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Design of Bionic Buffering and Vibration Reduction Foot for Legged Robots

Design of Bionic Buffering and Vibration Reduction Foot for Legged Robots Hindawi Applied Bionics and Biomechanics Volume 2021, Article ID 5510993, 9 pages https://doi.org/10.1155/2021/5510993 Research Article Design of Bionic Buffering and Vibration Reduction Foot for Legged Robots 1,2 1 1 1 3 3 4 Qian Cong, Xiaojie Shi, Ju Wang, Yu Xiong, Bo Su, Lei Jiang, Ming Li, and Weijun Tian Key Laboratory of Bionic Engineering, Ministry of Education, China, Jilin University, Changchun 130022, China State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130022, China North-Vehicle Research, Fengtai District, Beijing 100072, China Sany Group Co. Ltd., Changsha, Hunan, China Correspondence should be addressed to Weijun Tian; tianweijun@jlu.edu.cn Received 6 February 2021; Revised 25 April 2021; Accepted 27 May 2021; Published 10 June 2021 Academic Editor: Guowu Wei Copyright © 2021 Qian Cong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. When legged robots walk on rugged roads, they would suffer from strong impact from the ground. The impact would cause the legged robots to vibrate, which would affect their normal operation. Therefore, it is necessary to take measures to absorb impact energy and reduce vibration. As an important part of a goat’s foot, the hoof capsule can effectively buffer the impact from the ground in the goat’s running and jumping. The structure of the hoof capsules and its principle of buffering and vibration reduction were studied. Inspired by the unique shape and internal structure of the hoof capsules, a bionic foot was designed. Experimental results displayed that the bionic foot could effectively use friction to consume impact energy and ensured the stability of legged robot walking. In addition, the bionic foot had a lower natural vibration frequency, which was beneficial to a wide range of vibration reduction. This work brings a new solution to the legged robot to deal with the ground impact, which helps it adapt to a variety of complex terrain. 1. Introduction sive biped walking robot, with a particular focus on the feet-ground contact interaction. They evaluated different Mobile robots had received much attention in the past few kinds of contact forces in robot walking by several force years because they could play an important role in rescue models. The experiment result displayed that a dissipative nonlinear Flores contact force model worked best [10]. operation, space exploration, and so on [1–4]. Though wheeled and tracked robots could run well in flat terrain, These feet-ground contact impacts would cause the leg- most of them could not adapt to working in complex ged robot to vibrate, which would affect their walking stabil- and cluttered terrain. The legged robots have more poten- ity, control precision, and service life [11–13]. Researchers tial to walking on almost all the earth surfaces in different and engineers proposed a variety of methods to absorb terrains, just like humans and animals [5–7]. When legged impact energy and reduce vibration such as flexible feet robots walk or jump, they need to face many problems [14]. Li et al. designed a flexible foot for the humanoid robot, such as contact impact with friction from the ground. It which included a landing impact absorption mechanism and is a complex work to characterize the contact impact a foot attitude estimation system [15]. The rubber bushes and because there are a lot of factors that need to be taken pads were utilized for absorbing impacts. Hashimoto et al. into account such as material properties and contacting reported a foot cushion device for the WL-16 robot. It surfaces [8, 9]. Scientists proposed many different types adopted a cam self-locking mechanism, which could be of contact force models. Corral et al. reported a general actively adjusted and controlled according to the force feed- approach for the dynamic modeling and analysis of a pas- back of the contact position. This mechanism successfully 2 Applied Bionics and Biomechanics So toe pillow Hard nail Hard nail So toe pillow (a) (b) Figure 1: The picture of the goats’ hoof capsules: the bottom (a) and the top (b). (a) (b) Figure 2: The design and bionic prototype of foot sole:(a) the touchdown contour of nails and (b) the bionic foot sole. (a) (b) (c) (d) Figure 3: SEM pictures: the hoof capsules (a), the inclined holes in the hoof capsules (b), the diameter of the inclined holes (c), and the bottom of hoof capsules (d). helped the robot to reduce the vibration [16]. Zhu designed a caused by uneven ground. The foot intelligently adjusted its novel kind of flexible robotic foot. The bottom of the robot position according to the force and moment of the sole foot was integrated with a spring-damping system, which [18]. Although the traditional buffering and vibration reduc- was composed of spring, damper, rubber pad, etc. The system tion mechanism for legged robots has made good progress, not only had a good vibration reduction effect but also had an there are still some problems to solve such as high cost and excellent service life [17]. Kim and Yoon proposed an intelli- complex manufacturing. By finding out excellent cushioning gent robot foot which could greatly reduce the vibration and vibration reduction features of biological structures, Applied Bionics and Biomechanics 3 (a) (b) Figure 4: The schematic diagram: the bionic cushion (a) and the angle of oblique holes (b). Connecting block Bionic cushion Bionic foot sole Steel ball Ball cap Screw (a) (b) Figure 5: The bionic foot: the unassembled model (a) and the assembled model (b). reduce the vibration caused by the impact of the ground [20]. Jiang et al. designed a bionic multijoint vibration con- trol platform based on the human legs. The platform achieved vibration reduction by the knee joint mechanism composed of rods and springs. The experimental results dis- played that it had excellent nonlinear vibration damping effects in the low-frequency range [21]. In the last million years, quadrupeds have evolved a lot of unique biological structures, which help them to adapt to various environments and terrains [22]. As a typical quadru- ped, goats have an excellent ability to move, jump, and run on unstructured terrain [23, 24]. As an important part of goats that directly contacts the ground, the hoof capsule could withstand a great external impact instantly, absorb the impact, and effectively reduce the vibration brought by the impact [25–27] The hoof capsule was dissected, and its internal structure was studied. Based on the above works, a bionic buffering and vibration reduction foot was designed. 2. Bionic Foot Based on the Hoof Figure 6: Ordinary robot foot. Capsules of Goats scientists and engineers have designed and manufactured lots 2.1. Treatment of Biomaterials. Adult and healthy white goats of bionic vibration reduction devices [19]. Chang et al. pro- without limitation to gender (40 ± 0:5 kg) were bought from posed a bionic robot foot based on the bone structure of the an abattoir of Changchun City. Their hoof capsules were cut German shepherd dog. It could transform the rigid contact off and made into samples. Firstly, the samples were washed between the robot and the ground into flexible contact and with ultrapure water to remove dust. They were then washed 4 Applied Bionics and Biomechanics Table 1: Material parameters of bionic cushion, bionic foot sole, ground, and mass block. Modulus of elasticity Poisson’s Density Model (MPa) ratio (kg/m ) 100 Bionic 7.84 0.47 1200 cushion Foot sole 2:1×10 0.3 7800 4×10 The ground 0.25 2500 Mass block 2:1×10 0.3 50000 02 46 8 Time (ms) Ordinary robot foot Bionic foot with 90° inclined holes Bionic foot with 60° inclined holes Bionic foot with 30° inclined holes Figure 9: Time curves of ground impact force of different robot feet. with anhydrous ethanol and acetone to remove grease and other contaminants. The above steps were repeated three –5 times. After that, the samples were put in anhydrous ethanol 0 2 4 6 8 10 12 and sonicated for 20 min and then placed in a drying cabinet Time (ms) for 24 h. The hoof capsules finally were placed in vacuum film deposition equipment for gold spraying for 30 s, followed by Ordinary robot foot observation under an EVO 18 scanning electron microscope Bionic foot with 90° inclined holes (SEM, Carl Zeiss Microscopy GmbH, Jena, Germany). Bionic foot with 60° inclined holes Bionic foot with 30° inclined holes 2.2. Design of the Bionic Foot. As shown in Figure 1, the hoof capsules consisted of a hard nail and soft toe pillow, present- Figure 7: Kinetic energy-time curves of different robot feet. ing an inverted V shape. This shape could help goats acquire a bigger contact area and friction [23, 28]. The combination 2.5 of nails and toe pillows allowed the goat to adapt to hard rock surfaces and soft soil surfaces. When goats walk on hard 2.0 ground like rocks or cliffs, the sunken soft toe pillow fitted with the hard ground to obtain a large contact area, further 1.5 increasing friction and reducing impact pressure. When they move on soft ground such as muddy roads and sand, the hard 1.0 nails would insert into them. Goats also get a larger contact area and friction, which helps them use friction to consume 0.5 impact energy. As an important part of the bionic foot, the robot foot 0.0 sole needs to help the robot obtain greater friction force and contact area to ensure the stability of walking. Therefore, –0.5 the touch curve of the hoof capsules was used to design the 02468 10 sole of the bionic foot. To obtain the contact curve, the hoof Time (ms) capsule coated with ink on the bottom was pressed firmly at a suitable position in the grid paper to obtain an imprint. The Ordinary robot foot imprint was then scanned to obtain the contact contour Bionic foot with 90° inclined holes (Figure 2(a)). The spline curve was used to fit the hoof cap- Bionic foot with 60° inclined holes sules’ contact contour. According to the feature that the nail Bionic foot with 30° inclined holes was higher than the toe pillow, the bionic sole with protru- sion was designed (Figure 2(b)). The shape of the protrusion Figure 8: Time curves of frictional dissipation energy of different was derived from the unilateral spline curve of the hoof cap- robot feet. sules’ contact contour. The design of the bionic sole could Kinetic energy (mJ) Frictional dissipation energy (mJ) Ground impact force (N) Applied Bionics and Biomechanics 5 ° ° 5 holes was between 35 and 80 . The cornified epidermal layer can resist the instant impact from the ground. The oblique hole layer of hoof capsules can store, release, and dissipate the impact energy by deforming itself [28]. They cooperate with each other to realize the excellent buffering and vibra- 2 tion reduction function of the hoof capsules. Based on the special structure of hoof capsules, a novel bionic cushion for the robot was proposed (Figure 4(a)). The bionic cushion was a hollow cylinder with evenly distrib- uted oblique holes. The angle between the oblique hole and –1 the horizontal direction was θ (Figure 4(b)). When the robot was impacted by the ground, the designed cushion with obli- que holes could deform in the annular direction, which Time (ms) caused a rotation moment. This rotational torque was trans- Ordinary robot foot mitted to the sole, so that the sole and the ground rotated rel- ative to each other. At this time, the sliding friction force Bionic foot with 90° inclined holes would consume part of the impact energy. In this process, Bionic foot with 60° inclined holes part of the impact energy was converted into the internal Bionic foot with 30° inclined holes energy of the cushion, and the other part was consumed by Figure 10: The displacement curves of the mass block on the bionic friction. feet and the ordinary foot after impact. Inspired by the unique biological structure of the hoof capsule, a new bionic vibration damping foot was designed 1200 (Figure 5). The bionic foot was composed of the connecting block, bionic cushion, bionic foot sole, steel ball, ball cap, and screw. The bionic foot sole was used to imitate inverted V shape of hoof capsules. Bionic cushion mimicked an obli- que hole layer to store energy. In addition, the steel ball, ball cover, and other parts were used to form a similar bearing structure, which ensured that the robot legs would not rotate when the impact energy was consumed by friction. The bionic foot was located at the bottom of the leg robot, which was the part of the robot direct to the ground. It was bolted to the calf of the legged robot. The bionic foot had to withstand the weight of the entire robot and the impact from the ground. 02 4 6 8 10 Order number 3. Simulation Analysis of Bionic Foot Ordinary robot foot The Abaqus was used to make the finite element simulation Bionic foot with 90° inclined holes analysis. The inclined hole angle (θ) of bionic vibration Bionic foot with 60° inclined holes ° ° ° damping feet was set as 30 ,60 , and 90 , respectively. There Bionic foot with 30° inclined holes was no bionic foot sole and cushion with holes in the ordi- nary foot (Figure 6). An equivalent mass block was added Figure 11: Natural frequencies of the bionic feet and ordinary foot to the upper part of the bionic vibration damping feet, whose varying with orders. mass was equal to the mass of a normal robot. The distance between the bottom of the bionic foot and the ground was set as 1 mm. The robot foot crashed into the ground at 1 ensure that the robot can obtain a large contact area and bet- m/s to imitate the situation where the robot’s foot was ter consume the impact energy from the ground through impacted by the ground. The coefficient of friction between friction. the robot’s feet and the ground was set to 0.1. The material The SEM pictures of hoof capsules are displayed in parameters of FEM models in the Abaqus are displayed in Figure 3. The hoof capsule was composed of two layers of tis- Table 1. The soft linear elastic material was used as the mate- sue. There were a lot of cornified tissues on the bottom of the rial of the bionic cushion to facilitate its ability to absorb hoof capsules, showing a layered shape. At the top of the hoof impact energy. The material of the bionic sole and the mass capsules, there was a layer of inclined holes with hexagonal block was steel while the material of the ground was rock. distribution, which were round or oval. The distance between The kinetic energy, frictional dissipation energy, and two adjacent holes was 140 μm-250 μm. The thickness of the ground reaction force were selected as indexes to evaluate inclined holes was about 1.1 mm-1.3 mm. The aperture was the buffering effect of the reported bionic foot. The kinetic between 50 μm-110 μm, and the inclination angle of inclined energy-time curves of the impact process are shown in Frequency values (Hz) Distance (mm) 6 Applied Bionics and Biomechanics Table 2: Participation coefficients of all vibration modes of the ordinary foot. Mode XY Z X‐RY‐RZ‐R 1 0.57566 −8:06E − 09 0.65584 −2:29E − 03 2:18E − 02 2:01E − 03 1:95E − 08 2:01E − 03 1:60E − 03 2:29E − 03 2 0.65584 -0.57566 3 2:02E − 09 −2:36E − 06 −1:84E − 08 4:20E − 08 1:16E − 02 4:13E − 08 4:92E − 08 1:00E − 05 1:93E − 09 −1:79E − 07 7:48E − 10 −1:76E − 07 −6:19E − 07 −1:52E − 07 −7:35E − 07 −2:30E − 09 −2:39E − 08 4:88E − 09 6:96E − 07 1:56E − 07 −6:66E − 07 −5:05E − 09 6:87E − 10 −7:83E − 09 7 −3:01E − 06 −1:61E − 07 −3:07E − 06 −4:48E − 08 −1:07E − 07 5:06E − 08 −3:04E − 06 −1:45E − 07 3:04E − 06 5:08E − 08 −1:08E − 09 4:98E − 08 8:59E − 07 8:22E − 09 8:66E − 07 1:06E − 08 3:05E − 08 −1:03E − 08 8:64E − 07 7:10E − 09 −8:63E − 07 −1:03E − 08 2:62E − 10 −1:09E − 08 Table 3: Participation coefficients of all vibration modes of the bionic foot with 90 inclined holes. Mode XY Z X‐RY‐RZ‐R 8:71E − 07 −2:65E − 03 3:68E − 03 −1:88E − 03 1 -0.53999 0.75897 −1:63E − 07 −1:88E − 03 2:30E − 02 2:65E − 03 2 0.75896 0.53999 3 −2:52E − 06 −2:73E − 03 3:25E − 06 4:87E − 05 1:13E − 02 4:79E − 05 −3:39E − 06 −8:44E − 07 −2:00E − 02 1:81E − 05 −1:97E − 02 4 1.122 −2:01E − 06 −1:69E − 02 2:03E − 06 3:01E − 04 −3:38E − 06 2:96E − 04 4:92E − 03 −8:08E − 07 −7:04E − 03 −1:95E − 04 −3:56E − 05 −1:14E − 04 7 −7:03E − 03 9:64E − 06 −4:93E − 03 −1:14E − 04 −2:12E − 04 1:95E − 04 −1:07E − 06 −5:36E − 06 1:81E − 06 1:50E − 07 1:49E − 08 1:27E − 07 −1:49E − 06 3:41E − 03 9:02E − 07 −6:07E − 05 3:82E − 06 −5:97E − 05 1:85E − 03 5:20E − 07 2:49E − 03 7:73E − 05 7:65E − 05 −6:28E − 05 Figure 7. When the robot feet are not in contact with the inclination angle was related to the amount of consumed ground, there was no change in kinetic energy. After the and stored energy of the bionic cushion. When the inclina- impact, the kinetic energy began to decline sharply, then tion angle of the bionic cushion was smaller, it was better at increased, and fluctuated steadily. The residual kinetic energy absorbing and consuming impact energy. Compared with of bionic vibration reduction robot feet was smaller than that the ordinary foot, the bionic feet had a longer cushion time, of the ordinary one, and the residual kinetic energy decreased which was beneficial to the stable operation of the robot. with the reduction of angle. This suggested that the proposed All the above results indicated that the proposed bionic feet bionic structure worked, allowing the bionic foot to consume had good cushion effect. more kinetic energy than the ordinary foot. The frictional In order to evaluate vibration reduction performances of dissipation energy-time curves of bionic vibration reduction the proposed bionic foot, the displacement change of robots feet in the impact process are displayed in Figure 8. The fric- after impact and the natural frequency were selected as tional dissipation energy of the bionic vibration damping feet indexes to make vibration response analysis. The displace- was greater than that of the ordinary one, and they increased ment curves of the mass block on the bionic feet and the ordi- with the decrease of inclination. This indicated that the buff- nary foot after impact are displayed in Figure 10. The ering effect of bionic feet increased with the decrease of the displacement change of the mass block on the bionic feet angle of inclined holes. As can be seen from Figure 9, the was smaller than that of the ordinary one. There was a little 90 hole structure was not suitable for the buffering and difference in the displacement change of the bionic foot with ° ° vibration reduction of the bionic foot in the vertical direction. 90 holes and the ordinary one. The bionic foot with 30 This was consistent with the results of previous studies [27]. inclined holes has the smallest change in displacement. This The time curves of the ground impact force that an ordi- indicated that the bionic foot could better reduce the vibra- nary foot and bionic feet suffer from are shown in Figure 9. tion caused by ground impact. The first ten-order natural fre- The peak impact force of bionic feet was less than that of quencies of the bionic feet and ordinary foot were obtained the ordinary foot, and the peak force decreased with the through modal analysis (Figure 11). It could be seen from decrease of the inclination angle. This displayed that the Figure 11 that the first three-order natural frequency of Applied Bionics and Biomechanics 7 Table 4: Participation coefficients of all vibration modes of the bionic foot with 60 inclined holes. Mode XY Z X‐RY‐RZ‐R 1 0.99313 1:69E − 05 0.38694 −9:03E − 04 2:45E − 02 3:81E − 03 −2:33E − 05 −3:81E − 03 1:05E − 02 −9:03E − 04 2 -0.38693 0.99313 3 6:34E − 05 -0.19575 −2:51E − 05 3:49E − 03 1:09E − 02 3:43E − 03 4:37E − 05 8:29E − 05 −2:01E − 02 1:49E − 03 −1:97E − 02 4 1.1251 −2:83E − 05 9:73E − 03 8:98E − 04 3:19E − 03 5 -0.31171 0.36829 −5:76E − 04 3:20E − 03 1:20E − 02 −9:71E − 03 6 0.36827 0.31159 7 1:39E − 04 9:18E − 02 7:17E − 04 −1:62E − 03 1:82E − 04 −1:62E − 03 −7:79E − 02 1:12E − 03 1:93E − 02 9:91E − 04 −1:05E − 03 1:32E − 03 −2:04E − 02 1:33E − 03 −7:79E − 02 −1:36E − 03 −1:73E − 03 1:01E − 03 −4:37E − 04 −9:85E − 04 1:38E − 03 4:80E − 05 1:48E − 05 1:40E − 05 Table 5: Participation coefficients of all vibration modes of the bionic foot with 30 inclined holes. Mode XY Z X‐RY‐RZ‐R 1:09E − 05 −1:69E − 03 2:27E − 02 3:48E − 03 1 0.74848 0.53125 2 -0.53126 −1:00E − 05 0.74849 −3:48E − 03 3:65E − 03 −1:69E − 03 4:60E − 06 5:75E − 06 4:95E − 03 1:03E − 02 4:87E − 03 3 -0.27758 4 −5:27E − 05 1.0762 −4:47E − 06 −1:92E − 02 2:10E − 03 −1:89E − 02 1:66E − 04 −1:16E − 03 1:16E − 02 −9:12E − 03 5 0.47678 0.17528 6 0.17526 1:42E − 05 -0.47668 −9:12E − 03 −5:23E − 03 1:16E − 03 −3:48E − 05 5:77E − 05 −5:28E − 05 −1:43E − 06 −1:35E − 06 −9:43E − 08 8 −3:96E − 02 3:18E − 04 −8:42E − 02 −8:59E − 04 −2:18E − 03 9:57E − 04 8:41E − 02 4:06E − 05 −3:95E − 02 −9:62E − 04 8:07E − 04 −8:53E − 04 3:63E − 05 7:08E − 02 1:78E − 04 −1:26E − 03 3:27E − 04 −1:24E − 03 bionic feet was smaller than those of the ordinary foot, and frequencies, which help it to obtain a larger damping range. the natural frequency gradually decreased with the decrease According to the parameters of vibration mode, the structure of the angle of inclined holes. of the inclined hole changed the main vibration form of the The parameters of the first ten-order vibration model for third order. The bionic structure transformed the main a normal foot and bionic feet are displayed in Tables 2–5. vibration mode of the third order from rotation in the Y After being impacted, the first-order and second-order vibra- direction into translational motion. This may be because tion modes of the robot foot were mainly translational move- the structure reduced the stiffness of the bionic foot in the ments of X and Z. In other words, the first-order and second- Y direction. In summary, the inclined hole feature changed order vibration of the ordinary foot and bionic feet was the natural frequency of the bionic foot, expanded the fre- mainly translational motion in the x‐z plane. For buffering quency range of vibration reduction, and facilitated the ° ° and vibration reduction feet with 30 and 60 inclined holes, absorption of vibration energy. the translational motion in the Y direction played a leading role in the third-order and fourth-order modes. For the ordi- 4. Conclusions nary foot and bionic foot with 90 inclined holes, the main vibration mode of the third order was the rotation in the Y The microstructure of goats’ hoof capsules was carefully direction. Their fourth-order vibration mode was similar to observed. The unique shape of hoof capsules increased the ° ° that of the bionic feet with 30 and 60 inclined holes. The contact area with the ground and friction, which was better vibration in the translational direction of Y played an impor- to reduce impact power. The internal oblique hole features tant role. The vibration mode after the fourth order was com- enabled the hoof capsules to absorb energy through appro- plex and changeable where the vibration participation priate changes after impact. Based on the above research, a coefficient was small, so its vibration influence can be bionic foot for buffering and vibration reduction of legged ignored. robots was proposed. Compared with the ordinary foot, Compared with the normal foot, bionic vibration reduc- bionic feet could better use elastic deformation and the fric- tion feet with inclined holes had smaller first three natural tion force to consume the impact energy, which was better 8 Applied Bionics and Biomechanics [10] E. Corral, M. J. G. García, C. Castejon, J. Meneses, and for the walking stability of legged robots. In addition, the R. Gismeros, “Dynamic modeling of the dissipative contact bionic foot effectively reduced the vibration of the robot and friction forces of a passive biped-walking robot,” Applied caused by impact. The natural frequency of the bionic foot Sciences, vol. 10, no. 7, article 2342, 2020. was smaller than that of the ordinary foot, which ensured [11] H. Song and K. Kong, “Analysis of vibrations transmitted to that the bionic foot has a wider range of vibration reduction. the quadruped robot body during trotting with different stiff- ness of feet,” in 2018 18th International Conference on Control, Data Availability Automation and Systems (ICCAS 2018), PyeongChang, Gang- Won Province, Korea, 2018. The data used to support the findings of this study are avail- [12] F. Ma, L. Ni, L. Wei, J. Nie, L. Wu, and W. Jia, “Posture control able from the corresponding author upon request. of all terrain mobile robot with vibration isolation system,” in Advances in Dynamics of Vehicles on Roads and Tracks. IAVSD Conflicts of Interest 2019. Lecture Notes in Mechanical Engineering, M. Klomp, F. Bruzelius, J. Nielsen, and A. Hillemyr, Eds., Springer, Cham, The authors declare that there is no conflict of interests regarding the publication of this paper. [13] J. Yin, “Design of foot cam vibration damping system for forest walking robot,” in Big Data Analytics for Cyber-Physical Sys- tem in Smart City. BDCPS 2020. Advances in Intelligent Sys- Acknowledgments tems and Computing, vol 1303, M. Atiquzzaman, N. Yen, and Z. Xu, Eds., Springer, Singapore, 2021. The authors gratefully acknowledge the support of the Foun- [14] A. David, J. R. Chardonnet, A. Kheddar, K. Kaneko, and dation of State Key Laboratory of Automotive Simulation K. Yokoi, “Study of an external passive shock-absorbing mech- and Control (Grant No. 20171115), the National Natural Sci- anism for walking robots,” in Humanoids 2008 - 8th IEEE-RAS ence Foundation of China (Grant Nos. 91748211 and International Conference on Humanoid Robots, Daejeon, 51305157), and the project of the 13th Five-Year Common Korea (South), December 2009. Technology (Grant No. 41412040101). [15] J. Li, Q. Huang, W. Zhang, Z. Yu, and K. Li, “Flexible foot design for a humanoid robot,,” in IEEE International Confer- References ence on Automation & Logistics, Qingdao, China, September [1] K. Ito and Y. Ishigaki, “Semiautonomous centipede-like robot [16] K. Hashimoto, T. Hosobata, Y. Sugahara et al., “Development for rubble - development of an actual scale robot for rescue of foot System of biped walking robot capable of maintaining operation,” International Journal of Advanced Mechatronic four-point contact,” in 2005 IEEE/RSJ International Confer- Systems, vol. 6, no. 2/3, p. 75, 2015. ence on Intelligent Robots and Systems, Edmonton, AB, Can- [2] P. Biswal and P. K. Mohanty, “Development of quadruped ada, August 2005. walking robots: a review,” Ain Shams Engineering Journal, [17] Q. Zhu, Humanoid Robot Mechanical Design and Analysis, vol. 32, 2020. Zhejiang University, 2011. [3] S. A. A. Moosavian, R. Rastegarij, and E. Papadopoulos, “Mul- [18] G. Kim and J. Yoon, “Development of intelligent foot with six- tiple impedance control for space free-flying robots,” Journal axis force/moment sensors for humanoid robot,” in 2008 IEEE of Guidance, Control, and Dynamics, vol. 28, no. 5, pp. 939– International Conference on Robotics and Biomimetics, Bang- 947, 2005. kok, Thailand, February 2009. [4] Y. Li, M. Li, H. Zhu et al., “Development and applications of [19] S. M. Sun, D. S. Ye, and X. Wu, “Research on vibration reduc- rescue robots for explosion accidents in coal mines,” Journal tion mechanism for robot joints by imitating the owl surface of Robotic Systems, vol. 37, no. 3, pp. 466–489, 2020. characteristics,” Applied Mechanics and Materials, vol. 539, [5] A. N. Sarmah, A. Boruah, D. Kalita, D. Neog, and S. Paul, “A pp. 13–17, 2014. bio-inspired implementation of walking and stair climbing [20] T. Chang, X. Liu, G. U. Xincen, and Z. Guo, “Design of bionic on a quadruped robot,” Procedia Computer Science, vol. 143, quadruped robot and stress analysis for foot end with kinemat- pp. 671–677, 2018. ics,” Computer Engineering, vol. 4, 2017. [6] V.-G. Loc, I. M. Koo, D. T. Tran, S. Park, H. Moon, and H. R. [21] G. Jiang, X. Jing, and Y. Guo, “A novel bio-inspired multi-joint Choi, “Improving traversability of quadruped walking robots anti-vibration structure and its nonlinear HSLDS properties,” using body movement in 3D rough terrains,” Robotics and Mechanical Systems and Signal Processing, vol. 138, article Autonomous Systems, vol. 59, no. 12, pp. 1036–1048, 2011. 106552, 2020. [7] P. M. James, A. Prakash, V. Kalburgi, and P. Sreedharan, [22] M. A. Woodward and M. Sitti, “Morphological intelligence “Design, analysis, manufacturing of four-legged walking robot counters foot slipping in the desert locust and dynamic with insect type leg,” Materials Today: Proceedings, vol. 46, robots,” Proceedings of the National Academy of Sciences of the United State of America, vol. 115, no. 36, pp. E8358– [8] E. Corral, R. G. Moreno, M. J. G. García, and C. Castejón, E8367, 2018. “Nonlinear phenomena of contact in multibody systems dynamics: a review,” Nonlinear Dynamics, vol. 104, no. 2, [23] Q. Zhang, X. L. Ding, K. Xu, and H. Chen, “Design and kine- matics analysis of a bionic mechanical goat hoof,” Applied pp. 1269–1295, 2021. Mechanics & Materials, vol. 461, pp. 191–200, 2014. [9] P. Flores and H. M. Lankarani, Contact Force Models for Multi- body Dynamics: Contact Force Models for Multibody Dynam- [24] G. Zhang, Research On Bionic Goat Mechanism On Sloping ics, SMIA, 2016. Fields, Henan University of Science and Technology, 2011. Applied Bionics and Biomechanics 9 [25] H. Kui, X. Liu, J. Liu et al., “The passive contact stability of blue sheep hoof based on structure, mechanical properties, and sur- face morphology,” Frontiers in Bioengineering and Biotechnol- ogy, vol. 8, 2020. [26] W. Tian, H. Liu, Q. Zhang, B. Su, W. Xu, and Q. Cong, “Cush- ion mechanism of goat hoof bulb tissues,” Applied Bionics and Biomechanics, vol. 2019, Article ID 3021576, 11 pages, 2019. [27] W. J. Tian, J. Y. Wang, M. Li, and Q. Cong, “Design and opti- mization of vibration reduction structure imitating pore struc- ture in goat Capsula ungulae,” Zhendong Gongcheng Xuebao/journal of Vibration Engineering, vol. 31, no. 2, pp. 352–357, 2018. [28] W. J. Tian, Y. J. Xu, W. Xu, P. Xu, Q. Zhang, and Q. Cong, “Bionic design and anti-slip characteristics study of quadruped robot foot,” Journal of Physics Conference Series, vol. 1507, arti- cle 052008, 2020. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Bionics and Biomechanics Hindawi Publishing Corporation

Design of Bionic Buffering and Vibration Reduction Foot for Legged Robots

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Hindawi Applied Bionics and Biomechanics Volume 2021, Article ID 5510993, 9 pages https://doi.org/10.1155/2021/5510993 Research Article Design of Bionic Buffering and Vibration Reduction Foot for Legged Robots 1,2 1 1 1 3 3 4 Qian Cong, Xiaojie Shi, Ju Wang, Yu Xiong, Bo Su, Lei Jiang, Ming Li, and Weijun Tian Key Laboratory of Bionic Engineering, Ministry of Education, China, Jilin University, Changchun 130022, China State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130022, China North-Vehicle Research, Fengtai District, Beijing 100072, China Sany Group Co. Ltd., Changsha, Hunan, China Correspondence should be addressed to Weijun Tian; tianweijun@jlu.edu.cn Received 6 February 2021; Revised 25 April 2021; Accepted 27 May 2021; Published 10 June 2021 Academic Editor: Guowu Wei Copyright © 2021 Qian Cong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. When legged robots walk on rugged roads, they would suffer from strong impact from the ground. The impact would cause the legged robots to vibrate, which would affect their normal operation. Therefore, it is necessary to take measures to absorb impact energy and reduce vibration. As an important part of a goat’s foot, the hoof capsule can effectively buffer the impact from the ground in the goat’s running and jumping. The structure of the hoof capsules and its principle of buffering and vibration reduction were studied. Inspired by the unique shape and internal structure of the hoof capsules, a bionic foot was designed. Experimental results displayed that the bionic foot could effectively use friction to consume impact energy and ensured the stability of legged robot walking. In addition, the bionic foot had a lower natural vibration frequency, which was beneficial to a wide range of vibration reduction. This work brings a new solution to the legged robot to deal with the ground impact, which helps it adapt to a variety of complex terrain. 1. Introduction sive biped walking robot, with a particular focus on the feet-ground contact interaction. They evaluated different Mobile robots had received much attention in the past few kinds of contact forces in robot walking by several force years because they could play an important role in rescue models. The experiment result displayed that a dissipative nonlinear Flores contact force model worked best [10]. operation, space exploration, and so on [1–4]. Though wheeled and tracked robots could run well in flat terrain, These feet-ground contact impacts would cause the leg- most of them could not adapt to working in complex ged robot to vibrate, which would affect their walking stabil- and cluttered terrain. The legged robots have more poten- ity, control precision, and service life [11–13]. Researchers tial to walking on almost all the earth surfaces in different and engineers proposed a variety of methods to absorb terrains, just like humans and animals [5–7]. When legged impact energy and reduce vibration such as flexible feet robots walk or jump, they need to face many problems [14]. Li et al. designed a flexible foot for the humanoid robot, such as contact impact with friction from the ground. It which included a landing impact absorption mechanism and is a complex work to characterize the contact impact a foot attitude estimation system [15]. The rubber bushes and because there are a lot of factors that need to be taken pads were utilized for absorbing impacts. Hashimoto et al. into account such as material properties and contacting reported a foot cushion device for the WL-16 robot. It surfaces [8, 9]. Scientists proposed many different types adopted a cam self-locking mechanism, which could be of contact force models. Corral et al. reported a general actively adjusted and controlled according to the force feed- approach for the dynamic modeling and analysis of a pas- back of the contact position. This mechanism successfully 2 Applied Bionics and Biomechanics So toe pillow Hard nail Hard nail So toe pillow (a) (b) Figure 1: The picture of the goats’ hoof capsules: the bottom (a) and the top (b). (a) (b) Figure 2: The design and bionic prototype of foot sole:(a) the touchdown contour of nails and (b) the bionic foot sole. (a) (b) (c) (d) Figure 3: SEM pictures: the hoof capsules (a), the inclined holes in the hoof capsules (b), the diameter of the inclined holes (c), and the bottom of hoof capsules (d). helped the robot to reduce the vibration [16]. Zhu designed a caused by uneven ground. The foot intelligently adjusted its novel kind of flexible robotic foot. The bottom of the robot position according to the force and moment of the sole foot was integrated with a spring-damping system, which [18]. Although the traditional buffering and vibration reduc- was composed of spring, damper, rubber pad, etc. The system tion mechanism for legged robots has made good progress, not only had a good vibration reduction effect but also had an there are still some problems to solve such as high cost and excellent service life [17]. Kim and Yoon proposed an intelli- complex manufacturing. By finding out excellent cushioning gent robot foot which could greatly reduce the vibration and vibration reduction features of biological structures, Applied Bionics and Biomechanics 3 (a) (b) Figure 4: The schematic diagram: the bionic cushion (a) and the angle of oblique holes (b). Connecting block Bionic cushion Bionic foot sole Steel ball Ball cap Screw (a) (b) Figure 5: The bionic foot: the unassembled model (a) and the assembled model (b). reduce the vibration caused by the impact of the ground [20]. Jiang et al. designed a bionic multijoint vibration con- trol platform based on the human legs. The platform achieved vibration reduction by the knee joint mechanism composed of rods and springs. The experimental results dis- played that it had excellent nonlinear vibration damping effects in the low-frequency range [21]. In the last million years, quadrupeds have evolved a lot of unique biological structures, which help them to adapt to various environments and terrains [22]. As a typical quadru- ped, goats have an excellent ability to move, jump, and run on unstructured terrain [23, 24]. As an important part of goats that directly contacts the ground, the hoof capsule could withstand a great external impact instantly, absorb the impact, and effectively reduce the vibration brought by the impact [25–27] The hoof capsule was dissected, and its internal structure was studied. Based on the above works, a bionic buffering and vibration reduction foot was designed. 2. Bionic Foot Based on the Hoof Figure 6: Ordinary robot foot. Capsules of Goats scientists and engineers have designed and manufactured lots 2.1. Treatment of Biomaterials. Adult and healthy white goats of bionic vibration reduction devices [19]. Chang et al. pro- without limitation to gender (40 ± 0:5 kg) were bought from posed a bionic robot foot based on the bone structure of the an abattoir of Changchun City. Their hoof capsules were cut German shepherd dog. It could transform the rigid contact off and made into samples. Firstly, the samples were washed between the robot and the ground into flexible contact and with ultrapure water to remove dust. They were then washed 4 Applied Bionics and Biomechanics Table 1: Material parameters of bionic cushion, bionic foot sole, ground, and mass block. Modulus of elasticity Poisson’s Density Model (MPa) ratio (kg/m ) 100 Bionic 7.84 0.47 1200 cushion Foot sole 2:1×10 0.3 7800 4×10 The ground 0.25 2500 Mass block 2:1×10 0.3 50000 02 46 8 Time (ms) Ordinary robot foot Bionic foot with 90° inclined holes Bionic foot with 60° inclined holes Bionic foot with 30° inclined holes Figure 9: Time curves of ground impact force of different robot feet. with anhydrous ethanol and acetone to remove grease and other contaminants. The above steps were repeated three –5 times. After that, the samples were put in anhydrous ethanol 0 2 4 6 8 10 12 and sonicated for 20 min and then placed in a drying cabinet Time (ms) for 24 h. The hoof capsules finally were placed in vacuum film deposition equipment for gold spraying for 30 s, followed by Ordinary robot foot observation under an EVO 18 scanning electron microscope Bionic foot with 90° inclined holes (SEM, Carl Zeiss Microscopy GmbH, Jena, Germany). Bionic foot with 60° inclined holes Bionic foot with 30° inclined holes 2.2. Design of the Bionic Foot. As shown in Figure 1, the hoof capsules consisted of a hard nail and soft toe pillow, present- Figure 7: Kinetic energy-time curves of different robot feet. ing an inverted V shape. This shape could help goats acquire a bigger contact area and friction [23, 28]. The combination 2.5 of nails and toe pillows allowed the goat to adapt to hard rock surfaces and soft soil surfaces. When goats walk on hard 2.0 ground like rocks or cliffs, the sunken soft toe pillow fitted with the hard ground to obtain a large contact area, further 1.5 increasing friction and reducing impact pressure. When they move on soft ground such as muddy roads and sand, the hard 1.0 nails would insert into them. Goats also get a larger contact area and friction, which helps them use friction to consume 0.5 impact energy. As an important part of the bionic foot, the robot foot 0.0 sole needs to help the robot obtain greater friction force and contact area to ensure the stability of walking. Therefore, –0.5 the touch curve of the hoof capsules was used to design the 02468 10 sole of the bionic foot. To obtain the contact curve, the hoof Time (ms) capsule coated with ink on the bottom was pressed firmly at a suitable position in the grid paper to obtain an imprint. The Ordinary robot foot imprint was then scanned to obtain the contact contour Bionic foot with 90° inclined holes (Figure 2(a)). The spline curve was used to fit the hoof cap- Bionic foot with 60° inclined holes sules’ contact contour. According to the feature that the nail Bionic foot with 30° inclined holes was higher than the toe pillow, the bionic sole with protru- sion was designed (Figure 2(b)). The shape of the protrusion Figure 8: Time curves of frictional dissipation energy of different was derived from the unilateral spline curve of the hoof cap- robot feet. sules’ contact contour. The design of the bionic sole could Kinetic energy (mJ) Frictional dissipation energy (mJ) Ground impact force (N) Applied Bionics and Biomechanics 5 ° ° 5 holes was between 35 and 80 . The cornified epidermal layer can resist the instant impact from the ground. The oblique hole layer of hoof capsules can store, release, and dissipate the impact energy by deforming itself [28]. They cooperate with each other to realize the excellent buffering and vibra- 2 tion reduction function of the hoof capsules. Based on the special structure of hoof capsules, a novel bionic cushion for the robot was proposed (Figure 4(a)). The bionic cushion was a hollow cylinder with evenly distrib- uted oblique holes. The angle between the oblique hole and –1 the horizontal direction was θ (Figure 4(b)). When the robot was impacted by the ground, the designed cushion with obli- que holes could deform in the annular direction, which Time (ms) caused a rotation moment. This rotational torque was trans- Ordinary robot foot mitted to the sole, so that the sole and the ground rotated rel- ative to each other. At this time, the sliding friction force Bionic foot with 90° inclined holes would consume part of the impact energy. In this process, Bionic foot with 60° inclined holes part of the impact energy was converted into the internal Bionic foot with 30° inclined holes energy of the cushion, and the other part was consumed by Figure 10: The displacement curves of the mass block on the bionic friction. feet and the ordinary foot after impact. Inspired by the unique biological structure of the hoof capsule, a new bionic vibration damping foot was designed 1200 (Figure 5). The bionic foot was composed of the connecting block, bionic cushion, bionic foot sole, steel ball, ball cap, and screw. The bionic foot sole was used to imitate inverted V shape of hoof capsules. Bionic cushion mimicked an obli- que hole layer to store energy. In addition, the steel ball, ball cover, and other parts were used to form a similar bearing structure, which ensured that the robot legs would not rotate when the impact energy was consumed by friction. The bionic foot was located at the bottom of the leg robot, which was the part of the robot direct to the ground. It was bolted to the calf of the legged robot. The bionic foot had to withstand the weight of the entire robot and the impact from the ground. 02 4 6 8 10 Order number 3. Simulation Analysis of Bionic Foot Ordinary robot foot The Abaqus was used to make the finite element simulation Bionic foot with 90° inclined holes analysis. The inclined hole angle (θ) of bionic vibration Bionic foot with 60° inclined holes ° ° ° damping feet was set as 30 ,60 , and 90 , respectively. There Bionic foot with 30° inclined holes was no bionic foot sole and cushion with holes in the ordi- nary foot (Figure 6). An equivalent mass block was added Figure 11: Natural frequencies of the bionic feet and ordinary foot to the upper part of the bionic vibration damping feet, whose varying with orders. mass was equal to the mass of a normal robot. The distance between the bottom of the bionic foot and the ground was set as 1 mm. The robot foot crashed into the ground at 1 ensure that the robot can obtain a large contact area and bet- m/s to imitate the situation where the robot’s foot was ter consume the impact energy from the ground through impacted by the ground. The coefficient of friction between friction. the robot’s feet and the ground was set to 0.1. The material The SEM pictures of hoof capsules are displayed in parameters of FEM models in the Abaqus are displayed in Figure 3. The hoof capsule was composed of two layers of tis- Table 1. The soft linear elastic material was used as the mate- sue. There were a lot of cornified tissues on the bottom of the rial of the bionic cushion to facilitate its ability to absorb hoof capsules, showing a layered shape. At the top of the hoof impact energy. The material of the bionic sole and the mass capsules, there was a layer of inclined holes with hexagonal block was steel while the material of the ground was rock. distribution, which were round or oval. The distance between The kinetic energy, frictional dissipation energy, and two adjacent holes was 140 μm-250 μm. The thickness of the ground reaction force were selected as indexes to evaluate inclined holes was about 1.1 mm-1.3 mm. The aperture was the buffering effect of the reported bionic foot. The kinetic between 50 μm-110 μm, and the inclination angle of inclined energy-time curves of the impact process are shown in Frequency values (Hz) Distance (mm) 6 Applied Bionics and Biomechanics Table 2: Participation coefficients of all vibration modes of the ordinary foot. Mode XY Z X‐RY‐RZ‐R 1 0.57566 −8:06E − 09 0.65584 −2:29E − 03 2:18E − 02 2:01E − 03 1:95E − 08 2:01E − 03 1:60E − 03 2:29E − 03 2 0.65584 -0.57566 3 2:02E − 09 −2:36E − 06 −1:84E − 08 4:20E − 08 1:16E − 02 4:13E − 08 4:92E − 08 1:00E − 05 1:93E − 09 −1:79E − 07 7:48E − 10 −1:76E − 07 −6:19E − 07 −1:52E − 07 −7:35E − 07 −2:30E − 09 −2:39E − 08 4:88E − 09 6:96E − 07 1:56E − 07 −6:66E − 07 −5:05E − 09 6:87E − 10 −7:83E − 09 7 −3:01E − 06 −1:61E − 07 −3:07E − 06 −4:48E − 08 −1:07E − 07 5:06E − 08 −3:04E − 06 −1:45E − 07 3:04E − 06 5:08E − 08 −1:08E − 09 4:98E − 08 8:59E − 07 8:22E − 09 8:66E − 07 1:06E − 08 3:05E − 08 −1:03E − 08 8:64E − 07 7:10E − 09 −8:63E − 07 −1:03E − 08 2:62E − 10 −1:09E − 08 Table 3: Participation coefficients of all vibration modes of the bionic foot with 90 inclined holes. Mode XY Z X‐RY‐RZ‐R 8:71E − 07 −2:65E − 03 3:68E − 03 −1:88E − 03 1 -0.53999 0.75897 −1:63E − 07 −1:88E − 03 2:30E − 02 2:65E − 03 2 0.75896 0.53999 3 −2:52E − 06 −2:73E − 03 3:25E − 06 4:87E − 05 1:13E − 02 4:79E − 05 −3:39E − 06 −8:44E − 07 −2:00E − 02 1:81E − 05 −1:97E − 02 4 1.122 −2:01E − 06 −1:69E − 02 2:03E − 06 3:01E − 04 −3:38E − 06 2:96E − 04 4:92E − 03 −8:08E − 07 −7:04E − 03 −1:95E − 04 −3:56E − 05 −1:14E − 04 7 −7:03E − 03 9:64E − 06 −4:93E − 03 −1:14E − 04 −2:12E − 04 1:95E − 04 −1:07E − 06 −5:36E − 06 1:81E − 06 1:50E − 07 1:49E − 08 1:27E − 07 −1:49E − 06 3:41E − 03 9:02E − 07 −6:07E − 05 3:82E − 06 −5:97E − 05 1:85E − 03 5:20E − 07 2:49E − 03 7:73E − 05 7:65E − 05 −6:28E − 05 Figure 7. When the robot feet are not in contact with the inclination angle was related to the amount of consumed ground, there was no change in kinetic energy. After the and stored energy of the bionic cushion. When the inclina- impact, the kinetic energy began to decline sharply, then tion angle of the bionic cushion was smaller, it was better at increased, and fluctuated steadily. The residual kinetic energy absorbing and consuming impact energy. Compared with of bionic vibration reduction robot feet was smaller than that the ordinary foot, the bionic feet had a longer cushion time, of the ordinary one, and the residual kinetic energy decreased which was beneficial to the stable operation of the robot. with the reduction of angle. This suggested that the proposed All the above results indicated that the proposed bionic feet bionic structure worked, allowing the bionic foot to consume had good cushion effect. more kinetic energy than the ordinary foot. The frictional In order to evaluate vibration reduction performances of dissipation energy-time curves of bionic vibration reduction the proposed bionic foot, the displacement change of robots feet in the impact process are displayed in Figure 8. The fric- after impact and the natural frequency were selected as tional dissipation energy of the bionic vibration damping feet indexes to make vibration response analysis. The displace- was greater than that of the ordinary one, and they increased ment curves of the mass block on the bionic feet and the ordi- with the decrease of inclination. This indicated that the buff- nary foot after impact are displayed in Figure 10. The ering effect of bionic feet increased with the decrease of the displacement change of the mass block on the bionic feet angle of inclined holes. As can be seen from Figure 9, the was smaller than that of the ordinary one. There was a little 90 hole structure was not suitable for the buffering and difference in the displacement change of the bionic foot with ° ° vibration reduction of the bionic foot in the vertical direction. 90 holes and the ordinary one. The bionic foot with 30 This was consistent with the results of previous studies [27]. inclined holes has the smallest change in displacement. This The time curves of the ground impact force that an ordi- indicated that the bionic foot could better reduce the vibra- nary foot and bionic feet suffer from are shown in Figure 9. tion caused by ground impact. The first ten-order natural fre- The peak impact force of bionic feet was less than that of quencies of the bionic feet and ordinary foot were obtained the ordinary foot, and the peak force decreased with the through modal analysis (Figure 11). It could be seen from decrease of the inclination angle. This displayed that the Figure 11 that the first three-order natural frequency of Applied Bionics and Biomechanics 7 Table 4: Participation coefficients of all vibration modes of the bionic foot with 60 inclined holes. Mode XY Z X‐RY‐RZ‐R 1 0.99313 1:69E − 05 0.38694 −9:03E − 04 2:45E − 02 3:81E − 03 −2:33E − 05 −3:81E − 03 1:05E − 02 −9:03E − 04 2 -0.38693 0.99313 3 6:34E − 05 -0.19575 −2:51E − 05 3:49E − 03 1:09E − 02 3:43E − 03 4:37E − 05 8:29E − 05 −2:01E − 02 1:49E − 03 −1:97E − 02 4 1.1251 −2:83E − 05 9:73E − 03 8:98E − 04 3:19E − 03 5 -0.31171 0.36829 −5:76E − 04 3:20E − 03 1:20E − 02 −9:71E − 03 6 0.36827 0.31159 7 1:39E − 04 9:18E − 02 7:17E − 04 −1:62E − 03 1:82E − 04 −1:62E − 03 −7:79E − 02 1:12E − 03 1:93E − 02 9:91E − 04 −1:05E − 03 1:32E − 03 −2:04E − 02 1:33E − 03 −7:79E − 02 −1:36E − 03 −1:73E − 03 1:01E − 03 −4:37E − 04 −9:85E − 04 1:38E − 03 4:80E − 05 1:48E − 05 1:40E − 05 Table 5: Participation coefficients of all vibration modes of the bionic foot with 30 inclined holes. Mode XY Z X‐RY‐RZ‐R 1:09E − 05 −1:69E − 03 2:27E − 02 3:48E − 03 1 0.74848 0.53125 2 -0.53126 −1:00E − 05 0.74849 −3:48E − 03 3:65E − 03 −1:69E − 03 4:60E − 06 5:75E − 06 4:95E − 03 1:03E − 02 4:87E − 03 3 -0.27758 4 −5:27E − 05 1.0762 −4:47E − 06 −1:92E − 02 2:10E − 03 −1:89E − 02 1:66E − 04 −1:16E − 03 1:16E − 02 −9:12E − 03 5 0.47678 0.17528 6 0.17526 1:42E − 05 -0.47668 −9:12E − 03 −5:23E − 03 1:16E − 03 −3:48E − 05 5:77E − 05 −5:28E − 05 −1:43E − 06 −1:35E − 06 −9:43E − 08 8 −3:96E − 02 3:18E − 04 −8:42E − 02 −8:59E − 04 −2:18E − 03 9:57E − 04 8:41E − 02 4:06E − 05 −3:95E − 02 −9:62E − 04 8:07E − 04 −8:53E − 04 3:63E − 05 7:08E − 02 1:78E − 04 −1:26E − 03 3:27E − 04 −1:24E − 03 bionic feet was smaller than those of the ordinary foot, and frequencies, which help it to obtain a larger damping range. the natural frequency gradually decreased with the decrease According to the parameters of vibration mode, the structure of the angle of inclined holes. of the inclined hole changed the main vibration form of the The parameters of the first ten-order vibration model for third order. The bionic structure transformed the main a normal foot and bionic feet are displayed in Tables 2–5. vibration mode of the third order from rotation in the Y After being impacted, the first-order and second-order vibra- direction into translational motion. This may be because tion modes of the robot foot were mainly translational move- the structure reduced the stiffness of the bionic foot in the ments of X and Z. In other words, the first-order and second- Y direction. In summary, the inclined hole feature changed order vibration of the ordinary foot and bionic feet was the natural frequency of the bionic foot, expanded the fre- mainly translational motion in the x‐z plane. For buffering quency range of vibration reduction, and facilitated the ° ° and vibration reduction feet with 30 and 60 inclined holes, absorption of vibration energy. the translational motion in the Y direction played a leading role in the third-order and fourth-order modes. For the ordi- 4. Conclusions nary foot and bionic foot with 90 inclined holes, the main vibration mode of the third order was the rotation in the Y The microstructure of goats’ hoof capsules was carefully direction. Their fourth-order vibration mode was similar to observed. The unique shape of hoof capsules increased the ° ° that of the bionic feet with 30 and 60 inclined holes. The contact area with the ground and friction, which was better vibration in the translational direction of Y played an impor- to reduce impact power. The internal oblique hole features tant role. The vibration mode after the fourth order was com- enabled the hoof capsules to absorb energy through appro- plex and changeable where the vibration participation priate changes after impact. Based on the above research, a coefficient was small, so its vibration influence can be bionic foot for buffering and vibration reduction of legged ignored. robots was proposed. Compared with the ordinary foot, Compared with the normal foot, bionic vibration reduc- bionic feet could better use elastic deformation and the fric- tion feet with inclined holes had smaller first three natural tion force to consume the impact energy, which was better 8 Applied Bionics and Biomechanics [10] E. Corral, M. J. G. García, C. Castejon, J. Meneses, and for the walking stability of legged robots. In addition, the R. Gismeros, “Dynamic modeling of the dissipative contact bionic foot effectively reduced the vibration of the robot and friction forces of a passive biped-walking robot,” Applied caused by impact. The natural frequency of the bionic foot Sciences, vol. 10, no. 7, article 2342, 2020. was smaller than that of the ordinary foot, which ensured [11] H. Song and K. Kong, “Analysis of vibrations transmitted to that the bionic foot has a wider range of vibration reduction. the quadruped robot body during trotting with different stiff- ness of feet,” in 2018 18th International Conference on Control, Data Availability Automation and Systems (ICCAS 2018), PyeongChang, Gang- Won Province, Korea, 2018. The data used to support the findings of this study are avail- [12] F. Ma, L. Ni, L. Wei, J. Nie, L. Wu, and W. Jia, “Posture control able from the corresponding author upon request. of all terrain mobile robot with vibration isolation system,” in Advances in Dynamics of Vehicles on Roads and Tracks. IAVSD Conflicts of Interest 2019. Lecture Notes in Mechanical Engineering, M. Klomp, F. Bruzelius, J. Nielsen, and A. Hillemyr, Eds., Springer, Cham, The authors declare that there is no conflict of interests regarding the publication of this paper. [13] J. Yin, “Design of foot cam vibration damping system for forest walking robot,” in Big Data Analytics for Cyber-Physical Sys- tem in Smart City. BDCPS 2020. Advances in Intelligent Sys- Acknowledgments tems and Computing, vol 1303, M. Atiquzzaman, N. Yen, and Z. Xu, Eds., Springer, Singapore, 2021. The authors gratefully acknowledge the support of the Foun- [14] A. David, J. R. Chardonnet, A. Kheddar, K. Kaneko, and dation of State Key Laboratory of Automotive Simulation K. Yokoi, “Study of an external passive shock-absorbing mech- and Control (Grant No. 20171115), the National Natural Sci- anism for walking robots,” in Humanoids 2008 - 8th IEEE-RAS ence Foundation of China (Grant Nos. 91748211 and International Conference on Humanoid Robots, Daejeon, 51305157), and the project of the 13th Five-Year Common Korea (South), December 2009. Technology (Grant No. 41412040101). [15] J. Li, Q. Huang, W. Zhang, Z. Yu, and K. Li, “Flexible foot design for a humanoid robot,,” in IEEE International Confer- References ence on Automation & Logistics, Qingdao, China, September [1] K. Ito and Y. Ishigaki, “Semiautonomous centipede-like robot [16] K. Hashimoto, T. Hosobata, Y. Sugahara et al., “Development for rubble - development of an actual scale robot for rescue of foot System of biped walking robot capable of maintaining operation,” International Journal of Advanced Mechatronic four-point contact,” in 2005 IEEE/RSJ International Confer- Systems, vol. 6, no. 2/3, p. 75, 2015. ence on Intelligent Robots and Systems, Edmonton, AB, Can- [2] P. Biswal and P. K. Mohanty, “Development of quadruped ada, August 2005. walking robots: a review,” Ain Shams Engineering Journal, [17] Q. Zhu, Humanoid Robot Mechanical Design and Analysis, vol. 32, 2020. Zhejiang University, 2011. [3] S. A. A. Moosavian, R. Rastegarij, and E. Papadopoulos, “Mul- [18] G. Kim and J. Yoon, “Development of intelligent foot with six- tiple impedance control for space free-flying robots,” Journal axis force/moment sensors for humanoid robot,” in 2008 IEEE of Guidance, Control, and Dynamics, vol. 28, no. 5, pp. 939– International Conference on Robotics and Biomimetics, Bang- 947, 2005. kok, Thailand, February 2009. [4] Y. Li, M. Li, H. Zhu et al., “Development and applications of [19] S. M. Sun, D. S. Ye, and X. Wu, “Research on vibration reduc- rescue robots for explosion accidents in coal mines,” Journal tion mechanism for robot joints by imitating the owl surface of Robotic Systems, vol. 37, no. 3, pp. 466–489, 2020. characteristics,” Applied Mechanics and Materials, vol. 539, [5] A. N. Sarmah, A. Boruah, D. Kalita, D. Neog, and S. Paul, “A pp. 13–17, 2014. bio-inspired implementation of walking and stair climbing [20] T. Chang, X. Liu, G. U. Xincen, and Z. Guo, “Design of bionic on a quadruped robot,” Procedia Computer Science, vol. 143, quadruped robot and stress analysis for foot end with kinemat- pp. 671–677, 2018. ics,” Computer Engineering, vol. 4, 2017. [6] V.-G. Loc, I. M. Koo, D. T. Tran, S. Park, H. Moon, and H. R. [21] G. Jiang, X. Jing, and Y. Guo, “A novel bio-inspired multi-joint Choi, “Improving traversability of quadruped walking robots anti-vibration structure and its nonlinear HSLDS properties,” using body movement in 3D rough terrains,” Robotics and Mechanical Systems and Signal Processing, vol. 138, article Autonomous Systems, vol. 59, no. 12, pp. 1036–1048, 2011. 106552, 2020. [7] P. M. James, A. Prakash, V. Kalburgi, and P. Sreedharan, [22] M. A. Woodward and M. Sitti, “Morphological intelligence “Design, analysis, manufacturing of four-legged walking robot counters foot slipping in the desert locust and dynamic with insect type leg,” Materials Today: Proceedings, vol. 46, robots,” Proceedings of the National Academy of Sciences of the United State of America, vol. 115, no. 36, pp. E8358– [8] E. Corral, R. G. Moreno, M. J. G. García, and C. Castejón, E8367, 2018. “Nonlinear phenomena of contact in multibody systems dynamics: a review,” Nonlinear Dynamics, vol. 104, no. 2, [23] Q. Zhang, X. L. Ding, K. Xu, and H. Chen, “Design and kine- matics analysis of a bionic mechanical goat hoof,” Applied pp. 1269–1295, 2021. Mechanics & Materials, vol. 461, pp. 191–200, 2014. [9] P. Flores and H. M. Lankarani, Contact Force Models for Multi- body Dynamics: Contact Force Models for Multibody Dynam- [24] G. Zhang, Research On Bionic Goat Mechanism On Sloping ics, SMIA, 2016. Fields, Henan University of Science and Technology, 2011. Applied Bionics and Biomechanics 9 [25] H. Kui, X. Liu, J. Liu et al., “The passive contact stability of blue sheep hoof based on structure, mechanical properties, and sur- face morphology,” Frontiers in Bioengineering and Biotechnol- ogy, vol. 8, 2020. [26] W. Tian, H. Liu, Q. Zhang, B. Su, W. Xu, and Q. Cong, “Cush- ion mechanism of goat hoof bulb tissues,” Applied Bionics and Biomechanics, vol. 2019, Article ID 3021576, 11 pages, 2019. [27] W. J. Tian, J. Y. Wang, M. Li, and Q. Cong, “Design and opti- mization of vibration reduction structure imitating pore struc- ture in goat Capsula ungulae,” Zhendong Gongcheng Xuebao/journal of Vibration Engineering, vol. 31, no. 2, pp. 352–357, 2018. [28] W. J. Tian, Y. J. Xu, W. Xu, P. Xu, Q. Zhang, and Q. Cong, “Bionic design and anti-slip characteristics study of quadruped robot foot,” Journal of Physics Conference Series, vol. 1507, arti- cle 052008, 2020.

Journal

Applied Bionics and BiomechanicsHindawi Publishing Corporation

Published: Jun 10, 2021

References