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Footstep Planning for Hexapod Robots Based on 3D Quasi-static Equilibrium Support Region

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Abstract

The hexapod robots equipped with six legs have higher stability and adaptability to challenging terrains than other legged robots with fewer legs. The ability of hexapods to traverse challenging terrains largely depends on practical planning approaches on their footstep sequence. However, suppose the stability of the robotic system is insufficiently considered with the footstep planning method, it cannot track the planning results in some extremely complex terrains, e.g., foot slippage or robot overturn. In this work, we develop a quasi-static equilibrium footstep planning method for hexapod robots to traverse challenging terrains. The core of this planning method is the proposed 3D quasi-static equilibrium support region (3D QESR), which can be employed as a constraint for the planning method to ensure the quasi-static stability of the hexapod robots. A new graph search algorithm for footstep sequence planning is also presented. The simulation and experiment results show that the proposed 3D QESR method has superior performance in bypassing unstable irregular regions compared with the widely used support polygon method.

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References

  1. Belter, D., Labecki, P., Skrzypczynski, P.: Adaptive motion planning for autonomous rough terrain traversal with a walking robot. J. Field Robot. 33(3), 337–370 (2016)

    Article  Google Scholar 

  2. Belter, D., Wietrzykowski, J., Skrzypczyński, P.: Employing natural terrain semantics in motion planning for a multi-legged robot. J. Intell. Robot. Syst. 93(3), 723 (2019)

    Article  Google Scholar 

  3. Perrin, N., Stasse, O., Lamiraux, F., Kim, Y. J., Manocha, D: Real-time footstep planning for humanoid robots among 3D obstacles using a hybrid bounding box. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 977–982 (2012)

  4. Perrin, N., Ott, C., Englsberger, J., Stasse, O., Lamiraux, F., Caldwell, D. G.: Continuous Legged Locomotion Planning. IEEE Trans. Robot. 33(1), 234 (2017)

    Article  Google Scholar 

  5. Cizek, P., Masri, D., Faigl, J: Foothold placement planning with a hexapod crawling robot. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 4096–4101. https://doi.org/10.1109/IROS.2017.8206267 (2017)

  6. Fankhauser, P., Bjelonic, M., Bellicoso, D., Miki, T., Hutter, M.: Robust Rough-Terrain Locomotion with a Quadrupedal Robot. In: Proceedings of the IEEE International Conference on Robotics and Automation (Brisbane Australia), pp. 5761–5768 (2018)

  7. Fankhauser, P.: Perceptive Locomotion for Legged Robots in Rough Terrain. Ph.D. thesis, ETH Zurich (2018)

  8. Chestnutt, J., Lau, M., Cheung, G., Kuffner, J., Hodgins, J., Kanade, T.: Footstep Planning for the Honda ASIMO Humanoid. In: Proceedings of the IEEE International Conference on Robotics and Automation (Barcelona Spain), pp. 629–634 (2005)

  9. Chestnutt, J., Nishiwaki, K., Kuffner, J., Kagamiy, S.: Interactive control of humanoid navigation. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, St. Louis, pp. 3519–3524 (2009)

  10. Nishiwaki, K., Chestnutt, J., Kagami, S.: Autonomous navigation of a humanoid robot over unknown rough terrain using a laser range sensor. Int. J. Robot. Res. 31(11), 1251 (2012)

    Article  Google Scholar 

  11. Estremera, J., Gonzalez de Santos, P.: Free Gaits for Quadruped Robots over Irregular Terrain. Int. J. Robot. Res. 21(2), 115 (2016)

    Article  Google Scholar 

  12. Kalakrishnan, M., Buchli, J., Pratt, J., Roy, N., Buchli, J., Pastor, P., Mistry, M., Schaal, S.: Learning, planning, and control for quadruped locomotion over challenging terrain. Int. J. Robot. Res. 30(2), 236 (2010)

    Article  Google Scholar 

  13. Kalakrishnan, M., Buchli, J., Pastor, P., Mistry, M., Schaal, S.: Fast, robust quadruped locomotion over challenging terrain. In: In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 2665–2670. https://doi.org/10.1109/ROBOT.2010.5509805 (2010)

  14. Bjelonic, M., Kottege, N., Homberger, T., Borges, P., Beckerle, P., Chli, M.: Weaver: Hexapod robot for autonomous navigation on unstructured terrain. J. Field Robot. 35(7), 1063 (2018)

    Article  Google Scholar 

  15. De Viragh, Y., Bjelonic, M., Bellicoso, C. D., Jenelten, F., Hutter, M.: Trajectory Optimization for Wheeled-Legged Quadrupedal Robots Using Linearized ZMP Constraints. IEEE Robot. Autom. Lett. 4(2), 1633 (2019)

    Article  Google Scholar 

  16. Bretl, T., Lall, S.: Testing static equilibrium for legged robots. IEEE Trans. Robot. 24(4), 794 (2008)

    Article  Google Scholar 

  17. Hauser, K., Bretl, T., Latombe, J. C., Harada, K., Wilcox, B.: Motion planning for legged robots on varied terrain. Int. J. Robot. Res. 27(11–12), 1325 (2008)

    Article  Google Scholar 

  18. Audren, H., Kheddar, A.: . IEEE Trans. Robot. 34(2), 388 (2018). https://doi.org/10.1109/TRO.2017.2786683

    Article  Google Scholar 

  19. Escande, A., Kheddar, A., Miossec, S.: . Robot. Auton. Syst. 61(5), 428 (2013)

    Article  Google Scholar 

  20. Orsolino, R., Focchi, M., Mastalli, C., Dai, H., Caldwell, D. G., Semini, C.: . IEEE Robot. Autom. Lett. 3(4), 3363 (2018)

    Article  Google Scholar 

  21. Orsolino, R., Focchi, M., Caron, S., Raiola, G., Barasuol, V., Caldwell, D. G., Semini, C.: . IEEE Trans. Robot. 36(4), 1239 (2020)

    Article  Google Scholar 

  22. Mesesan, G., Englsberger, J., Ott, C., Albu-schäffer, A.: . IEEE Robot. Autom. Lett. 3(4), 3449 (2018)

    Article  Google Scholar 

  23. Fernbach, P., Tonneau, S., Stasse, O., Carpentier, J., Taïx, M.: . IEEE Trans. Robot. 36(3), 676 (2020)

    Article  Google Scholar 

  24. Zucker, M., Ratliff, N., Dragan, A. D., Pivtoraiko, M., Klingensmith, M., Dellin, C. M., Bagnell, J. A., Srinivasa, S. S.: Chomp: Covariant hamiltonian optimization for motion planning. Int. J. Robot. Res. 32(9–10), 1164 (2013)

    Article  Google Scholar 

  25. Shkolnik, A., Buchli, J., Pratt, J., Roy, N., Levashov, M., Manchester, I. R., Tedrake, R.: Bounding on rough terrain with the littledog robot. Int. J. Robot. Res. 30(2), 192 (2010)

    Article  Google Scholar 

  26. Shkolnik, A. C.: Sample-based motion planning in high-dimensional and differentially-constrained systems. Ph.D. thesis Massachusetts Institute of Technology (2010)

  27. Lin, Y. C., Ponton, B., Righetti, L., Berenson, D.: Efficient humanoid contact planning using learned centroidal dynamics prediction. In: Proceedings of the IEEE International Conference on Robotics and Automation, Montreal, Canada, pp. 5280–5286 (2019)

  28. Winkler, A. W., Bellicoso, C. D., Hutter, M., Buchli, J.: Gait and trajectory optimization for legged systems through phase-based end-effector parameterization. IEEE Robot. Autom. Lett. 3(3), 1560 (2018)

    Article  Google Scholar 

  29. Winkler, A. W.: Optimization-Based Motion Planning for Legged Robots. Thesis, ETH Zurich (2018)

  30. Klamt, T., Behnke, S.: Anytime hybrid driving-stepping locomotion planning. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, pp 4444–4451 (2017)

  31. Liu, Z., Zhuang, H. C., Gao, H. B., Deng, Z. Q., Ding, L.: Static force analysis of foot of electrically driven heavy-duty six-legged robot under tripod gait. Chin. J. Mech. Eng. 31(1), 63 (2018). https://doi.org/10.1109/IROS.2017.8206310

    Article  Google Scholar 

  32. Liu, Y., Gao, H., Ding, L., Liu, G., Deng, Z., Li, N.: State estimation of a heavy-duty hexapod robot with passive compliant ankles based on the leg kinematics and IMU data fusion. J. Mech. Sci. Technol. 32(8), 3885–3897 (2018)

    Article  Google Scholar 

  33. Gao, H., Liu, Y., Ding, L., Liu, G., Deng, Z., Liu, Y., Yu, H.: Low impact force and energy consumption motion planning for hexapod robot with passive compliant ankles. J. Intell. Robot. Syst. 94(2), 349 (2019)

    Article  Google Scholar 

  34. Zha, F., Chen, C., Guo, W., Zheng, P., Shi, J.: A free gait controller designed for a heavy load hexapod robot. Adv. Mech. Eng. 11(3), 1–17 (2019)

    Article  Google Scholar 

  35. Gao, F., Wu, W., Lin, Y., Shen, S.: Online Safe Trajectory Generation for Quadrotors Using Fast Marching Method and Bernstein Basis Polynomial. In: Proceedings of the IEEE International Conference on Robotics and Automation, Brisbane, Australia, pp. 344–351 (2018)

  36. Aguero, C., Koenig, N., Chen, I., Boyer, H., Peters, S., Hsu, J., Gerkey, B., Paepcke, S., Rivero, J., Manzo, J., Krotkov, E., Pratt, G.: Inside the virtual robotics challenge: simulating real-time robotic disaster response. IEEE Trans. Autom. Sci. Eng. 12(2), 494 (2015)

    Article  Google Scholar 

  37. Fankhauser, P., Hutter, M.: A Universal Grid Map Library: Implementation and Use Case for Rough Terrain Navigation. In: Robot Operating System (ROS) – The Complete Reference, vol. 1. Springer, chap. 5. https://doi.org/10.1007/978-3-319-26054-9_5 (2016)

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Funding

This research was supported by the National Key Research and Development Program of China (Grant No. SQ2019YFB130016), the National Natural Science Foundation of China (Grant No. 91948202, 51822502), and the “111” Project (Grant No. B07018).

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Authors and Affiliations

  1. State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, Heilongjiang, China

    Liang Ding, Guanyu Wang, Haibo Gao, Huaiguang Yang & Zongquan Deng

  2. Department of Aerospace Engineering, Ryerson University, Toronto, Canada

    Guangjun Liu

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  1. Liang Ding
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  2. Guanyu Wang
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  3. Haibo Gao
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  4. Guangjun Liu
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  5. Huaiguang Yang
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  6. Zongquan Deng
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Contributions

All authors contributed to the research. Liang Ding, Guanyu Wang and Huaiguang Yang performed the experiments; Guanyu Wang performed the simulations; Guangjun Liu, Haibo Gao and Zongquan Deng edited and reviewed the manuscript.

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Correspondence to Guanyu Wang.

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Ding, L., Wang, G., Gao, H. et al. Footstep Planning for Hexapod Robots Based on 3D Quasi-static Equilibrium Support Region. J Intell Robot Syst 103, 25 (2021). https://doi.org/10.1007/s10846-021-01469-0

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