Realization & application of skeletonization based on wave propagation with the grassfire algorithm for path planning

Realization & application of skeletonization based on wave propagation with the grassfire algorithm for path planning | 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 Research Article Realization & application of skeletonization based on wave propagation with the grassfire algorithm for path planning Md Hasibuzzaman, Gene Eu Jan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6780178/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 Path Planning is a key problem in autonomous navigation requiring efficient, safe traversal, and real-time responses. This paper introduces a new method of realizing and implementing skeletonization based on wave propagation using the Grassfire Algorithm. The Grassfire Algorithm uses the traditional method of skeletonization and enhances it by taking the most optimized path, which prioritizes the longest common points, to find an optimized path of travel that exhibits navigation methods. In the absence of any common points at distance, the algorithm limits degradation by using the synchronization, repetition rules, or fallback of wave propagation. Our proposed algorithm can support adaptable responses from the system that allows for the cancellation of path offset, and simultaneous response to changes in the environment, while maintaining skeleton shape even in cluttered or dynamic environments. The experimental results of the proposed algorithm on various grid maps demonstrate the proposed method's ability to generate collision-free, geometrically-related paths appropriate for complex, real-world applications, such as UAV, or multi-agent systems. The Grassfire Method, then, is both a light-weight, topological method with potential for improving real-time robotic path planning in autonomous systems. Robotics Path Planning Autonomous Navigation Skeletonization Grassfire Algorithm Wave Propagation Medial Axis Transform Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1 Introduction Path planning will always be essential to any autonomous navigation scenario, allowing robots and agents to effectively plan for safe navigation in complex environments [ 1 ]. Many planners, such as A* and D*, are mostly grid-based and commonly used, but they become computationally expensive in more variable and cluttered spaces, meaning we require lightweight topological representations [ 2 ]. Skeletonization of environmental spaces is a common way of converting a free space into the intersection of a network of medial axes, so that it can be closely examined while still preserving connectivity in the planning space [ 3 ]. Skeletonizing free space can be especially effective with wave propagation techniques or sub-methods such as grassfire algorithms, where wave propagation is used to simulate the collision of wavefronts, resulting in a first collision location that serves as a skeletal point [ 4 ]. Skeletonization techniques originate from Blum's medial axis transform (MAT) [ 5 ]. While they offer geometric robustness, they do require some attention to the specific application domain when deployed (for instance, noise concerns and real-time performance) [ 6 ]. While recent developments to wavefront-driven skeletonization have focused on improving efficiency, particularly with parallelization [ 7 ], and hybridizing skeletonization algorithms with heuristic search algorithms [ 8 ], many researchers and practitioners still leverage wavefront methods such as grassfire for real-time planning purposes. One specific implementation of wavefront methods is similar to the process used in geometric combustion. The grassfire algorithm propagates a distance field from obstacles to define how far away a path is from an obstacle, and then distills the relevant information in the form of a collision-free corridor [ 9 ]. Unfortunately, current algorithms based on two-dimensional geometries are still hampered by issues with irregular geometries and dynamic updates of obstacles, meaning real-world deployment tasks like UAV navigation in three-dimensional environments or multi-agent systems are still limited in their functionality [ 10 ]. We implement a new approach to study the realization and implementation of skeletonization based upon wave propagation using the grassfire algorithm for path planning, adopting a more novel approach to make even more effective, obstacle-aware navigation. The primary contribution was formulating a skeletonization rule in order to identify common points based on large distances to generate a path optimization. The procedure that was realized systematically increased the distance from the lower to the higher, constructive common point threshold, and utilized a fallback methodology employing wave propagation if no common point threshold existed. This method resulted in path planning that was realized with flexible and functional methods associated with complex problem domains. The grassfire algorithm was also modified to utilize rules of repetition, transverse, and synchronization in order to remedy path offsets and reduce unnecessary movement. Where the path was not remedied by even the standard technique, we utilized our wave propagation mechanism, which allowed for skeletonization continuity and preserved the paths. We even tested a variety of grid maps in order to assess how our method performed, which produced compelling evidence that it produced correct skeleton paths to avoid obstacles. Overall, we supplied evidence that skeletonization combined with adaptive wave propagation has a remarkable advancement with true path planning for real-time applications, and possibly further implications to the field of robotics and autonomous navigation systems. 2 Related Works Skeletonization is well established in simplifying spatial representations for robotics and computer vision. The skeleton extraction was adapted from the medial axis transform (MAT), which models wavefront progression from the boundary [ 11 ]; the extraction process was refined using Hamilton-Jacobi equations to develop a better skeletal representation [ 12 ]. The MAT and the grassfire algorithm, a discrete version of the MAT, were applied to more complex environments that could be interpreted as grid-based [ 13 ]; this is important in robotics and computer vision to maintain speed in computation, but there was a lag in the exploration of noise and how to increase generalizability beyond examples. Wave propagation approaches (e.g., fast marching) [ 14 ] emerged as a means to create skeletonization workflows in continuous spaces using Eikonal equations, propelling its applications in 3D body models [ 15 ]. In robotics, skeletonization has been fused with corridor maps to develop collision-free paths [ 16 ], and work has been published on improving wavefront propagation for dynamic environments in real-time [ 17 ]. Skeletonization frames explored another area with adaptive thresholding to remove over-skeletonization in the presence of noise when representing brute force Cartesian data in mapping scenarios [ 18 ]. The grassfire algorithm has picked up traction for performing path planning in autonomous systems recently. It has successfully contributed to UAV flight in GPS-denied spaces, where obstacle proximity is important [ 19 ], and has also been used in reinforcement learning approaches for improving exploration efficiency in multi-robot systems [ 20 ]. Several hurdles remain—the challenge of balancing computational speed with topological preservation while maintaining robust performance in response to sensor noise. While skeletonization is a realized solution in the literature, a gap remains in its implementation in deployments. 3 The Proposed New Approach In path planning, there are various methods of wave propagation that can be used to identify the shortest or most efficient path while avoiding obstacles. Point wave propagation is the simplest and most useful method and can be utilized most effectively in simple cases with just one obstacle between the start and goal point. Another method is object propagation, which can be further developed by using the grassfire algorithm and would then adopt the skeletonization method for more advanced path planning. 3.1 Point Wave Propagation As illustrated in Fig. 2 , the wave starts from the starting node, node 0 (green node), and propagates in all directions, selecting the nearest nodes that yield the shortest distance to the goal node, node 6 (red node). By traversing all directions and making decisions based on proximity, the wave is able to effectively navigate through the environment towards the goal, travelling in a minimum number of steps while avoiding any collisions. In this example, the wave has determined an optimal route from point 0 to point 6. To help solidify the concept, Fig. 1 presents a much simpler example. The wave starts at point 0 and rolls out and around a single obstacle. The wave travelled in the 0, 4, 5, 6 intermediate nodes prior to reaching the obstacle. Node 6 is the furthest point of the wave prior to hitting the obstacle, which is the extent of this iteration of wave propagation. Moreover, Fig. 2 illustrates that there are two possible shortest paths leading to the destination. One path goes to the left of point 0, the other goes left after moving horizontally then turning toward the goal. Both paths are shortest routes, demonstrating that point wave propagation can intelligently calibrate even in a simple environment. 3.2 Object Wave Propagation Wave propagation emanates from the boundary of the obstacle, as shown in Fig. 3 below, which can take any number of forms. The wave propagates outward by adding a distance value of one, until the wave can no longer fill up cells in the free space. The first illustration shows obstacles represented as 1 and free space as 0. For the distance propagation I will have to reverse this meaning: the distances will use a continually increasing value (1, 2, 3,, and so on) while the inside of the obstacle will represent either a 0 or ∞ (inaccessible space). As shown below, Fig. 4 , the contour lines are multi-colored to represent the wavefront propagating from a contour around an obstacle. Distance propagation begins from contoured boundary to fill in free space by minimum distance values on the first accessible cells. 3.3 Skeletonization Using the Enhanced Grassfire Method Skeletonization refers to the process of reducing a shape or object in an image to an essential structure or "skeleton" by preserving the geometry and connectivity. The Enhanced Grassfire Method will be considered as it is an improvement to traditional skeletonization by mimicking a wavefront propagation away from the boundary of the object and inward. This method uses a prioritized approach in which it begins with the farthest common points in order to capture the broader structural details associated with the object first. When there are no common points at the greatest distance, it uses the repeated values of the greater distances. When there are no boundaries or obstacles, the algorithm continues marking in the direction of highlighting away from the object until valid points are found while using the largest distance metrics. The process continues to wavefront towards an obstacle. If the previous techniques do not yield results it will default to wave propagation techniques. The enhanced method also provides a more robust and accurate extraction of the skeleton, especially in complex shapes, thus improving accuracy for shape analysis, object recognition, and pathfinding. See Fig. 2 . 3.4 Optimal path finding Figure 5 shows two possible paths from the starting point to the goal. To find the optimal route from the two paths, the algorithm should select the one with the least distance. When traversing, the path should proceed through the center point of each pixel at all times - both to ensure accuracy and smoothness. The same rule should be applied for corner movement too (corner moves would also have to be with the principle of remaining aligned with the pixel’s center point for continuity). This is beneficial for precision in skeleton-based navigation networks or grid-based navigation systems, and avoids the risk of nonsensical transitions and provides the most direct, geometrically sound path for the navigation. 4 Algorithm and Illustration This section shows the algorithm and its pictorial representation to show how the `upgraded' Grassfire can provide an efficient path plan from here to there as a consequence of constructing the skeleton of a binary image and finding the shortest path to the target point. 4.1 Algorithm The Wave-Guided Skeletonization Path Planning algorithm provides a foundation for efficient path planning for robotic agents through the combined application of an improved skeletonization technique and wave propagation, specifically the Grassfire algorithm. The algorithm process begins by tagging the starting position of the robot and keeping track of all previously visited points along the robot’s path. While executing the algorithm, it traces a skeletal representation of the environment derived from the position of obstacles within the grid or arena. The algorithm also generates a list of anticipated common points existing between the skeleton of the robot’s current position and the desired goal, all being derived from the skeletal representation. In the situation where larger distances to common points were found, they were considered first to guarantee that the robot is following an optimal central path. In the case that the common points were minimal in (value) diversity from the goal, the algorithm would revert to other existing methods utilizing the skeleton representation and flexibly synchronized distance considerations, path retracers (repeating path), or just plain wave propagation techniques. The resulting structure of nested methods allows the fluid offering and adaptation to the current context, whether dynamic or accumulated clutter exists. Additionally, the number of potential collisions is reviewed just prior to every movement in the environment, and then the velocity commands are adjusted accordingly. And so delivers a smooth path allowing for advancing in an obstacle-free way that embraces the geometry of the environment. This method provides a lightweight, flexible solution for complex path planning, demonstrating effective methods in the columnar grid of approach maps and providing a real-world opportunity for real-time or projected implementation of these efforts towards UAVs and multi-agent systems. 4.2 Illustration: The graphic provided in Fig. 6 illustrates the use of the Wave-Guided Skeletonization Path Planning algorithm in a grid environment, with the focus on robotics pathfinding around obstacles efficiently. The grid is filled with the different colored paths and boxes, and the red boxes are obstacles. The different colored lines (green, yellow, purple) are differing skeleton paths generated by the medial-axis transform. The robot begins to move left of it in the left most gray cell, labeled as the start, and the goal is cell 5, green, in the lower-left corner. The blue arrows that totally represent the actual path of travel the robot did, which are generated by the Grassfire wave propagation algorithm. Starting at the gray cell, the robot calculates the distance of the cells from the starting position in a unified wavefront across all accessible grid cells. This allowed the robot to discover what the closest distance the robot can travel, while maintaining a trajectory that allows the robot to center on the middle of so that it is not getting too close to or potentially hitting an obstacle. The skeletonization establishes a path, enhancing the movement of the robot along a central corridor with certain constraints. The robot starts each columnation by seeking the farthest common point or the closest common point between the current skeleton path and goal. If the first skeleton path isn't sufficient, the robot selects a closer or same skeleton path. Regardless of the choice made, the robot should always be working toward the direction of the goal. If the open space allows the algorithm to skeletonize the path, the algorithm will skeletonize to the goal. If the skeletonization is poor and there are many paths that do not generate adequate skeletons, redundancy will occur until the robot can make a proper connection to the goal. Adjusting dynamically will minimize collisions and help create better paths. 5 Results and Conclusion In this section, we compare our proposed method with other widely used path planning algorithms and conclude by highlighting its advantages and overall effectiveness." 5.1 Results In below Table 1, we discuss about comparison of our methods and others methods. The Wave-Guided Skeletonization Path Planning algorithm is a well-balanced and adaptively supportive tool helpful for robotic navigation in dynamic and cluttered environments. This algorithm is somewhat unique in its use of wave propagation, using the Grassfire algorithm, along with skeletonization to create a central focused path that navigates around obstacles. Pathfinder algorithms such as A* and Dijkstra’s methods rely on cost or uniform propagation on a grid map. The Grassfire method can consider and check for obstacles dynamically, and ultimately navigate along medial-axis paths to have a more ‘natural’ motion in the navigation of obstacles, and include a real time velocity. RRT algorithms primarily focus on exploration and subsequently provide path solutions that will likely not yield optimum path quality, while Bug algorithms can provide a simple strategy for boundary following—enough for robots that are limited in resources. What is unique to this algorithm is it's ability to ‘recover’ as it utilizes path repetition, have fallback options, and a centrality awareness—navigating challenging terrain (but not to be confused with travel along an obstacle) making it suited for UAVs and multi-agent systems. While it does have a nominally high computational demand relative classical algorithms, there are fewer lookup delays for the robot to question and recover from, and the layered logic provides reliability, adaptive flexibility, and the capability to match the realities of the real world. Table 1 Feature / Method Wave-Guided Skeletonization (Ours) A* Dijkstra's RRT Bug Algorithm Path Type Skeletonized central path Optimal cost-based path Uniform-cost path Random tree-based path Boundary-following Obstacle Handling Dynamic check + skeleton avoidance Avoids via cost Avoids via cost Avoids probabilistically Reactive obstacle avoidance Environment Representation Grid + Skeleton + Distance Map Grid-based Grid-based Continuous space Grid or continuous Wave Propagation (Grassfire) Yes – fallback method Heuristic search Cost-only propagation No No Adaptability to Cluttered Environments High – uses layered logic with skeleton & propagation fallback Medium Low–Medium High (but non-optimal paths) Medium Path Centrality / Smoothness High – favors medial axis & avoids corners Low–Medium Low Very Low Very Low Velocity Adjustment (Real-time) Yes – adjusts before each move No No No No Repetitive Path Recovery Yes – uses repetition on skeleton if needed No No No No Optimality Approximate optimal via skeleton and wave High High Low Very Low Computational Efficiency Medium – layered logic with fallback strategies High Medium Very High Very High Use Case Suitability UAVs, multi-agent, dynamic, cluttered spaces General robotics, navigation General pathfinding High DOF, exploration tasks Simple, low-resource robots 5.2 Conclusion In this paper, we presented a novel path planning process that combines skeletonization with wave propagation through the Grassfire algorithm to navigate successfully, efficiently and collision-free in complicated environments. In our process, we addressed numerous flaws and limitations particularly present within traditional algorithms such as A* and Dijkstra Modulo and the associated path planning that cannot directly represent collision-free medial axis, do not account for geometrics in their model and favor the shortest distance instead of the most optimal or 'smooth' path, while not supporting movement through complex environments or those featuring a number of dynamic obstacles. Each approach suffered from limitations others did not. What we were most excited about with our process, was seeking out the right 'area' to check the starting point compared to the goal, applying rules of synchronization, and repetition of the check, and ultimately falling back to wave propagation when needed. Further, it is needed to state that this 'layered logic' based approach also helps with numerous hurdles when needing consistent path optimization and other pathing obstacles while developing spatial decision making skills in real time applications. The algorithm showed excellent capability to compensate for obstacles, maintain a stable trajectory, and update trajectories in real-time all while maintaining the continuity of the skeleton through extensive simulation in grid-like environments. The main path characteristics, velocity modulation, and recovery mechanism make the algorithm particularly amenable to autonomous mobile robots, UAVs, and multi-agent coordination applications where the vehicle's location and trajectory must be deemed acceptable. As opposed to reactive or random methods of traversing an environment an algorithm based on structural decomposition ensures an acceptable tradeoff between computational speed and path quality. Future work will focus on expanding this type of method into working effectively in 3D stationary and dynamic spaces, both of which are critical for aerial and underwater robotics. We will explore how we could improve computational performance through hardware-level parallelism and also through GPU-based parallel computing. Another important area to expand into is how to incorporate real-time sensory input, such as LiDAR or vision systems, into generating algorithms with the capability to intelligently react to unstructured or changing environments. The final area we would like to explore would be applying these methods to decentralized multi-agent systems, where hosted, collaborative skeletonization and local wave propagation may facilitate distributed yet coordinated path planning. This research provides a strong foundation for advancing realistic real-time navigation focused initially on autonomous systems and, overall, to combine lightweight computation with smart geometry-based spatial awareness. Declarations Acknowledgment Supporter: This research was supported by my advisor, Prof. Gene-Eu Jan but no funding was available for publishing it as open access. Author’s Contribution: Md Hasibuzzaman has contributed to writing the Introduction, Related work, The proposed New Approach, Algorithm and Illustration, Results, and Conclusion. Prof. Gene Eu Jan contributes to giving the idea, revision. Data availability: Data availability. The datasets used or analyzed during the current study are available from the corresponding author on reasonable request. Ethical Approval: No human was involved, and all the research was carried out in an ethical manner. Consent to Participate: I hereby give my consent for the **participate** if any information is required. Consent for Publication: I hereby give my consent for the results of this study to be published. Conflict of Interests: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. The subscription-based publishing model: "I prefer to publish under the subscription-based model, as there is currently no available funding to support Open Access publication fees References S. M. LaValle, Planning algorithms . Cambridge university press, 2006. H. Choset and J. Burdick, "Sensor-based exploration: The hierarchical generalized voronoi graph," The International Journal of Robotics Research, vol. 19, no. 2, pp. 96-125, 2000. R. Geraerts and M. H. Overmars, "The corridor map method: Real-time high-quality path planning," in Proceedings 2007 IEEE International Conference on Robotics and Automation , 2007: IEEE, pp. 1023-1028. J. A. Sethian, "Fast marching methods," SIAM review, vol. 41, no. 2, pp. 199-235, 1999. H. 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Geraerts, "Planning short paths with clearance using explicit corridors," in 2010 IEEE international conference on robotics and automation , 2010: IEEE, pp. 1997-2004. B. Lau, C. Sprunk, and W. Burgard, "Efficient grid-based spatial representations for robot navigation in dynamic environments," Robotics and Autonomous Systems, vol. 61, no. 10, pp. 1116-1130, 2013. H. Zhao, X. Li, Z. Chen, and J. Hu, "Skeletonization-scheme-based adaptive near field sampling for radio frequency source reconstruction," IEEE Internet of Things Journal, vol. 6, no. 6, pp. 10219-10228, 2019. W. Meng, X. Zhang, L. Zhou, H. Guo, and X. Hu, "Advances in UAV Path Planning: A Comprehensive Review of Methods, Challenges, and Future Directions," Drones, vol. 9, no. 5, p. 376, 2025. [Online]. Available: https://www.mdpi.com/2504-446X/9/5/376. G. Calzolari, V. Sumathy, C. Kanellakis, and G. Nikolakopoulos, "Reinforcement Learning Driven Multi-Robot Exploration via Explicit Communication and Density-Based Frontier Search," arXiv preprint arXiv:2412.20049, 2024. Additional Declarations The authors declare no competing interests. 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. 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07:04:55","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1626793,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6780178/v1/dcce8f43-ebcc-47bc-b9a3-fb3dd3d9f797.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eRealization \u0026amp; application of skeletonization based on wave propagation with the grassfire algorithm for path planning\u003c/p\u003e","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003ePath planning will always be essential to any autonomous navigation scenario, allowing robots and agents to effectively plan for safe navigation in complex environments [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Many planners, such as A* and D*, are mostly grid-based and commonly used, but they become computationally expensive in more variable and cluttered spaces, meaning we require lightweight topological representations [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Skeletonization of environmental spaces is a common way of converting a free space into the intersection of a network of medial axes, so that it can be closely examined while still preserving connectivity in the planning space [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Skeletonizing free space can be especially effective with wave propagation techniques or sub-methods such as grassfire algorithms, where wave propagation is used to simulate the collision of wavefronts, resulting in a first collision location that serves as a skeletal point [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Skeletonization techniques originate from Blum's medial axis transform (MAT) [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. While they offer geometric robustness, they do require some attention to the specific application domain when deployed (for instance, noise concerns and real-time performance) [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. While recent developments to wavefront-driven skeletonization have focused on improving efficiency, particularly with parallelization [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], and hybridizing skeletonization algorithms with heuristic search algorithms [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], many researchers and practitioners still leverage wavefront methods such as grassfire for real-time planning purposes. One specific implementation of wavefront methods is similar to the process used in geometric combustion. The grassfire algorithm propagates a distance field from obstacles to define how far away a path is from an obstacle, and then distills the relevant information in the form of a collision-free corridor [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Unfortunately, current algorithms based on two-dimensional geometries are still hampered by issues with irregular geometries and dynamic updates of obstacles, meaning real-world deployment tasks like UAV navigation in three-dimensional environments or multi-agent systems are still limited in their functionality [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. We implement a new approach to study the realization and implementation of skeletonization based upon wave propagation using the grassfire algorithm for path planning, adopting a more novel approach to make even more effective, obstacle-aware navigation. The primary contribution was formulating a skeletonization rule in order to identify common points based on large distances to generate a path optimization. The procedure that was realized systematically increased the distance from the lower to the higher, constructive common point threshold, and utilized a fallback methodology employing wave propagation if no common point threshold existed. This method resulted in path planning that was realized with flexible and functional methods associated with complex problem domains. The grassfire algorithm was also modified to utilize rules of repetition, transverse, and synchronization in order to remedy path offsets and reduce unnecessary movement. Where the path was not remedied by even the standard technique, we utilized our wave propagation mechanism, which allowed for skeletonization continuity and preserved the paths. We even tested a variety of grid maps in order to assess how our method performed, which produced compelling evidence that it produced correct skeleton paths to avoid obstacles. Overall, we supplied evidence that skeletonization combined with adaptive wave propagation has a remarkable advancement with true path planning for real-time applications, and possibly further implications to the field of robotics and autonomous navigation systems.\u003c/p\u003e"},{"header":"2 Related Works","content":"\u003cp\u003eSkeletonization is well established in simplifying spatial representations for robotics and computer vision. The skeleton extraction was adapted from the medial axis transform (MAT), which models wavefront progression from the boundary [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]; the extraction process was refined using Hamilton-Jacobi equations to develop a better skeletal representation [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. The MAT and the grassfire algorithm, a discrete version of the MAT, were applied to more complex environments that could be interpreted as grid-based [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]; this is important in robotics and computer vision to maintain speed in computation, but there was a lag in the exploration of noise and how to increase generalizability beyond examples. Wave propagation approaches (e.g., fast marching) [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] emerged as a means to create skeletonization workflows in continuous spaces using Eikonal equations, propelling its applications in 3D body models [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. In robotics, skeletonization has been fused with corridor maps to develop collision-free paths [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], and work has been published on improving wavefront propagation for dynamic environments in real-time [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Skeletonization frames explored another area with adaptive thresholding to remove over-skeletonization in the presence of noise when representing brute force Cartesian data in mapping scenarios [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. The grassfire algorithm has picked up traction for performing path planning in autonomous systems recently. It has successfully contributed to UAV flight in GPS-denied spaces, where obstacle proximity is important [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], and has also been used in reinforcement learning approaches for improving exploration efficiency in multi-robot systems [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Several hurdles remain\u0026mdash;the challenge of balancing computational speed with topological preservation while maintaining robust performance in response to sensor noise. While skeletonization is a realized solution in the literature, a gap remains in its implementation in deployments.\u003c/p\u003e"},{"header":"3 The Proposed New Approach","content":"\u003cp\u003eIn path planning, there are various methods of wave propagation that can be used to identify the shortest or most efficient path while avoiding obstacles. Point wave propagation is the simplest and most useful method and can be utilized most effectively in simple cases with just one obstacle between the start and goal point. Another method is object propagation, which can be further developed by using the grassfire algorithm and would then adopt the skeletonization method for more advanced path planning.\u003c/p\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1 Point Wave Propagation\u003c/h2\u003e\n \u003cp\u003eAs illustrated in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, the wave starts from the starting node, node 0 (green node), and propagates in all directions, selecting the nearest nodes that yield the shortest distance to the goal node, node 6 (red node). By traversing all directions and making decisions based on proximity, the wave is able to effectively navigate through the environment towards the goal, travelling in a minimum number of steps while avoiding any collisions. In this example, the wave has determined an optimal route from point 0 to point 6. To help solidify the concept, Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e presents a much simpler example. The wave starts at point 0 and rolls out and around a single obstacle. The wave travelled in the 0, 4, 5, 6 intermediate nodes prior to reaching the obstacle. Node 6 is the furthest point of the wave prior to hitting the obstacle, which is the extent of this iteration of wave propagation.\u003c/p\u003e\n \u003cp\u003eMoreover, Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates that there are two possible shortest paths leading to the destination. One path goes to the left of point 0, the other goes left after moving horizontally then turning toward the goal. Both paths are shortest routes, demonstrating that point wave propagation can intelligently calibrate even in a simple environment.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n \u003ch2\u003e3.2 Object Wave Propagation\u003c/h2\u003e\n \u003cp\u003eWave propagation emanates from the boundary of the obstacle, as shown in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e below, which can take any number of forms. The wave propagates outward by adding a distance value of one, until the wave can no longer fill up cells in the free space. The first illustration shows obstacles represented as 1 and free space as 0. For the distance propagation I will have to reverse this meaning: the distances will use a continually increasing value (1, 2, 3,, and so on) while the inside of the obstacle will represent either a 0 or \u0026infin; (inaccessible space). As shown below, Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e, the contour lines are multi-colored to represent the wavefront propagating from a contour around an obstacle. Distance propagation begins from contoured boundary to fill in free space by minimum distance values on the first accessible cells.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003e3.3 Skeletonization Using the Enhanced Grassfire Method\u003c/h2\u003e\n \u003cp\u003eSkeletonization refers to the process of reducing a shape or object in an image to an essential structure or \u0026quot;skeleton\u0026quot; by preserving the geometry and connectivity. The Enhanced Grassfire Method will be considered as it is an improvement to traditional skeletonization by mimicking a wavefront propagation away from the boundary of the object and inward. This method uses a prioritized approach in which it begins with the farthest common points in order to capture the broader structural details associated with the object first. When there are no common points at the greatest distance, it uses the repeated values of the greater distances. When there are no boundaries or obstacles, the algorithm continues marking in the direction of highlighting away from the object until valid points are found while using the largest distance metrics. The process continues to wavefront towards an obstacle. If the previous techniques do not yield results it will default to wave propagation techniques. The enhanced method also provides a more robust and accurate extraction of the skeleton, especially in complex shapes, thus improving accuracy for shape analysis, object recognition, and pathfinding. See Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n \u003ch2\u003e3.4 Optimal path finding\u003c/h2\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e shows two possible paths from the starting point to the goal. To find the optimal route from the two paths, the algorithm should select the one with the least distance. When traversing, the path should proceed through the center point of each pixel at all times - both to ensure accuracy and smoothness. The same rule should be applied for corner movement too (corner moves would also have to be with the principle of remaining aligned with the pixel\u0026rsquo;s center point for continuity). This is beneficial for precision in skeleton-based navigation networks or grid-based navigation systems, and avoids the risk of nonsensical transitions and provides the most direct, geometrically sound path for the navigation.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4 Algorithm and Illustration","content":"\u003cp\u003eThis section shows the algorithm and its pictorial representation to show how the `upgraded\u0026apos; Grassfire can provide an efficient path plan from here to there as a consequence of constructing the skeleton of a binary image and finding the shortest path to the target point.\u003c/p\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n \u003ch2\u003e4.1 Algorithm\u003c/h2\u003e\n \u003cp\u003e\u003cimg 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\" style=\"width: 1039px;\" width=\"1039\" height=\"893\"\u003e\u003cbr\u003e\u003c/p\u003e\n \u003cp\u003eThe Wave-Guided Skeletonization Path Planning algorithm provides a foundation for efficient path planning for robotic agents through the combined application of an improved skeletonization technique and wave propagation, specifically the Grassfire algorithm. The algorithm process begins by tagging the starting position of the robot and keeping track of all previously visited points along the robot\u0026rsquo;s path. While executing the algorithm, it traces a skeletal representation of the environment derived from the position of obstacles within the grid or arena. The algorithm also generates a list of anticipated common points existing between the skeleton of the robot\u0026rsquo;s current position and the desired goal, all being derived from the skeletal representation. In the situation where larger distances to common points were found, they were considered first to guarantee that the robot is following an optimal central path. In the case that the common points were minimal in (value) diversity from the goal, the algorithm would revert to other existing methods utilizing the skeleton representation and flexibly synchronized distance considerations, path retracers (repeating path), or just plain wave propagation techniques. The resulting structure of nested methods allows the fluid offering and adaptation to the current context, whether dynamic or accumulated clutter exists. Additionally, the number of potential collisions is reviewed just prior to every movement in the environment, and then the velocity commands are adjusted accordingly. And so delivers a smooth path allowing for advancing in an obstacle-free way that embraces the geometry of the environment. This method provides a lightweight, flexible solution for complex path planning, demonstrating effective methods in the columnar grid of approach maps and providing a real-world opportunity for real-time or projected implementation of these efforts towards UAVs and multi-agent systems.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n \u003ch2\u003e4.2 Illustration:\u003c/h2\u003e\n \u003cp\u003eThe graphic provided in Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e illustrates the use of the Wave-Guided Skeletonization Path Planning algorithm in a grid environment, with the focus on robotics pathfinding around obstacles efficiently. The grid is filled with the different colored paths and boxes, and the red boxes are obstacles. The different colored lines (green, yellow, purple) are differing skeleton paths generated by the medial-axis transform. The robot begins to move left of it in the left most gray cell, labeled as the start, and the goal is cell 5, green, in the lower-left corner. The blue arrows that totally represent the actual path of travel the robot did, which are generated by the Grassfire wave propagation algorithm. Starting at the gray cell, the robot calculates the distance of the cells from the starting position in a unified wavefront across all accessible grid cells. This allowed the robot to discover what the closest distance the robot can travel, while maintaining a trajectory that allows the robot to center on the middle of so that it is not getting too close to or potentially hitting an obstacle. The skeletonization establishes a path, enhancing the movement of the robot along a central corridor with certain constraints. The robot starts each columnation by seeking the farthest common point or the closest common point between the current skeleton path and goal. If the first skeleton path isn\u0026apos;t sufficient, the robot selects a closer or same skeleton path. Regardless of the choice made, the robot should always be working toward the direction of the goal. If the open space allows the algorithm to skeletonize the path, the algorithm will skeletonize to the goal. If the skeletonization is poor and there are many paths that do not generate adequate skeletons, redundancy will occur until the robot can make a proper connection to the goal. Adjusting dynamically will minimize collisions and help create better paths.\u003c/p\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003c/div\u003e"},{"header":"5 Results and Conclusion","content":"\u003cp\u003eIn this section, we compare our proposed method with other widely used path planning algorithms and conclude by highlighting its advantages and overall effectiveness.\u0026quot;\u003c/p\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n \u003ch2\u003e5.1 Results\u003c/h2\u003e\n \u003cp\u003eIn below Table\u0026nbsp;1, we discuss about comparison of our methods and others methods. The Wave-Guided Skeletonization Path Planning algorithm is a well-balanced and adaptively supportive tool helpful for robotic navigation in dynamic and cluttered environments. This algorithm is somewhat unique in its use of wave propagation, using the Grassfire algorithm, along with skeletonization to create a central focused path that navigates around obstacles. Pathfinder algorithms such as A* and Dijkstra\u0026rsquo;s methods rely on cost or uniform propagation on a grid map. The Grassfire method can consider and check for obstacles dynamically, and ultimately navigate along medial-axis paths to have a more \u0026lsquo;natural\u0026rsquo; motion in the navigation of obstacles, and include a real time velocity. RRT algorithms primarily focus on exploration and subsequently provide path solutions that will likely not yield optimum path quality, while Bug algorithms can provide a simple strategy for boundary following\u0026mdash;enough for robots that are limited in resources. What is unique to this algorithm is it\u0026apos;s ability to \u0026lsquo;recover\u0026rsquo; as it utilizes path repetition, have fallback options, and a centrality awareness\u0026mdash;navigating challenging terrain (but not to be confused with travel along an obstacle) making it suited for UAVs and multi-agent systems. While it does have a nominally high computational demand relative classical algorithms, there are fewer lookup delays for the robot to question and recover from, and the layered logic provides reliability, adaptive flexibility, and the capability to match the realities of the real world.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cdiv align=\"left\" class=\"colspec\" style=\"text-align: center;\"\u003eTable 1\u003c/div\u003e\u0026nbsp;\u003ctable id=\"Tabb\" border=\"1\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFeature / Method\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eWave-Guided Skeletonization (Ours)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eA*\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDijkstra\u0026apos;s\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRRT\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBug Algorithm\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePath Type\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSkeletonized central path\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eOptimal cost-based path\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eUniform-cost path\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRandom tree-based path\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBoundary-following\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eObstacle Handling\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDynamic check\u0026thinsp;+\u0026thinsp;skeleton avoidance\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAvoids via cost\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAvoids via cost\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAvoids probabilistically\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eReactive obstacle avoidance\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eEnvironment Representation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGrid\u0026thinsp;+\u0026thinsp;Skeleton\u0026thinsp;+\u0026thinsp;Distance Map\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGrid-based\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGrid-based\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eContinuous space\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGrid or continuous\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWave Propagation (Grassfire)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eYes \u0026ndash; fallback method\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHeuristic search\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCost-only propagation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAdaptability to Cluttered Environments\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHigh \u0026ndash; uses layered logic with skeleton \u0026amp; propagation fallback\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMedium\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLow\u0026ndash;Medium\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHigh (but non-optimal paths)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMedium\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePath Centrality / Smoothness\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHigh \u0026ndash; favors medial axis \u0026amp; avoids corners\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLow\u0026ndash;Medium\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eVery Low\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eVery Low\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eVelocity Adjustment (Real-time)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eYes \u0026ndash; adjusts before each move\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRepetitive Path Recovery\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eYes \u0026ndash; uses repetition on skeleton if needed\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eOptimality\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eApproximate optimal via skeleton and wave\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHigh\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHigh\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eVery Low\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eComputational Efficiency\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMedium \u0026ndash; layered logic with fallback strategies\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHigh\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMedium\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eVery High\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eVery High\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eUse Case Suitability\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eUAVs, multi-agent, dynamic, cluttered spaces\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGeneral robotics, navigation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGeneral pathfinding\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHigh DOF, exploration tasks\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSimple, low-resource robots\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n \u003ch2\u003e5.2 Conclusion\u003c/h2\u003e\n \u003cp\u003eIn this paper, we presented a novel path planning process that combines skeletonization with wave propagation through the Grassfire algorithm to navigate successfully, efficiently and collision-free in complicated environments. In our process, we addressed numerous flaws and limitations particularly present within traditional algorithms such as A* and Dijkstra Modulo and the associated path planning that cannot directly represent collision-free medial axis, do not account for geometrics in their model and favor the shortest distance instead of the most optimal or \u0026apos;smooth\u0026apos; path, while not supporting movement through complex environments or those featuring a number of dynamic obstacles. Each approach suffered from limitations others did not. What we were most excited about with our process, was seeking out the right \u0026apos;area\u0026apos; to check the starting point compared to the goal, applying rules of synchronization, and repetition of the check, and ultimately falling back to wave propagation when needed. Further, it is needed to state that this \u0026apos;layered logic\u0026apos; based approach also helps with numerous hurdles when needing consistent path optimization and other pathing obstacles while developing spatial decision making skills in real time applications. The algorithm showed excellent capability to compensate for obstacles, maintain a stable trajectory, and update trajectories in real-time all while maintaining the continuity of the skeleton through extensive simulation in grid-like environments. The main path characteristics, velocity modulation, and recovery mechanism make the algorithm particularly amenable to autonomous mobile robots, UAVs, and multi-agent coordination applications where the vehicle\u0026apos;s location and trajectory must be deemed acceptable. As opposed to reactive or random methods of traversing an environment an algorithm based on structural decomposition ensures an acceptable tradeoff between computational speed and path quality. Future work will focus on expanding this type of method into working effectively in 3D stationary and dynamic spaces, both of which are critical for aerial and underwater robotics. We will explore how we could improve computational performance through hardware-level parallelism and also through GPU-based parallel computing. Another important area to expand into is how to incorporate real-time sensory input, such as LiDAR or vision systems, into generating algorithms with the capability to intelligently react to unstructured or changing environments. The final area we would like to explore would be applying these methods to decentralized multi-agent systems, where hosted, collaborative skeletonization and local wave propagation may facilitate distributed yet coordinated path planning. This research provides a strong foundation for advancing realistic real-time navigation focused initially on autonomous systems and, overall, to combine lightweight computation with smart geometry-based spatial awareness.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgment\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupporter:\u003c/strong\u003e This research was supported by my advisor, Prof. Gene-Eu Jan but no funding was available for publishing it as open access.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor\u0026rsquo;s Contribution:\u0026nbsp;\u003c/strong\u003eMd Hasibuzzaman has contributed to writing the Introduction, Related work, The proposed New Approach, Algorithm and Illustration, Results, and Conclusion.\u003c/p\u003e\n\u003cp\u003eProf. Gene Eu Jan contributes to giving the idea, revision.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability:\u0026nbsp;\u003c/strong\u003eData availability. The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthical Approval:\u003c/strong\u003e No human was involved, and all the research was carried out in an ethical manner.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to Participate:\u003c/strong\u003e I hereby give my consent for the **participate** if any information is required.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for Publication:\u0026nbsp;\u003c/strong\u003eI hereby give my consent for the results of this study to be published.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of Interests:\u0026nbsp;\u003c/strong\u003eThe author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eThe subscription-based\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003epublishing model:\u003c/strong\u003e \u0026quot;I prefer to publish under the subscription-based model, as there is currently no available funding to support Open Access publication fees\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eS. 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Nikolakopoulos, \u0026quot;Reinforcement Learning Driven Multi-Robot Exploration via Explicit Communication and Density-Based Frontier Search,\u0026quot; \u003cem\u003earXiv preprint arXiv:2412.20049, \u003c/em\u003e2024.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Asia University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"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},"keywords":"Path Planning, Autonomous Navigation, Skeletonization, Grassfire Algorithm, Wave Propagation, Medial Axis Transform","lastPublishedDoi":"10.21203/rs.3.rs-6780178/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6780178/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePath Planning is a key problem in autonomous navigation requiring efficient, safe traversal, and real-time responses. This paper introduces a new method of realizing and implementing skeletonization based on wave propagation using the Grassfire Algorithm. The Grassfire Algorithm uses the traditional method of skeletonization and enhances it by taking the most optimized path, which prioritizes the longest common points, to find an optimized path of travel that exhibits navigation methods. In the absence of any common points at distance, the algorithm limits degradation by using the synchronization, repetition rules, or fallback of wave propagation. Our proposed algorithm can support adaptable responses from the system that allows for the cancellation of path offset, and simultaneous response to changes in the environment, while maintaining skeleton shape even in cluttered or dynamic environments. The experimental results of the proposed algorithm on various grid maps demonstrate the proposed method's ability to generate collision-free, geometrically-related paths appropriate for complex, real-world applications, such as UAV, or multi-agent systems. The Grassfire Method, then, is both a light-weight, topological method with potential for improving real-time robotic path planning in autonomous systems.\u003c/p\u003e","manuscriptTitle":"Realization \u0026amp; application of skeletonization based on wave propagation with the grassfire algorithm for path planning","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-03 06:40:50","doi":"10.21203/rs.3.rs-6780178/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":"aaf03788-b770-4f09-8542-de85ca76135d","owner":[],"postedDate":"June 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":49323086,"name":"Robotics"}],"tags":[],"updatedAt":"2025-06-17T11:23:30+00:00","versionOfRecord":[],"versionCreatedAt":"2025-06-03 06:40:50","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6780178","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6780178","identity":"rs-6780178","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}