long symmetric corridor-like roadway scenario because of the lack of detectable geometric features. In addition, intersections with similar structure can easily bring up with spurious loop closures. The simulated scenario mapping results through Lidar-based SLAM is shown in Fig. 17 (b). While, with the fusion of IMU data and wheel odometry information of the robot, the Lidar-inertial-based SLAM can estimate the robot odometry more accurately and obtain better mapping results, as shown in Fig. 17 (c). However, subject to the cumulative errors, the robot odometry obtained by the algorithm inevitably drifts to a certain extent after a long driving route and several sharp turns, which leads to deviations in the mapping result. Finally, in the virtual underground scenario, the proposed integrated-odometry-based SLAM algorithm of the paper is tested and proved to be effective in eliminating cumulative errors and obtaining accurate mapping result, as shown in Fig. 17 (d). Under the help of priori localization vision markers and sparse global position signals provided by virtual UWB beacons installed in roadway intersections, more accurate and robust robot position and odometry can be acquired through combining Lidar-inertial odometry, visual-inertial odometry and wheel odometry. Furthermore, the robot odometry obtained by different algorithms are put into the same coordinate system and compared with the ground truth of the robot trajectory, as shown in Fig. 18 . The results shows that the proposed integrated-odometry-based localization solution and motion control strategy of the robot are feasible and effective in the simulated scenario of underground coal mine auxiliary transport roadways. (a)shows the result of Visual-based SLAM; (b) shows the result of Lidar-based SLAM; (c) shows the result of Lidar-inertial-based SLAM; (d) shows the result of integrated-odometry-based SLAM. 7. Conclusions and Future Work In this work, a new type of transport robot system MTATBOTS is introduced for intelligent auxiliary transportation of underground coal mine, aiming at executing automated and unmanned subterranean transport task. The robot system is specially designed for the explosion-proof, long-range and perception-degraded underground roadway scenario. The paper describes structural composition of the robot system and the functional implementation of the robot autopilot system. To solve the perception and localization challenges of GNSS-denied subterranean roadway environment, the Integrated-odometry-based SLAM solution is proposed and applied in the robot localization strategy. The proposed algorithm can achieve accurate and robust robot odometry and mapping result by considering Lidar-inertial odometry, visual-inertial odometry and wheel odometry simultaneously. And in order to mitigate the influence of accumulative errors of onboard sensors, the global position information provided by UWB beacons sparsely arranged in underground roadways are also taken into account in the localization algorithm. Furthermore, the robot path-following motion control strategy is presented based on the dynamic model of the robot. Finally, in order to validate the proposed localization algorithm and motion control strategy, the robot virtual model and the simulated underground coal mine auxiliary transport roadways scenario are established. The simulation results indicates that the proposed localization solution and control strategy of the robot are suitable for the auxiliary transport roadway of underground coal mine. Considering the complexity of underground transport roadway conditions, it is difficult for the simulated test scenario to reproduce the actual operating environment of the robot system. In the future, the proposed algorithms and control strategies need to be tested and modified under the real subterranean coal mine environment. As shown in Fig. 19 , the physical prototype of EWTBOT has been manufactured based on the paper’s design and simulation test results. Further testing and validation work will be carried out on the basis of the prototype. Additionally, the current robot control strategy mainly focuses on the tracking of the planning route, and the safe and smooth control strategy of autonomous collision avoidance maneuver in the narrow, space-constrained underground roadway needs to be further improved and optimized. Declarations Conflicts of Interest: The authors declare that there is no conflict of interest regarding the publication of this paper. Author Contribution Hao, Ren and Ji wrote the main manuscript text. Yuan , Bi and Zhao conducted the experiment of the manuscript . All authors reviewed the manuscript. Acknowledgement This work is supported by the Shanxi Province Key Research and Development Program Projects of China(201803D121121), the Taiyuan Institute of Technology Scientific Research Initial Funding(2022KJ095). Data Availability The experimental data used to support the findings of this study are available from the corresponding author upon request. References Hao, Y. et al. 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Optimal Trajectory Generation for Dynamic Street Scenarios in a Fren´et Frame, International Conference on Robotics and Automation , pp. 987–993, May (2010). Paden, B., ˇC´ap, M., Yong, S. Z., Yershov, D. & Frazzoli, E. A Survey of Motion Planning and Control Techniques for Self-Driving Urban Vehicles. IEEE Trans. Intell. Veh. 1 (1), 33–55 (Mar. 2016). Yang, H., Cocquempot, V. & Jiang, B. Optimal Fault-Tolerant Path-Tracking Control for 4WS4WD Electric Vehicles, IEEE Transactions on Intelligent Transportation Systems , vol. 11, no. 1, pp. 237–243, Mar. (2010). Guo, H. et al. Dual-envelop-oriented moving horizon path tracking control for fully automated vehicles, Mechatronics , vol. 50, pp. 422–433, (2018). Li, X., Sun, Z., Chen, Q. & Liu, D. An Adaptive Preview Path Tracker for Off-Road Autonomous Driving, IEEE International Conference on Control and Automation , pp. 1718–1723, (2013). González, D., Pérez, J., Milanés, V. & Nashashibi, F. Apr., A Review of Motion Planning Techniques for Automated Vehicles. IEEE Trans. Intell. Transp. Syst. , 17 , 4, (2016). Hang, P., Chen, X., Zhang, B. & Tang, T. Longitudinal Velocity Tracking Control of a 4WID Electric Vehicle. Int. Federation Automatic Control , pp. 790–795, (2018). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4955671","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":360469650,"identity":"ae6956f0-6f23-4687-8c53-285d4848d103","order_by":0,"name":"Mingrui Hao","email":"","orcid":"","institution":"China University of Mining and Technology Beijing Campus School of Mechanical Electronic and Information Engineering","correspondingAuthor":false,"prefix":"","firstName":"Mingrui","middleName":"","lastName":"Hao","suffix":""},{"id":360469652,"identity":"1ddde6ec-05f4-4c93-a078-77bb77ba2a65","order_by":1,"name":"Xiaoming Yuan","email":"","orcid":"","institution":"China Coal Technology \u0026 Engineering Group Taiyuan Research Institute Co. Ltd","correspondingAuthor":false,"prefix":"","firstName":"Xiaoming","middleName":"","lastName":"Yuan","suffix":""},{"id":360469654,"identity":"3c2733af-b6fc-4a44-aae4-3a464a6e0103","order_by":2,"name":"Jie Ren","email":"","orcid":"","institution":"Taiyuan Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Jie","middleName":"","lastName":"Ren","suffix":""},{"id":360469657,"identity":"bb12a229-6b5a-4ba2-abbb-7d99fcabf067","order_by":3,"name":"Yueqi Bi","email":"","orcid":"","institution":"China Coal Technology \u0026 Engineering Group Taiyuan Research Institute Co. Ltd","correspondingAuthor":false,"prefix":"","firstName":"Yueqi","middleName":"","lastName":"Bi","suffix":""},{"id":360469659,"identity":"1d439448-32b1-4aab-9486-a7f9f9316e80","order_by":4,"name":"Xiaodong Ji","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIie3OsQrCMBCA4SuFuNwDRET7CikFEfRhUgp2UREEcXCIFOpScK1TX6EuugqFTHV39BE6Oqnp5hQzOuSHgwTugwOw2f4wR4D/4JvJQL2ZGteIBKyppwEQU6Iado9pFQpj4uZR2UPixkWRnClsxqHo3K76wzK5DBDJvJRkTaGOQ4ELrif7jEVIcV4SHFKnvZAi05MEWYWMxl7akpcJ2Wf+LueMg2yJMCGZXEFz5X4pp6sRl3GQ4kxP/Dy6PMPX2/OS6nRvtuP+oVP/IOL7x9UQ7b7K+7Vgs9lsNvgAlWVCZtsL5jwAAAAASUVORK5CYII=","orcid":"","institution":"Shijiazhuang Tiedao University","correspondingAuthor":true,"prefix":"","firstName":"Xiaodong","middleName":"","lastName":"Ji","suffix":""},{"id":360469660,"identity":"7fb68c4e-a544-4e93-ad66-83f28dddd6ad","order_by":5,"name":"Sihai Zhao","email":"","orcid":"","institution":"China University of Mining and Technology Beijing Campus School of Mechanical Electronic and Information Engineering","correspondingAuthor":false,"prefix":"","firstName":"Sihai","middleName":"","lastName":"Zhao","suffix":""},{"id":360469661,"identity":"f4664d22-a6b6-4e1a-a01b-261dbfebd35e","order_by":6,"name":"Miao Wu","email":"","orcid":"","institution":"China University of Mining and Technology Beijing Campus School of Mechanical Electronic and Information Engineering","correspondingAuthor":false,"prefix":"","firstName":"Miao","middleName":"","lastName":"Wu","suffix":""}],"badges":[],"createdAt":"2024-08-22 06:39:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4955671/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4955671/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":65863602,"identity":"899fa4b7-75c6-42f4-a37b-99cb1df743c3","added_by":"auto","created_at":"2024-10-03 16:53:03","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":51203,"visible":true,"origin":"","legend":"\u003cp\u003eExplosion-proof rubber wheeled vehicles used in the underground coal mine\u003c/p\u003e\n\u003cp\u003e(a) shows the traditional explosion-proof rubber wheeled vehicle for material transport; (b) shows the autonomous driving prototype of underground coal mine transport vehicle\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/ad23a401653e5ff7e001f911.jpg"},{"id":65862931,"identity":"f371c2bd-98c5-437a-8db6-a0effbd279f0","added_by":"auto","created_at":"2024-10-03 16:37:02","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":64491,"visible":true,"origin":"","legend":"\u003cp\u003eThe trackless auxiliary transportation robot system used for material distribution in underground coal mine\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/7a1688811b871ecd45e9ccd7.jpg"},{"id":65862934,"identity":"714b44ca-98bc-4d63-99b2-d546a193a157","added_by":"auto","created_at":"2024-10-03 16:37:03","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":76797,"visible":true,"origin":"","legend":"\u003cp\u003eStructural configuration of the explosion-proof wheeled transport robot\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/cd1b004a93e9469052985a5e.jpg"},{"id":65864215,"identity":"df7efe45-1879-4259-a35a-91d6d64da2fe","added_by":"auto","created_at":"2024-10-03 17:01:03","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":66223,"visible":true,"origin":"","legend":"\u003cp\u003ePowertrain arrangement of the explosion-proof wheeled transport robot.\u003c/p\u003e\n\u003cp\u003e①Explosion-proof electric steering gear; ②Steering swing arm; ③Steering tie rod; ④Wheel-side enclosed wet brake; ⑤Drive axle shaft; ⑥Reducer and differential gear; ⑦Explosion-proof permanent magnet motor.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/d9b7da5939ab7cea6324e251.jpg"},{"id":65863380,"identity":"e8e1b431-b00f-48d4-8ae5-520be304e468","added_by":"auto","created_at":"2024-10-03 16:45:03","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":78372,"visible":true,"origin":"","legend":"\u003cp\u003eMulti-type material containers of the trackless auxiliary transportation robot system\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/4d742904e0c0642ca2595f52.jpg"},{"id":65863598,"identity":"312e95b1-55a0-4829-95d1-2bd8a818adde","added_by":"auto","created_at":"2024-10-03 16:53:03","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":61073,"visible":true,"origin":"","legend":"\u003cp\u003eAutopilot system configuration of the trackless auxiliary transportation robot system\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/2a467a8b4de71f0874925702.jpg"},{"id":65862932,"identity":"34ee66e3-768b-46b4-9dc9-97bd21798f42","added_by":"auto","created_at":"2024-10-03 16:37:03","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":23234,"visible":true,"origin":"","legend":"\u003cp\u003ePerceptually-degraded environment of auxiliary transport roadway in underground coal mine\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/ad0904dbde4cf7914cd621d5.jpg"},{"id":65863378,"identity":"3031ed40-51d3-41b4-881e-df62eff23a8c","added_by":"auto","created_at":"2024-10-03 16:45:03","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":44813,"visible":true,"origin":"","legend":"\u003cp\u003eThe sensors’ arrangement of environment perception system in explosion-proof electric boxes.\u003c/p\u003e\n\u003cp\u003e(a) shows the main explosion-proof electric box; (b) shows the corner explosion-proof electric box.\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/1a3d1a218c316e7d3d3d31f4.jpg"},{"id":65863600,"identity":"8f823d46-e8e0-428a-b243-6c6d4a15142b","added_by":"auto","created_at":"2024-10-03 16:53:03","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":52949,"visible":true,"origin":"","legend":"\u003cp\u003eDetection range of EWTBOT environment perception system. Top: Birds eye view of Lidar and millimeter wave radar horizon on EWTBOT; Bottom: Birds eye view of RGB-D cameras and laser distance sensors horizon on EWTBOT.\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/fc18d16e3369b745f0392114.jpg"},{"id":65862946,"identity":"f5783fb9-0c4e-4100-a40f-d43ff757b93a","added_by":"auto","created_at":"2024-10-03 16:37:03","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":120760,"visible":true,"origin":"","legend":"\u003cp\u003eArchitecture overview of EWTBOT localization strategy\u003c/p\u003e","description":"","filename":"10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/df39ed2e5bcbb989dcad2c61.jpg"},{"id":65863382,"identity":"7f65bf1d-1194-4fad-9249-6be34ee2b63a","added_by":"auto","created_at":"2024-10-03 16:45:03","extension":"jpg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":44554,"visible":true,"origin":"","legend":"\u003cp\u003eFactor graph and range measurements of EWTBOT\u003c/p\u003e","description":"","filename":"11.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/57a7aa86596affe9b1e89b0d.jpg"},{"id":65862939,"identity":"73ab8e91-f877-49d7-9a16-b3e220d5abf1","added_by":"auto","created_at":"2024-10-03 16:37:03","extension":"jpg","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":54641,"visible":true,"origin":"","legend":"\u003cp\u003eMulti-type motion forms of the explosion-proof wheeled transport robot. \u003cem\u003eG\u003c/em\u003e is the robot CoG, positioned at \u003cem\u003eX\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eY\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e in the global Cartesian coordinate system \u003cem\u003eXOY\u003c/em\u003e. \u003cem\u003exGy\u003c/em\u003e is the robot body coordinate system with the robot’ longitudinal axis as \u003cem\u003ex\u003c/em\u003e-axis and its lateral direction as \u003cem\u003ey\u003c/em\u003e-axis. \u003cem\u003eL\u003c/em\u003e is the robot axis distance. \u003cem\u003eD\u003c/em\u003e is the robot wheel distance. \u003cem\u003eP\u003c/em\u003e is the instantaneous center of steering of the robot. \u003cimg width=\"10\" height=\"21\" src=\"file:///C:/Users/adr8178/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif\"/\u003eis the yaw angle of the robot. \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003emin\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e\u003cem\u003e\u003cstrong\u003e \u003c/strong\u003e\u003c/em\u003e\u003c/sub\u003eis the robot minimum turning radius. \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e\u003cem\u003e\u003cstrong\u003e \u003c/strong\u003e\u003c/em\u003e\u003c/sub\u003eis the robot maximum turning radius.\u003c/p\u003e","description":"","filename":"12.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/448620333924ca02d53ead40.jpg"},{"id":65862949,"identity":"6a2da6a1-2db4-4b87-bdb9-1c199f16a409","added_by":"auto","created_at":"2024-10-03 16:37:04","extension":"jpg","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":59600,"visible":true,"origin":"","legend":"\u003cp\u003eTwo-degree-of-freedom model of the explosion-proof wheeled transport robot. \u003cem\u003eG\u003c/em\u003e is the robot CoG; \u003cem\u003eP\u003c/em\u003e is the instantaneous center of steering of the robot; \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eyf\u003c/em\u003e\u003c/sub\u003e\u003cstrong\u003e \u003c/strong\u003eand \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eyr\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e \u003c/sub\u003eare the lateral tire forces of the front and rear axle; \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003exf\u003c/em\u003e\u003c/sub\u003e\u003cstrong\u003e \u003c/strong\u003eand \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003exr\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e \u003c/sub\u003eare the components of force provided by the front and rear tires, respectively, in their direction of rolling; \u003cem\u003eV \u003c/em\u003eis the robot velocity vector in the center of gravity, which has a longitudinal component \u003cem\u003ev\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e\u003cstrong\u003e \u003c/strong\u003e\u003c/em\u003eand a lateral component \u003cem\u003ev\u003c/em\u003e\u003csub\u003e\u003cem\u003ey \u003c/em\u003e\u003c/sub\u003e, which identify the sideslip angle \u003cem\u003e\u003cstrong\u003eβ\u003c/strong\u003e\u003c/em\u003e; \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e\u003csub\u003e\u003cem\u003e\u003cstrong\u003e \u003c/strong\u003e\u003c/em\u003e\u003c/sub\u003eis the front tire velocity vector; \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003er \u003c/em\u003e\u003c/sub\u003eis the rear tire velocity vector.\u003c/p\u003e","description":"","filename":"13.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/c25ce657cb1875e0fb739d44.jpg"},{"id":65864216,"identity":"b78b1d29-2808-497a-8cd8-23cea5e20d99","added_by":"auto","created_at":"2024-10-03 17:01:03","extension":"jpg","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":17693,"visible":true,"origin":"","legend":"\u003cp\u003ePath-following error dynamics model of the explosion-proof wheeled transport robot. v is the robot actual velocity vector；\u003cem\u003eG\u003c/em\u003e is the robot CoG; \u003cem\u003eQ\u003c/em\u003e is the orthogonal projection point of \u003cem\u003eG\u003c/em\u003eon the desired path; \u003cem\u003ed\u003c/em\u003e is the distance from \u003cem\u003eG\u003c/em\u003e to \u003cem\u003eQ\u003c/em\u003e.\u003c/p\u003e","description":"","filename":"14.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/4cc79ab87d080e86060466cc.jpg"},{"id":65863385,"identity":"09a38ecc-8c5e-4a0a-8499-f56c40440439","added_by":"auto","created_at":"2024-10-03 16:45:03","extension":"jpg","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":67766,"visible":true,"origin":"","legend":"\u003cp\u003eMotion control scheme framework of EWTBOT\u003c/p\u003e","description":"","filename":"15.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/5e01e70a5fa5d74db1b0f0bd.jpg"},{"id":65862947,"identity":"92921874-9aeb-4a92-b99d-3e0b22e574f9","added_by":"auto","created_at":"2024-10-03 16:37:03","extension":"jpg","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":23447,"visible":true,"origin":"","legend":"\u003cp\u003eSimulation testing model of MTATBOTS.\u003c/p\u003e","description":"","filename":"16.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/a61ce2acea0a740b766041ca.jpg"},{"id":65862945,"identity":"8a5e1629-ab98-45e3-b8cb-2494fadf8cbb","added_by":"auto","created_at":"2024-10-03 16:37:03","extension":"jpg","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":48412,"visible":true,"origin":"","legend":"\u003cp\u003eSimulation tests of EWTBOT simultaneous localization and mapping solutions.\u003c/p\u003e\n\u003cp\u003e(a)shows the result of Visual-based SLAM; (b) shows the result ofLidar-based SLAM; (c) shows the result of Lidar-inertial-based SLAM; (d) shows the result of integrated-odometry-based SLAM.\u003c/p\u003e","description":"","filename":"17.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/c628c41eeb67d2b509a5e482.jpg"},{"id":65862941,"identity":"979fab9b-ffd9-43f3-8d90-b4822d3a5311","added_by":"auto","created_at":"2024-10-03 16:37:03","extension":"jpg","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":44205,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of EWTBOT trajectories based on different odometry information with the Ground Truth: (a) shows the comparative results at three-dimensional scale; (b) shows the comparative results at planar scale.\u003c/p\u003e","description":"","filename":"18.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/b1276e41ab4f488e7ddb9959.jpg"},{"id":65862948,"identity":"48006919-6b3f-4171-8501-33c961732752","added_by":"auto","created_at":"2024-10-03 16:37:03","extension":"jpg","order_by":19,"title":"Figure 19","display":"","copyAsset":false,"role":"figure","size":80897,"visible":true,"origin":"","legend":"\u003cp\u003ePhysical prototype of EWTBOT\u003c/p\u003e","description":"","filename":"19.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/6af63be8e3de2a0d69d0baab.jpg"},{"id":66058361,"identity":"cc637963-8a67-4ebd-a7c1-1e13f3c437e8","added_by":"auto","created_at":"2024-10-07 09:39:46","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2497854,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4955671/v1/9b54b1a9-6ff0-439e-849a-22ca9e68e846.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Trackless Auxiliary Transportation Robot System for Unmanned Material Distribution of Underground Coal Mine","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eCoal mine intellectualization is the core technical support for the high-quality development of coal industry. Especially for the underground coal mine, the hash working condition, heavy labor intensity and frequent mining accidents make it increasingly difficult for enterprises to recruit employees engaged in subterranean environment works. Hereby, the construction of production automation, equipment robotization and unmanned operation based on the application of artificial intelligence, robot technology, industrial Internet, cloud platform and other labor-saving technologies in the whole underground mining process has become the main development goal of coal industry in the future[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Compared to the main transportation system which is responsible for the coal transportation, the auxiliary transportation system of underground coal mine is in charge of the transport of production consumables, working equipment and subterranean personnel. Because of the diverse transport objects, complex driving environments and heavy transport tasks, the auxiliary transportation system has become one of the most labor-intensive and accident-prone parts in the whole underground mining process. Therefore, an intelligent and unmanned auxiliary transportation system can effectively reduce the subterranean labors, increase the mining efficiency and lower the mining accident rate. Correspondingly, in the intelligent development plan for coal mines proposed by the Chinese government, the intelligent underground auxiliary transportation development goal with features of standardized loading, intelligent distribution, automatic transfer and unmanned transportation is proposed to promote the development of coal industry[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eHowever, the current auxiliary transportation of underground coal mine mainly uses manually driven vehicles to perform transport tasks. Depending on different transportation conditions, auxiliary transport equipment can be broadly classified into two categories: railed locomotives and trackless vehicles. Compared with railed locomotives, the trackless auxiliary vehicles can perform transport task from point to point, avoiding transshipment process, which is more efficient, flexible and labor-saving. Currently, trackless auxiliary transportation mainly depends on explosion-proof rubber wheeled vehicles. However, these vehicles are mainly driven by explosion-proof diesel engines, depending on hydraulic or mechanical transmission, relying on human operation, which are hard to achieve automatic control and unmanned transportation. In addition, the existing trackless auxiliary transport system adopts different types of vehicles for diverse transport objects, resulting in a wide variety of transport equipment and heavy maintenance work. In short, relying on the existing equipment base, it is difficult to support the standardization and automation of underground transportation.\u003c/p\u003e \u003cp\u003eIn response to above problems, in this paper, a trackless auxiliary transportation robot system (MTATBOTS) used for material and consumables distribution in the underground coal mine is introduced, which is powered by explosion-proof lithium batteries and equipped with explosion-proof wired control system. The robot can be controlled by remote operation platform or onboard autopilot system to execute unmanned underground transportation. The paper describes the system composition and functional implementation of MTATBOTS, aiming at providing an intelligent transport terminal and feasible solution for intelligent auxiliary transportation of underground coal mine.\u003c/p\u003e \u003cp\u003eThe remainder of the paper is organized as follows: Section 2 presents an overview of the related unmanned technology and equipment development of intelligent mining; The general structure of MTATBOTS is shown in Section 3; Section 4 describes the autopilot system design of the robot; The robot dynamic model and control strategy are presented in Section 5; In Section 6, the simulation test results of the robot virtual model are presented; The paper ends with a conclusion in section 7.\u003c/p\u003e"},{"header":"2. Prior Works and Technical Challenges","content":"\u003cp\u003eIn order to improve transportation efficiency and reduce labor intensity, various types of automated and unmanned transport equipment are gradually put into the mining process of both coal mine and other mines. Generally speaking, the mining area is considered to be an ideal experimental site and technology landing scenario for some advanced technologies, such as autonomous driving. Because it can provide a specific enclosed area with no legal barriers and a regular route for vehicles driving at a low speed. In recent years, the autonomous driving has made big progress in some mining and machinery companies, especially in some open-pit mines. The productivity benefits of the autonomous open-pit mining truck fleet have helped reduced costs by around 20 per cent, and the autonomous trucks effectively shield employees from dangerous situations[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. In the open-pit mining area, benefiting from the advantages of global navigation satellite system (GNSS), the autonomous driving system can more easily get the accurate location information of mining trucks, which is the premise and basis of automatic and unmanned transportation. In addition, the transport objects of open-pit mines are relatively fixed, mainly focusing on coal or other ores, which makes it easier to achieve standardized and automated transport process. However, considering that GNSS signals cannot spread in subterranean environment, precise localization of autonomous driving vehicles in underground terrain must be solved in other solutions. Additionally, the special features of underground coal mine environment pose challenges to the autonomous driving vehicle, including limited line-of-sight, large variations in illumination, obscurants (e.g., dust, fog, and moisture), restricted working space, self-similarity long-narrow roadways, degraded perception and sensing, constrained communication, radio frequency propagation challenges, explosion-proof requirements of electric components, increasingly complicated environment with the mining operations. And most challenging of all, however is the combination of all the above features.\u003c/p\u003e \u003cp\u003eThus, researchers have done much work to promote the application of relative technologies. Dong \u003cem\u003eet al.\u003c/em\u003e proposed analytical and iterative velocity-free localization methods in complex and dynamic mining conditions[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Through the utilization of active sources, laser rangefinders, proximity sensor, in conjunction with the localization method, realize the accurate localization of autonomous rock drilling jumbo and explosive charging vehicle in deep underground mine. But the method relies on the sensor network deployed in advance, which will increase economic cost and infrastructure investment when used in large-scale underground coal mine roadways. Ebadi \u003cem\u003eet al.\u003c/em\u003e presented a large-scale autonomous mapping and positioning method for exploration of perceptually-degraded subterranean environments based on the technology of simultaneous localization and mapping SLAM[\u003cspan additionalcitationids=\"CR6\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Depending on the centralized multi-robot SLAM system, robust estimate of the trajectories of multiple robots in large-scale, unknown, and complex subterranean environment can be obtained. Another algorithm named range-aided pose-graph-based SLAM was introduced by Funabiki \u003cem\u003eet al.\u003c/em\u003e to execute position estimate in subterranean perceptual degraded environment under the help of sparsely deployed ranging beacons[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Kim \u003cem\u003eet al.\u003c/em\u003e developed an autonomous driving robot that drives and returns along a planned route in an underground mine tunnel through a machine-vision-based road sign recognition algorithm[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Stefaniak \u003cem\u003eet al\u003c/em\u003e. integrated the inertial measurement unit IMU and dynamic time warping DTW algorithms to locate the underground mine LHD and obtained robust performance[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. A search-and-rescue robot system with explosion-proof and waterproof function used for remote sensing of the underground coal mine environment was introduced by Zhao \u003cem\u003eet al.\u003c/em\u003e [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. In addition, the ultra-wide band UWB technology is increasingly being used to locate personnel and equipment in underground coal mines[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], and it is also considered to be helpful for underground driverless vehicle. However, limited by the features of underground coal mine roadway, the construction of UWB positioning network covering the entire auxiliary transportation roadways is hard to implement and high cost. And considering the relative high speed and high safety requirements of underground transport vehicles, the dynamic positioning accuracy and signal stability of UWB in the underground environment need to be further testified and improved. Briefly, the above state-of-art solutions provide useful and positive references for intelligent unmanned auxiliary transportation of underground coal mine.\u003c/p\u003e \u003cp\u003eMoreover, in recent years, several kinds of autonomous driving technology validation models of underground coal mine transport vehicles have been developed by equipment manufacturers and research institutions in China, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. These models are mainly converted from the existing explosion-proof trackless rubber wheeled vehicles by adding environmental sensors, such as Lidar, camera and millimeter wave radar. Some autonomous driving algorithms for underground coal mine environment were developed and testified depending on these prototypes. However, the automatic driving modification of existing explosion-proof trackless vehicles can hardly meet the standardized, continuous and unmanned requirements of intelligent auxiliary transport systems. MTATBOTS introduced in the paper is a new type of robotized coal mine auxiliary transport system, which is specially designed for the unmanned material distribution of underground coal mine. In the following article, the structural composition and functional design of the robot system will be described in details.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e(a) shows the traditional explosion-proof rubber wheeled vehicle for material transport; (b) shows the autonomous driving prototype of underground coal mine transport vehicle\u003c/p\u003e"},{"header":"3. General Structure of MTATBOTS","content":"\u003cp\u003eMTATBOTS is designed for automated and unmanned transportation in underground coal mine. With modular structural design, MTATBOTS breaks through the conventional structure of explosion-proof trackless vehicles and divides the transport operations into different functional units. For different transport objects, the required functional units can be combined into a suitable transport vehicle, thus reducing the variety of vehicle types and facilitating standardized transportation. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, MTATBOTS consists of three main parts, including: Remote Monitoring Platform, Explosion-proof Wheeled Transport Robot and Multi-type Material Containers.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Remote Monitoring Platform\u003c/h2\u003e \u003cp\u003eRemote monitoring platform is the command and dispatch center of MTATBOTS. The platform can be independently arranged in the ground control center or integrated into the comprehensive dispatching system of coal mine. Remote monitoring platform has three main functions. First, it\u0026rsquo;s in charge of processing task information of required material type, underground destination and location of available wheeled transport robot. The robot can perform the transport task will be identified based on the information. Secondly, the remote monitoring platform is also responsible for calculating the global planning path of the robot from its current location to the required destination based on real-time underground traffic condition. The generated global planning path is then released to the identified robot as the task navigation information via the wireless communication network of coal mine. Third, the platform can monitor the robot\u0026rsquo;s operational status and execute remote takeover as needed to ensure transportation safety.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Explosion-proof Wheeled Transport Robot\u003c/h2\u003e \u003cp\u003eAn explosion-proof wheeled transport robot (EWTBOT) used as automated-guided-vehicle is the transport actuator of MTATBOTS. EWTBOT is designed for the complex operating environment and special working conditions of underground coal mine, which equipped with the autopilot system as its control center and the explosion-proof wheeled electric chassis as its walking device. The configuration structure and chief components of the explosion-proof wheeled electric chassis are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The chassis is designed with a front-to-back symmetrical structure to achieve good maneuverability and bi-directional travel capability. Meanwhile, considering the limited underground working space, the chassis adopts a low-profile design with the dimensions of length 4500 mm, width 2000 mm, height 1000 mm. The chassis is powered by batteries and has zero emissions. Two blocks of explosion-proof lithium batteries are mounted in the middle of chassis, providing 64 kWh energy. The onboard energy system gives the robot a maximum driving range of 80 km to meet the demand of at least one round trip of material transportation in a large-scale underground coal mine. Furthermore, in order to solve the problems of driving range anxiety and excessive charging time faced by current explosion-proof electric vehicles, the chassis has battery quick-change function that allows it replace battery packs in ten minutes. In addition, the robot is equipped with a four-wheeled independent suspension system to achieve good driving stability when travelling in underground complicated road conditions. Hydraulic system of the chassis is powered by an explosion-proof oil pump motor to perform the braking function of the robot.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe autopilot system of EWTBOT mainly includes environment perception system and decision control system. Two explosion-proof electric control boxes are symmetrically placed at the front and rear ends of the chassis to host onboard electric components and computing units. Four explosion-proof electric control boxes are arranged separately at the corners of the chassis, in which the sensors required for the environment perception system are placed. Powertrain system arrangement of EWTBOT is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. The robot is equipped with two sets of driving units, each consisting of a 46 \u003cem\u003ekW\u003c/em\u003e explosion-proof permanent magnet motor and a reducer with differential function. The power system enables the robot reach a maximum travel speed of 40 \u003cem\u003ekm/h\u003c/em\u003e and a maximum climbing capacity of 14\u0026deg;. Meanwhile, in order to obtain good passing ability in the underground limited space, the robot is equipped with two set of Ackerman steering mechanisms to perform four-wheel steering function and small turning radius. Moreover, each tire of the robot is equipped with a wheel-side enclosed wet brake. Considering the safety of braking, the brake adopts a safety type operating mode of spring-applied and hydraulically released that will be automatically locked when the robot loses power. In addition, the robot is equipped with polyurethane filled tires, increasing its adaptability to complex subterranean road conditions. The main characterized parameters of EWTBOT are listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eTechnical specifications of Explosion-proof Wheeled Transport Robot\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItems\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eParameters\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRobot Mass\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5000 kg\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaximum Load Capacity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5000 kg\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRobot Body Sizes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4500\u0026times;2000\u0026times;1000 mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaximum Speed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40 km/h\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eClimbing Capacity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e14\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTurning Radius\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026le;\u0026thinsp;5400(outer) / \u0026ge;2800(inner) mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaximum Driving Range\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e80 km\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBattery Capacity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e64 kWh\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInstalled Power\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2\u0026times;46 kW\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePerception Range\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e360\u0026deg;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePerception Distance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026ge;\u0026thinsp;20 m\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e①Explosion-proof electric steering gear; ②Steering swing arm; ③Steering tie rod; ④Wheel-side enclosed wet brake; ⑤Drive axle shaft; ⑥Reducer and differential gear; ⑦Explosion-proof permanent magnet motor.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Multi-type Material Containers\u003c/h2\u003e \u003cp\u003eMuti-type material containers is a series of removable top loading devices which could be quickly changed and installed on EWTBOT. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, several kinds of material containers are designed to meet the transportation needs of various materials during underground production in coal mines, such as anchor rods, anchor cables, building materials, pipes, meals and other spare parts or consumables. The volume and shape of the containers can be customized according to different mines\u0026rsquo; demands. All kinds of loading containers are equipped with a unified installation interface and easy to be installed on the robot. After receiving the transportation order from the remote monitoring platform, EWTBOT selects a suitable container according to the task requirement, and then executes the material delivery task. Therefore, the robot system is conductive to the standardization and centralization of coalmine materials management and effective reduction of transport vehicle types. What\u0026rsquo;s more, the material containers can be replaced with other operating agency, such as robotic arms, lifting platforms and cable reels, to make the robot become a mobile operating platform.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Autopilot System of MTATBOTS","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Autopilot System Configuration\u003c/h2\u003e \u003cp\u003eMTATBOTS has two working modes: the remote-control mode and the autopilot mode. When it\u0026rsquo;s in the autopilot mode, the robot can automatically perform underground transportation. The autopilot system configuration of MTATBOTS is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, including remote monitoring platform, autopilot software platform, reference hardware platform and explosion-proof wheeled electric chassis. Except for remote monitoring platform, all the other systems are arranged on EWTBOT. Reference hardware platform mainly consists of sensing devices, positioning modules and computing unit. Autopilot software platform can be further divided into three parts: real time operating system, runtime framework and functional modules. The real time operating system adopts Ubuntu embedded operating system based on Linux core, using as interaction interface between software system and hardware platform. The runtime framework adopts robot operating system (ROS) that can provide complete development toolkit, flexible computing scheduling model and rich debugging tools. The functional modules include a series of software packages that are mainly used to implement application-level algorithms and procedures for autopilot functions, such as perception, localization, path planning and motion control. Explosion-proof wheeled electric chassis is the actuator of the autopilot system, which adopts explosion proof wire control technology to realize the horizontal and vertical motion of the robot.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eCompared to the variable ground transportation environment, the transport path of underground coal mine is relatively fixed. When MTATBOTS receives the transport task and destination information, its remote monitoring platform will calculate the global planning path based on the information of current underground traffic condition and available EWTBOT\u0026rsquo;s location. After receiving the start command, the identified EWTBOT will perform transport task along the global planning path. At the same time, considering that the underground coal mine roadway is an environment shared by equipment and personnel, the actual trajectory of the robot must take into account the changes of ahead obstacle information. Therefore, the implementation of MTATBOTS autopilot mode mainly depends on the EWTBOT autopilot system.\u003c/p\u003e \u003cp\u003eThe autopilot system equipped on EWTBOT adopts a four-level functional architecture, including the sensing layer, the perception layer, the decision layer and the execution layer. The sensing layer mainly consists of several kinds of sensors such as Lidar, Radar, RGB-D camera and IMU, providing the information of obstacles distribution and robot posture parameters. The perception layer calculates and fuses the collected information to estimate the robot\u0026rsquo;s location and obstacle distance. The decision layer determines the obstacle avoidance strategy and calculates the certain future period trajectory of the robot based on the above information. The execution layer is in charge of controlling the robot to travel along the local planning path provided by decision layer.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Environment Perception System of EWTBOT\u003c/h2\u003e \u003cp\u003eAccurate and fast environment perception is the premise and foundation for the safe and autonomous driving of EWTBOT in underground coal mine. Unfortunately, the auxiliary transportation roadway environment EWTBOT worked is often perceptual degradation, such as low or zero illumination, self-similar visual and geometric environment, and sometimes obscurants (fog, dust), as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. Meanwhile, considering the large scale of underground coal mine auxiliary transportation roadways (some of roadways are dozens of kilometers long), these conditions make it difficult to achieve desired perception results through traditional methods. Furthermore, due to the explosion-proof requirement of underground coal mine, the commonly used detection sensors, such as Lidar and camera, can\u0026rsquo;t be directly applied in EWTBOT.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe environment perception system of EWTBOT is specially designed for the conditions of underground transportation roadways. In order to get good perception performance in the underground perceptual degradation roadways, the combination of multi-type sensors, including Lidar, RGB-D Camera, Radar and IMU, is applied in EWTBOT\u0026rsquo;s environment perception system. In addition, all the sensors are specially explosion-proof designed for the underground coal mine environment. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e, all the optical sensors have been enclosed in explosion-proof electric boxes on EWTBOT. Under the help of specially designed explosion-proof glasses, the sensors can work normally in underground roadways of wet, dusty and explosive-risk atmosphere.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e(a) shows the main explosion-proof electric box; (b) shows the corner explosion-proof electric box.\u003c/p\u003e \u003cp\u003eThe arrangement and detection range of perception sensors applied on EWTBOT are depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e. EWTBOT equips with two Lidar at the front and rear, each with a field of detection horizon of 270 degrees, thus achieving full coverage of the robot's surrounding environment detection. Meanwhile, two millimeter-wave radars are installed separately in the front and rear of EWTBOT, mainly for the detection and tracking of moving objects in the forward direction of the robot. Additionally, a total of 10 RGB-D cameras are arranged around the vehicle to achieve video coverage in the main directions of the robot. Additionally, several laser distance sensors are arranged on both sides of the robot, which can quickly obtain the real-time distance information between the body and both sidewalls of the roadways, using for the judgement of the robot\u0026rsquo;s lateral position in the tunnel.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Localization strategy of EWTBOT\u003c/h2\u003e \u003cp\u003eAccurate estimation of self-localization in underground coal mine transport roadways is another challenge for autopilot system of EWTBOT. Because GNSS-based localization is not applicable in subterranean environment, simultaneous localization and mapping based on the information collected by environment perception system is essential for the robot localization. However, the perceptual degradation of underground roadway environment is typically challenging for no matter Lidar-based or visual-based SLAM. In order to increase the localization accuracy, our approach is to use Lidar-centric SLAM solution fused by visual, IMU and wheel rotation information, which can obtain more accurate and robust robot odometry. Moreover, in order to mitigate the inevitable accumulation of global drift over large-scale underground roadways when using SLAM to position the robot, auxiliary localization methods are simultaneously introduced into the strategy.\u003c/p\u003e \u003cp\u003eIt is important to note that when the robot travels in underground coal mine, its driving range is strictly limited between the sidewalls of the roadway. Compared with the length along the roadway direction, the roadway width (generally no more than 6\u003cem\u003em\u003c/em\u003e) is almost negligible. Therefore, the localization of EWTBOT mainly depends on its accurate odometry along the subterranean roadway direction. For above reason, our localization strategy is to use multi-modal information to obtain the accurate robot odometry, and then utilize effective auxiliary positioning methods to correct and optimize the robot trajectory and posture, aiming at achieving accurate vehicle position coordinates and heading angles to conduct the robot\u0026rsquo;s automatic motion control. Figure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e shows the overview of EWTBOT\u0026rsquo;s localization system architecture. As shown in the diagram, EWTBOT localization system mainly consists of two parts: onboard localization system and auxiliary localization system.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eA. Onboard Localization Solution\u003c/em\u003e \u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eDepending on EWTBOT\u0026rsquo;s onboard hardware platform, onboard localization solution is implemented through a complementary muti-modal SLAM system which includes two main components: the front-end and the back-end.\u003c/p\u003e \u003cp\u003e \u003cem\u003e1 Front-end: Integrated Odometry.\u003c/em\u003e The front-end of onboard SLAM system is in charge of abstracting the saw sensor data into the robot odometry. With the different type of data collected by relevant sensors, three components of the robot\u0026rsquo;s odometry information can be obtained separately, including Lidar-inertial odometry, wheel odometry and visual-inertial odometry. The Lidar-inertial odometry component can fuse the Lidar point cloud matching results with the IMU data to derive the robot position and trajectory[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Our solution develops on top of an existing open-source implementation LIO-SAM[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. This tightly-coupled Lidar inertial odometry framework can achieve accurate, real-time mobile robot trajectory estimation and map-building. In addition, the framework is suitable for multi-sensor fusion by formulating odometry atop a factor graph, thus additional sensor measurements, such as wheel odometry and UWB position information, can be incorporated into the framework as new factors to eliminate the sensor drift, which has significant importance especially in the large-scale underground roadway environment[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. The visual-inertial odometry component fuses the matching result of sparse ORB features[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] between consecutive images filmed by RGB-D camera and the IMU data to estimate the robot odometry while reconstructing the environment[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Our solution builds upon the existing open-source implementation ORB-SLAM3[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], which is state-of-the-art visual odometry framework can perform visual SLAM with RGB-D camera. But considering that the visual odometry is not reliable in the low-texture underground roadway environment and is susceptible to illumination, the visual odometry component plays an auxiliary and complementary role in our strategy. The wheel odometry component can figure out the robot driving range based on the robot speed and heading angle gathered by motor encoder and IMU.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eHowever, affected by perceptually-degraded subterranean environment and poor road surface condition, each kind of odometry information can be biased or even missing when the robot travelling along the roadway. For examples: Long-range, corridor-like subterranean roadways and similar-structure intersections make Lidar-based odometry prone to drift; Uneven and slippery roadway surface make the wheel odometry inaccurate; Poor and drastic change illumination, dust, water puddles and non-Lambertian surfaces render visual odometry unreliable[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Above all, it is hard to obtain accurate and robust localization result depends on single source odometry information. Therefore, Kalman Filter is introduced in our strategy to consider all the three odometry components simultaneously and the integrated odometry information of the robot which is more reliable and robust can be figured out accordingly.\u003c/p\u003e\u003cp\u003e \u003cem\u003e2. Back-end: Localization Optimization.\u003c/em\u003e The back-end of onboard SLAM system is in charge of optimizing robot trajectory and global map estimates by fusing the key frame information of integrated odometry from the front-end and the landmark position information from the priori roadway map via a nonlinear estimator approach named as pose graph optimization (PGO)[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. The priori map of underground roadways can be obtained from the geographic information system (GIS) of coal mine or mapped from the onboard SLAM system. Position information of significant landmarks, such as underground traffic signs and signals, key intersections, artificial markings, can be marked in the map as the priori localization markers. When the robot travels along subterranean roadways, these markers can be captured by onboard RGB-D cameras under the help of YOLO[\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. YOLO produces a 2D bounding box around the detected marker, and then the position of the marker can be estimated according to the range of the bounding box center measured by the depth channel of RGB-D camera.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eThe pose graph of EWTBOT is depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e. When the back-end receives the front-end odometry information, a serial of key frames is periodically instantiated in every 1\u003cem\u003em\u003c/em\u003e displacement and the corresponding poses and odometry edges are added to the robot\u0026rsquo;s pose graph. When the back-end receives the landmark measurements, a landmark point whose position can be obtained from the priori roadway map is instantiated in the pose graph and an edge is added between the landmark and the corresponding observation pose. Based on the landmark position, the robot\u0026rsquo;s trajectory can be optimized accordingly and spurious loop closure that occurred frequently in perceptually-degraded subterranean roadways can be mitigated effectively. Therefore, the problem of the optimization of the robot\u0026rsquo;s odometry and trajectory can be formulated as pose graph optimization by integrating the priori landmarks position constrains. And the problem is implemented in our strategy based on GTSAM[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] framework and use the Levenberg-Marquardt algorithm to solve the nonlinear least squares problem.\u003c/p\u003e \u003cp\u003e \u003cem\u003e5. Auxiliary Localization Solution\u003c/em\u003e \u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eIn order to increase the robustness and the accuracy of EWTBOT localization, more auxiliary positioning solutions should be added besides the priori subterranean roadway information. In the absence of sufficient landmarks information provided for the robot odometry optimization, the arrangement of radio beacons which can publish position information to the robot is an effective and economic way to realize localization optimization, because its omnidirectional observability, ease of deployment, and robustness to the perceptually degraded subterranean environment[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. In our strategy, UWB devices are adopted as radio beacons to provide the global positioning information for EWTBOT.\u003c/p\u003e \u003cp\u003eTypically, positioning method that use radio beacons require a dense distribution of beacons. However, considering that deployment of enough radio beacons for large-scale underground roadways will significantly increase economic cost and the effective radio-ranging of each beacon is also severely limited by subterranean roadway geography, a limited number of explosive-proof UWB ranging beacons are sparsely deployed in the roadways, mainly in sharp turns and roadway intersections. These ranging beacons can provide global position information for the robot to eliminate accumulated errors. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e, when the robot travels into the UWB beacon operation area, a beacon range edge will be added in pose graph between the beacon and the corresponding observation pose as a global constrain to correct the odometry and optimize the robot trajectory. In addition, all the UWB beacons are uniquely identified so that the robot can quickly locate itself when passing by, effectively reducing the computational burden and avoiding spurious loop closure.\u003c/p\u003e \u003cp\u003eFurthermore, the remote monitor platform of MTATBOTS can also interact with the robot trajectory through manually transmit position information to the robot in cases that the operator identifies a loop closure which has not been detected by the onboard SLAM system or correct the spurious loop closure.\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Motion Control of EWTBOT","content":"\u003cp\u003eDriving stabilization and collision avoidance are two of the most crucial concerns when EWTBOT works in the underground roadways of limited space and multiple traffic participants[\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. The motion control strategy of the robot adopts a hierarchical control architecture consisting of decision-making layer and motion execution layer. In decision-making layer, a smooth and collision-free driving trajectory that meets kinematic and dynamic constraints of the robot is calculated based on the changing environmental information. In motion execution layer, the robot motion is decoupled into the lateral and longitudinal motion under Frenet coordinate system[\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] with the planned driving path as the coordinate axis. The lateral motion controller manipulates the steering system according to the deviation between the robot actual position and the planned trajectory. The longitudinal controller controls the traction motor and the brake system to track the position and speed of the planned trajectory. In this section, the motion model of EWTBOT is described based on dynamics analysis, and then the motion control scheme of the robot is presented.\u003c/p\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Motion forms of EWTBOT\u003c/h2\u003e \u003cp\u003eEWTBOT is equipped with two sets of Ackerman steering mechanisms at the front and rear respectively, which can realize a variety of motion forms to improve its maneuverability. Three motions forms of the robot are shown in Fig.\u0026nbsp;12, including front/rear wheel steering, four-wheel steering and crab walking. Compared with front wheel steering or rear-wheel steering, four-wheel steering can effectively reduce the turning radius of the robot. Crab walking make the robot travel diagonally, i.e., the driving direction is deflected by an angle between the longitudinal axis of the vehicle. In the crab walking mode, the robot can easily perform obstacle avoidance maneuvers in subterranean roadways of limited space. Moreover, the two steering systems serve as a backup for each other. If one of the steering system fails, the robot can still complete the steering maneuver.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eFront/Rear wheel steering (b) Four-wheel steering (c) Crab walking\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eFigure 12. Multi-type motion forms of the explosion-proof wheeled transport robot. \u003cem\u003eG\u003c/em\u003e is the robot CoG, positioned at \u003cem\u003eX\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eY\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e in the global Cartesian coordinate system \u003cem\u003eXOY\u003c/em\u003e. \u003cem\u003exGy\u003c/em\u003e is the robot body coordinate system with the robot\u0026rsquo; longitudinal axis as \u003cem\u003ex\u003c/em\u003e-axis and its lateral direction as \u003cem\u003ey\u003c/em\u003e-axis. \u003cem\u003eL\u003c/em\u003e is the robot axis distance. \u003cem\u003eD\u003c/em\u003e is the robot wheel distance. \u003cem\u003eP\u003c/em\u003e is the instantaneous center of steering of the robot. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varphi\\:\\)\u003c/span\u003e\u003c/span\u003eis the yaw angle of the robot. \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003emin\u003c/em\u003e\u003c/sub\u003e is the robot minimum turning radius. \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e is the robot maximum turning radius.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Dynamic Model of EWTBOT\u003c/h2\u003e \u003cp\u003eThe effectiveness of motion control of EWTBOT should be based on correct and reliable vehicle model[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. A feasible local path planning trajectory generated by the decision-making layer needs to satisfy the kinematic and dynamic constraints of the robot[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. In order to develop a reasonable control scheme and mitigate the computational burden, a planar 2-DoF bicycle model[\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] is employed to represent the robot, depicted in Fig.\u0026nbsp;13(a), which utilizes small angle assumptions and the approximation that the tires on each axle can be lumped together. \u003cem\u003eG\u003c/em\u003e is the center of gravity of the robot, which positioned at \u003cem\u003eX\u003c/em\u003e\u003csub\u003e\u003cb\u003eh\u003c/b\u003e\u003c/sub\u003e and \u003cem\u003eY\u003c/em\u003e\u003csub\u003e\u003cb\u003eh\u003c/b\u003e\u003c/sub\u003e in the global Cartesian coordinate system \u003cem\u003eXOY\u003c/em\u003e. And \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varphi\\:\\)\u003c/span\u003e\u003c/span\u003e is the robot yaw angle between the earth coordinate system \u003cem\u003eX\u003c/em\u003e-axis and the robot longitudinal \u003cem\u003ex\u003c/em\u003e-axis. Thus, the robot position and posture in the earth fixed coordinate system can be defined by the vector \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:[\\begin{array}{ccc}{X}_{h}\u0026amp;\\:{Y}_{h}\u0026amp;\\:\\varphi\\:\\end{array}{]}^{T}\\)\u003c/span\u003e\u003c/span\u003e. Assuming that the robot drives at a constant speed \u003cb\u003ev\u003c/b\u003e\u003csub\u003e\u003cb\u003ex\u003c/b\u003e\u003c/sub\u003e in the direction of the robot\u0026rsquo;s longitudinal \u003cem\u003ex\u003c/em\u003e-axis, the bicycle model consisting of the lateral and yaw dynamics in the robot body coordinate system \u003cem\u003exGy\u003c/em\u003e, the force and the torque equilibrium of the 2-DOF bicycle model in lateral direction can be derived as follows according to geometric relationships and dynamic analysis:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\sum\\:{F}_{y}=m({\\dot{v}}_{y}+{v}_{x}\\cdot\\:\\dot{\\varphi\\:})={F}_{yf}{cos}{\\delta\\:}_{f}+{F}_{yr}{cos}{\\delta\\:}_{r}\\approx\\:{C}_{\\alpha\\:f}\\cdot\\:{\\alpha\\:}_{f}+{C}_{\\alpha\\:r}\\cdot\\:{\\alpha\\:}_{r}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\sum\\:M={I}_{z}\\ddot{\\varphi\\:}=a\\cdot\\:{F}_{yf}{cos}{\\delta\\:}_{f}-b\\cdot\\:{F}_{yr}{cos}{\\delta\\:}_{r}\\approx\\:a\\cdot\\:{C}_{\\alpha\\:f}\\cdot\\:{\\alpha\\:}_{f}-b\\cdot\\:{C}_{\\alpha\\:r}\\cdot\\:{\\alpha\\:}_{r}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e is the force of the model in the direction of the robot lateral \u003cem\u003ey\u003c/em\u003e-axis; \u003cem\u003eM\u003c/em\u003e is the turning torque about the \u003cem\u003ez\u003c/em\u003e-axis; \u003cem\u003em\u003c/em\u003e is the robot mass; \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e is the moment of inertia about the \u003cem\u003ez\u003c/em\u003e-axis;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varphi\\:\\)\u003c/span\u003e\u003c/span\u003eis yaw angle; \u003cem\u003ev\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ev\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e are the components of the velocity vector in the center of gravity along the \u003cem\u003ex\u003c/em\u003e-axis and the lateral \u003cem\u003ey\u003c/em\u003e-axis of the robot body coordinate system; \u003cb\u003eβ\u003c/b\u003e is the sideslip angle of the robot in the center of gravity. \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eyf\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eyr\u003c/em\u003e\u003c/sub\u003e are the lateral tire forces, perpendicular to the rolling direction of the tire, and proportional to the slip angle, \u003cb\u003eα\u003c/b\u003e, between the local velocity vector and its forward direction;\u003cb\u003eα\u003c/b\u003e\u003csub\u003e\u003cb\u003ef\u003c/b\u003e\u003c/sub\u003e and \u003cb\u003eα\u003c/b\u003e\u003csub\u003e\u003cb\u003er\u003c/b\u003e\u003c/sub\u003e respectively denote the front and rear tire slip angles; \u003cem\u003ea\u003c/em\u003e and \u003cem\u003eb\u003c/em\u003e are the distances from the center of gravity of the vehicle to the front and rear axles; \u003cem\u003eδ\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eδ\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e are the steering angles of the front and rear wheels with respect to the robot, which assumed to be small angles; \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003eαf\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003eαr\u003c/em\u003e\u003c/sub\u003e are the tire stiffness of the front and the rear tire pairs, respectively.\u003c/p\u003e \u003cp\u003eBased on the velocity vectors\u0026rsquo; geometric relationships of the robot\u0026rsquo;s center of gravity, the front and rear tire, depicted in Fig.\u0026nbsp;13(b), the slip angles can be obtained in the following equations:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{\\alpha\\:}_{f}=-\\left({\\delta\\:}_{f}-{\\theta\\:}_{f}\\right)=\\frac{\\dot{\\varphi\\:}\\cdot\\:a+{v}_{y}}{{v}_{x}}-{\\delta\\:}_{f}\\approx\\:\\beta\\:+\\frac{\\dot{\\varphi\\:}\\cdot\\:a}{{v}_{x}}-{\\delta\\:}_{f}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{\\alpha\\:}_{r}=-\\left(\\frac{\\dot{\\varphi\\:}\\cdot\\:b-{v}_{y}}{{v}_{x}}-{\\delta\\:}_{r}\\right)\\approx\\:\\beta\\:+{\\delta\\:}_{r}-\\frac{\\dot{\\varphi\\:}\\cdot\\:b}{{v}_{x}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{v}_{y}/{v}_{x}={tan}\\beta\\:\\approx\\:\\beta\\:\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eDynamic analysis of the 2-DOF model.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eVelocity vectors geometrical relationship of the model\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eFigure 13. Two-degree-of-freedom model of the explosion-proof wheeled transport robot. \u003cem\u003eG\u003c/em\u003e is the robot CoG; \u003cem\u003eP\u003c/em\u003e is the instantaneous center of steering of the robot; \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eyf\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eyr\u003c/em\u003e\u003c/sub\u003e are the lateral tire forces of the front and rear axle; \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003exf\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003exr\u003c/em\u003e\u003c/sub\u003e are the components of force provided by the front and rear tires, respectively, in their direction of rolling; \u003cem\u003eV\u003c/em\u003e is the robot velocity vector in the center of gravity, which has a longitudinal component \u003cem\u003ev\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e and a lateral component \u003cem\u003ev\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e, which identify the sideslip angle \u003cb\u003eβ\u003c/b\u003e; \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e is the front tire velocity vector; \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e is the rear tire velocity vector.\u003c/p\u003e \u003cp\u003eFurthermore, in order to meet the needs of the robot multiple motion forms, the control of the steering angles of the front and rear tire follows the following rule:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{\\delta\\:}_{r}=\\xi\\:\\cdot\\:{\\delta\\:}_{f}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\xi\\:\\in\\:\\)\u003c/span\u003e\u003c/span\u003e [-1,1], \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\xi\\:\\)\u003c/span\u003e\u003c/span\u003eis the control scale factor.\u003c/p\u003e \u003cp\u003eNext, by bringing Equations (\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), (\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) and (5) into Equations (\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) and (\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), the parametric 2-DOF vehicle model and the expression for the lateral position of the robot can be written as follows:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\left\\{\\begin{array}{c}\\ddot{y}=\\left(\\frac{{C}_{\\alpha\\:f}+{C}_{\\alpha\\:r}}{m{v}_{x}}\\right)\\dot{y}+\\left(\\frac{{C}_{\\alpha\\:f}\\cdot\\:a-{C}_{\\alpha\\:r}\\cdot\\:b}{m{v}_{x}}-{v}_{x}\\right)\\dot{\\varphi\\:}+\\left(\\frac{-{C}_{\\alpha\\:f}+\\xi\\:\\cdot\\:{C}_{\\alpha\\:r}}{m}\\right){\\delta\\:}_{f}\\\\\\:\\ddot{\\varphi\\:}=\\left(\\frac{a\\cdot\\:{C}_{\\alpha\\:f}-b\\cdot\\:{C}_{\\alpha\\:r}}{{I}_{z}{v}_{x}}\\right)\\dot{y}+\\left(\\frac{{a}^{2}\\cdot\\:{C}_{\\alpha\\:f}+{b}^{2}\\cdot\\:{C}_{\\alpha\\:r}}{{I}_{z}{v}_{x}}\\right)\\dot{\\varphi\\:}+\\left(\\frac{-a\\cdot\\:{C}_{\\alpha\\:f}-\\xi\\:\\cdot\\:b\\cdot\\:{C}_{\\alpha\\:r}}{{I}_{z}}\\right){\\delta\\:}_{f}\\end{array}\\right.$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e(6)\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003ey\u003c/em\u003e is the robot lateral displacement; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varphi\\:\\)\u003c/span\u003e\u003c/span\u003e is the yaw angle; \u003cb\u003eδ\u003c/b\u003e\u003csub\u003e\u003cb\u003ef\u003c/b\u003e\u003c/sub\u003e is the steering angle of the front wheel. By defining \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:X=[\\begin{array}{cc}\\dot{y}\u0026amp;\\:\\dot{\\varphi\\:}\\end{array}{]}^{T}\\)\u003c/span\u003e\u003c/span\u003eas the state vector and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:U=\\left[{\\delta\\:}_{f}\\right]\\)\u003c/span\u003e\u003c/span\u003e as the control vector, the robot model described in Eq.\u0026nbsp;(6) can be converted into the state equation as:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:\\dot{X}=AX+BU$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:A=\\left[\\begin{array}{cc}\\frac{{C}_{\\alpha\\:f}+{C}_{\\alpha\\:r}}{m{v}_{x}}\u0026amp;\\:\\frac{{C}_{\\alpha\\:f}\\cdot\\:a-{C}_{\\alpha\\:r}\\cdot\\:b}{m{v}_{x}}-{v}_{x}\\\\\\:\\frac{a\\cdot\\:{C}_{\\alpha\\:f}-b\\cdot\\:{C}_{\\alpha\\:r}}{{I}_{z}{v}_{x}}\u0026amp;\\:\\frac{{a}^{2}\\cdot\\:{C}_{\\alpha\\:f}+{b}^{2}\\cdot\\:{C}_{\\alpha\\:r}}{{I}_{z}{v}_{x}}\\end{array}\\right],\\:B=\\left[\\begin{array}{c}\\frac{-{C}_{\\alpha\\:f}+\\xi\\:\\cdot\\:{C}_{\\alpha\\:r}}{m}\\\\\\:\\frac{-a\\cdot\\:{C}_{\\alpha\\:f}-\\xi\\:\\cdot\\:b\\cdot\\:{C}_{\\alpha\\:r}}{{I}_{z}}\\end{array}\\right]$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e5.3 Path-following error dynamic model\u003c/h2\u003e \u003cp\u003eThe control objective of EWTBOT is to make the position and the heading angle of the robot track the planned reference path. Using the desired path as the reference line, the robot movement can be decoupled separately as the lateral and longitudinal motion based on Frenet coordinate system. In the coordinate system, the direction along the desired path is taken as the longitudinal axis, and the direction perpendicular to the reference path is taken as the lateral axis[\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e14\u003c/span\u003e, the reference desired path of EWTBOT, on which the robot is supposed to drive, is depicted as the curve \u003cem\u003es\u003c/em\u003e. In addition, \u003cem\u003ed\u003c/em\u003e represents the distance from the center of gravity of the robot to the closest point \u003cem\u003eQ\u003c/em\u003e on the desired path, i.e., the orthogonal projection point of \u003cem\u003eG\u003c/em\u003e on the reference path. Robot position under the Frenet coordinate system can be depicted as the longitudinal displacement \u003cem\u003es\u003c/em\u003e and the lateral displacement \u003cem\u003ed\u003c/em\u003e. Thus, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\dot{\\varvec{s}}\\)\u003c/span\u003e\u003c/span\u003e is the robot\u0026rsquo;s desired velocity at its projection point \u003cem\u003eQ\u003c/em\u003e, along the tangential direction of the desired path.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eUnder the global Cartesian coordinate system \u003cem\u003eXOY\u003c/em\u003e, the actual position and the desired position on the reference path of the robot can be represented separately in position vectors of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\overrightarrow{x}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\overrightarrow{x}}_{r}\\)\u003c/span\u003e\u003c/span\u003e. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\theta\\:\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\theta\\:}_{r}\\)\u003c/span\u003e\u003c/span\u003e respectively represent the robot\u0026rsquo;s actual heading angle and the desired heading angle on the reference trajectory. And then, defining \u003cem\u003ed\u003c/em\u003e as the lateral position error and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left(\\theta\\:-{\\theta\\:}_{r}\\right)\\)\u003c/span\u003e\u003c/span\u003eas the heading error of the robot, the objective of the robot\u0026rsquo;s later control is to globally asymptotically minimize the two kinds of path-following errors. Besides, defining \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left(\\left|\\overrightarrow{v}\\right|-\\left|\\dot{s}\\right|\\right)\\)\u003c/span\u003e\u003c/span\u003e as the robot\u0026rsquo;s velocity magnitude error, the objective of the robot\u0026rsquo;s longitudinal control is to minimize the longitudinal position error and the velocity error. In addition, assuming that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\overrightarrow{\\tau\\:},\\overrightarrow{n}\\)\u003c/span\u003e\u003c/span\u003e are orthogonal unit vectors at point \u003cem\u003eG\u003c/em\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\overrightarrow{\\tau\\:}}_{r},{\\overrightarrow{n}}_{r}\\)\u003c/span\u003e\u003c/span\u003e are orthogonal unit vectors at point \u003cem\u003eQ\u003c/em\u003e, and the directions of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\overrightarrow{n}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\overrightarrow{n}}_{r}\\)\u003c/span\u003e\u003c/span\u003e are consistent with the vectors of the actual velocity and the desired velocity of the robot, the lateral displacement \u003cem\u003ed\u003c/em\u003e and the lateral velocity \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\dot{d}\\)\u003c/span\u003e\u003c/span\u003e can be attained as follows:\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:{\\overrightarrow{x}}_{r}+d{\\overrightarrow{n}}_{r}=\\overrightarrow{x}\\Rightarrow\\:d=\\left(\\overrightarrow{x}-{\\overrightarrow{x}}_{r}\\right)\\cdot\\:{\\overrightarrow{n}}_{r}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\:\\dot{d}=\\left(\\dot{\\overrightarrow{x}}-{\\dot{\\overrightarrow{x}}}_{r}\\right)\\cdot\\:{\\overrightarrow{n}}_{r}+\\left(\\overrightarrow{x}-{\\overrightarrow{x}}_{r}\\right)\\cdot\\:{\\dot{\\overrightarrow{n}}}_{r}=\\left|\\overrightarrow{v}\\right|{cos}⟨\\overrightarrow{\\tau\\:},{\\overrightarrow{n}}_{r}⟩=\\left|\\overrightarrow{v}\\right|{sin}\\left(\\theta\\:-{\\theta\\:}_{r}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\dot{\\overrightarrow{x}}=\\left|\\overrightarrow{v}\\right|\\overrightarrow{\\tau\\:}\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\dot{\\overrightarrow{x}}}_{r}=\\dot{s}{\\overrightarrow{\\tau\\:}}_{r}\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\dot{\\overrightarrow{n}}}_{r}=-\\kappa\\:{\\overrightarrow{\\tau\\:}}_{r}\\dot{s}\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\kappa\\:\\:\\)\u003c/span\u003e\u003c/span\u003erepresents the curvature of the desired path.\u003c/p\u003e \u003cp\u003eAnd the robot desired velocity can be calculated in the following equation:\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$$\\:\\dot{s}=\\frac{\\left|\\overrightarrow{v}\\right|\\text{cos}\\left(\\theta\\:-{\\theta\\:}_{r}\\right)}{1-\\kappa\\:\\cdot\\:d}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eConsidering that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\theta\\:=\\varphi\\:+\\beta\\:\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{v}_{x}=\\left|\\overrightarrow{v}\\right|{cos}\\beta\\:，{v}_{y}=\\left|\\overrightarrow{v}\\right|{sin}\\beta\\:\\)\u003c/span\u003e\u003c/span\u003e, the equations (\u003cspan refid=\"Equ8\" class=\"InternalRef\"\u003e9\u003c/span\u003e) and (\u003cspan refid=\"Equ9\" class=\"InternalRef\"\u003e10\u003c/span\u003e) can be written as follows:\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:\\dot{d}={v}_{y}\\text{cos}\\left(\\varphi\\:-{\\theta\\:}_{r}\\right)+{v}_{x}{sin}\\left(\\varphi\\:-{\\theta\\:}_{r}\\right)\\approx\\:{v}_{y}+{v}_{x}\\left(\\varphi\\:-{\\theta\\:}_{r}\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$$\\:\\dot{s}=\\frac{{v}_{x}\\text{cos}\\left(\\varphi\\:-{\\theta\\:}_{r}\\right)-{v}_{y}{sin}\\left(\\varphi\\:-{\\theta\\:}_{r}\\right)}{1-\\kappa\\:\\cdot\\:d}\\approx\\:\\frac{{v}_{x}-{v}_{y}\\left(\\varphi\\:-{\\theta\\:}_{r}\\right)}{1-\\kappa\\:\\cdot\\:d}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$$\\:\\left\\{\\begin{array}{c}\\dot{d}={v}_{y}\\text{c}\\text{o}\\text{s}\\left(\\varphi\\:-{\\theta\\:}_{r}\\right)+{v}_{x}{sin}\\left(\\varphi\\:-{\\theta\\:}_{r}\\right)\\approx\\:{v}_{y}+{v}_{x}\\left(\\varphi\\:-{\\theta\\:}_{r}\\right)\\\\\\:\\dot{s}=\\frac{{v}_{x}\\text{cos}\\left(\\varphi\\:-{\\theta\\:}_{r}\\right)-{v}_{y}{sin}\\left(\\varphi\\:-{\\theta\\:}_{r}\\right)}{1-\\kappa\\:\\cdot\\:d}\\approx\\:\\frac{{v}_{x}-{v}_{y}\\left(\\varphi\\:-{\\theta\\:}_{r}\\right)}{1-\\kappa\\:\\cdot\\:d}\\end{array}\\right.$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left(\\varphi\\:-{\\theta\\:}_{r}\\right)\\)\u003c/span\u003e\u003c/span\u003e is assumed as a small angle.\u003c/p\u003e \u003cp\u003eDefining that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{e}_{d}=d\\)\u003c/span\u003e\u003c/span\u003e is the lateral error and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{e}_{\\varphi\\:}=\\varphi\\:-{\\theta\\:}_{r}\\)\u003c/span\u003e\u003c/span\u003e is the heading error, the following equations can be attained:\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$$\\:{v}_{y}={\\dot{e}}_{d}-{v}_{x}{e}_{\\varphi\\:}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equf\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equf\" name=\"EquationSource\"\u003e\n$$\\:{\\dot{v}}_{y}={\\ddot{e}}_{d}-{v}_{x}{\\dot{e}}_{\\varphi\\:}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equg\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equg\" name=\"EquationSource\"\u003e\n$$\\:\\dot{\\varphi\\:}={\\dot{e}}_{\\varphi\\:}+{\\dot{\\theta\\:}}_{r}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ11\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ11\" name=\"EquationSource\"\u003e\n$$\\:\\ddot{\\varphi\\:}={\\ddot{e}}_{\\varphi\\:}+{\\ddot{\\theta\\:}}_{r}\\approx\\:{\\ddot{e}}_{\\varphi\\:}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equh\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equh\" name=\"EquationSource\"\u003e\n$$\\:\\left\\{\\begin{array}{c}{v}_{y}={\\dot{e}}_{d}-{v}_{x}{e}_{\\varphi\\:}\\\\\\:{\\dot{v}}_{y}={\\ddot{e}}_{d}-{v}_{x}{\\dot{e}}_{\\varphi\\:}\\\\\\:\\dot{\\varphi\\:}={\\dot{e}}_{\\varphi\\:}+{\\dot{\\theta\\:}}_{r}\\\\\\:\\ddot{\\varphi\\:}={\\ddot{e}}_{\\varphi\\:}+{\\ddot{\\theta\\:}}_{r}\\approx\\:{\\ddot{e}}_{\\varphi\\:}\\end{array}\\right.$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eNext, by bringing Equations (\u003cspan refid=\"Equ11\" class=\"InternalRef\"\u003e12\u003c/span\u003e) into Equations (6), the path-following error dynamics model of EWTBOT can be written as follows:\u003cdiv id=\"Equi\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equi\" name=\"EquationSource\"\u003e\n$$\\:{\\ddot{e}}_{d}-{v}_{x}{\\dot{e}}_{\\varphi\\:}=\\left(\\frac{{C}_{\\alpha\\:f}+{C}_{\\alpha\\:r}}{m{v}_{x}}\\right)\\left({\\dot{e}}_{d}-{v}_{x}{e}_{\\varphi\\:}\\right)+\\left(\\frac{{C}_{\\alpha\\:f}\\cdot\\:a-{C}_{\\alpha\\:r}\\cdot\\:b}{m{v}_{x}}-{v}_{x}\\right)\\left({\\dot{e}}_{\\varphi\\:}+{\\dot{\\theta\\:}}_{r}\\right)+\\left(\\frac{-{C}_{\\alpha\\:f}+\\xi\\:\\cdot\\:{C}_{\\alpha\\:r}}{m}\\right){\\delta\\:}_{f}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ12\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ12\" name=\"EquationSource\"\u003e\n$$\\:{\\ddot{e}}_{\\varphi\\:}=\\left(\\frac{a\\cdot\\:{C}_{\\alpha\\:f}-b\\cdot\\:{C}_{\\alpha\\:r}}{{I}_{z}{v}_{x}}\\right)\\left({\\dot{e}}_{d}-{v}_{x}{e}_{\\varphi\\:}\\right)+\\left(\\frac{{a}^{2}\\cdot\\:{C}_{\\alpha\\:f}+{b}^{2}\\cdot\\:{C}_{\\alpha\\:r}}{{I}_{z}{v}_{x}}\\right)\\left({\\dot{e}}_{\\varphi\\:}+{\\dot{\\theta\\:}}_{r}\\right)+\\left(\\frac{-a\\cdot\\:{C}_{\\alpha\\:f}-\\xi\\:\\cdot\\:b\\cdot\\:{C}_{\\alpha\\:r}}{{I}_{z}}\\right){\\delta\\:}_{f}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e13\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equj\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equj\" name=\"EquationSource\"\u003e\n$$\\:\\left\\{\\begin{array}{c}{\\ddot{e}}_{d}-{v}_{x}{\\dot{e}}_{\\varphi\\:}=\\left(\\frac{{C}_{\\alpha\\:f}+{C}_{\\alpha\\:r}}{m{v}_{x}}\\right)\\left({\\dot{e}}_{d}-{v}_{x}{e}_{\\varphi\\:}\\right)+\\left(\\frac{{C}_{\\alpha\\:f}\\cdot\\:a-{C}_{\\alpha\\:r}\\cdot\\:b}{m{v}_{x}}-{v}_{x}\\right)\\left({\\dot{e}}_{\\varphi\\:}+{\\dot{\\theta\\:}}_{r}\\right)+\\left(\\frac{-{C}_{\\alpha\\:f}+\\xi\\:\\cdot\\:{C}_{\\alpha\\:r}}{m}\\right){\\delta\\:}_{f}\\\\\\:{\\ddot{e}}_{\\varphi\\:}=\\left(\\frac{a\\cdot\\:{C}_{\\alpha\\:f}-b\\cdot\\:{C}_{\\alpha\\:r}}{{I}_{z}{v}_{x}}\\right)\\left({\\dot{e}}_{d}-{v}_{x}{e}_{\\varphi\\:}\\right)+\\left(\\frac{{a}^{2}\\cdot\\:{C}_{\\alpha\\:f}+{b}^{2}\\cdot\\:{C}_{\\alpha\\:r}}{{I}_{z}{v}_{x}}\\right)\\left({\\dot{e}}_{\\varphi\\:}+{\\dot{\\theta\\:}}_{r}\\right)+\\left(\\frac{-a\\cdot\\:{C}_{\\alpha\\:f}-\\xi\\:\\cdot\\:b\\cdot\\:{C}_{\\alpha\\:r}}{{I}_{z}}\\right){\\delta\\:}_{f}\\end{array}\\right.$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eBy defining \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{E}_{rr}={\\left[\\begin{array}{cccc}{e}_{d}\u0026amp;\\:{\\dot{e}}_{d}\u0026amp;\\:{e}_{\\varphi\\:}\u0026amp;\\:{\\dot{e}}_{\\varphi\\:}\\end{array}\\right]}^{T}\\)\u003c/span\u003e\u003c/span\u003eas the state vector, the path-following error dynamics model described in Eq.\u0026nbsp;(\u003cspan refid=\"Equ12\" class=\"InternalRef\"\u003e13\u003c/span\u003e) can be converted into the state equation as:\u003cdiv id=\"Equ13\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ13\" name=\"EquationSource\"\u003e\n$$\\:{\\dot{E}}_{rr}=\\stackrel{\\sim}{A}{E}_{rr}+\\stackrel{\\sim}{B}U+\\stackrel{\\sim}{C}{\\dot{\\theta\\:}}_{r}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e14\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere\u003cdiv id=\"Equk\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equk\" name=\"EquationSource\"\u003e\n$$\\:\\stackrel{\\sim}{A}=\\left(\\begin{array}{cccc}0\u0026amp;\\:1\u0026amp;\\:0\u0026amp;\\:0\\\\\\:0\u0026amp;\\:\\frac{{C}_{f}+{C}_{r}}{m{v}_{x}}\u0026amp;\\:-\\frac{{C}_{f}+{C}_{r}}{m}\u0026amp;\\:\\frac{a{C}_{f}-b{C}_{r}}{m{v}_{x}}\\\\\\:0\u0026amp;\\:0\u0026amp;\\:0\u0026amp;\\:1\\\\\\:0\u0026amp;\\:\\frac{a{C}_{f}-b{C}_{r}}{{I}_{z}{v}_{x}}\u0026amp;\\:-\\frac{a{C}_{f}-b{C}_{r}}{{I}_{z}}\u0026amp;\\:\\frac{{a}^{2}{C}_{f}+{b}^{2}{C}_{r}}{{I}_{z}{v}_{x}}\\end{array}\\right),\\stackrel{\\sim}{B}=\\left(\\begin{array}{c}0\\\\\\:\\frac{-{C}_{f}+\\xi\\:{C}_{r}}{m}\\\\\\:0\\\\\\:\\frac{-\\xi\\:b{C}_{r}-a{C}_{f}}{{I}_{z}}\\end{array}\\right),\\stackrel{\\sim}{C}=\\left(\\begin{array}{c}0\\\\\\:\\frac{a{C}_{f}-b{C}_{r}}{m{v}_{x}}-{v}_{x}\\\\\\:0\\\\\\:\\frac{{a}^{2}{C}_{f}+{b}^{2}{C}_{r}}{{I}_{z}{v}_{x}}\\end{array}\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eFurthermore, by using Euler\u0026rsquo;s approximation, Eq.\u0026nbsp;(\u003cspan refid=\"Equ13\" class=\"InternalRef\"\u003e14\u003c/span\u003e) can be discretised at sample time \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e, and the discrete-time state equation can be obtained as:\u003cdiv id=\"Equ14\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ14\" name=\"EquationSource\"\u003e\n$$\\:{E}_{rr}\\left(k+1\\right)={\\stackrel{\\sim}{A}}_{d}{E}_{rr}\\left(k\\right)+{\\stackrel{\\sim}{B}}_{d}U\\left(k\\right)+{\\stackrel{\\sim}{C}}_{d}{\\dot{\\theta\\:}}_{r}\\left(k\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e15\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{\\sim}{A}}_{d}={\\left(I-\\frac{\\stackrel{\\sim}{A}{t}_{s}}{2}\\right)}^{-1}\\left(I+\\frac{\\stackrel{\\sim}{A}{t}_{s}}{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{\\sim}{B}}_{d}={\\left(I-\\frac{\\stackrel{\\sim}{A}{t}_{s}}{2}\\right)}^{-1}\\stackrel{\\sim}{B}{t}_{s}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{\\sim}{C}}_{d}={\\left(I-\\frac{\\stackrel{\\sim}{A}{t}_{s}}{2}\\right)}^{-1}\\stackrel{\\sim}{C}{t}_{s}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cem\u003eI\u003c/em\u003e denotes the identity matrix.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e5.4 Motion Control Scheme\u003c/h2\u003e \u003cp\u003eDepending on the path-following error dynamics model, the control strategy of EWTBOT is developed as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e15\u003c/span\u003e. When EWTBOT receives the global planning path from Remote Monitoring Platform, the onboard decision-making layer of motion control system will generate a collision-free local planning path based on the global path. The local planning path is generated according to the distribution information of surrounding obstacles provided by the robot\u0026rsquo;s environment perception system. And the path consists of a series of adjacent discrete trajectory points, each of which contains the desired position coordinates and heading angle of the robot in certain planning moment, along with the information of the robot\u0026rsquo;s desired velocity and acceleration. Meanwhile, the current position and the heading angle of the robot can be acquired through the robot localization system. The above information, as well as the robot attribute parameters, will be passed into the path-following error dynamic model of EWTBOT as input data.\u003c/p\u003e \u003cp\u003eThe motion execution layer is responsible for manipulating the explosion-proof wire-controlled system to walk along the local planning path. In our strategy, the robot motion is decoupled into the lateral and longitudinal motion under Frenet coordinate frame. The lateral motion control of the robot can be figured out by minimizing the errors of the lateral displacement and the heading angle between the robot current state and the reference trajectory point. Accordingly, the robot lateral control output will be published to the corresponding steering motor, in terms of the front-wheel and rear-wheel turning angles. In the other hand, the longitudinal motion controller is in charge of tracking the desired velocity and acceleration of the reference trajectory point based on the robot\u0026rsquo;s actual speed and acceleration. Hereby, the robot longitudinal control outputs will be published in terms of throttle and brake pressure to the traction motors and the electro-hydraulic brake system separately.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"6. Simulation Testing","content":"\u003cp\u003eA simulated model of EWTBOT based on ROS and a virtual scenario of underground coal mine auxiliary transport roadways are established to facilitate the simulation testing of MTATBOTS, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e16\u003c/span\u003e. The virtual model of EWTBOT is build according to its real size and system configuration, which equipped with simulated environment perception system and motion control system. Under the control of the path-following algorithm based on the proposed motion control strategy, the virtual robot can travel along the desired trajectory in the simulated underground roadways. Meanwhile, with the help of SLAM algorithm, the environment perception system can estimate the motion state and position of the robot based on the acquired environment information and onboard sensor data. Accordingly, the robot trajectory and the roadway map can be obtained simultaneously. In order to testify the effectiveness of localization and control strategy of EWTBOT in the virtual underground scene, several kinds of SLAM solutions are implemented relying on the simulation model to estimate the robot odometry and build the scenario map. And the algorithms are tested separately by running at the same travelling route, hereby the robot odometry figured out through different localization solutions can be compared on the basis of actual robot trajectory.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eLeft: Virtual auxiliary transport roadway scenario of underground coal mine; Right: Simulated model of EWTBOT.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e17\u003c/span\u003e. shows the mapping results of the virtual underground roadways obtained through four different SLAM solutions. In the simulated underground roadway scenario, the vision-based SLAM can hardly execute the localization and mapping task independently, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e17\u003c/span\u003e(a), because of the featureless environment and varying illumination. As for the Lidar-based SLAM, it significantly underestimates the robot motion in long symmetric corridor-like roadway scenario because of the lack of detectable geometric features. In addition, intersections with similar structure can easily bring up with spurious loop closures. The simulated scenario mapping results through Lidar-based SLAM is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e17\u003c/span\u003e(b). While, with the fusion of IMU data and wheel odometry information of the robot, the Lidar-inertial-based SLAM can estimate the robot odometry more accurately and obtain better mapping results, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e17\u003c/span\u003e(c). However, subject to the cumulative errors, the robot odometry obtained by the algorithm inevitably drifts to a certain extent after a long driving route and several sharp turns, which leads to deviations in the mapping result.\u003c/p\u003e \u003cp\u003eFinally, in the virtual underground scenario, the proposed integrated-odometry-based SLAM algorithm of the paper is tested and proved to be effective in eliminating cumulative errors and obtaining accurate mapping result, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e17\u003c/span\u003e(d). Under the help of priori localization vision markers and sparse global position signals provided by virtual UWB beacons installed in roadway intersections, more accurate and robust robot position and odometry can be acquired through combining Lidar-inertial odometry, visual-inertial odometry and wheel odometry. Furthermore, the robot odometry obtained by different algorithms are put into the same coordinate system and compared with the ground truth of the robot trajectory, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e18\u003c/span\u003e. The results shows that the proposed integrated-odometry-based localization solution and motion control strategy of the robot are feasible and effective in the simulated scenario of underground coal mine auxiliary transport roadways.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e(a)shows the result of Visual-based SLAM; (b) shows the result of Lidar-based SLAM; (c) shows the result of Lidar-inertial-based SLAM; (d) shows the result of integrated-odometry-based SLAM.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"7. Conclusions and Future Work","content":"\u003cp\u003eIn this work, a new type of transport robot system MTATBOTS is introduced for intelligent auxiliary transportation of underground coal mine, aiming at executing automated and unmanned subterranean transport task. The robot system is specially designed for the explosion-proof, long-range and perception-degraded underground roadway scenario. The paper describes structural composition of the robot system and the functional implementation of the robot autopilot system. To solve the perception and localization challenges of GNSS-denied subterranean roadway environment, the Integrated-odometry-based SLAM solution is proposed and applied in the robot localization strategy. The proposed algorithm can achieve accurate and robust robot odometry and mapping result by considering Lidar-inertial odometry, visual-inertial odometry and wheel odometry simultaneously. And in order to mitigate the influence of accumulative errors of onboard sensors, the global position information provided by UWB beacons sparsely arranged in underground roadways are also taken into account in the localization algorithm. Furthermore, the robot path-following motion control strategy is presented based on the dynamic model of the robot. Finally, in order to validate the proposed localization algorithm and motion control strategy, the robot virtual model and the simulated underground coal mine auxiliary transport roadways scenario are established. The simulation results indicates that the proposed localization solution and control strategy of the robot are suitable for the auxiliary transport roadway of underground coal mine.\u003c/p\u003e \u003cp\u003eConsidering the complexity of underground transport roadway conditions, it is difficult for the simulated test scenario to reproduce the actual operating environment of the robot system. In the future, the proposed algorithms and control strategies need to be tested and modified under the real subterranean coal mine environment. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e19\u003c/span\u003e, the physical prototype of EWTBOT has been manufactured based on the paper\u0026rsquo;s design and simulation test results. Further testing and validation work will be carried out on the basis of the prototype. Additionally, the current robot control strategy mainly focuses on the tracking of the planning route, and the safe and smooth control strategy of autonomous collision avoidance maneuver in the narrow, space-constrained underground roadway needs to be further improved and optimized.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eConflicts of Interest:\u003c/h2\u003e \u003cp\u003eThe authors declare that there is no conflict of interest regarding the publication of this paper.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eHao, Ren and Ji wrote the main manuscript text. Yuan , Bi and Zhao conducted the experiment of the manuscript . All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThis work is supported by the Shanxi Province Key Research and Development Program Projects of China(201803D121121), the Taiyuan Institute of Technology Scientific Research Initial Funding(2022KJ095).\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe experimental data used to support the findings of this study are available from the corresponding author upon request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eHao, Y. et al. New insights on ground control in intelligent mining with Internet of Things. \u003cem\u003eComput. Commun.\u003c/em\u003e, \u003cb\u003e150\u003c/b\u003e, pp. 788\u0026ndash;798, Jan 15 2020.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang, K. et al. 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The robot is specially designed for long-range, space-constrained and explosion-proof underground coal mine environment. With onboard perception and autopilot system, the robot can perform automated and unmanned subterranean material transportation. The paper proposes an integrated-odometry-based method to improve position estimation and mitigate location ambiguities for simultaneous localization and mapping (SLAM) in large-scale, GNSS-denied and perceptually-degraded subterranean transport roadway scenario. Additionally, the paper analyzes the robot dynamic model and presents the nonlinear control strategy for the robot to autonomously tack a planned trajectory based on the path-following error dynamic model. Finally, the proposed algorithm and control strategy are tested and validated in a virtual underground transport roadway environment relying on the simulation model of the robot system. The test result indicates that the proposed algorithm can obtain more accurate and robust robot odometry and better underground roadway mapping result compared with other SLAM solutions.\u003c/p\u003e","manuscriptTitle":"A Trackless Auxiliary Transportation Robot System for Unmanned Material Distribution of Underground Coal Mine","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-10-03 16:36:58","doi":"10.21203/rs.3.rs-4955671/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"48665337-0841-4e96-a34f-b681d0568a6c","owner":[],"postedDate":"October 3rd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":38346324,"name":"Physical sciences/Engineering/Electrical and electronic engineering"},{"id":38346325,"name":"Physical sciences/Engineering/Mechanical engineering"},{"id":38346326,"name":"Physical sciences/Energy science and technology/Fossil fuels/Coal"}],"tags":[],"updatedAt":"2024-10-07T09:39:28+00:00","versionOfRecord":[],"versionCreatedAt":"2024-10-03 16:36:58","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4955671","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4955671","identity":"rs-4955671","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}