Footholds optimization for legged robots walking on complex terrain

Abstract

This paper proposes a novel continuous footholds optimization method for legged robots to expand their walking ability on complex terrains. The algorithm can efficiently run onboard and online by using terrain perception information to protect the robot against slipping or tripping on the edge of obstacles, and to improve its stability and safety when walking on complex terrain. By relying on the depth camera installed on the robot and obtaining the terrain heightmap, the algorithm converts the discrete grid heightmap into a continuous costmap. Then, it constructs an optimization function combined with the robot’s state information to select the next footholds and generate the motion trajectory to control the robot’s locomotion. Compared with most existing footholds selection algorithms that rely on discrete enumeration search, as far as we know, the proposed algorithm is the first to use a continuous optimization method. We successfully implemented the algorithm on a hexapod robot, and verified its feasibility in a walking experiment on a complex terrain.

Graphical abstract

Keywords

footholds optimization / legged robot / complex terrain adapting / hexapod robot / locomotion control

References

[1] Raibert M H, Tello E R. Legged robots that balance. IEEE Expert, 1986, 1(4): 89

[2] BledtG, Powell M J, KatzB, Di CarloJ, Wensing P M, KimS. MIT Cheetah 3: design and control of a robust, dynamic quadruped robot. In: Proceedings of 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems. Madrid: IEEE, 2018

[3] VernazaP, Likhachev M, BhattacharyaS, ChittaS, Kushleyev A, Lee D D. Search-based planning for a legged robot over rough terrain. In: Proceedings of 2009 IEEE International Conference on Robotics & Automation. Kobe: IEEE, 2009, 2380–2387

[4] KalakrishnanM, BuchliJ, PastorP, MistryM, Schaal S. Fast, robust quadruped locomotion over challenging terrain. In: Proceedings of 2010 IEEE International Conference on Robotics & Automation. Anchorage: IEEE, 2010, 2665–2670

[5] Semini C, Tsagarakis N G, Guglielmino E, Focchi M, Cannella F, Caldwell D G. Design of HyQ—a hydraulically and electrically actuated quadruped robot. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 2011, 225(6): 831–849

[6] WinklerA, Havoutis I, BazeilleS, OrtizJ, Focchi M, Dillmann R, Caldwell D, SeminiC. Path planning with force-based foothold adaptation and virtual model control for torque controlled quadruped robots. In: Proceedings of 2014 IEEE International Conference on Robotics & Automation (ICRA). Hong Kong: IEEE, 2014, 6476–6482

[7] HutterM, Gehring C, JudD, LauberA, Bellicoso C D, TsounisV, HwangboJ, BodieK, FankhauserP, Bloesch M, DiethelmR, BachmannS, MelzerA, HoepflingerM. ANYmal—a highly mobile and dynamic quadrupedal robot. In: Proceedings of 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Daejeon: IEEE, 2016, 38–44

[8] Winkler A W, Bellicoso C D, Hutter M, Buchli J. Gait and trajectory optimization for legged systems through phase-based end-effector parameterization. IEEE Robotics and Automation Letters, 2018, 3(3): 1560–1567

[9] MastalliC, Focchi M, HavoutisI, RadulescuA, Calinon S, Buchli J, Caldwell D G, SeminiC. Trajectory and foothold optimization using low-dimensional models for rough terrain locomotion. In: Proceedings of 2017 IEEE International Conference on Robotics & Automation (ICRA). Singapore: IEEE, 2017, 1096–1103

[10] Mastalli C, Havoutis I, Focchi M, Caldwell D G, Semini C. Motion planning for quadrupedal locomotion: coupled planning, terrain mapping and whole-body control. IEEE Transactions on Robotics, 2020, 36(6): 1635–1648

[11] MastalliC, Havoutis I, WinklerA W, CaldwellD G, SeminiC. On-line and on-board planning and perception for quadrupedal locomotion. In: Proceedings of 2015 IEEE International Conference on Technologies for Practical Robot Applications (TePRA). Woburn: IEEE, 2019, 1–7

[12] FankhauserP, Bjelonic M, BellicosoC D, MikiT, HutterM. Robust rough-terrain locomotion with a quadrupedal robot. In: Proceedings of 2018 IEEE International Conference on Robotics and Automation (ICRA). Brisbane: IEEE, 2018, 5761–5768

[13] Jenelten F, Miki T, Vijayan A E, Bjelonic M, Hutter M. Perceptive locomotion in rough terrain—online foothold optimization. IEEE Robotics and Automation Letters, 2020, 5(4): 5370–5376

[14] ChaiX, Gao F, XuY L. Perception-based gait planning for a hexapod robot walking on typical structured terrain. In: Zhang X M, Wang N F, Huang Y J, eds. Mechanism and Machine Science. Singapore: Springer, 2017, 169–181

[15] KimD, Carballo D, Di CarloJ, KatzB, Bledt G, Lim B, Kim S. Vision aided dynamic exploration of unstructured terrain with a small-scale quadruped robot. In: Proceedings of 2020 IEEE International Conference on Robotics and Automation (ICRA). Paris: IEEE, 2020, 2464–2470

[16] Mao L H, Tian Y, Gao F, Zhao Y. Novel method of gait switching in six-legged robot walking on continuous-nondifferentiable terrain by utilizing stability and interference criteria. Science China Technological Sciences, 2020, 63(12): 2527–2540

[17] Mao L H, Gao F, Tian Y, Zhao Y. Novel method for preventing shin-collisions in six-legged robots by utilising a robot–terrain interference model. Mechanism and Machine Theory, 2020, 151: 103897

[18] ZhaoY, Gao F, YinY P. Obstacle avoidance and terrain identification for a hexapod robot. Research Square, 2020, preprint

[19] Magaña O A V, Barasuol V, Camurri M, Franceschi L, Focchi M, Pontil M, Caldwell D G, Semini C. Fast and continuous foothold adaptation for dynamic locomotion through CNNs. IEEE Robotics and Automation Letters, 2019, 4(2): 2140–2147

[20] Miki T, Lee J, Hwangbo J, Wellhausen L, Koltun V, Hutter M. Learning robust perceptive locomotion for quadrupedal robots in the wild. Science Robotics, 2022, 7(62): eabk2822

[21] Tsounis V, Alge M, Lee J, Farshidian F, Hutter M. DeepGait: planning and control of quadrupedal gaits using deep reinforcement learning. IEEE Robotics and Automation Letters, 2020, 5(2): 3699–3706

[22] GehringC, Fankhauser P, IslerL, DiethelmR, Bachmann S, PotzM, GerstenbergL, HutterM. ANYmal in the field: solving industrial inspection of an offshore HVDC platform with a quadrupedal robot. In: Ishigami G, Yoshida K, eds. Field and Service Robotics. Singapore: Springer, 2021, 247–260

[23] LiuW, GaoY, GaoF, LiS Y. Trajectory adaptation and safety control via control barrier functions for legged robots. In: Proceedings of 2021 China Automation Congress (CAC). Beijing: IEEE, 2021, 5571–5576

[24] Park H W, Wensing P M, Kim S. Jumping over obstacles with MIT Cheetah 2. Robotics and Autonomous Systems, 2021, 136: 103703

[25] QiS H, Lin W C, HongZ J, ChenH, ZhangW. Perceptive autonomous stair climbing for quadrupedal robots. In: Proceedings of 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Prague: IEEE, 2021, 2313–2320

[26] GerumP. Xenomai—Implementing a RTOS emulation framework on GNU/Linux. White Paper, 2004, 81

[27] HintjensP. ZeroMQ: Messaging for Many Applications. O’Reilly Media, 2013

[28] Sun Q, Gao F, Chen X B. Towards dynamic alternating tripod trotting of a pony-sized hexapod robot for disaster rescuing based on multi-modal impedance control. Robotica, 2018, 36(7): 1048–1076

[29] EkstromM P. Digital Image Processing Techniques. 2nd ed. Academic Press, 2012

[30] Ranganathan A.. The Levenberg‒Marquardt algorithm. Tutoral on LM Algorithm, 2004, 11(1): 101–110

[31] BlöschMHutterMHöpflinger M ALeuteneggerSGehringCRemyC D SiegwartR Y. State estimation for legged robots—consistent fusion of leg kinematics and IMU. In: Proceedings of Robotics: Science and Systems Conference (RSS 2012). Sidney: Robotics: Science and Systems Conference, 2012

[32] Focchi M, Del Prete A, Havoutis I, Featherstone R, Caldwell D G, Semini C. High-slope terrain locomotion for torque-controlled quadruped robots. Autonomous Robots, 2017, 41(1): 259–272

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Higher Education Press