Study on bionic bouncing foot of a lunar environment jumping robot

Study on bionic bouncing foot of a lunar environment jumping robot | 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 Study on bionic bouncing foot of a lunar environment jumping robot Rui Zhang, 熙程 栗, Tao Li, Jiaqi Tang, Hua Zhang, Weijun Wang, Zhenyu Hu, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4280934/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 In the current study, we have designed a bouncing device, the bionic bouncing foot end, specifically for the lunar surface environment. The device uses its gravity to store energy in a spring and bounces when the spring releases the energy. We released the spring device from a fixed height and used a 3D capture device to record and analyse the height and angle of excursion of the foot to assess its bouncing performance. Given the important influence of the attachment performance of the foot end on the jumping performance, we designed a new bionic pattern of the bouncing foot end using the camel hoof and the ostrich papilla as bionic prototypes. Through validation, we demonstrated that the attachment performance of the bionic pattern is better than that of the traditional patterned foot end. For the application requirements of jumping robots in loose and soft media, we further optimised the design of the foot end pattern and verified it by simulation through multi-rigid body dynamics and discrete element simulation. These studies provide important theoretical and technical support for the study of high-performance jumping robots in the lunar surface environment. low gravity soft ground bionic hopping foot end Jumping Robot 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 The Moon is the closest natural satellite to mankind, rich in resources, and deep space exploration is of great significance to mankind(Flahaut, et al.2023). The more common lunar surface exploration tools are currently available. Wheeled lunar rovers move quickly, but have poor ability to cross obstacles and a limited range of movement. When on soft ground, the wheels tend to sink and slip. Tracked lunar rovers have greatly improved their adaptability to the surface, but are not suitable for planetary exploration due to their high weight and poor manoeuvrability. The flexibility of the footed walking robot has been greatly improved, and it has some ability to cross obstacles. However, it moves slowly and is complicated to control. Jumping robots have significant mobility advantages in soft, rocky and low-gravity lunar environments. The structure is simple to control, and in the low-gravity environment of the Moon, it can use its advantages to easily cross obstacles several times its height（Zhang, et al.2017）. It is a better choice for future deep space exploration robots on the Moon. Xiangxiao Liu et al. designed foot ends with rigid plantar fascia by mimicking human foot features to enhance the jumping performance of a humanoid robot(Liu, et al.2016). Lee, Jessica Sy Research focuses on bionic composite feet with vertebrae and footpads to improve jumping performance in flea robots（Lee, et al.2016）. Chuanku Yiz, on the other hand, has designed a humanoid foot with bionic bones and joints, drawing on the structure of the human foot end（Yi, et al.2022）. It is designed to reduce impact and absorb the shock of landing a jumping robot（Yi, et al.2024）. H Chai presents a foot-flexible jumping robot prototype with an optimised design that outperforms conventional foot designs in terms of flexible foot jump height and distance. Relatively little research has been conducted on the foot of jumping robots, mainly focussing on improving jumping performance on conventional ground surfaces. In contrast, there has been relatively little research on unconventional ground. The design of end-of-foot research for soft ground has focused more on the walking aspect, while applications in the field of jumping robots have not been fully explored. Christian M. Hubicki describes a mass-attachment model for the foot-end intrusion process into the soil and validates it with experiments that show the feasibility of computational time for leg design(Hubicki, et al.2016). Jerey Aguilar conducted a study of a simple spring-mass robot jumping system over a granular medium（Aguilar and Goldman2016）. Emphasis is placed on explaining how jump performance is affected by the interaction of nonlinear frictional and hydrodynamic drag, as well as additional mass modelling. Relevant principles in deformable ground environments and control are provided. Will Bosworth shows that ground characteristics have a significant effect on the stability of jumping robots through robot trials on soft and hard surfaces, and gives three parameters to evaluate ground characteristics（Bosworth, et al.2016）. By Keita KOBASHi A simulation based on the discrete element method was carried out to parametrically analyse the jumping motion with different particle parameters, focusing on the two characteristics of jumping velocity and jumping angle during the jumping motion（Kobashi, et al.2021）. Łukasz Wisniewski gives an overview of the effects of motion energy consumption of typical planetary exploration jumping robots and also suggests that energy dissipation due to contact with the terroir is also part of the current research（Wisniewski, et al.2021）. Kosuke Sakamoto designed a new footbed to improve jumping performance on soft soil by evaluating jumping performance in three terrain conditions（Sakamoto, et al.2019）. There is relatively little research on jumping robots for soft ground and relatively limited research on the foot-loam relationship between jumping robots and the ground. However, jump manoeuvrability is particularly important for robots that need to explore special terrain such as asteroids such as the Moon. These areas may be covered by a loose medium, making the design of the bouncing foot end, the only component in contact with the loose ground, particularly critical for the robot. Jumping robots are more appropriate for applications in deep space exploration. The morphology of the foot end affects the sand fixation ability and attachment performance of the foot end, which in turn affects the jumping performance of the foot end. Therefore, in this paper, a bionic bouncing foot end with high adhesion performance was developed by using engineering bionic technology, and the relationship between the jumping foot end and the sandy soil was explored through a series of experiments. 2 Materials and methods 2.1 A biomimetic study of the highly adherent pattern on the hemispherical foot tip Due to the sticky and plastic nature of the soft ground, to minimise the impact on its jumping performance, our jumping robot uses a spherically contoured footbed(El-Gendy, et al.2011). Ostriches in the desert have a superb resistance to slippage and subsidence. Careful observation and dissection of the ostrich foot can be found that a large number of papillae clusters are attached to the soles of the third and fourth toes of the ostrich foot. Pang Hao et al. from Jilin University did an in-depth study on ostrich papillae and found that they have the effect of increasing the coefficient of adhesion and applied them to lunar wheels（Pang, et al.2021）. Therefore, the foot end pattern in this study was designed as a biomimetic anti-slip foot pattern using the ostrich plantar papillae cluster as a biological model. The shape of the papillae was distributed concerning the shape of the camel's hoof. Camels can walk smoothly on desert surfaces without sinking and slipping. For example, Professor Zhuang Jide of Jilin University has designed a desert tyre based on the camel's hooves, which improves the vehicle's ability to pass in the deser. In this study, the jumping robot foot end morphology envelope is based on the shape of a camel's hoof as a biological model, and the bionic anti-slip convex-concave body cluster is distributed in the bionic anti-slip morphology envelope area and is arrayed into five parts, which are wrapped on the surface of the hemispherical foot end. Finally, the bionic foot end pattern is formed, and the pattern pattern is shown in Fig. 1 . 2.2 Static attachment experiment of foot end to loose medium The test equipment was a spring-loaded dynamometer. The samples were foot ends of the three different patterns mentioned above. To investigate the adhesion of the foot end at different angles, the test could not be completed with the normal design of the printed foot end. To solve this problem, different angular cuts were made in the design of the foot end, and a quantitative normal load was applied to these cuts during the test. The experimental procedure is shown in Fig. 2 . Two types of sandy soils, quartz sand and simulated lunar loam, were selected as the experimental media, both of which were in a naturally loose state. Through the test, the foot end adhesion of different patterns and different touchdown angles showed a tendency of increasing magnitude decreasing with the increase of load. Under the same loading conditions and the same test medium conditions, the greater the touchdown angle, the greater the foot-end adhesion. Foot end adhesion bionic pattern > block pattern > herringbone pattern. The foot-end adhesion at different angles with a normal load of 2.50 kg is taken as a sample for analysis, as shown in Fig. 3 below. Under quartz sand conditions, the adhesion of the block pattern improved by 8–20% over the herringbone pattern under the same conditions, and the adhesion of the bionic pattern improved by 32–55% over the herringbone pattern. Under simulated lunar soil conditions, the adhesion of the block pattern improved by 3–11% over the herringbone pattern and the adhesion of the bionic pattern improved by 39–41% over the herringbone pattern under the same conditions. 2.3 Dynamic adhesion test between foot end and sandy surface During the test, one end of the traction wire is connected to the foot end and the other end is connected to the tension sensor. By controlling the work of the testing machine through the control computer, the foot end is pulled forward by the traction wire(Li, et al.2023). The test samples are different patterns of the foot end and the test process is shown in Fig. 4 . By test. The increase in foot-end adhesion with increasing load decreases for different patterns and different touchdown angles. Under the same loading conditions and the same test medium conditions, the greater the touchdown angle, the greater the foot-end adhesion. Adhesion of foot end bionic pattern > block pattern > herringbone pattern. The foot end adhesion at different angles with a load of 200 g was taken as a sample for analysis under quartz sand conditions. The adhesion of the block pattern under the same conditions was improved by 4–13% over the herringbone pattern, as shown in Fig. 5 Bionic patterns are 22 to 31 per cent higher than herringbone patterns. Under simulated lunar soil conditions, block patterns improved adhesion by 5–9% over herringbone patterns, and bionic patterns improved by 22–26% over herringbone patterns. Comparing the two figures, it can be seen that the foot-end adhesion under simulated lunar soil is greater than that under quartz sand under the same conditions. 1.09–1.21 times that of quartz sand. The main reason may be the difference in particle size and inter-particle contact characteristics of the sand. There is a large difference in grain size between simulated moon soil and quartz sand, with quartz sand having about 10 times the grain size of simulated moon soil, and more grains can be cemented to the end of the same patterned foot under the same conditions. The fact that the stacking angle of the simulated lunar soil is greater than that of the quartz sand, further indicates that the fluidity of the particles of the quartz sand is greater than that of the simulated lunar soil, which reduces the adhesion on the quartz sand. 2.4 Braking distance test The braking test mainly tests the moving performance of the foot end under accelerated conditions and evaluates the attachment performance of the foot end by comparing the sliding distance when different foot ends stop. Test samples were selected from 0°15°30° herringbone, block and bionic foot ends. The tension rope on the rail test frame in the test is connected to the weights at one end and to the foot end at the other end. One person is responsible for adding loads to the foot end and the other person is responsible for adding the weights needed to drag the foot end forward, and after the weights dragging the foot end forward have touched the ground and come to rest, the foot end also slides a distance and then comes to rest. Measurement of the distance of slip of the foot end. The main condition orientated in this braking test is the foot-end emergency stop condition. The test procedure is shown in Fig. 6 It can be seen from Fig. 7 below that under the same medium conditions and the same touchdown angle the herringbone patterned foot end has the largest slip distance and the bionic patterned foot end has the smallest slip distance, indicating that the adhesion of the bionic patterned foot end is superior to that a herringbone patterned foot end and a block patterned foot end and that the block patterned foot end has a better attachment than that of the herringbone patterned foot end. Under the same pattern conditions, the larger the touchdown angle, the shorter the slip distance. This means that the larger the touchdown angle, the greater the adhesion. Comparison reveals that the slip distance at the foot end of the same pattern in the quartz sand condition is greater than that in the simulated lunar soil condition. The effect of touchdown angle and test medium on slip distance was greater than the effect of foot end pattern on slip distance. 3 Study on the jumping performance of bionic foot end A foot end with good jumping performance is selected through jumping tests and then optimised for that foot end. Keeping the basic shape of the end of the foot unchanged and adjusting the size of the pattern, the end of the foot is finally designed to jump with excellent jumping performance. The foot end in this study is ultimately oriented towards the low gravity environment on the lunar surface, which is difficult to test, whereas it can be easily implemented in the simulation software, so this part of the study is calculated in the simulation simulation. 3.1 Foot-end jumping test based on different patterns The test samples were a bionic pattern, herringbone pattern, and block pattern foot ends. The bouncing device is an idealised bouncing model. The lower part is the foot end of the bouncing device, the middle is the spring that stores and releases energy, and the upper part is the structure that balances the whole system. The different foot ends have the same mass. The bouncing device has no energy source of its own, mainly relying on its gravity to achieve bouncing after contact with the ground. When the test is lifted to the specified height, keep the end of the foot vertically down, to be stable after the free-fall movement, and the end of the foot and the sand contact with the soil after the spring up and down to the stationary state. As shown in Fig. 8 . The results showed that the bouncing height of the foot end was bionic pattern > block pattern > herringbone pattern, and the bouncing height of the foot end of the bionic pattern was 40.30% higher than that of the foot end of the non-patterned foot, 18.80% higher than that of the foot end of the herringbone pattern, and 10.70% higher than that of the foot end of the block pattern. The bionic pattern foot-end adhesion is consistent with the previous patterns of adhesion at the foot-end of different patterns, indicating a positive correlation between foot-end pattern adhesion and bounce height. Comparison of the above different foot ends in the simulated lunar soil foot end adhesion is greater than the quartz sand and quartz sand on the bouncing device of the bouncing height is greater than the simulated lunar soil, indicating that the test medium not only has an effect on the bouncing device foot end adhesion but also has an effect on the bouncing device foot end support force, and the effect on the foot end support force is greater than the effect on the foot end adhesion force. As shown in Fig. 9 . 3.2. Optimised design of orthogonal tests The jumping performance of the bionic foot end was finally found to be better than the other two conventional foot ends through the jumping test of different patterned foot ends. The foot-end pattern is further optimised. The shape and distribution of the papillae were not changed, but only the dimensions of the papillae were optimised, mainly including the radius of the papillae, the height of the papillae, and the angle of the papillae. An orthogonal experimental design was chosen to reduce the workload. Where 0°, 45° refers to the mastoid angle versus the angle with the vertical plane, and 90° refers to the mastoid angle versus the hemispherical facet angle. Table 1 Variable values for the three variables radius(mm) height(mm) angle(°) 0.5 1 0 1 3 45 1.5 5 90 The optimised nine-foot ends were drawn in 3D and the 3D model was 3D printed as a solid, as shown in Fig. 10 below, and then the jumping test was carried out. The jumping height and jumping stability are shown in Fig. 11 below. Taking the jump height as an example, the values of I, II, III, T and R were calculated for each factor. The results of the calculations are shown in the Table 2 Table 2 Calculation table for analysis of height test results factor A B C height(mm) test number 1 2 3 1 1 1 1 141 2 1 2 2 120 3 1 3 3 115 4 2 1 2 145 5 2 2 3 131 6 2 3 1 102 7 3 1 3 150 8 3 2 1 119 9 3 3 2 108 Ⅰ 376 436 362 T = 1131 Ⅱ 378 370 373 Ⅲ 377 325 396 R 2 111 34 The order of priority of the factors is B > C > A For each factor, take the number of levels as the horizontal coordinate, and the corresponding I, II, and III as the vertical coordinate, and draw a trend graph as shown in Fig. 12 , the greater the height, the better, and the resulting optimal bionic design should be 1.5mm (radius) − 1mm (height) − 90° (angle). Deviation angles are analysed in the same way. 3.3 Simulation of foot-end jumping in low-gravity Joint simulation using RecurDyn and EDEM. Gravity environment and low gravity environment respectively. The optimised model 1.5mm (height)-1mm (height)-90° (angle) is taken as the object of study. As shown in Fig. 13 . The jump height of the bouncing device in low gravity is much higher than that of the bouncing device in gravity, because the low gravity environment makes it easier for the jumping robot to jump, allowing it to easily cross larger obstacles and reduce energy consumption. The deviation angles under different gravity conditions are shown on the right, and it can be seen that the slopes of the bouncing device under low gravity are smaller than those of the bouncing device under gravity under the same moment conditions, which indicates that the bouncing under low gravity is a bit more stable. Consideration has to do with the contact between the foot end and the soil in low gravity, the contact between the foot end and the sandy soil in low gravity is softer, and the disturbance to the soil is a bit smaller, which is more favourable to the adjustment of the state of the whole system. From the analysis of the particle velocity field at the same position of the foot end, the range of particle perturbation under the velocity field of gravity environment is the largest, the range of velocity field perturbation under low gravity environment is the smallest, the direction of particle flow is directed to the bottom of the foot end, and the particle velocity field under gravity soil is more concentrated compared with that under low gravity. The velocity field of particles under gravity is more concentrated compared to that under low gravity. 4 Conclusion The moon's surface is characterised by soft lunar soil and low gravity environment, and the jumping robot has superior motion performance in the moon surface environment, which will have an important application prospect in the moon surface exploration mission. To study the high-performance foot end suitable for the lunar surface environment, this paper combines experiment and simulation to research the bouncing performance of foot ends with different curvature radii, the attachment performance of foot ends with different patterns, the bouncing performance of foot ends with different patterns, and the bouncing performance of the foot ends under different gravitational environments, and obtains the following main conclusions: A bionic patterned bouncing foot end is designed using camel hooves and ostrich papillae as bionic prototypes. Two conventional patterned foot ends were used as a comparison. Adhesion tests verified that the bionic patterned ends had better adhesion properties than the conventional patterned ends. The adhesion performance was improved by 22–31%. The bouncing performance test showed that the bionic patterned foot end had better-bouncing performance than the conventional patterned foot end, with the height performance improved by 10.7%-18.8% and the stability performance improved by 10.4%-25.4%. The dimensions of the foot end pattern were optimised for the best combination of 1.5mm (radius) − 1mm (height) − 90° (angle) for height performance and 0.5mm (radius) − 5mm (height) − 0° (angle) for stability performance. Through coupled simulation, the bouncing situation of the bouncing device under the low gravity environment on the lunar surface is investigated. The bouncing performance of the bionic bouncing foot is compared between the low-gravity and gravity environments, and the bionic bouncing foot is finally developed for the low-gravity soft lunar surface environment. Declarations Conflicts of Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Author Contribution Rui Zhang：Conceptualization, Methodology, Software, Investigation, Formal Analysis, Writing - Original Draft;Xicheng Li：Data Curation, Writing - Original Draft;Tao Li：Visualization, Investigation;Jiaqi Tang：Resources, Supervision;Hua Zhang：Software, Validation；Weijun Wang：Visualization, Writing - Review & Editing；Zhenyu Hu：Software, Validation；Lige Wen：Resources, Supervision; Acknowledgements We thank the support of the National Natural Science Foundation of China (No. 52275287), the Opening Project of Aerospace System Engineering Shanghai (YY-F805202108002), the Opening Project of the Key Laboratory of Bionic Engineering (Ministry of Education), Jilin University (No. KF20211009) References J. Flahaut, C. H. van der Bogert, I. A. Crawford and S. 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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-4280934","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":292302678,"identity":"0f5704c9-feda-49c1-bc36-0c12e1ddaca2","order_by":0,"name":"Rui 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09:37:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4280934/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4280934/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":55104500,"identity":"ffeea1a4-ca7d-45bb-988b-1a2000f403cc","added_by":"auto","created_at":"2024-04-22 16:22:30","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":26321,"visible":true,"origin":"","legend":"\u003cp\u003eMorphological study of highly attached bionic foot ends\u003c/p\u003e","description":"","filename":"floatimage1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4280934/v1/28d16e73bbcfe3ddea5d9f57.jpg"},{"id":55104503,"identity":"6f9d3f63-47f5-4074-9e10-e28ef2efa9a9","added_by":"auto","created_at":"2024-04-22 16:22:30","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":24599,"visible":true,"origin":"","legend":"\u003cp\u003eStatic attachment test procedure\u003c/p\u003e","description":"","filename":"floatimage2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4280934/v1/0104f51937584b7c9dec9154.jpg"},{"id":55104502,"identity":"2da0b2f0-987e-4943-a24c-6b55b1633c55","added_by":"auto","created_at":"2024-04-22 16:22:30","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":682659,"visible":true,"origin":"","legend":"\u003cp\u003eFoot-end adhesion under quartz sand media (left) simulating lunar soil (right)\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4280934/v1/89f5e2fd0de4413f917f4863.jpeg"},{"id":55104507,"identity":"834f7720-76d2-418e-a773-c92ba273b4db","added_by":"auto","created_at":"2024-04-22 16:22:31","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":30770,"visible":true,"origin":"","legend":"\u003cp\u003eUTM friction tester test process\u003c/p\u003e","description":"","filename":"floatimage4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4280934/v1/0cc01d0595c72d5d9778a35a.jpg"},{"id":55104508,"identity":"a04bd51e-65e8-4447-95c8-a400f8a1f4ad","added_by":"auto","created_at":"2024-04-22 16:22:31","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":676394,"visible":true,"origin":"","legend":"\u003cp\u003eFoot-end adhesion under quartz sand (left) simulated lunar soil (right)\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4280934/v1/0973406c705a20bd7219033f.jpeg"},{"id":55104834,"identity":"08c8104e-0e0c-45e3-a216-4dfe04708a20","added_by":"auto","created_at":"2024-04-22 16:30:30","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":20440,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of the braking distance test process\u003c/p\u003e","description":"","filename":"floatimage6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4280934/v1/e4eeb5d6d96cd525c6da974b.jpg"},{"id":55104511,"identity":"42600948-3f4f-41c5-b6e6-5372d1c1803c","added_by":"auto","created_at":"2024-04-22 16:22:31","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":617443,"visible":true,"origin":"","legend":"\u003cp\u003eFoot-end slip in quartz sand (left) simulated lunar soil (right) conditions\u003c/p\u003e","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4280934/v1/d9cb82e28cddae13c0450e45.jpeg"},{"id":55104501,"identity":"f5887ab0-aabe-49a6-9364-3ebd2f46a099","added_by":"auto","created_at":"2024-04-22 16:22:30","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":8147,"visible":true,"origin":"","legend":"\u003cp\u003eFoot-end bouncing device\u003c/p\u003e","description":"","filename":"floatimage8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4280934/v1/c7c121946b2b4597e27a9049.jpg"},{"id":55104509,"identity":"b8c2b1af-fedf-486d-b8dd-64a7e724e13c","added_by":"auto","created_at":"2024-04-22 16:22:31","extension":"jpeg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":648100,"visible":true,"origin":"","legend":"\u003cp\u003eBounce height (left) deviation angle (right) at the foot end of different patterns\u003c/p\u003e","description":"","filename":"floatimage9.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4280934/v1/d9ac585317e7043372921609.jpeg"},{"id":55104835,"identity":"1f28d9cb-4b03-46d3-b54f-de07523dffe9","added_by":"auto","created_at":"2024-04-22 16:30:31","extension":"jpeg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":104106,"visible":true,"origin":"","legend":"\u003cp\u003ePatterns in three different sizes\u003c/p\u003e","description":"","filename":"floatimage10.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4280934/v1/e5920b5924f4892ff1158ba4.jpeg"},{"id":55104514,"identity":"b03a1f24-9445-4b10-a503-9473118fdb16","added_by":"auto","created_at":"2024-04-22 16:22:31","extension":"jpeg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":833746,"visible":true,"origin":"","legend":"\u003cp\u003eBounce height (left) deviation angle (right) for nine-foot ends\u003c/p\u003e","description":"","filename":"floatimage11.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4280934/v1/0be61e44a38c49391d842a4f.jpeg"},{"id":55104506,"identity":"ef68f70c-2882-4d84-bf58-7f38c80728ec","added_by":"auto","created_at":"2024-04-22 16:22:31","extension":"jpg","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":27474,"visible":true,"origin":"","legend":"\u003cp\u003eTrends in factor levels\u003c/p\u003e","description":"","filename":"floatimage12.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4280934/v1/ea7b01653252cacd0008566c.jpg"},{"id":55104513,"identity":"35cc4fc9-2c20-463b-b1da-af21d7a9a92a","added_by":"auto","created_at":"2024-04-22 16:22:31","extension":"jpeg","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":763245,"visible":true,"origin":"","legend":"\u003cp\u003eBounce height (left) offset angle (right) for different gravity conditions\u003c/p\u003e","description":"","filename":"floatimage13.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4280934/v1/44fdcc7bda01c2b25d78ec8c.jpeg"},{"id":55104512,"identity":"b397373f-70a0-4191-a985-d777fe149c2f","added_by":"auto","created_at":"2024-04-22 16:22:31","extension":"jpeg","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":179596,"visible":true,"origin":"","legend":"\u003cp\u003eVelocity field in gravity environment (left) and low gravity environment (right)\u003c/p\u003e","description":"","filename":"floatimage14.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4280934/v1/9780152301d8d6c52322059e.jpeg"},{"id":57513249,"identity":"b01940fe-fbee-4ca4-b4df-3abd51c3a581","added_by":"auto","created_at":"2024-05-31 17:54:43","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5074077,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4280934/v1/080a5f87-c109-4f4c-8258-06f7f5d4bab7.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Study on bionic bouncing foot of a lunar environment jumping robot","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eThe Moon is the closest natural satellite to mankind, rich in resources, and deep space exploration is of great significance to mankind(Flahaut, et al.2023). The more common lunar surface exploration tools are currently available. Wheeled lunar rovers move quickly, but have poor ability to cross obstacles and a limited range of movement. When on soft ground, the wheels tend to sink and slip. Tracked lunar rovers have greatly improved their adaptability to the surface, but are not suitable for planetary exploration due to their high weight and poor manoeuvrability. The flexibility of the footed walking robot has been greatly improved, and it has some ability to cross obstacles. However, it moves slowly and is complicated to control. Jumping robots have significant mobility advantages in soft, rocky and low-gravity lunar environments. The structure is simple to control, and in the low-gravity environment of the Moon, it can use its advantages to easily cross obstacles several times its height（Zhang, et al.2017）. It is a better choice for future deep space exploration robots on the Moon.\u003c/p\u003e\n\u003cp\u003eXiangxiao Liu et al. designed foot ends with rigid plantar fascia by mimicking human foot features to enhance the jumping performance of a humanoid robot(Liu, et al.2016). Lee, Jessica Sy Research focuses on bionic composite feet with vertebrae and footpads to improve jumping performance in flea robots（Lee, et al.2016）. Chuanku Yiz, on the other hand, has designed a humanoid foot with bionic bones and joints, drawing on the structure of the human foot end（Yi, et al.2022）. It is designed to reduce impact and absorb the shock of landing a jumping robot（Yi, et al.2024）. H Chai presents a foot-flexible jumping robot prototype with an optimised design that outperforms conventional foot designs in terms of flexible foot jump height and distance. Relatively little research has been conducted on the foot of jumping robots, mainly focussing on improving jumping performance on conventional ground surfaces. In contrast, there has been relatively little research on unconventional ground. The design of end-of-foot research for soft ground has focused more on the walking aspect, while applications in the field of jumping robots have not been fully explored.\u003c/p\u003e\n\u003cp\u003eChristian M. Hubicki describes a mass-attachment model for the foot-end intrusion process into the soil and validates it with experiments that show the feasibility of computational time for leg design(Hubicki, et al.2016). Jerey Aguilar conducted a study of a simple spring-mass robot jumping system over a granular medium（Aguilar and Goldman2016）. Emphasis is placed on explaining how jump performance is affected by the interaction of nonlinear frictional and hydrodynamic drag, as well as additional mass modelling. Relevant principles in deformable ground environments and control are provided. Will Bosworth shows that ground characteristics have a significant effect on the stability of jumping robots through robot trials on soft and hard surfaces, and gives three parameters to evaluate ground characteristics（Bosworth, et al.2016）. By Keita KOBASHi A simulation based on the discrete element method was carried out to parametrically analyse the jumping motion with different particle parameters, focusing on the two characteristics of jumping velocity and jumping angle during the jumping motion（Kobashi, et al.2021）. Łukasz Wisniewski gives an overview of the effects of motion energy consumption of typical planetary exploration jumping robots and also suggests that energy dissipation due to contact with the terroir is also part of the current research（Wisniewski, et al.2021）. Kosuke Sakamoto designed a new footbed to improve jumping performance on soft soil by evaluating jumping performance in three terrain conditions（Sakamoto, et al.2019）. There is relatively little research on jumping robots for soft ground and relatively limited research on the foot-loam relationship between jumping robots and the ground. However, jump manoeuvrability is particularly important for robots that need to explore special terrain such as asteroids such as the Moon. These areas may be covered by a loose medium, making the design of the bouncing foot end, the only component in contact with the loose ground, particularly critical for the robot. Jumping robots are more appropriate for applications in deep space exploration. The morphology of the foot end affects the sand fixation ability and attachment performance of the foot end, which in turn affects the jumping performance of the foot end. Therefore, in this paper, a bionic bouncing foot end with high adhesion performance was developed by using engineering bionic technology, and the relationship between the jumping foot end and the sandy soil was explored through a series of experiments.\u003c/p\u003e"},{"header":"2 Materials and methods","content":"\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e\n\u003ch3\u003e2.1 A biomimetic study of the highly adherent pattern on the hemispherical foot tip\u003c/h3\u003e\n\u003cp\u003eDue to the sticky and plastic nature of the soft ground, to minimise the impact on its jumping performance, our jumping robot uses a spherically contoured footbed(El-Gendy, et al.2011). Ostriches in the desert have a superb resistance to slippage and subsidence. Careful observation and dissection of the ostrich foot can be found that a large number of papillae clusters are attached to the soles of the third and fourth toes of the ostrich foot. Pang Hao et al. from Jilin University did an in-depth study on ostrich papillae and found that they have the effect of increasing the coefficient of adhesion and applied them to lunar wheels（Pang, et al.2021）. Therefore, the foot end pattern in this study was designed as a biomimetic anti-slip foot pattern using the ostrich plantar papillae cluster as a biological model. The shape of the papillae was distributed concerning the shape of the camel's hoof. Camels can walk smoothly on desert surfaces without sinking and slipping. For example, Professor Zhuang Jide of Jilin University has designed a desert tyre based on the camel's hooves, which improves the vehicle's ability to pass in the deser. In this study, the jumping robot foot end morphology envelope is based on the shape of a camel's hoof as a biological model, and the bionic anti-slip convex-concave body cluster is distributed in the bionic anti-slip morphology envelope area and is arrayed into five parts, which are wrapped on the surface of the hemispherical foot end. Finally, the bionic foot end pattern is formed, and the pattern pattern is shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003ch3\u003e2.2 Static attachment experiment of foot end to loose medium\u003c/h3\u003e\n\u003cp\u003eThe test equipment was a spring-loaded dynamometer. The samples were foot ends of the three different patterns mentioned above. To investigate the adhesion of the foot end at different angles, the test could not be completed with the normal design of the printed foot end. To solve this problem, different angular cuts were made in the design of the foot end, and a quantitative normal load was applied to these cuts during the test. The experimental procedure is shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e. Two types of sandy soils, quartz sand and simulated lunar loam, were selected as the experimental media, both of which were in a naturally loose state.\u003c/p\u003e\n\u003cp\u003eThrough the test, the foot end adhesion of different patterns and different touchdown angles showed a tendency of increasing magnitude decreasing with the increase of load. Under the same loading conditions and the same test medium conditions, the greater the touchdown angle, the greater the foot-end adhesion. Foot end adhesion bionic pattern\u0026thinsp;\u0026gt;\u0026thinsp;block pattern\u0026thinsp;\u0026gt;\u0026thinsp;herringbone pattern.\u003c/p\u003e\n\u003cp\u003eThe foot-end adhesion at different angles with a normal load of 2.50 kg is taken as a sample for analysis, as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e below. Under quartz sand conditions, the adhesion of the block pattern improved by 8\u0026ndash;20% over the herringbone pattern under the same conditions, and the adhesion of the bionic pattern improved by 32\u0026ndash;55% over the herringbone pattern. Under simulated lunar soil conditions, the adhesion of the block pattern improved by 3\u0026ndash;11% over the herringbone pattern and the adhesion of the bionic pattern improved by 39\u0026ndash;41% over the herringbone pattern under the same conditions.\u003c/p\u003e\n\u003ch3\u003e2.3 Dynamic adhesion test between foot end and sandy surface\u003c/h3\u003e\n\u003cp\u003eDuring the test, one end of the traction wire is connected to the foot end and the other end is connected to the tension sensor. By controlling the work of the testing machine through the control computer, the foot end is pulled forward by the traction wire(Li, et al.2023). The test samples are different patterns of the foot end and the test process is shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eBy test. The increase in foot-end adhesion with increasing load decreases for different patterns and different touchdown angles. Under the same loading conditions and the same test medium conditions, the greater the touchdown angle, the greater the foot-end adhesion. Adhesion of foot end bionic pattern\u0026thinsp;\u0026gt;\u0026thinsp;block pattern\u0026thinsp;\u0026gt;\u0026thinsp;herringbone pattern.\u003c/p\u003e\n\u003cp\u003eThe foot end adhesion at different angles with a load of 200 g was taken as a sample for analysis under quartz sand conditions. The adhesion of the block pattern under the same conditions was improved by 4\u0026ndash;13% over the herringbone pattern, as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e Bionic patterns are 22 to 31 per cent higher than herringbone patterns. Under simulated lunar soil conditions, block patterns improved adhesion by 5\u0026ndash;9% over herringbone patterns, and bionic patterns improved by 22\u0026ndash;26% over herringbone patterns. Comparing the two figures, it can be seen that the foot-end adhesion under simulated lunar soil is greater than that under quartz sand under the same conditions. 1.09\u0026ndash;1.21 times that of quartz sand. The main reason may be the difference in particle size and inter-particle contact characteristics of the sand. There is a large difference in grain size between simulated moon soil and quartz sand, with quartz sand having about 10 times the grain size of simulated moon soil, and more grains can be cemented to the end of the same patterned foot under the same conditions. The fact that the stacking angle of the simulated lunar soil is greater than that of the quartz sand, further indicates that the fluidity of the particles of the quartz sand is greater than that of the simulated lunar soil, which reduces the adhesion on the quartz sand.\u003c/p\u003e\n\u003ch3\u003e2.4 Braking distance test\u003c/h3\u003e\n\u003cp\u003eThe braking test mainly tests the moving performance of the foot end under accelerated conditions and evaluates the attachment performance of the foot end by comparing the sliding distance when different foot ends stop. Test samples were selected from 0\u0026deg;15\u0026deg;30\u0026deg; herringbone, block and bionic foot ends. The tension rope on the rail test frame in the test is connected to the weights at one end and to the foot end at the other end. One person is responsible for adding loads to the foot end and the other person is responsible for adding the weights needed to drag the foot end forward, and after the weights dragging the foot end forward have touched the ground and come to rest, the foot end also slides a distance and then comes to rest. Measurement of the distance of slip of the foot end. The main condition orientated in this braking test is the foot-end emergency stop condition. The test procedure is shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eIt can be seen from Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e below that under the same medium conditions and the same touchdown angle the herringbone patterned foot end has the largest slip distance and the bionic patterned foot end has the smallest slip distance, indicating that the adhesion of the bionic patterned foot end is superior to that a herringbone patterned foot end and a block patterned foot end and that the block patterned foot end has a better attachment than that of the herringbone patterned foot end. Under the same pattern conditions, the larger the touchdown angle, the shorter the slip distance. This means that the larger the touchdown angle, the greater the adhesion.\u003c/p\u003e\n\u003cp\u003eComparison reveals that the slip distance at the foot end of the same pattern in the quartz sand condition is greater than that in the simulated lunar soil condition. The effect of touchdown angle and test medium on slip distance was greater than the effect of foot end pattern on slip distance.\u003c/p\u003e"},{"header":"3 Study on the jumping performance of bionic foot end","content":"\u003cp\u003eA foot end with good jumping performance is selected through jumping tests and then optimised for that foot end. Keeping the basic shape of the end of the foot unchanged and adjusting the size of the pattern, the end of the foot is finally designed to jump with excellent jumping performance. The foot end in this study is ultimately oriented towards the low gravity environment on the lunar surface, which is difficult to test, whereas it can be easily implemented in the simulation software, so this part of the study is calculated in the simulation simulation.\u003c/p\u003e\n\u003ch3\u003e3.1 Foot-end jumping test based on different patterns\u003c/h3\u003e\n\u003cp\u003eThe test samples were a bionic pattern, herringbone pattern, and block pattern foot ends. The bouncing device is an idealised bouncing model. The lower part is the foot end of the bouncing device, the middle is the spring that stores and releases energy, and the upper part is the structure that balances the whole system. The different foot ends have the same mass. The bouncing device has no energy source of its own, mainly relying on its gravity to achieve bouncing after contact with the ground. When the test is lifted to the specified height, keep the end of the foot vertically down, to be stable after the free-fall movement, and the end of the foot and the sand contact with the soil after the spring up and down to the stationary state. As shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eThe results showed that the bouncing height of the foot end was bionic pattern\u0026thinsp;\u0026gt;\u0026thinsp;block pattern\u0026thinsp;\u0026gt;\u0026thinsp;herringbone pattern, and the bouncing height of the foot end of the bionic pattern was 40.30% higher than that of the foot end of the non-patterned foot, 18.80% higher than that of the foot end of the herringbone pattern, and 10.70% higher than that of the foot end of the block pattern. The bionic pattern foot-end adhesion is consistent with the previous patterns of adhesion at the foot-end of different patterns, indicating a positive correlation between foot-end pattern adhesion and bounce height. Comparison of the above different foot ends in the simulated lunar soil foot end adhesion is greater than the quartz sand and quartz sand on the bouncing device of the bouncing height is greater than the simulated lunar soil, indicating that the test medium not only has an effect on the bouncing device foot end adhesion but also has an effect on the bouncing device foot end support force, and the effect on the foot end support force is greater than the effect on the foot end adhesion force. As shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e.\u003c/p\u003e\n\u003ch3\u003e3.2. Optimised design of orthogonal tests\u003c/h3\u003e\n\u003cp\u003eThe jumping performance of the bionic foot end was finally found to be better than the other two conventional foot ends through the jumping test of different patterned foot ends. The foot-end pattern is further optimised. The shape and distribution of the papillae were not changed, but only the dimensions of the papillae were optimised, mainly including the radius of the papillae, the height of the papillae, and the angle of the papillae. An orthogonal experimental design was chosen to reduce the workload. Where 0\u0026deg;, 45\u0026deg; refers to the mastoid angle versus the angle with the vertical plane, and 90\u0026deg; refers to the mastoid angle versus the hemispherical facet angle.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab1\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eVariable values for the three variables\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eradius(mm)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eheight(mm)\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eangle(\u0026deg;)\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e45\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e90\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eThe optimised nine-foot ends were drawn in 3D and the 3D model was 3D printed as a solid, as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e below, and then the jumping test was carried out. The jumping height and jumping stability are shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e below.\u003c/p\u003e\n\u003cp\u003eTaking the jump height as an example, the values of I, II, III, T and R were calculated for each factor. The results of the calculations are shown in the Table\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab2\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003eCalculation table for analysis of height test results\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003efactor\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eA\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eB\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eC\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eheight(mm)\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003etest number\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e141\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e120\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e115\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e145\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e131\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e102\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e7\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e150\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e8\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e119\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e9\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e108\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eⅠ\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e376\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e436\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e362\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"4\" align=\"left\"\u003e\n\u003cp\u003eT\u0026thinsp;=\u0026thinsp;1131\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eⅡ\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e378\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e370\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e373\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eⅢ\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e377\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e325\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e396\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eR\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e111\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e34\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eThe order of priority of the factors is B\u0026thinsp;\u0026gt;\u0026thinsp;C\u0026thinsp;\u0026gt;\u0026thinsp;A For each factor, take the number of levels as the horizontal coordinate, and the corresponding I, II, and III as the vertical coordinate, and draw a trend graph as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e, the greater the height, the better, and the resulting optimal bionic design should be 1.5mm (radius) \u0026minus;\u0026thinsp;1mm (height) \u0026minus;\u0026thinsp;90\u0026deg; (angle). Deviation angles are analysed in the same way.\u003c/p\u003e\n\u003ch3\u003e3.3 Simulation of foot-end jumping in low-gravity\u003c/h3\u003e\n\u003cp\u003eJoint simulation using RecurDyn and EDEM. Gravity environment and low gravity environment respectively. The optimised model 1.5mm (height)-1mm (height)-90\u0026deg; (angle) is taken as the object of study. As shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003e. The jump height of the bouncing device in low gravity is much higher than that of the bouncing device in gravity, because the low gravity environment makes it easier for the jumping robot to jump, allowing it to easily cross larger obstacles and reduce energy consumption.\u003c/p\u003e\n\u003cp\u003eThe deviation angles under different gravity conditions are shown on the right, and it can be seen that the slopes of the bouncing device under low gravity are smaller than those of the bouncing device under gravity under the same moment conditions, which indicates that the bouncing under low gravity is a bit more stable. Consideration has to do with the contact between the foot end and the soil in low gravity, the contact between the foot end and the sandy soil in low gravity is softer, and the disturbance to the soil is a bit smaller, which is more favourable to the adjustment of the state of the whole system.\u003c/p\u003e\n\u003cp\u003eFrom the analysis of the particle velocity field at the same position of the foot end, the range of particle perturbation under the velocity field of gravity environment is the largest, the range of velocity field perturbation under low gravity environment is the smallest, the direction of particle flow is directed to the bottom of the foot end, and the particle velocity field under gravity soil is more concentrated compared with that under low gravity. The velocity field of particles under gravity is more concentrated compared to that under low gravity.\u003c/p\u003e"},{"header":"4 Conclusion","content":"\u003cp\u003eThe moon's surface is characterised by soft lunar soil and low gravity environment, and the jumping robot has superior motion performance in the moon surface environment, which will have an important application prospect in the moon surface exploration mission. To study the high-performance foot end suitable for the lunar surface environment, this paper combines experiment and simulation to research the bouncing performance of foot ends with different curvature radii, the attachment performance of foot ends with different patterns, the bouncing performance of foot ends with different patterns, and the bouncing performance of the foot ends under different gravitational environments, and obtains the following main conclusions:\u003c/p\u003e \u003cp\u003eA bionic patterned bouncing foot end is designed using camel hooves and ostrich papillae as bionic prototypes. Two conventional patterned foot ends were used as a comparison. Adhesion tests verified that the bionic patterned ends had better adhesion properties than the conventional patterned ends. The adhesion performance was improved by 22\u0026ndash;31%.\u003c/p\u003e \u003cp\u003eThe bouncing performance test showed that the bionic patterned foot end had better-bouncing performance than the conventional patterned foot end, with the height performance improved by 10.7%-18.8% and the stability performance improved by 10.4%-25.4%. The dimensions of the foot end pattern were optimised for the best combination of 1.5mm (radius) \u0026minus;\u0026thinsp;1mm (height) \u0026minus;\u0026thinsp;90\u0026deg; (angle) for height performance and 0.5mm (radius) \u0026minus;\u0026thinsp;5mm (height) \u0026minus;\u0026thinsp;0\u0026deg; (angle) for stability performance.\u003c/p\u003e \u003cp\u003eThrough coupled simulation, the bouncing situation of the bouncing device under the low gravity environment on the lunar surface is investigated. The bouncing performance of the bionic bouncing foot is compared between the low-gravity and gravity environments, and the bionic bouncing foot is finally developed for the low-gravity soft lunar surface environment.\u003c/p\u003e"},{"header":"Declarations","content":" \u003ch2\u003eConflicts of Interest\u003c/h2\u003e \u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e \u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eRui Zhang：Conceptualization, Methodology, Software, Investigation, Formal Analysis, Writing - Original Draft;Xicheng Li：Data Curation, Writing - Original Draft;Tao Li：Visualization, Investigation;Jiaqi Tang：Resources, Supervision;Hua Zhang：Software, Validation；Weijun Wang：Visualization, Writing - Review \u0026amp; Editing；Zhenyu Hu：Software, Validation；Lige Wen：Resources, Supervision;\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eWe thank the support of the National Natural Science Foundation of China (No. 52275287), the Opening Project of Aerospace System Engineering Shanghai (YY-F805202108002), the Opening Project of the Key Laboratory of Bionic Engineering (Ministry of Education), Jilin University (No. KF20211009)\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eJ. 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Song,(2023)Foot Bionics Research Based on Reindeer Hoof Attachment Mechanism and Macro/Microstructures.Journal815. 10.3390/biomimetics8080600\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":"low gravity, soft ground, bionic hopping foot end, Jumping Robot","lastPublishedDoi":"10.21203/rs.3.rs-4280934/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4280934/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn the current study, we have designed a bouncing device, the bionic bouncing foot end, specifically for the lunar surface environment. The device uses its gravity to store energy in a spring and bounces when the spring releases the energy. We released the spring device from a fixed height and used a 3D capture device to record and analyse the height and angle of excursion of the foot to assess its bouncing performance. Given the important influence of the attachment performance of the foot end on the jumping performance, we designed a new bionic pattern of the bouncing foot end using the camel hoof and the ostrich papilla as bionic prototypes. Through validation, we demonstrated that the attachment performance of the bionic pattern is better than that of the traditional patterned foot end. For the application requirements of jumping robots in loose and soft media, we further optimised the design of the foot end pattern and verified it by simulation through multi-rigid body dynamics and discrete element simulation. These studies provide important theoretical and technical support for the study of high-performance jumping robots in the lunar surface environment.\u003c/p\u003e","manuscriptTitle":"Study on bionic bouncing foot of a lunar environment jumping robot","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-22 16:22:26","doi":"10.21203/rs.3.rs-4280934/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 22nd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-05-31T17:46:35+00:00","versionOfRecord":[],"versionCreatedAt":"2024-04-22 16:22:26","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4280934","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4280934","identity":"rs-4280934","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}