Slip-resistant mechanism of bio-inspired foot end based on particle morphology and friction on ice and frozen ground

Slip-resistant mechanism of bio-inspired foot end based on particle morphology and friction on ice and frozen ground | 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 Slip-resistant mechanism of bio-inspired foot end based on particle morphology and friction on ice and frozen ground Guoyu Li, Rui Zhang, Kaixiang Chen, Hao Pang, Rui Zhang, Lige Wen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4251682/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 The attachment characteristics of the mechanical foot end are crucial for enhancing the traversability and locomotion of robots on extreme terrains. In this study targeting the reindeer touchdown unit, four bio-inspired foot ends and one conventional multi-baffle foot end were designed. Dynamic friction data of the bio-inspired foot ends were collected under various ground conditions, and the macro- and micro-structures of these surfaces were analyzed. The impacts of multiple factors on the attachment performances of the bio-inspired foot ends were explored, including the moisture content and compactness of frozen soil, and the ridges and convex crowns of foot ends. Additionally, a sliding/rolling friction conversion model was proposed to describe the interaction between the foot ends and frozen soil. When the ends interacted with the frozen ground and simulant for water-ice lunar soil, the attachment of the bio-inspired ribbed foot end and convex-crown was the best, and its dynamic coefficient of friction (DCOF) increased by 24.19%-44.68% and 35.14%-51.47% than the multi-baffle foot end. Upon interacting with the ice surface, the bio-inspired ribless foot end and non-convex crown demonstrated the best attachment performance. The DCOFs of these designs increased by about 24% compared to the multi-baffle foot end. The attachment performances of foot ends were more affected by moisture content compared with the compacted state of frozen ground. Compared to the ribless and non-convex-crown structures, the structures of ribs and convex-crown increased DCOF by 1%-15% and 18%-42%, respectively. Therefore, the effect of convex-crowns was greater than that of ribs. This study can improve the adaptability and traversability of robots on extreme terrains, which is of great significance for their applications in exploring polar regions, the moon, and other harsh environments. reindeer hoof bio-inspired foot end ice and frozen ground friction test slip-resistant mechanism 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 1 Introduction With the development of artificial intelligence, robots have gradually entered daily life, replacing humans to complete production and manufacturing. For example, digit robots can carry out logistics and parcel delivery (Kuindersma et al., 2016 , Zhang 2021 ). Unmanned military equipment has become an inevitable trend, and various military robots are increasingly widely used. For instance, Packbot robots can complete reconnaissance, exploration, and handling of explosive devices (Mller et al., 2021 ). As the only part in contact with the ground, the end of the mechanical foot is of great significance to improve the traversability and mobility of the robot on extreme ground. Bio-inspired legged robots have high movement flexibility and environmental adaptability on unconventional ground owing to the discrete point contacts and flexible limb structures. They have been used in exploration and transportation under high-risk environments, such as frozen ground ( Zhang et al., 2019). BigDog, the military quadruped robot developed by Boston Dynamics, is equipped with advanced controllers (e.g., terrain sensors, dynamic control) to coordinate leg movements and ensure movement balance and stability. Its controllers adapt to terrain changes through terrain measurement and attitude control ( Nelson et al., 2006). Researchers from Massachusetts Institute of Technology analyzed the kinetics, energy consumption and speed of quadrupeds during movement, and designed a bio-inspired lightweight mechanical foot simulating cheetah hindlimbs based on the principle of tendon-bone copositioning. This mechanical foot with less weight meets the premise of stiffness and strength, avoids large bending moments and improves energy efficiency, which contribute to high-speed movement ( Kim et al., 2006). The second-generation Atlas has made breakthroughs in portability and balance. The internal sensors and lidar positioning allow this robot to avoid obstacles, maintain balance and complete movements outdoors ( Koolen et al., 2016). However, the robot will still slip upon walking on snow, and can only collect posture data through sensors and adjust its motion to keep body balance. Because of the control algorithm, image measurement and gait adjustment endow the foot robot with an anti-interference ability and the ability to walk on frozen ground to certain extent. However, the robot is limited by low walking stability and a relatively simple foot structure, and there is little research on design of bio-inspired feet on frozen ground. Frozen grounds, a type of extreme ground, are widely distributed in the world with a total area ~ 35 million km 2 , accounting for 25% of the entire earth area. Frozen grounds are more widely found in the northern hemisphere. As scientists explored the moon in recent decades, they have discovered that water ice exists on the moon, but the specific location and content of water ice are still at the research stage ( Spudis et al., 2013). The NASA and ESA detected water ice in the permanent shadow areas (craters) of the north and south lunar poles using lunar probes, such as Clementine, Lunar Prospector and SMART-1, and initially concluded that water ice may exist ( Richard et al., 1999, Feldman et al., 1998, Racca et al., 2002). Besides, LCROSS and LRO cooperated in impacting the moon. Through thermal imaging, near-infrared spectroscopy, ultraviolet spectroscopy and other technologies, they detected water vapor in impact sputters, and successfully proved the existence of water ice on the moon (Neish et al., 2011 ). In 2010, the Mini-star radar mounted on Chandrayaan-1 detected more than 40 craters containing water ice in the lunar north pole, and the content of water ice was estimated to be about 0.6 billion tons (Deutsch et al., 2017 ). Lunar water ice is not only a hot spot for international exploration, but also a future strategic resource. At present, all the global major space powers have formulated plans to detect and sample lunar water ice. The ESA is aimed to build a lunar village. China plans to conduct multiple detection and samples of lunar water ice by 2030 ( Green 2011). Lunar water ice mainly exists in craters, which are difficult for wheeled robots to pass through. In comparison, footed robots with excellent active adaptability and foot attachment have good application prospects ( Asif and Iqbal 2012). Under the law of natural selection, the foot structures, movements, and functions of animals have evolved to adapt to the environment. Engineering application of special structures of animal feet based on bio-inspireds has long been a source to solve problems and find inspiration (Zhao et al., 2023 ). Mechanical feet designed with hoofed animals as bio-inspired prototypes show excellent adaptability and movement characteristics in various grounds. Abad designed a goat-hoof-like mechanical foot with flexible joints, strong attachment, and cushioning vibration reduction. The hoof anterior and convex-crown pattern of the mechanical foot improve the attachment performance by embedding into the ground and enlarging the contact area respectively. The pattern structure is stuck in rocks or soil and can provide an additional braking effect ( Zhong et al., 2019). Horse feet have mobility, load-bearing capacity and endurance during movement. Garcia et al. simulated the horse muscle system by connecting elastic elements and excitation units in series, designed a bio-inspired mechanical foot based on effective leg length, kinematics, and foot mass distribution, and studied the key influence factors on the agility of the mechanical foot ( Sanz et al., 2015). Reindeer ( Rangifer tartandus ), a typical polar migratory animal, belongs to Cervidae, Artiodactyla and has a hoof structure suitable for migration in complex environments ( Zhang et al., 2019). In particular, reindeer hooves have good traversability on frozen ground ( Wareing et al., 2021). The ungula structure and plantar fur of the hooves can enlarge the contact area with the ground and play an anti-slip role when walking on frozen ground (Raesaenen et al., 2007 ). Reindeer migrate seasonally over long distances on land, and some populations even migrate farther than other terrestrial mammals ( Fancy et al., 1989). In this study, the particle compositions of original soil and simulant lunar soil were analyzed microscopically, and the effects of particle compositions on the surface roughness of frozen ground were revealed. Based on the microstructure and macrostructure of stance units, four bio-inspired attachment foot ends and an ordinary multi-baffle foot end were designed. The attachment performances of the five foot ends on ice and frozen ground were comparatively tested using a friction testing machine, and the slip-resistant mechanism was revealed. The influence factors including moisture content, compaction state, crown and rib on the dynamic coefficient of friction (DCOF) in frozen ground were analyzed. 2 Materials and methods 2.1 Construction and micromorphology of ice and frozen ground The physical properties of the collected original soil and simulant lunar soil were analyzed, and the effect of the micromorphology of ice or frozen ground was observed. 2.1.1 Particle compositions The samples of original soil and simulant lunar soil were observed under a BT-1600 image particle analyzer, and the particle morphology is shown in Figs. 1 and 2 . The particles can be categorized by the structure and outline into spherical, elongated, and polygonal shapes. Both the original soil and the simulant lunar soil have more polygonal particles, which also indicates the irregularity of the particles in the soil samples. Both the original soil and the simulant lunar soil were dark gray. Soil particle diameter was detected using the sieving method, and the main equipment included soil sieves (holes of 0.15, 0.3, 0.45, 0.63, 1, 2, and 4 mm), a high-frequency vibrating sifter, and an electronic balance. About 1000 g of soil was dried, sieved and weighed. The original soil sieved at particle sizes of > 4, 2–4, 1–2, 0.63-1, 0.45–0.63, 0.3–0.45, 0.15–0.3 and < 0.15 mm accounted for about 1.55%, 11.94%, 21.55%, 24.65%, 2.63%, 17.91%, 11.08% and 8.68%, respectively (Fig. 3 A). The particle size of the original soil was concentrated in 0.3-2 mm. The simulant lunar soil fell in the particle sizes of > 1, 0.63-1, 0.45–0.63, 0.3–0.45, 0.15–0.3, 0.097–0.15, 0.075–0.097 and < 0.075 mm, which accounted for about 0.60%, 2.28%, 0.27%, 5.69%, 5.09%, 13.86%, 34.96% and 37.24%, respectively (Fig. 3 B). Compared with the original soil, the particle size distribution of the simulant lunar soil was more concentrated and was mainly < 0.15 mm. The mechanical properties of soil are closely related to its particle size and gradation. Results show the original soil is distributed more discretely and has larger particles. Therefore, the surface of frozen ground is rougher under the same preparation conditions. 2.1.2 Microscopic surface structure of frozen ground Ice and frozen ground was categorized into three types: frozen ground, Simulant for water-ice lunar soil, and ice. According to ESA, the moisture content of frozen ground in lunar polar regions is below 11.9% ( Song et al., 2021). Mechanical mixing of water or ice particles with dry simulant lunar soil is commonly used to make Simulant for water-ice lunar soil ( Koemle et al., 2016). To study the physical properties of the Simulant for water-ice lunar soil, we mixed the simulant lunar soil with water-ice particles to form soil with 8% moisture and froze it in a freezer at -20°C. In addition, ice surface was made. Based on moisture content, the frozen ground was divided into four types: 16.3% (original frozen), 20%, 35%, and 50% moisture. Based on the compacted state, the frozen ground was divided into two types: loose and tight. The Simulant for water-ice lunar soil was divided into two types: water-soil mixed, and ice-soil mixed. Based on the contact relationship between soil particles and ice structure, the surface structure of frozen ground was analyzed (Fig. 4 ). As the original loose frozen ground, the gaps between soil particles were large and contained only a few ice crystals. At the moisture content of 20%, the gaps of the loose frozen ground were connected by a slightly larger number of ice crystals than in the original frozen ground. The small gaps were filled with ice crystals and the large gaps were still interstitial. At the moisture content of 35%, many ice crystals appeared on the gaps of the loose frozen ground, and ice crystals almost completely filled in the gaps between soil particles. At the moisture content of 50%, many ice crystals still existed on the gaps of the loose frozen ground, and ice crystals fully filled in the gaps between soil particles. In addition, a smooth ice surface was formed on the gaps due to the consolidation of the ice crystals. As the moisture content increased, ice crystals were formed on the gaps of the soil particles, and a number of ice crystals consolidated to form a smooth ice surface. Under the same moisture content, the surface consolidation of the gaps on tight frozen ground was similar to that on loose frozen ground (Fig. 5 ). However, the surface of the tight frozen ground was flatter due to compaction. The surface structure of the dry simulant lunar soil was shown in Fig. 6 A. As the simulant lunar soil was mixed with water and ice, the Simulant for water-ice lunar soil was more compact than the dry simulant lunar soil (Fig. 6 B and C). The ice surface is the smoothest, because it has fewer convex structures and is almost flat (Fig. 6 D). The particle size of the simulant lunar soil was smaller than that of the original soil, so the Simulant for water-ice lunar soil was smoother than the frozen ground. 2.2 Design of bio-inspired attachment foot ends Targeting at reindeer hooves, we designed four bio-inspired foot ends, and an ordinary multi-baffle foot end based on the typical curves of the ungula edge, the ball surface of the ungula capsule, and the microstructure of the hooves. 2.2.1 Bio-inspired prototype Four reindeer hindlimbs were selected from naturally dead adult male reindeer in the Ewenki tribe in Genhe City, China. The ungulae were free from disease or any surgical treatment, or other invasive manipulations (Fig. 7 A). Before the test, the reindeer ungulae were cleaned with distilled water to remove any surface dirt from the samples. Then the samples were left to dry naturally and subjected to CT scanning (220 KV, 220 MA, 1.25 mm layer thickness). The hoof model after CT scanning was mesh-healed, relaxed, and smoothed in Geomagic Studio to generate a 3D model (Fig. 7 B). In winter, the reindeer hooves are the only part in contact with the ice and frozen ground (Nichol et al., 2004 ). The microstructure of the reindeer ungula cusp was jagged ribs, and many cracks existed in the severely worn area. The width and length of the ribs were measured with a ratio of 0.65:1 (Fig. 7 C). On the ungula edge, the ribs were longitudinally distributed and the surface was rough. The width and distance of the ribs were measured with a ratio of 3:1 (Fig. 7 D). In addition, the scales of the plantar fur were closely arranged, and the scale ripples were largely undulated (Fig. 7 E). On the ice and frozen ground, these specific structures were served as an attachment function for the reindeer. 2.2.2 Structural and functional design of the bio-inspired foot front end The reindeer plantar feature plays a crucial role in the slip resistance on frozen ground, such as the typical curves of the ungula edge (Fig. 8 A). After the ungula cusp and inner and outer edge curves were equidistantly spaced inward by 3.6 mm, the curves were stretched by 18.0 mm and the inner groove was stretched by 1.2 mm. Then the 3D model of the bio-inspired foot front end was established (Fig. 8 B). 2.2.3 Structural and functional design of bio-inspired ribs The bio-inspired ribbed part at the ungula cusp and edge was designed according to the microstructure ratio of the reindeer hooves. The bio-inspired ribs of the foot front end consisted of serrated ribs at the ungula cusp and longitudinal ribs at the ungula edge (Fig. 8 C, D, and E). 2.2.4 Structural and Functional Design of bio-inspired convex-crown The ungula capsule of reindeer, which critically contributes to the attachment characteristics, was further converted into a 3D model (Fig. 8 F). Given the basic dimensions of the bio-inspired convex-crown, the number of bio-inspired pattern designs shall ensure a moderate distribution of density. The number of bio-inspired patterns of 10 is reasonable. The plantar fur at the proximal capsule of the reindeer ungula is denser than at the distal capsule. Combining with the sparse distribution of plantar fur, we arranged four and six bio-inspired crowns at the distal and proximal convexes of the bio-inspired foot end, respectively. Given the distribution angle of the plantar fur, the bio-inspired crowns were distributed to both sides at an angle of ~ 30° to the centerline of the convex. 2.2.5 Structural design of the ordinary multi-baffle foot end As is well-known, the multi-baffle foot end has good attachment characteristics ( Poerschke et al., 2021). An ordinary multi-baffle foot was designed by combining with the specific dimensions of the bio-inspired foot end (Fig. 8 G and H). The height, upper surface area, and lower surface contact area of the multi-baffle foot end are consistent with the bio-inspired foot ends (Table 1 ). Table 1 Dimensions of the bio-inspired and ordinary foot ends Height (mm) Upper surface area (mm 2 ) Lower surface contact area (mm 2 ) Bio-inspired foot ends 25.00 14307.10 2324.00 Multi-baffle foot end 25.00 14224.20 2326.21 2.3 Experiment design of foot ends on ice and frozen ground 2.3.1 Processing of foot ends Bio-inspired foot end A is composed of a bio-inspired ribbed foot end and a non-convex-crown (Fig. 9 A). Bio-inspired foot end B consists of a bio-inspired ribbed foot end and a bio-inspired convex-crown (Fig. 9 B). Bio-inspired foot end C is composed of a bio-inspired ribless foot end and a non-convex-crown (Fig. 9 C). Bio-inspired foot end D consists of a bio-inspired ribless foot end and a convex-crown (Fig. 9 D). Multi-baffle foot end E is of the same size (Fig. 9 E). 2.3.2 Experiment conditions Frozen ground attachment experiments were done with a UTM friction testing machine (Fig. 10 ). The tray with frozen ground was fixed on the machine. One end of the traction line was connected to the attachment foot, and the other end was linked to a tension sensor on the lifting rod. The sensor accuracy was 0.0001. The position of the lifting rod was adjusted to keep the traction line horizontal. After the lifting rod was fixed, it moved horizontally and uniformly on the electric track. The moving speed range and maximum moving distance were 10–500 mm/min and 200 mm respectively. The experiment was conducted in a cold room with the temperature controlled around − 10°C. During the experiment, the room was closed to avoid the influence of wind, and the surface temperature of the frozen ground was stable at ± 0.5°C. The signals of friction force and displacement were detected using force and displacement sensors and transmitted to a computer. 2.4 Data processing and analysis The sliding friction between a bio-inspired foot end and the frozen ground was collected using a UTM friction tester. The mean and standard deviation of the DCOF of five successful tests under each condition were obtained on Origin 9.1. The effects of moisture content (20% vs. 50%), compacted state (loose vs. tight), ribs (ribbed vs. ribless) and convex-crown (convex-crown vs. non-convex-crown) on the attachment characteristics of the bio-inspired foot end were tested via two-way analysis of variance (ANOVA). Then the interaction effects were analyzed. The significance level was set at P < 0.05. 3 Results and discussion 3.1 Slip-resistant mechanism of bio-inspired foot end on frozen ground 3.1.1 Attachment experiments on original frozen ground The DCOFs and the changing patterns of the five foot ends on the original frozen ground (16.4% moisture) are shown in Fig. 11 . The DCOFs of the five foot ends on loose original frozen ground rank as foot end B > foot end D > multi-baffle foot end E > foot end A > foot end C (Fig. 11 A). The DCOFs of the five foot ends on tight original frozen ground rank as foot end B > foot end D > foot end A > multi-baffle foot end E > foot end C (Fig. 11 B). Compared with multi-baffled foot end E , the DCOFs of bio-inspired foot ends B and D increased by 11.43%-31.75% and 2.86%-17.46%, respectively. Hence, bio-inspired foot ends B and D acted as good attachments. Upon interacting with the original frozen ground, the ribs and convex of a bio-inspired foot end all can embed into the frozen ground (Fig. 11 C). Bio-inspired foot end B increased the embedding depth through the bio-inspired crown, and the bio-inspired ribs had better grip performance, so its attachment performance was the optimal. The embedding of the foot end into the frozen soil caused the frozen surface to loosen, increasing soil particles. Upon interaction with the foot end, these soil particles began to roll, converting sliding friction into rolling friction, which reduced the attachment performance of the foot end. Given the variance in preparation methods between the original frozen soil and other frozen soils (20%, 35%, and 50% moisture), we then comparatively analyzed the factors. 3.1.2 Attachment comparison of foot ends on frozen ground The changes of DCOF in the five foot ends on frozen ground (20%, 35%, and 50% moisture) are shown in Fig. 12 A. With the increasing moisture content in frozen soil, the DCOF of the foot ends consistently rose. Compared with the moisture content, the compacted state of the frozen ground had a relatively minor impact on the attachment performance of the foot ends. Under the same conditions, the adhesion performance was the highest in bio-inspired foot end B , followed by bio-inspired foot end D , and was the lowest in bio-inspired foot end C . The difference in attachment performance between bio-inspired foot end A and multi-baffle foot end E was relatively minor. The DCOF of foot end E was larger than that of foot end A under the loose ground conditions of 35% and 50% moisture, but was smaller in other conditions. The attachment properties of bio-inspired foot ends B and D were much greater than that of multi-baffled foot end E, and foot end B was superior over foot end D (Table 2 ). Under the loose frozen grounds with 20%, 35%, and 50% moisture, the DCOFs of foot end B are 1.10, 1.10, and 1.15 times those of foot end D , respectively. Under tight frozen grounds with 20%, 35% and 50% moisture, the DCOFs of foot end B are 1.09, 1.13, and 1.14 times those of foot end D , respectively. Table 2 Improvement in attachment performance of bio-inspired foot ends compared to multi-baffle foot end Ratio between foot ends B and E (%) Ratio between foot ends D and E (%) Tight frozen ground 20% moisture 41.18 29.41 35% moisture 36.84 22.81 50% moisture 28.85 11.54 Loose frozen ground 20% moisture 40.58 27.54 35% moisture 24.19 14.52 50% moisture 44.68 25.53 Upon interaction with frozen grounds with 20%, 35%, and 50% moisture, the bio-inspired foot ends can be hardly embedded into the ground. However, under the same load, the bio-inspired crown exhibited a smaller surface area but higher pressure, creating strong friction with the non-smooth surface of the frozen ground and thus enhancing the attachment performance. Additionally, the bio-inspired ribs provided good traction, making bio-inspired foot end B have the optimal attachment performance (Fig. 12 B). 3.1.3 Effects of moisture content and compacted state on attachment characteristics Significant differences were tested with the moisture content and compacted state of frozen ground. The P values indicate moisture content more significantly affected the attachment performances of the five foot ends. The moisture content of frozen ground significantly affected the attachment performances of all five foot ends, whereas the compacted state did not significantly affect bio-inspired foot ends B and D . These results suggest the bio-inspired convex-crown may reduce the effect of frozen ground compacted state on the attachment characteristics of foot ends (Table 3 ). Table 3 Two-way ANOVA for moisture content (20% vs. 50%) and compacted state (loose vs. tight) Moisture content Compacted state Interaction F P F P F P Foot end A 125.35 3.63 x 10 − 6 7.80 2.34 x 10 − 2 0.20 0.66 Foot end B 211.36 4.91 x 10 − 7 0.34 0.58 6.01 x 10 − 3 0.94 Foot end C 83.07 1.69 x 10 − 5 5.63 4.51 x 10 − 2 1.84 0.21 Foot end D 119.52 4.35 x 10 − 6 2.85 x 10 − 2 0.87 9.41 x 10 − 6 1.00 Multi-baffle foot end E 136.44 2.63 x 10 − 6 8.44 1.97 x 10 − 2 15.76 4.12 x 10 − 3 Further experiments revealed that the DCOFs of the foot ends were more pronounced with respect to moisture content compared to the compacted state of the frozen ground. The DCOFs of the foot ends increased with the higher moisture content of the frozen ground. The changing patterns in DCOFs for the five foot ends on the frozen ground with varying moisture content are shown in Fig. 13 . The ice structure content of the frozen ground in a loose state increased with the higher moisture content, leading to a decrease in the DCOFs of the bio-inspired foot ends (Fig. 13 A). In the tight state, the effect of moisture content on the attachment performance of the foot ends is similar to that in the loose state (Fig. 13 B). The impact of water content on the attachment performance of the foot ends was quantitatively described in both the loose and compacted states of frozen ground. The percentage of DCOF reduction in the foot ends as water content increasing from 20–35% and from 35–50% was shown in Table 4 . The attachment performance of the bio-inspired foot ends decreased with the increasing moisture content in frozen ground. The reason was that ice crystals were formed on the ground surface, and the ice structure solidified and encapsulated soil particles. In the gaps, the ice structure formed a smooth ice surface. The increase of ice content led to a downtrend in the DCOFs of the foot ends on frozen ground. Table 4 Quantitative analysis of the effect of moisture content on the attachment properties of foot ends Loose frozen ground Tight frozen ground 20–35% moisture 35–50% moisture 20–35% moisture 35–50% moisture Foot end A 25.38 23.03 32.69 8.13 Foot end B 25.76 14.73 22.51 17.81 Foot end C 9.44 13.76 22.06 8.18 Foot end D 25.02 20.43 26.35 19.47 Multi-baffle foot end E 12.09 29.68 18.61 10.37 Note: Unit in % 3.1.4 Effects of bio-inspired ribs and bio-inspired convex-crowns on attachment characteristics Statistical analysis revealed a significant difference between bio-inspired rids and bio-inspired convex-crown. Both bio-inspired rids and convex-crown significantly impacted the attachment performance of the bio-inspired foot ends under all conditions, except for the loose ground with 50% moisture. Notably, convex-crown more significantly affected the attachment performance of the bio-inspired foot ends compared to rids, as indicated by the P-values in Table 5 . Table 5 Two-way ANOVA for bio-inspired ribs (ribs vs. ribless) and convex-crown (convex-crown vs. non-convex-crown) Ribs Convex-crown Interaction F P F P F P Tight frozen ground 20% moisture 31.10 5.24 x 10 − 4 111.06 5.73 x 10 − 6 1.82 0.21 35% moisture 26.33 8.95 x 10 − 4 156.75 1.55 x 10 − 6 1.21 0.30 50% moisture 16.33 3.73 x 10 − 3 38.05 2.68 x 10 − 4 0.80 0.40 Loose frozen ground 20% moisture 58.47 6.03 x 10 − 5 318.63 9.94 x 10 − 8 2.52 0.15 35% moisture 8.41 1.99 x 10 − 2 91.03 1.20 x 10 − 5 0.56 0.47 50% moisture 1.74 0.22 23.45 1.28 x 10 − 3 2.09 0.19 Further experiments showed that the DCOFs of the foot ends were associated with the ribs and convex-crown (Fig. 13 ). In the loose state of ground, the DCOF was larger in the ribbed foot ends than the ribless foot ends, and in convex-crown foot ends than in non-convex-crown foot ends. In the compact state of ground, the influence of ridges and crowns on the attachment performance of the bio-inspired foot ends is similar to that on loose ground (Fig. 13 D). The effects of ribs and convex-crowns on the attachment performance of the foot ends were quantitatively described in Table 6 . Under the tested conditions, the DCOF of the convex-crown foot end was 1.18–1.48 times that of the non-convex-crown foot end, and the DCOF of the ribbed foot end was 1.01–1.23 times higher than that of the ribless foot end. Table 6 Quantitative analysis of effects of ribs and convex-crown on the attachment performance of bio-inspired foot ends Ratio between ribs and ribless Ratio between convex-crown and non-convex-crown Bio-inspired foot with convex-crown Bio-inspired foot with non-convex-crown Bio-inspired foot with ribs Bio-inspired foot with ribless Tight frozen ground 20% moisture 1.09 1.20 1.22 1.34 35% moisture 1.13 1.11 1.32 1.31 50% moisture 1.14 1.11 1.22 1.18 Loose frozen ground 20% moisture 1.10 1.23 1.33 1.48 35% moisture 1.10 1.07 1.32 1.30 50% moisture 1.15 1.01 1.42 1.23 Note: Unit in times 3.2 Slip-resistant mechanism of bio-inspired foot ends on ice and simulant for water-ice lunar soil The DCOFs of the five foot ends on ice surface rank as foot end C > foot end E > foot end B > foot end D > foot end A (Fig. 14 A). Compared to multi-baffle foot end E , foot end C increased the DCOF by about 24%. The ribless and non-convex-crown bio-inspired foot end C exhibited good attachment performance. When the bio-inspired foot ends interacted with ice surface, only the convex-crown and the ribs contacted due to their limited deformation. Consequently, the contact area of the foot ends was reduced, which in turn weakened the attachment performance (Fig. 14 B). In contrast, foot end C and multi-baffle foot end E maintained the largest contact areas with the ice surface. The ribs of foot end C were designed from the microstructure of reindeer ungula cusp, which enhanced its attachment performance. Consequently, foot end C exhibited the optimal attachment performance when interacting with the ice surface. On simulant for water-ice lunar soil (ice-soil mixture), the DCOFs rank as foot end B > foot end D > foot end E > foot end A > foot end C (Fig. 14 C). On simulant for water-ice lunar soil (water-soil mixture), the DCOFs rank as foot end B > foot end D > foot end A > foot end C > foot end E (Fig. 14 D). Foot ends B and D increased the DCOFs by 35.14%-51.47% and 6.76%-36.76%, respectively, compared to multi-baffled foot end E on simulant for water-ice lunar soil (ice-soil mixture). Similarly, on simulant for water-ice lunar soil (water-soil mixture), foot ends B and D improved the DCOFs by 35.14%-51.47% and 6.76%-36.76%, respectively. In both cases, bio-inspired foot ends B and D demonstrated excellent attachment performance. The slip-resistant mechanism of the foot ends on simulant for water-ice lunar soil is similar to that on frozen ground (Fig. 14 E). Under the synergistic action of the bio-inspired convex-crown and bio-inspired ribs, the attachment performance of bio-inspired foot end B is the optimal. 4 Conclusions The attachment characteristics of the mechanical foot end are critical for enhancing robot adaptability and traversal on extreme terrains. In this study, inspired by the reindeer touchdown unit, we designed four bio-inspired foot ends and one conventional multi-baffle foot end. Through friction tests on various ground surfaces, including ice and frozen ground, we explored the attachment performances of these bio-inspired foot ends. The bio-inspired ribbed foot end and convex-crown exhibited the best attachment performance on frozen ground and simulant lunar soil, increasing the dynamic coefficient of friction (DCOF) from 24.19–44.68% and 35.14–51.47%, respectively, compared to the multi-baffle foot end. This highlights the effectiveness of bio-inspired designs in enhancing attachment on challenging surfaces. The performance of the bio-inspired foot ends varied based on the moisture content of the frozen ground. As the water content increased, the attachment performance improved, indicating the importance of considering environmental conditions in foot end design. The slip-resistant mechanism of the foot ends was influenced by their structural features. Both the convex crown and ribs contributed to reducing the contact area of the foot end, leading to improved attachment performance. However, the convex crown had a greater effect than ribs, suggesting that this feature plays a crucial role in enhancing attachment on icy and rough surfaces. The results of this study demonstrate the effectiveness of bio-inspired foot end designs in improving robot traversal on extreme terrains. Future work could focus on further optimizing the design of bio-inspired foot ends for specific environmental conditions and exploring additional biomimetic features that could enhance attachment performance. Though our study provides valuable insights, there are limitations, such as the simplified nature of our models and the need for further validation in real-world environments. Declarations Conflicts of Interest: The authors declare no conflict of interest. Funding: This work is financially supported by the Science and Technology Research Planning Project of Jilin Provincial Department of Education (No. JJKH20220980KJ), the Science and Technology Development Planning Project of Jilin Province of China (No. 20220101014JC, 20230203198SF) and 2022 Key Laboratory Project of Ministry of Culture and Tourism. References Asif, U., Iqbal, J., 2012. On the improvement of multi-legged locomotion over difficult terrains using a balance stabilization method. Int. J. Adv. Robot. Syst. 9, 6-10. https://doi.org/ 10.5772/7789. Deutsch, A.N., Neumann, G.A., Head, J.W., 2017. 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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-4251682","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":290360662,"identity":"651b265f-b0fa-42d1-a970-83366af7ba31","order_by":0,"name":"Guoyu Li","email":"","orcid":"","institution":"School of Mechanical Engineering, Shanghai Dianji University","correspondingAuthor":false,"prefix":"","firstName":"Guoyu","middleName":"","lastName":"Li","suffix":""},{"id":290360663,"identity":"f0cc3f65-937b-496e-bfaa-f87081dc90c2","order_by":1,"name":"Rui Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA10lEQVRIie3PIQvCQBTA8TcGWg5W39hkX2EwmMKCX2VLV4ZRDIaDwap1oJ/DZLjjYGl2q8VsUUzibprPrQneP7xX3o/jAEymXwzfizggWbvtAcRlYiCBkFs9SbAtLufbQfqRECXCKsnY+Mi1xNrV08i/SBJzRRqaMbJItcTGNPaQf4hVyowhCbVkhPTekYgp8uxBCOaxe21JCIqwHgQxX3rAKUEuilla06gkuZ4EFd27D57MnUqK03WdTDbjRk9UNune4wCp+t3X+zbroabD+tyaTCbTP/YCOtxE2Tqc5JkAAAAASUVORK5CYII=","orcid":"","institution":"Key Laboratory of Bionic Engineering, Ministry of Education, Jilin University","correspondingAuthor":true,"prefix":"","firstName":"Rui","middleName":"","lastName":"Zhang","suffix":""},{"id":290360664,"identity":"89eaf1d9-65e2-4c65-a4a5-c81aeec42616","order_by":2,"name":"Kaixiang Chen","email":"","orcid":"","institution":"Key Laboratory of Bionic Engineering, Ministry of Education, Jilin 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University","correspondingAuthor":false,"prefix":"","firstName":"Lige","middleName":"","lastName":"Wen","suffix":""}],"badges":[],"createdAt":"2024-04-11 10:00:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4251682/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4251682/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":54762146,"identity":"0d00f28e-8bd6-44bc-9bd2-4a7f1577a1df","added_by":"auto","created_at":"2024-04-16 11:40:21","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":492719,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMorphology of original soil particles. \u003c/strong\u003e(A) \u0026gt;4 mm, (B) 2-4 mm, (C) 1-2 mm, (D) 0.63-1 mm, (E) 0.45-0.63 mm, (F) 0.3-0.45 mm, (G) 0.15-0.3 mm, (H) \u0026lt;0.15 mm\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4251682/v1/67c3957cf1768b842dba1e0a.png"},{"id":54762147,"identity":"cbf3a41f-bd8b-498b-87a4-7e0442b5f391","added_by":"auto","created_at":"2024-04-16 11:40:21","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":539856,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMorphology of simulant lunar soil particles. \u003c/strong\u003e(A) \u0026gt;1 mm, (B) 0.63-1 mm, (C) 0.45-0.63 mm, (D) 0.3-0.45 mm, (E) 0.15-0.3 mm, (F) 0.097 -0.15 mm, (G) 0.075-0.097 mm, (H) \u0026lt;0.075 mm\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4251682/v1/7094d15530cd4bafea558975.png"},{"id":54762148,"identity":"ff9ad1cf-75bf-40e8-86cb-c377bc0c2024","added_by":"auto","created_at":"2024-04-16 11:40:21","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":250653,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSoil particle diameter. \u003c/strong\u003e(A) Original soil, (B) simulant lunar soil\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-4251682/v1/3c1104f8eaf03057fc483e25.png"},{"id":54762149,"identity":"32d4b947-8e5b-46e0-bb42-1259fab6af51","added_by":"auto","created_at":"2024-04-16 11:40:21","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1307538,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eLoose frozen ground. \u003c/strong\u003e(A) 16.4% moisture (original frozen ground ), (B) 20% moisture, (C) 35% moisture, (D) 50% moisture\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4251682/v1/c848aa2bc8636f8e281d3eb6.png"},{"id":54762150,"identity":"3f8a7375-7f35-427a-9c13-f65d2eb3420a","added_by":"auto","created_at":"2024-04-16 11:40:21","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":1445646,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTight frozen ground. \u003c/strong\u003e(A) 16.4% moisture (original frozen ground), (B) 20% moisture, (C) 35% moisture, (D) 50% moisture\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-4251682/v1/f49f24030bc9ebad7f916138.png"},{"id":54762156,"identity":"a125de5c-c8fc-419f-97fb-76ebe8b011b2","added_by":"auto","created_at":"2024-04-16 11:40:21","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":1318603,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSimulant for water-ice lunar soil and ice surface. \u003c/strong\u003e(A) Dry simulant lunar soil, (B) Water-soil mixed simulant lunar soil, (C) Ice-soil mixed simulant lunar soil, (D) Ice surface\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-4251682/v1/eea59c9abd90f97b13d0fa30.png"},{"id":54762154,"identity":"f5e0d0b9-99b7-49ce-9753-8d02c3804843","added_by":"auto","created_at":"2024-04-16 11:40:21","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":1000429,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eReindeer samples and hooves macro/microstructures.\u003c/strong\u003e (A) Reindeer, (B) 3D of the ungula; Microstructures of (C) ungulae cusp, (D) Hoof edge and (E) plantar fur\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-4251682/v1/c7e91ad6a08d90cce73ecbb8.png"},{"id":54762152,"identity":"3f8d84a3-d451-4b4a-96c9-dcf0b61a6f62","added_by":"auto","created_at":"2024-04-16 11:40:21","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":552212,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eStructure design of bio-inspired foot ends.\u003c/strong\u003e (A) Reindeer ungula, (B) 3D model of bio-inspired foot front end, (C) Main view, (D) side view, and (E) top view of the bio-inspired ribbed foot front end, (F) 3D model of bio-inspired convex, (G) Top view and (H) main view of the multi-baffle foot end\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-4251682/v1/201afc87c0d6b25167b44035.png"},{"id":54762153,"identity":"9dd2d0c6-6474-4d22-b65b-9b3dfbdc9b2a","added_by":"auto","created_at":"2024-04-16 11:40:21","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":376521,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eProcessing of bio-inspired foot ends and multi-baffled foot end.\u003c/strong\u003e (A - D) Bio-inspired foot ends \u003cem\u003eA\u003c/em\u003e, \u003cem\u003eB\u003c/em\u003e, \u003cem\u003eC\u003c/em\u003e, and \u003cem\u003eD\u003c/em\u003e respectively, (E) Multi-baffle foot end\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-4251682/v1/eb58a2507ca3d33848f32344.png"},{"id":54762159,"identity":"26ddca2f-8f5f-4889-bcd4-8fc46097bc8f","added_by":"auto","created_at":"2024-04-16 11:40:21","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":288988,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFrozen ground attachment test procedure. \u003c/strong\u003e1 - Track, 2 - Lift bar, 3 - Tension transducer, 4 - Traction line, 5 - Frozen ground, 6 - Attachment foot end, 7 - Weights\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-4251682/v1/2b39d35c1554a44d5725065f.png"},{"id":54762151,"identity":"65a8f91f-2538-469e-a0d8-7d7a2c1885f5","added_by":"auto","created_at":"2024-04-16 11:40:21","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":274459,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComparison of the attachment properties among five foot ends on original frozen ground. \u003c/strong\u003e(A) Loose ground, (B) Tight ground, (C) Slip-resistant mechanism of bio-inspired foot ends on original frozen ground\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-4251682/v1/45e7aaf183c0b4e4012aecfd.png"},{"id":54762155,"identity":"fc1c4d04-9324-4083-a538-90f7d722f770","added_by":"auto","created_at":"2024-04-16 11:40:21","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":301459,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComparison of attachment properties among five foot ends on frozen ground. \u003c/strong\u003e(A) DCOF of frozen ground in different moisture contents and compacted states, (B) Slip-resistant mechanism of bio-inspired foot ends on frozen ground\u003c/p\u003e","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-4251682/v1/60f554736208176de313210a.png"},{"id":54762157,"identity":"aa893c6c-c973-4394-bf7b-f76d6335bedc","added_by":"auto","created_at":"2024-04-16 11:40:21","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":445642,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eEffects of moisture content, bio-inspired ribs, and convex-crown on foot end attachment properties. \u003c/strong\u003eEffects of moisture content on (A) loose and (B) tight frozen ground. Effects of bio-inspired ribs and convex-crown on (C) loose and (D) tight frozen ground\u003c/p\u003e","description":"","filename":"floatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-4251682/v1/50e6c1bb5ab88b22eca99bac.png"},{"id":54762158,"identity":"d41f8203-8b33-4606-980b-7a9e88014697","added_by":"auto","created_at":"2024-04-16 11:40:21","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":160941,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComparison of the attachment properties among the five foot ends on ice and simulant for water-ice lunar soil. \u003c/strong\u003e(A) Ice surface; slip-resistant mechanism of bio-inspired foot ends on (B) Ice, (C) Simulant for water-ice lunar soil (ice-soil mixture), (D) Simulant for water-ice lunar soil (water-soil mixture), (E) Slip-resistant mechanism of bio-inspired foot ends on simulant for water-ice lunar soil\u003c/p\u003e","description":"","filename":"floatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-4251682/v1/dbd2af148307789da8420b2b.png"},{"id":61424579,"identity":"89daf3bd-51c4-45cd-8add-3d8b33220c86","added_by":"auto","created_at":"2024-07-30 14:31:54","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":12407083,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4251682/v1/ae769bf4-eb32-4f40-b8e1-51c81687ef16.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Slip-resistant mechanism of bio-inspired foot end based on particle morphology and friction on ice and frozen ground","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eWith the development of artificial intelligence, robots have gradually entered daily life, replacing humans to complete production and manufacturing. For example, digit robots can carry out logistics and parcel delivery (Kuindersma et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2016\u003c/span\u003e, Zhang \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Unmanned military equipment has become an inevitable trend, and various military robots are increasingly widely used. For instance, Packbot robots can complete reconnaissance, exploration, and handling of explosive devices (Mller et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). As the only part in contact with the ground, the end of the mechanical foot is of great significance to improve the traversability and mobility of the robot on extreme ground.\u003c/p\u003e \u003cp\u003eBio-inspired legged robots have high movement flexibility and environmental adaptability on unconventional ground owing to the discrete point contacts and flexible limb structures. They have been used in exploration and transportation under high-risk environments, such as frozen ground (\u003csup\u003eZhang\u003c/sup\u003e et al., 2019). BigDog, the military quadruped robot developed by Boston Dynamics, is equipped with advanced controllers (e.g., terrain sensors, dynamic control) to coordinate leg movements and ensure movement balance and stability. Its controllers adapt to terrain changes through terrain measurement and attitude control (\u003csup\u003eNelson\u003c/sup\u003e et al., 2006). Researchers from Massachusetts Institute of Technology analyzed the kinetics, energy consumption and speed of quadrupeds during movement, and designed a bio-inspired lightweight mechanical foot simulating cheetah hindlimbs based on the principle of tendon-bone copositioning. This mechanical foot with less weight meets the premise of stiffness and strength, avoids large bending moments and improves energy efficiency, which contribute to high-speed movement (\u003csup\u003eKim\u003c/sup\u003e et al., 2006). The second-generation Atlas has made breakthroughs in portability and balance. The internal sensors and lidar positioning allow this robot to avoid obstacles, maintain balance and complete movements outdoors (\u003csup\u003eKoolen\u003c/sup\u003e et al., 2016). However, the robot will still slip upon walking on snow, and can only collect posture data through sensors and adjust its motion to keep body balance. Because of the control algorithm, image measurement and gait adjustment endow the foot robot with an anti-interference ability and the ability to walk on frozen ground to certain extent. However, the robot is limited by low walking stability and a relatively simple foot structure, and there is little research on design of bio-inspired feet on frozen ground.\u003c/p\u003e \u003cp\u003eFrozen grounds, a type of extreme ground, are widely distributed in the world with a total area\u0026thinsp;~\u0026thinsp;35\u0026nbsp;million km\u003csup\u003e2\u003c/sup\u003e, accounting for 25% of the entire earth area. Frozen grounds are more widely found in the northern hemisphere. As scientists explored the moon in recent decades, they have discovered that water ice exists on the moon, but the specific location and content of water ice are still at the research stage (\u003csup\u003eSpudis\u003c/sup\u003e et al., 2013). The NASA and ESA detected water ice in the permanent shadow areas (craters) of the north and south lunar poles using lunar probes, such as Clementine, Lunar Prospector and SMART-1, and initially concluded that water ice may exist (\u003csup\u003eRichard\u003c/sup\u003e et al., 1999, \u003csup\u003eFeldman\u003c/sup\u003e et al., 1998, \u003csup\u003eRacca\u003c/sup\u003e et al., 2002). Besides, LCROSS and LRO cooperated in impacting the moon. Through thermal imaging, near-infrared spectroscopy, ultraviolet spectroscopy and other technologies, they detected water vapor in impact sputters, and successfully proved the existence of water ice on the moon (Neish et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). In 2010, the Mini-star radar mounted on Chandrayaan-1 detected more than 40 craters containing water ice in the lunar north pole, and the content of water ice was estimated to be about 0.6\u0026nbsp;billion tons (Deutsch et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Lunar water ice is not only a hot spot for international exploration, but also a future strategic resource. At present, all the global major space powers have formulated plans to detect and sample lunar water ice. The ESA is aimed to build a lunar village. China plans to conduct multiple detection and samples of lunar water ice by 2030 (\u003csup\u003eGreen\u003c/sup\u003e 2011). Lunar water ice mainly exists in craters, which are difficult for wheeled robots to pass through. In comparison, footed robots with excellent active adaptability and foot attachment have good application prospects (\u003csup\u003eAsif\u003c/sup\u003e and \u003csup\u003eIqbal\u003c/sup\u003e 2012).\u003c/p\u003e \u003cp\u003eUnder the law of natural selection, the foot structures, movements, and functions of animals have evolved to adapt to the environment. Engineering application of special structures of animal feet based on bio-inspireds has long been a source to solve problems and find inspiration (Zhao et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Mechanical feet designed with hoofed animals as bio-inspired prototypes show excellent adaptability and movement characteristics in various grounds. Abad designed a goat-hoof-like mechanical foot with flexible joints, strong attachment, and cushioning vibration reduction. The hoof anterior and convex-crown pattern of the mechanical foot improve the attachment performance by embedding into the ground and enlarging the contact area respectively. The pattern structure is stuck in rocks or soil and can provide an additional braking effect (\u003csup\u003eZhong\u003c/sup\u003e et al., 2019). Horse feet have mobility, load-bearing capacity and endurance during movement. Garcia et al. simulated the horse muscle system by connecting elastic elements and excitation units in series, designed a bio-inspired mechanical foot based on effective leg length, kinematics, and foot mass distribution, and studied the key influence factors on the agility of the mechanical foot (\u003csup\u003eSanz\u003c/sup\u003e et al., 2015).\u003c/p\u003e \u003cp\u003eReindeer (\u003cem\u003eRangifer tartandus\u003c/em\u003e), a typical polar migratory animal, belongs to Cervidae, Artiodactyla and has a hoof structure suitable for migration in complex environments (\u003csup\u003eZhang\u003c/sup\u003e et al., 2019). In particular, reindeer hooves have good traversability on frozen ground (\u003csup\u003eWareing\u003c/sup\u003e et al., 2021). The ungula structure and plantar fur of the hooves can enlarge the contact area with the ground and play an anti-slip role when walking on frozen ground (Raesaenen et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). Reindeer migrate seasonally over long distances on land, and some populations even migrate farther than other terrestrial mammals (\u003csup\u003eFancy\u003c/sup\u003e et al., 1989).\u003c/p\u003e \u003cp\u003eIn this study, the particle compositions of original soil and simulant lunar soil were analyzed microscopically, and the effects of particle compositions on the surface roughness of frozen ground were revealed. Based on the microstructure and macrostructure of stance units, four bio-inspired attachment foot ends and an ordinary multi-baffle foot end were designed. The attachment performances of the five foot ends on ice and frozen ground were comparatively tested using a friction testing machine, and the slip-resistant mechanism was revealed. The influence factors including moisture content, compaction state, crown and rib on the dynamic coefficient of friction (DCOF) in frozen ground were analyzed.\u003c/p\u003e"},{"header":"2 Materials and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Construction and micromorphology of ice and frozen ground\u003c/h2\u003e \u003cp\u003eThe physical properties of the collected original soil and simulant lunar soil were analyzed, and the effect of the micromorphology of ice or frozen ground was observed.\u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section3\"\u003e \u003ch2\u003e2.1.1 Particle compositions\u003c/h2\u003e \u003cp\u003eThe samples of original soil and simulant lunar soil were observed under a BT-1600 image particle analyzer, and the particle morphology is shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The particles can be categorized by the structure and outline into spherical, elongated, and polygonal shapes. Both the original soil and the simulant lunar soil have more polygonal particles, which also indicates the irregularity of the particles in the soil samples.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eBoth the original soil and the simulant lunar soil were dark gray. Soil particle diameter was detected using the sieving method, and the main equipment included soil sieves (holes of 0.15, 0.3, 0.45, 0.63, 1, 2, and 4 mm), a high-frequency vibrating sifter, and an electronic balance. About 1000 g of soil was dried, sieved and weighed. The original soil sieved at particle sizes of \u0026gt;\u0026thinsp;4, 2\u0026ndash;4, 1\u0026ndash;2, 0.63-1, 0.45\u0026ndash;0.63, 0.3\u0026ndash;0.45, 0.15\u0026ndash;0.3 and \u0026lt;\u0026thinsp;0.15 mm accounted for about 1.55%, 11.94%, 21.55%, 24.65%, 2.63%, 17.91%, 11.08% and 8.68%, respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA). The particle size of the original soil was concentrated in 0.3-2 mm.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe simulant lunar soil fell in the particle sizes of \u0026gt;\u0026thinsp;1, 0.63-1, 0.45\u0026ndash;0.63, 0.3\u0026ndash;0.45, 0.15\u0026ndash;0.3, 0.097\u0026ndash;0.15, 0.075\u0026ndash;0.097 and \u0026lt;\u0026thinsp;0.075 mm, which accounted for about 0.60%, 2.28%, 0.27%, 5.69%, 5.09%, 13.86%, 34.96% and 37.24%, respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB). Compared with the original soil, the particle size distribution of the simulant lunar soil was more concentrated and was mainly\u0026thinsp;\u0026lt;\u0026thinsp;0.15 mm. The mechanical properties of soil are closely related to its particle size and gradation. Results show the original soil is distributed more discretely and has larger particles. Therefore, the surface of frozen ground is rougher under the same preparation conditions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e \u003ch2\u003e2.1.2 Microscopic surface structure of frozen ground\u003c/h2\u003e \u003cp\u003eIce and frozen ground was categorized into three types: frozen ground, Simulant for water-ice lunar soil, and ice. According to ESA, the moisture content of frozen ground in lunar polar regions is below 11.9% (\u003csup\u003eSong\u003c/sup\u003e et al., 2021). Mechanical mixing of water or ice particles with dry simulant lunar soil is commonly used to make Simulant for water-ice lunar soil (\u003csup\u003eKoemle\u003c/sup\u003e et al., 2016). To study the physical properties of the Simulant for water-ice lunar soil, we mixed the simulant lunar soil with water-ice particles to form soil with 8% moisture and froze it in a freezer at -20\u0026deg;C. In addition, ice surface was made. Based on moisture content, the frozen ground was divided into four types: 16.3% (original frozen), 20%, 35%, and 50% moisture. Based on the compacted state, the frozen ground was divided into two types: loose and tight. The Simulant for water-ice lunar soil was divided into two types: water-soil mixed, and ice-soil mixed.\u003c/p\u003e \u003cp\u003eBased on the contact relationship between soil particles and ice structure, the surface structure of frozen ground was analyzed (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). As the original loose frozen ground, the gaps between soil particles were large and contained only a few ice crystals. At the moisture content of 20%, the gaps of the loose frozen ground were connected by a slightly larger number of ice crystals than in the original frozen ground. The small gaps were filled with ice crystals and the large gaps were still interstitial. At the moisture content of 35%, many ice crystals appeared on the gaps of the loose frozen ground, and ice crystals almost completely filled in the gaps between soil particles. At the moisture content of 50%, many ice crystals still existed on the gaps of the loose frozen ground, and ice crystals fully filled in the gaps between soil particles. In addition, a smooth ice surface was formed on the gaps due to the consolidation of the ice crystals. As the moisture content increased, ice crystals were formed on the gaps of the soil particles, and a number of ice crystals consolidated to form a smooth ice surface.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eUnder the same moisture content, the surface consolidation of the gaps on tight frozen ground was similar to that on loose frozen ground (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). However, the surface of the tight frozen ground was flatter due to compaction.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe surface structure of the dry simulant lunar soil was shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eA. As the simulant lunar soil was mixed with water and ice, the Simulant for water-ice lunar soil was more compact than the dry simulant lunar soil (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eB and C). The ice surface is the smoothest, because it has fewer convex structures and is almost flat (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eD). The particle size of the simulant lunar soil was smaller than that of the original soil, so the Simulant for water-ice lunar soil was smoother than the frozen ground.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Design of bio-inspired attachment foot ends\u003c/h2\u003e \u003cp\u003eTargeting at reindeer hooves, we designed four bio-inspired foot ends, and an ordinary multi-baffle foot end based on the typical curves of the ungula edge, the ball surface of the ungula capsule, and the microstructure of the hooves.\u003c/p\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e2.2.1 Bio-inspired prototype\u003c/h2\u003e \u003cp\u003eFour reindeer hindlimbs were selected from naturally dead adult male reindeer in the Ewenki tribe in Genhe City, China. The ungulae were free from disease or any surgical treatment, or other invasive manipulations (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eA). Before the test, the reindeer ungulae were cleaned with distilled water to remove any surface dirt from the samples. Then the samples were left to dry naturally and subjected to CT scanning (220 KV, 220 MA, 1.25 mm layer thickness). The hoof model after CT scanning was mesh-healed, relaxed, and smoothed in Geomagic Studio to generate a 3D model (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eB).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn winter, the reindeer hooves are the only part in contact with the ice and frozen ground (Nichol et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2004\u003c/span\u003e). The microstructure of the reindeer ungula cusp was jagged ribs, and many cracks existed in the severely worn area. The width and length of the ribs were measured with a ratio of 0.65:1 (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eC). On the ungula edge, the ribs were longitudinally distributed and the surface was rough. The width and distance of the ribs were measured with a ratio of 3:1 (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eD). In addition, the scales of the plantar fur were closely arranged, and the scale ripples were largely undulated (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eE). On the ice and frozen ground, these specific structures were served as an attachment function for the reindeer.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e2.2.2 Structural and functional design of the bio-inspired foot front end\u003c/h2\u003e \u003cp\u003eThe reindeer plantar feature plays a crucial role in the slip resistance on frozen ground, such as the typical curves of the ungula edge (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eA). After the ungula cusp and inner and outer edge curves were equidistantly spaced inward by 3.6 mm, the curves were stretched by 18.0 mm and the inner groove was stretched by 1.2 mm. Then the 3D model of the bio-inspired foot front end was established (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eB).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e2.2.3 Structural and functional design of bio-inspired ribs\u003c/h2\u003e \u003cp\u003eThe bio-inspired ribbed part at the ungula cusp and edge was designed according to the microstructure ratio of the reindeer hooves. The bio-inspired ribs of the foot front end consisted of serrated ribs at the ungula cusp and longitudinal ribs at the ungula edge (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eC, D, and E).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e \u003ch2\u003e2.2.4 Structural and Functional Design of bio-inspired convex-crown\u003c/h2\u003e \u003cp\u003eThe ungula capsule of reindeer, which critically contributes to the attachment characteristics, was further converted into a 3D model (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eF). Given the basic dimensions of the bio-inspired convex-crown, the number of bio-inspired pattern designs shall ensure a moderate distribution of density. The number of bio-inspired patterns of 10 is reasonable. The plantar fur at the proximal capsule of the reindeer ungula is denser than at the distal capsule. Combining with the sparse distribution of plantar fur, we arranged four and six bio-inspired crowns at the distal and proximal convexes of the bio-inspired foot end, respectively. Given the distribution angle of the plantar fur, the bio-inspired crowns were distributed to both sides at an angle of ~\u0026thinsp;30\u0026deg; to the centerline of the convex.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e2.2.5 Structural design of the ordinary multi-baffle foot end\u003c/h2\u003e \u003cp\u003eAs is well-known, the multi-baffle foot end has good attachment characteristics (\u003csup\u003ePoerschke\u003c/sup\u003e et al., 2021). An ordinary multi-baffle foot was designed by combining with the specific dimensions of the bio-inspired foot end (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eG and H). The height, upper surface area, and lower surface contact area of the multi-baffle foot end are consistent with the bio-inspired foot ends (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\u003eDimensions of the bio-inspired and ordinary foot ends\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHeight (mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUpper surface area (mm\u003csup\u003e2\u003c/sup\u003e )\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLower surface contact area (mm\u003csup\u003e2\u003c/sup\u003e )\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eBio-inspired foot ends\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e25.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e14307.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2324.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMulti-baffle foot end\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e25.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e14224.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2326.21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Experiment design of foot ends on ice and frozen ground\u003c/h2\u003e \u003cdiv id=\"Sec13\" class=\"Section3\"\u003e \u003ch2\u003e2.3.1 Processing of foot ends\u003c/h2\u003e \u003cp\u003eBio-inspired foot end \u003cem\u003eA\u003c/em\u003e is composed of a bio-inspired ribbed foot end and a non-convex-crown (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eA). Bio-inspired foot end \u003cem\u003eB\u003c/em\u003e consists of a bio-inspired ribbed foot end and a bio-inspired convex-crown (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eB). Bio-inspired foot end \u003cem\u003eC\u003c/em\u003e is composed of a bio-inspired ribless foot end and a non-convex-crown (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eC). Bio-inspired foot end \u003cem\u003eD\u003c/em\u003e consists of a bio-inspired ribless foot end and a convex-crown (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eD). Multi-baffle foot end \u003cem\u003eE\u003c/em\u003e is of the same size (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eE).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e \u003ch2\u003e2.3.2 Experiment conditions\u003c/h2\u003e \u003cp\u003eFrozen ground attachment experiments were done with a UTM friction testing machine (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e). The tray with frozen ground was fixed on the machine. One end of the traction line was connected to the attachment foot, and the other end was linked to a tension sensor on the lifting rod. The sensor accuracy was 0.0001. The position of the lifting rod was adjusted to keep the traction line horizontal. After the lifting rod was fixed, it moved horizontally and uniformly on the electric track. The moving speed range and maximum moving distance were 10\u0026ndash;500 mm/min and 200 mm respectively.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe experiment was conducted in a cold room with the temperature controlled around \u0026minus;\u0026thinsp;10\u0026deg;C. During the experiment, the room was closed to avoid the influence of wind, and the surface temperature of the frozen ground was stable at \u0026plusmn;\u0026thinsp;0.5\u0026deg;C. The signals of friction force and displacement were detected using force and displacement sensors and transmitted to a computer.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Data processing and analysis\u003c/h2\u003e \u003cp\u003eThe sliding friction between a bio-inspired foot end and the frozen ground was collected using a UTM friction tester. The mean and standard deviation of the DCOF of five successful tests under each condition were obtained on Origin 9.1. The effects of moisture content (20% vs. 50%), compacted state (loose vs. tight), ribs (ribbed vs. ribless) and convex-crown (convex-crown vs. non-convex-crown) on the attachment characteristics of the bio-inspired foot end were tested via two-way analysis of variance (ANOVA). Then the interaction effects were analyzed. The significance level was set at P\u0026thinsp;\u0026lt;\u0026thinsp;0.05.\u003c/p\u003e \u003c/div\u003e"},{"header":"3 Results and discussion","content":"\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Slip-resistant mechanism of bio-inspired foot end on frozen ground\u003c/h2\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003e3.1.1 Attachment experiments on original frozen ground\u003c/h2\u003e \u003cp\u003eThe DCOFs and the changing patterns of the five foot ends on the original frozen ground (16.4% moisture) are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e. The DCOFs of the five foot ends on loose original frozen ground rank as foot end \u003cem\u003eB\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;foot end \u003cem\u003eD\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;multi-baffle foot end \u003cem\u003eE\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;foot end \u003cem\u003eA\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;foot end \u003cem\u003eC\u003c/em\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003eA). The DCOFs of the five foot ends on tight original frozen ground rank as foot end \u003cem\u003eB\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;foot end \u003cem\u003eD\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;foot end \u003cem\u003eA\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;multi-baffle foot end \u003cem\u003eE\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;foot end \u003cem\u003eC\u003c/em\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003eB). Compared with multi-baffled foot end \u003cem\u003eE\u003c/em\u003e, the DCOFs of bio-inspired foot ends \u003cem\u003eB\u003c/em\u003e and \u003cem\u003eD\u003c/em\u003e increased by 11.43%-31.75% and 2.86%-17.46%, respectively. Hence, bio-inspired foot ends \u003cem\u003eB\u003c/em\u003e and \u003cem\u003eD\u003c/em\u003e acted as good attachments.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eUpon interacting with the original frozen ground, the ribs and convex of a bio-inspired foot end all can embed into the frozen ground (Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003eC). Bio-inspired foot end \u003cem\u003eB\u003c/em\u003e increased the embedding depth through the bio-inspired crown, and the bio-inspired ribs had better grip performance, so its attachment performance was the optimal. The embedding of the foot end into the frozen soil caused the frozen surface to loosen, increasing soil particles. Upon interaction with the foot end, these soil particles began to roll, converting sliding friction into rolling friction, which reduced the attachment performance of the foot end. Given the variance in preparation methods between the original frozen soil and other frozen soils (20%, 35%, and 50% moisture), we then comparatively analyzed the factors.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section3\"\u003e \u003ch2\u003e3.1.2 Attachment comparison of foot ends on frozen ground\u003c/h2\u003e \u003cp\u003eThe changes of DCOF in the five foot ends on frozen ground (20%, 35%, and 50% moisture) are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003eA. With the increasing moisture content in frozen soil, the DCOF of the foot ends consistently rose. Compared with the moisture content, the compacted state of the frozen ground had a relatively minor impact on the attachment performance of the foot ends. Under the same conditions, the adhesion performance was the highest in bio-inspired foot end \u003cem\u003eB\u003c/em\u003e, followed by bio-inspired foot end \u003cem\u003eD\u003c/em\u003e, and was the lowest in bio-inspired foot end \u003cem\u003eC\u003c/em\u003e. The difference in attachment performance between bio-inspired foot end \u003cem\u003eA\u003c/em\u003e and multi-baffle foot end \u003cem\u003eE\u003c/em\u003e was relatively minor. The DCOF of foot end \u003cem\u003eE\u003c/em\u003e was larger than that of foot end \u003cem\u003eA\u003c/em\u003e under the loose ground conditions of 35% and 50% moisture, but was smaller in other conditions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe attachment properties of bio-inspired foot ends \u003cem\u003eB\u003c/em\u003e and \u003cem\u003eD\u003c/em\u003e were much greater than that of multi-baffled foot end E, and foot end \u003cem\u003eB\u003c/em\u003e was superior over foot end \u003cem\u003eD\u003c/em\u003e (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Under the loose frozen grounds with 20%, 35%, and 50% moisture, the DCOFs of foot end \u003cem\u003eB\u003c/em\u003e are 1.10, 1.10, and 1.15 times those of foot end \u003cem\u003eD\u003c/em\u003e, respectively. Under tight frozen grounds with 20%, 35% and 50% moisture, the DCOFs of foot end \u003cem\u003eB\u003c/em\u003e are 1.09, 1.13, and 1.14 times those of foot end \u003cem\u003eD\u003c/em\u003e, respectively.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eImprovement in attachment performance of bio-inspired foot ends compared to multi-baffle foot end\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\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 \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRatio between foot ends \u003cem\u003eB\u003c/em\u003e and \u003cem\u003eE\u003c/em\u003e (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRatio between foot ends \u003cem\u003eD\u003c/em\u003e and \u003cem\u003eE\u003c/em\u003e (%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u003cb\u003eTight frozen ground\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e20% moisture\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e41.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e29.41\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e35% moisture\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e36.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e22.81\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e50% moisture\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e28.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e11.54\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u003cb\u003eLoose frozen ground\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e20% moisture\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e40.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e27.54\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e35% moisture\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e24.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e14.52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e50% moisture\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e44.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25.53\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\u003eUpon interaction with frozen grounds with 20%, 35%, and 50% moisture, the bio-inspired foot ends can be hardly embedded into the ground. However, under the same load, the bio-inspired crown exhibited a smaller surface area but higher pressure, creating strong friction with the non-smooth surface of the frozen ground and thus enhancing the attachment performance. Additionally, the bio-inspired ribs provided good traction, making bio-inspired foot end B have the optimal attachment performance (Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003eB).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section3\"\u003e \u003ch2\u003e3.1.3 Effects of moisture content and compacted state on attachment characteristics\u003c/h2\u003e \u003cp\u003eSignificant differences were tested with the moisture content and compacted state of frozen ground. The \u003cem\u003eP\u003c/em\u003e values indicate moisture content more significantly affected the attachment performances of the five foot ends. The moisture content of frozen ground significantly affected the attachment performances of all five foot ends, whereas the compacted state did not significantly affect bio-inspired foot ends \u003cem\u003eB\u003c/em\u003e and \u003cem\u003eD\u003c/em\u003e. These results suggest the bio-inspired convex-crown may reduce the effect of frozen ground compacted state on the attachment characteristics of foot ends (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eTwo-way ANOVA for moisture content (20% vs. 50%) and compacted state (loose vs. tight)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eMoisture content\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eCompacted state\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eInteraction\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eF\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eF\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eF\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFoot end\u003c/b\u003e \u003cb\u003eA\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e125.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.63 x 10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.34 x 10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.66\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFoot end\u003c/b\u003e \u003cb\u003eB\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e211.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.91 x 10\u003csup\u003e\u0026minus;\u0026thinsp;7\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e6.01 x 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.94\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFoot end\u003c/b\u003e \u003cb\u003eC\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e83.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.69 x 10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.51 x 10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFoot end\u003c/b\u003e \u003cb\u003eD\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e119.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.35 x 10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.85 x 10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e9.41 x 10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMulti-baffle foot end\u003c/b\u003e \u003cb\u003eE\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e136.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.63 x 10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.97 x 10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e15.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4.12 x 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\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\u003eFurther experiments revealed that the DCOFs of the foot ends were more pronounced with respect to moisture content compared to the compacted state of the frozen ground. The DCOFs of the foot ends increased with the higher moisture content of the frozen ground. The changing patterns in DCOFs for the five foot ends on the frozen ground with varying moisture content are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e. The ice structure content of the frozen ground in a loose state increased with the higher moisture content, leading to a decrease in the DCOFs of the bio-inspired foot ends (Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003eA). In the tight state, the effect of moisture content on the attachment performance of the foot ends is similar to that in the loose state (Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003eB).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe impact of water content on the attachment performance of the foot ends was quantitatively described in both the loose and compacted states of frozen ground. The percentage of DCOF reduction in the foot ends as water content increasing from 20\u0026ndash;35% and from 35\u0026ndash;50% was shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. The attachment performance of the bio-inspired foot ends decreased with the increasing moisture content in frozen ground. The reason was that ice crystals were formed on the ground surface, and the ice structure solidified and encapsulated soil particles. In the gaps, the ice structure formed a smooth ice surface. The increase of ice content led to a downtrend in the DCOFs of the foot ends on frozen ground.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eQuantitative analysis of the effect of moisture content on the attachment properties of foot ends\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\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 \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eLoose frozen ground\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eTight frozen ground\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20\u0026ndash;35% moisture\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e35\u0026ndash;50% moisture\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e20\u0026ndash;35% moisture\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e35\u0026ndash;50% moisture\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFoot end\u003c/b\u003e \u003cb\u003eA\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e25.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e23.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e32.69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFoot end\u003c/b\u003e \u003cb\u003eB\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e25.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e14.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e22.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e17.81\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFoot end\u003c/b\u003e \u003cb\u003eC\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e13.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e22.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eFoot end\u003c/b\u003e \u003cb\u003eD\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e25.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e20.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e26.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e19.47\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMulti-baffle foot end\u003c/b\u003e \u003cb\u003eE\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e12.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e29.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e18.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e10.37\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"5\" nameend=\"c5\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eNote: Unit in %\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec21\" class=\"Section3\"\u003e \u003ch2\u003e3.1.4 Effects of bio-inspired ribs and bio-inspired convex-crowns on attachment characteristics\u003c/h2\u003e \u003cp\u003eStatistical analysis revealed a significant difference between bio-inspired rids and bio-inspired convex-crown. Both bio-inspired rids and convex-crown significantly impacted the attachment performance of the bio-inspired foot ends under all conditions, except for the loose ground with 50% moisture. Notably, convex-crown more significantly affected the attachment performance of the bio-inspired foot ends compared to rids, as indicated by the P-values in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eTwo-way ANOVA for bio-inspired ribs (ribs vs. ribless) and convex-crown (convex-crown vs. non-convex-crown)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\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 \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eRibs\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003eConvex-crown\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003eInteraction\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eF\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eF\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003eF\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u003cb\u003eTight frozen ground\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e20% moisture\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e31.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.24 x 10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e111.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.73 x 10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e35% moisture\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e26.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.95 x 10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e156.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.55 x 10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e50% moisture\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e16.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.73 x 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e38.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.68 x 10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u003cb\u003eLoose frozen ground\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e20% moisture\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e58.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.03 x 10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e318.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e9.94 x 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e35% moisture\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.99 x 10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e91.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.20 x 10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.47\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e50% moisture\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e23.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.28 x 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.19\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\u003eFurther experiments showed that the DCOFs of the foot ends were associated with the ribs and convex-crown (Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e). In the loose state of ground, the DCOF was larger in the ribbed foot ends than the ribless foot ends, and in convex-crown foot ends than in non-convex-crown foot ends. In the compact state of ground, the influence of ridges and crowns on the attachment performance of the bio-inspired foot ends is similar to that on loose ground (Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003eD). The effects of ribs and convex-crowns on the attachment performance of the foot ends were quantitatively described in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. Under the tested conditions, the DCOF of the convex-crown foot end was 1.18\u0026ndash;1.48 times that of the non-convex-crown foot end, and the DCOF of the ribbed foot end was 1.01\u0026ndash;1.23 times higher than that of the ribless foot end.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eQuantitative analysis of effects of ribs and convex-crown on the attachment performance of bio-inspired foot ends\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\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 \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eRatio between ribs and ribless\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003eRatio between convex-crown and non-convex-crown\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBio-inspired foot with convex-crown\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBio-inspired foot with non-convex-crown\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBio-inspired foot with ribs\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eBio-inspired foot with ribless\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u003cb\u003eTight frozen ground\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e20% moisture\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.34\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e35% moisture\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e50% moisture\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u003cb\u003eLoose frozen ground\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e20% moisture\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.48\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e35% moisture\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e50% moisture\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.23\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eNote: Unit in times\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec22\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Slip-resistant mechanism of bio-inspired foot ends on ice and simulant for water-ice lunar soil\u003c/h2\u003e \u003cp\u003eThe DCOFs of the five foot ends on ice surface rank as foot end \u003cem\u003eC\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;foot end \u003cem\u003eE\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;foot end \u003cem\u003eB\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;foot end \u003cem\u003eD\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;foot end \u003cem\u003eA\u003c/em\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003eA). Compared to multi-baffle foot end \u003cem\u003eE\u003c/em\u003e, foot end \u003cem\u003eC\u003c/em\u003e increased the DCOF by about 24%. The ribless and non-convex-crown bio-inspired foot end \u003cem\u003eC\u003c/em\u003e exhibited good attachment performance.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWhen the bio-inspired foot ends interacted with ice surface, only the convex-crown and the ribs contacted due to their limited deformation. Consequently, the contact area of the foot ends was reduced, which in turn weakened the attachment performance (Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003eB). In contrast, foot end \u003cem\u003eC\u003c/em\u003e and multi-baffle foot end \u003cem\u003eE\u003c/em\u003e maintained the largest contact areas with the ice surface. The ribs of foot end \u003cem\u003eC\u003c/em\u003e were designed from the microstructure of reindeer ungula cusp, which enhanced its attachment performance. Consequently, foot end \u003cem\u003eC\u003c/em\u003e exhibited the optimal attachment performance when interacting with the ice surface.\u003c/p\u003e \u003cp\u003eOn simulant for water-ice lunar soil (ice-soil mixture), the DCOFs rank as foot end \u003cem\u003eB\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;foot end \u003cem\u003eD\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;foot end \u003cem\u003eE\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;foot end \u003cem\u003eA\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;foot end \u003cem\u003eC\u003c/em\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003eC). On simulant for water-ice lunar soil (water-soil mixture), the DCOFs rank as foot end \u003cem\u003eB\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;foot end \u003cem\u003eD\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;foot end \u003cem\u003eA\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;foot end \u003cem\u003eC\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;foot end \u003cem\u003eE\u003c/em\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003eD). Foot ends \u003cem\u003eB\u003c/em\u003e and \u003cem\u003eD\u003c/em\u003e increased the DCOFs by 35.14%-51.47% and 6.76%-36.76%, respectively, compared to multi-baffled foot end \u003cem\u003eE\u003c/em\u003e on simulant for water-ice lunar soil (ice-soil mixture). Similarly, on simulant for water-ice lunar soil (water-soil mixture), foot ends \u003cem\u003eB\u003c/em\u003e and \u003cem\u003eD\u003c/em\u003e improved the DCOFs by 35.14%-51.47% and 6.76%-36.76%, respectively. In both cases, bio-inspired foot ends \u003cem\u003eB\u003c/em\u003e and \u003cem\u003eD\u003c/em\u003e demonstrated excellent attachment performance. The slip-resistant mechanism of the foot ends on simulant for water-ice lunar soil is similar to that on frozen ground (Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003eE). Under the synergistic action of the bio-inspired convex-crown and bio-inspired ribs, the attachment performance of bio-inspired foot end \u003cem\u003eB\u003c/em\u003e is the optimal.\u003c/p\u003e \u003c/div\u003e"},{"header":"4 Conclusions","content":"\u003cp\u003eThe attachment characteristics of the mechanical foot end are critical for enhancing robot adaptability and traversal on extreme terrains. In this study, inspired by the reindeer touchdown unit, we designed four bio-inspired foot ends and one conventional multi-baffle foot end. Through friction tests on various ground surfaces, including ice and frozen ground, we explored the attachment performances of these bio-inspired foot ends. The bio-inspired ribbed foot end and convex-crown exhibited the best attachment performance on frozen ground and simulant lunar soil, increasing the dynamic coefficient of friction (DCOF) from 24.19\u0026ndash;44.68% and 35.14\u0026ndash;51.47%, respectively, compared to the multi-baffle foot end. This highlights the effectiveness of bio-inspired designs in enhancing attachment on challenging surfaces. The performance of the bio-inspired foot ends varied based on the moisture content of the frozen ground. As the water content increased, the attachment performance improved, indicating the importance of considering environmental conditions in foot end design. The slip-resistant mechanism of the foot ends was influenced by their structural features. Both the convex crown and ribs contributed to reducing the contact area of the foot end, leading to improved attachment performance. However, the convex crown had a greater effect than ribs, suggesting that this feature plays a crucial role in enhancing attachment on icy and rough surfaces.\u003c/p\u003e \u003cp\u003eThe results of this study demonstrate the effectiveness of bio-inspired foot end designs in improving robot traversal on extreme terrains. Future work could focus on further optimizing the design of bio-inspired foot ends for specific environmental conditions and exploring additional biomimetic features that could enhance attachment performance. Though our study provides valuable insights, there are limitations, such as the simplified nature of our models and the need for further validation in real-world environments.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eConflicts of Interest:\u003c/strong\u003e The authors declare no conflict of interest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding:\u003c/strong\u003e This work is financially supported by the Science and Technology Research Planning Project of Jilin Provincial Department of Education (No. JJKH20220980KJ), the Science and Technology Development Planning Project of Jilin Province of China (No. 20220101014JC, 20230203198SF) and 2022 Key Laboratory Project of Ministry of Culture and Tourism.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAsif, U., Iqbal, J., 2012. On the improvement of multi-legged locomotion over difficult terrains using a balance stabilization method. Int. J. Adv. Robot. 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Syst. 16, 1729881419844148. https://doi.org/ 10.1177/1729881419844148.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","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":"reindeer hoof, bio-inspired foot end, ice and frozen ground, friction test, slip-resistant mechanism","lastPublishedDoi":"10.21203/rs.3.rs-4251682/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4251682/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe attachment characteristics of the mechanical foot end are crucial for enhancing the traversability and locomotion of robots on extreme terrains. In this study targeting the reindeer touchdown unit, four bio-inspired foot ends and one conventional multi-baffle foot end were designed. Dynamic friction data of the bio-inspired foot ends were collected under various ground conditions, and the macro- and micro-structures of these surfaces were analyzed. The impacts of multiple factors on the attachment performances of the bio-inspired foot ends were explored, including the moisture content and compactness of frozen soil, and the ridges and convex crowns of foot ends. Additionally, a sliding/rolling friction conversion model was proposed to describe the interaction between the foot ends and frozen soil. When the ends interacted with the frozen ground and simulant for water-ice lunar soil, the attachment of the bio-inspired ribbed foot end and convex-crown was the best, and its dynamic coefficient of friction (DCOF) increased by 24.19%-44.68% and 35.14%-51.47% than the multi-baffle foot end. Upon interacting with the ice surface, the bio-inspired ribless foot end and non-convex crown demonstrated the best attachment performance. The DCOFs of these designs increased by about 24% compared to the multi-baffle foot end. The attachment performances of foot ends were more affected by moisture content compared with the compacted state of frozen ground. Compared to the ribless and non-convex-crown structures, the structures of ribs and convex-crown increased DCOF by 1%-15% and 18%-42%, respectively. Therefore, the effect of convex-crowns was greater than that of ribs. This study can improve the adaptability and traversability of robots on extreme terrains, which is of great significance for their applications in exploring polar regions, the moon, and other harsh environments.\u003c/p\u003e","manuscriptTitle":"Slip-resistant mechanism of bio-inspired foot end based on particle morphology and friction on ice and frozen ground","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-16 11:40:16","doi":"10.21203/rs.3.rs-4251682/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":"0ce79298-30eb-4b16-97df-77581fa193df","owner":[],"postedDate":"April 16th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-07-30T14:23:42+00:00","versionOfRecord":[],"versionCreatedAt":"2024-04-16 11:40:16","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4251682","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4251682","identity":"rs-4251682","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}