skip to main content
research-article

Fast and flexible multilegged locomotion using learned centroidal dynamics

Published:12 August 2020Publication History
Skip Abstract Section

Abstract

We present a flexible and efficient approach for generating multilegged locomotion. Our model-predictive control (MPC) system efficiently generates terrain-adaptive motions, as computed using a three-level planning approach. This leverages two commonly-used simplified dynamics models, an inverted pendulum on a cart model (IPC) and a centroidal dynamics model (CDM). Taken together, these ensure efficient computation and physical fidelity of the resulting motion. The final full-body motion is generated using a novel momentum-mapped inverse kinematics solver and is responsive to external pushes by using CDM forward dynamics. For additional efficiency and robustness, we then learn a predictive model that then replaces two of the intermediate steps. We demonstrate the rich capabilities of the method by applying it to monopeds, bipeds, and quadrupeds, and showing that it can generate a very broad range of motions at interactive rates, including banked variable-terrain walking and running, hurdles, jumps, leaps, stepping stones, monkey bars, implicit quadruped gait transitions, moon gravity, push-responses, and more.

Skip Supplemental Material Section

Supplemental Material

a46-kwon.mp4

mp4

49.3 MB

3386569.3392432.mp4

Presentation video

mp4

145.6 MB

References

  1. Yeuhi Abe, Marco da Silva, and Jovan Popović. 2007. Multiobjective Control with Frictional Contacts. In Proceedings of the 2007 ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 249--258.Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. Bernardo Aceituno-Cabezas, Carlos Mastalli, Hongkai Dai, Michele Focchi, Andreea Radulescu, Darwin G Caldwell, José Cappelletto, Juan C Grieco, Gerardo Fernández-López, and Claudio Semini. 2018. Simultaneous Contact, Gait, and Motion Planning for Robust Multilegged Locomotion via Mixed-Integer Convex Optimization. IEEE Robotics and Automation Letters 3, 3 (2018), 2531--2538.Google ScholarGoogle Scholar
  3. Mazen Al Borno, Martin De Lasa, and Aaron Hertzmann. 2013. Trajectory optimization for full-body movements with complex contacts. IEEE transactions on visualization and computer graphics 19, 8 (2013), 1405--1414.Google ScholarGoogle Scholar
  4. Mazen Al Borno, Michiel Van De Panne, and Eugene Fiume. 2017. Domain of attraction expansion for physics-based character control. ACM Transactions on Graphics (TOG) 36, 2 (2017), 17.Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. G. E. P. Box and G. C. Tiao. 1992. Bayesian Inference in Statistical Analysis. John Wiley & Sons, New York.Google ScholarGoogle Scholar
  6. Armin Bruderlin and Lance Williams. 1995. Motion Signal Processing. In SIGGRAPH. 97--104.Google ScholarGoogle Scholar
  7. Justin Carpentier, Steve Tonneau, Maximilien Naveau, Olivier Stasse, and Nicolas Mansard. 2016. A versatile and efficient pattern generator for generalized legged locomotion. In 2016 IEEE International Conference on Robotics and Automation (ICRA). 3555--3561.Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. Djork-Arné Clevert, Thomas Unterthiner, and Sepp Hochreiter. 2016. Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs). arXiv:1511.07289 [cs] (Feb. 2016). arXiv: 1511.07289.Google ScholarGoogle Scholar
  9. Stelian Coros, Philippe Beaudoin, and Michiel van de Panne. 2010. Generalized biped walking control. ACM Transactions on Graphics 29, 4 (2010), 130.Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Stelian Coros, Andrej Karpathy, Ben Jones, Lionel Reveret, and Michiel Van De Panne. 2011. Locomotion skills for simulated quadrupeds. In ACM Transactions on Graphics (TOG), Vol. 30. ACM, 59.Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. H. Dai, A. Valenzuela, and R. Tedrake. 2014. Whole-body motion planning with centroidal dynamics and full kinematics. In 2014 IEEE-RAS International Conference on Humanoid Robots. 295--302.Google ScholarGoogle Scholar
  12. Martin de Lasa, Igor Mordatch, and Aaron Hertzmann. 2010. Feature-based locomotion controllers. ACM Transactions on Graphics 29, 4 (2010), 131.Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. Peter Dorato, Vito Cerone, and Chaouki Abdallah. 1994. Linear-Quadratic Control: An Introduction. Simon & Schuster.Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. Johannes Englsberger, Christian Ott, and Alin Albu-SchÃd'ffer. 2015. Three-Dimensional Bipedal Walking Control Based on Divergent Component of Motion. IEEE Transactions on Robotics 31, 2 (April 2015), 355--368.Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Tom Erez, Kendall Lowrey, Yuval Tassa, Vikash Kumar, Svetoslav Kolev, and Emanuel Todorov. 2013. An integrated system for real-time model predictive control of humanoid robots. In 2013 IEEE-RAS International Conference on Humanoid Robots. IEEE, 292--299.Google ScholarGoogle ScholarCross RefCross Ref
  16. Farbod Farshidian, Edo Jelavić, Asutosh Satapathy, Markus Giftthaler, and Jonas Buchli. 2017. Real-time motion planning of legged robots: A model predictive control approach. In 2017 IEEE-RAS International Conference on Humanoid Robots.Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Martin L Felis and Katja Mombaur. 2016. Synthesis of full-body 3-D human gait using optimal control methods. In 2016 IEEE International Conference on Robotics and Automation (ICRA). 1560--1566.Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Thomas Geijtenbeek and Nicolas Pronost. 2012. Interactive character animation using simulated physics: A state-of-the-art review. In Computer Graphics Forum, Vol. 31. Wiley Online Library, 2492--2515.Google ScholarGoogle Scholar
  19. Sehoon Ha, Yuting Ye, and C. Karen Liu. 2012. Falling and landing motion control for character animation. ACM Transactions on Graphics 31, 6 (2012), 155.Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Perttu Hämäläinen, Sebastian Eriksson, Esa Tanskanen, Ville Kyrki, and Jaakko Lehtinen. 2014. Online motion synthesis using sequential monte carlo. ACM Transactions on Graphics (TOG) 33, 4 (2014), 51.Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. Perttu Hämäläinen, Joose Rajamäki, and C Karen Liu. 2015. Online control of simulated humanoids using particle belief propagation. ACM Transactions on Graphics (TOG) 34, 4 (2015), 81.Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Daseong Han, Haegwang Eom, Junyong Noh, and Joseph S Shin. 2016. Data-guided model predictive control based on smoothed contact dynamics. In Computer Graphics Forum, Vol. 35. Wiley Online Library, 533--543.Google ScholarGoogle Scholar
  23. Nikolaus Hansen and Andreas Ostermeier. 1996. Adapting Arbitrary Normal Mutation Distributions in Evolution Strategies: The Covariance Matrix Adaptation. In International Conference on Evolutionary Computation. 312--317.Google ScholarGoogle Scholar
  24. Nicolas Heess, Srinivasan Sriram, Jay Lemmon, Josh Merel, Greg Wayne, Yuval Tassa, Tom Erez, Ziyu Wang, Ali Eslami, Martin Riedmiller, et al. 2017. Emergence of locomotion behaviours in rich environments. arXiv preprint arXiv:1707.02286 (2017).Google ScholarGoogle Scholar
  25. Alexander Herzog, Stefan Schaal, and Ludovic Righetti. 2016. Structured contact force optimization for kino-dynamic motion generation. In 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). 2703--2710.Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Jessica K. Hodgins, Wayne L. Wooten, David C. Brogan, and James F. O'Brien. 1995. Animating human athletics. In ACM SIGGRAPH. 71--78.Google ScholarGoogle Scholar
  27. Daniel Holden, Taku Komura, and Jun Saito. 2017. Phase-functioned Neural Networks for Character Control. ACM Transactions on Graphics 36, 4 (2017), 42:1--42:13.Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. Seokpyo Hong, Daseong Han, Kyungmin Cho, Joseph S Shin, and Junyong Noh. 2019. Physics-based Full-body Soccer Motion Control for Dribbling and Shooting. ACM Transactions on Graphics 38, 4 (2019).Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. Marco Hutter, Christian Gehring, Dominic Jud, Andreas Lauber, C. Dario Bellicoso, Vassilios Tsounis, Jemin Hwangbo, Karen Bodie, Peter Fankhauser, Michael Bloesch, Remo Diethelm, Samuel Bachmann, Amir Melzer, and Mark Hoepflinger. 2016. ANYmal - a highly mobile and dynamic quadrupedal robot. In 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). 38--44.Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. Jaepyung Hwang, Jongmin Kim, Il Hong Suh, and Taesoo Kwon. 2018. Real-time Locomotion Controller using an Inverted-Pendulum-based Abstract Model. 37, 2 (2018), 287--296.Google ScholarGoogle Scholar
  31. Satoru Ishigaki, Timothy White, Victor B Zordan, and C Karen Liu. 2009. Performance-based control interface for character animation. In ACM Transactions on Graphics (TOG), Vol. 28. ACM, 61.Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. Sumit Jain, Yuting Ye, and C Karen Liu. 2009. Optimization-based interactive motion synthesis. ACM Transactions on Graphics (TOG) 28, 1 (2009), 10.Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. Shuuji Kajita, Fumio Kanehiro, Kenji Kaneko, Kiyoshi Fujiwara, Kensuke Harada, Kazuhito Yokoi, and Hirohisa Hirukawa. 2003. Biped walking pattern generation by using preview control of zero-moment point. In Proceedings of the 2003 IEEE International Conference on Robotics and Automation. 1620--1626.Google ScholarGoogle ScholarCross RefCross Ref
  34. Jonas Koenemann, Andrea Del Prete, Yuval Tassa, Emanuel Todorov, Olivier Stasse, Maren Bennewitz, and Nicolas Mansard. 2015. Whole-body model-predictive control applied to the HRP-2 humanoid. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2015). 8p.Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. Taesoo Kwon and Jessica Hodgins. 2010. Control systems for human running using an inverted pendulum model and a reference motion capture sequence. In Proc. ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 129--138.Google ScholarGoogle Scholar
  36. Taesoo Kwon and Jessica K. Hodgins. 2017. Momentum-Mapped Inverted Pendulum Models for Controlling Dynamic Human Motions. ACM Transactions on Graphics 36, 4 (2017).Google ScholarGoogle ScholarDigital LibraryDigital Library
  37. Yoonsang Lee, Sungeun Kim, and Jehee Lee. 2010. Data-driven biped control. ACM Transactions on Graphics 29, 4 (2010), 129.Google ScholarGoogle ScholarDigital LibraryDigital Library
  38. Sergey Levine and Vladlen Koltun. 2013. Guided policy search. In International Conference on Machine Learning. 1--9.Google ScholarGoogle ScholarDigital LibraryDigital Library
  39. C Karen Liu and Zoran Popović. 2002. Synthesis of complex dynamic character motion from simple animations. ACM Transactions on Graphics (TOG) 21, 3 (2002), 408--416.Google ScholarGoogle ScholarDigital LibraryDigital Library
  40. Libin Liu and Jessica Hodgins. 2018. Learning basketball dribbling skills using trajectory optimization and deep reinforcement learning. ACM Transactions on Graphics (TOG) 37, 4 (2018), 142.Google ScholarGoogle ScholarDigital LibraryDigital Library
  41. Libin Liu, Michiel van de Panne, and KangKang Yin. 2016. Guided Learning of Control Graphs for Physics-Based Characters. ACM Transactions on Graphics 35, 3 (2016).Google ScholarGoogle ScholarDigital LibraryDigital Library
  42. Libin Liu, KangKang Yin, and Baining Guo. 2015. Improving Sampling-based Motion Control. In Computer Graphics Forum, Vol. 34. Wiley Online Library, 415--423.Google ScholarGoogle Scholar
  43. Libin Liu, KangKang Yin, Michiel van de Panne, and Baining Guo. 2012. Terrain runner: control, parameterization, composition, and planning for highly dynamic motions. ACM Transactions on Graphics 31, 6 (2012), 154--1.Google ScholarGoogle ScholarDigital LibraryDigital Library
  44. Libin Liu, KangKang Yin, Michiel van de Panne, Tianjia Shao, and Weiwei Xu. 2010. Sampling-based contact-rich motion control. ACM Transactions on Graphics 29, 4 (2010), 128.Google ScholarGoogle ScholarDigital LibraryDigital Library
  45. Kendall Lowrey, Aravind Rajeswaran, Sham Kakade, Emanuel Todorov, and Igor Mordatch. 2018. Plan Online, Learn Offline: Efficient Learning and Exploration via Model-Based Control. arXiv preprint arXiv:1811.01848 (2018).Google ScholarGoogle Scholar
  46. Adriano Macchietto, Victor Zordan, and Christian R. Shelton. 2009. Momentum control for balance. ACM Transactions on Graphics 28, 3 (2009), 1--8.Google ScholarGoogle ScholarDigital LibraryDigital Library
  47. Igor Mordatch, Martin de Lasa, and Aaron Hertzmann. 2010. Robust physics-based locomotion using low-dimensional planning. ACM Transactions on Graphics 29, 4 (2010), 71.Google ScholarGoogle ScholarDigital LibraryDigital Library
  48. Igor Mordatch, Kendall Lowrey, Galen Andrew, Zoran Popovic, and Emanuel V Todorov. 2015. Interactive control of diverse complex characters with neural networks. In Advances in Neural Information Processing Systems. 3132--3140.Google ScholarGoogle Scholar
  49. Igor Mordatch, Emanuel Todorov, and Zoran Popović. 2012. Discovery of complex behaviors through contact-invariant optimization. ACM Transactions on Graphics (TOG) 31, 4 (2012), 43.Google ScholarGoogle ScholarDigital LibraryDigital Library
  50. Uldarico Muico, Yongjoon Lee, Jovan Popović, and Zoran Popović. 2009. Contact-aware nonlinear control of dynamic characters. ACM Transactions on Graphics 28, 3 (2009), 1--9.Google ScholarGoogle ScholarDigital LibraryDigital Library
  51. David E Orin, Ambarish Goswami, and Sung-Hee Lee. 2013. Centroidal dynamics of a humanoid robot. Autonomous Robots 35, 2-3 (2013), 161--176.Google ScholarGoogle ScholarDigital LibraryDigital Library
  52. Soohwan Park, Hoseok Ryu, Seyoung Lee, Sunmin Lee, and Jehee Lee. 2019. Learning predict-and-simulate policies from unorganized human motion data. ACM Transactions on Graphics (TOG) (2019).Google ScholarGoogle Scholar
  53. Xue Bin Peng, Pieter Abbeel, Sergey Levine, and Michiel van de Panne. 2018. DeepMimic: Example-Guided Deep Reinforcement Learning of Physics-Based Character Skills. ACM Transactions on Graphics (TOG) 37, 4 (2018).Google ScholarGoogle ScholarDigital LibraryDigital Library
  54. Xue Bin Peng, Glen Berseth, and Michiel Van de Panne. 2016. Terrain-adaptive locomotion skills using deep reinforcement learning. ACM Transactions on Graphics (TOG) 35, 4 (2016), 81.Google ScholarGoogle ScholarDigital LibraryDigital Library
  55. Xue Bin Peng, Glen Berseth, KangKang Yin, and Michiel Van De Panne. 2017. Deeploco: Dynamic locomotion skills using hierarchical deep reinforcement learning. ACM Transactions on Graphics (TOG) 36, 4 (2017), 41.Google ScholarGoogle ScholarDigital LibraryDigital Library
  56. Sarah Pilliner, Samantha Elmhurst, and Zoe Davies. 2009. The Horse In Motion. Blackwell Science.Google ScholarGoogle Scholar
  57. B. Ponton, A. Herzog, S. Schaal, and L. Righetti. 2016. A convex model of humanoid momentum dynamics for multi-contact motion generation. In 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids). 842--849.Google ScholarGoogle Scholar
  58. Joose Rajamäki and Perttu Hämäläinen. 2017. Augmenting sampling based controllers with machine learning. In Proceedings of the 2017 ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 1--9.Google ScholarGoogle ScholarDigital LibraryDigital Library
  59. Diana Serra, Camille Brasseur, Alexander Sherikov, Dimitar Dimitrov, and Pierre-Brice Wieber. 2016. A Newton method with always feasible iterates for Nonlinear Model Predictive Control of walking in a multi-contact situation. In 2016 IEEE-RAS International Conference on Humanoid Robots. IEEE, 932--937.Google ScholarGoogle ScholarDigital LibraryDigital Library
  60. Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. 2014. Dropout: A Simple Way to Prevent Neural Networks from Overfitting. Journal of Machine Learning Research 15 (2014), 1929--1958.Google ScholarGoogle ScholarDigital LibraryDigital Library
  61. Toru Takenaka, Takashi Matsumoto, and Takahide Yoshiike. 2009. Real time motion generation and control for biped robot - 1st report: Walking gait pattern generation-. In IEEE/RSJ International Conference on Intelligent Robots and Systems. 1084--1091.Google ScholarGoogle Scholar
  62. Jie Tan, Tingnan Zhang, Erwin Coumans, Atil Iscen, Yunfei Bai, Danijar Hafner, Steven Bohez, and Vincent Vanhoucke. 2018. Sim-to-Real: Learning Agile Locomotion For Quadruped Robots. arXiv:1804.10332 [cs] (May 2018). arXiv: 1804.10332.Google ScholarGoogle Scholar
  63. Yuval Tassa, Tom Erez, and Emanuel Todorov. 2012. Synthesis and stabilization of complex behaviors through online trajectory optimization. In Intelligent Robots and Systems (IROS), 2012 IEEE/RSJ International Conference on. 4906--4913.Google ScholarGoogle ScholarCross RefCross Ref
  64. Steve Tonneau, Pierre Fernbach, Andrea Del Prete, Julien Pettré, and Nicolas Mansard. 2018. 2PAC: Two-Point Attractors for Center Of Mass Trajectories in Multi-Contact Scenarios. ACM Transactions on Graphics (TOG) 37, 5 (2018), 176.Google ScholarGoogle ScholarDigital LibraryDigital Library
  65. Yao-Yang Tsai, Wen-Chieh Lin, Kuangyou B Cheng, Jehee Lee, and Tong-Yee Lee. 2010. Real-time physics-based 3d biped character animation using an inverted pendulum model. IEEE Trans. Visualization and Computer Graphics 16, 2 (2010), 325--337.Google ScholarGoogle ScholarDigital LibraryDigital Library
  66. Pierre-Brice Wieber, Russ Tedrake, and Scott Kuindersma. 2016. Modeling and control of legged robots. In Springer handbook of robotics. Springer, 1203--1234.Google ScholarGoogle Scholar
  67. Alexander W Winkler, C Dario Bellicoso, Marco Hutter, and Jonas Buchli. 2018. Gait and trajectory optimization for legged systems through phase-based end-effector parameterization. IEEE Robotics and Automation Letters 3, 3 (2018), 1560--1567.Google ScholarGoogle ScholarCross RefCross Ref
  68. Zhaoming Xie, Patrick Clary, Jeremy Dao, Pedro Morais, Jonathan Hurst, and Michiel van de Panne. 2019. Iterative Reinforcement Learning Based Design of Dynamic Locomotion Skills for Cassie. arXiv:1903.09537 [cs] (March 2019). arXiv: 1903.09537.Google ScholarGoogle Scholar
  69. Yuting Ye and C Karen Liu. 2010. Optimal feedback control for character animation using an abstract model. ACM Transactions on Graphics 29, 4 (2010), 74.Google ScholarGoogle ScholarDigital LibraryDigital Library
  70. KangKang Yin, Kevin Loken, and Michiel van de Panne. 2007. SIMBICON: simple biped locomotion control. ACM Transactions on Graphics 26, 3 (2007), 105.Google ScholarGoogle ScholarDigital LibraryDigital Library
  71. Wenhao Yu, Greg Turk, and C Karen Liu. 2018. Learning symmetric and low-energy locomotion. ACM Transactions on Graphics (TOG) 37, 4 (2018), 144.Google ScholarGoogle ScholarDigital LibraryDigital Library
  72. He Zhang, Sebastian Starke, Taku Komura, and Jun Saito. 2018. Mode-adaptive neural networks for quadruped motion control. ACM Transactions on Graphics (TOG) 37, 4 (2018), 145.Google ScholarGoogle ScholarDigital LibraryDigital Library
  73. Tianhao Zhang, Gregory Kahn, Sergey Levine, and Pieter Abbeel. 2016. Learning deep control policies for autonomous aerial vehicles with mpc-guided policy search. In 2016 IEEE international conference on robotics and automation (ICRA). 528--535.Google ScholarGoogle ScholarDigital LibraryDigital Library
  74. Daniel Zimmermann, Stelian Coros, Yuting Ye, Robert W Sumner, and Markus Gross. 2015. Hierarchical planning and control for complex motor tasks. In Proceedings of the 14th ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 73--81.Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Fast and flexible multilegged locomotion using learned centroidal dynamics

      Recommendations

      Comments

      Login options

      Check if you have access through your login credentials or your institution to get full access on this article.

      Sign in

      Full Access

      • Published in

        cover image ACM Transactions on Graphics
        ACM Transactions on Graphics  Volume 39, Issue 4
        August 2020
        1732 pages
        ISSN:0730-0301
        EISSN:1557-7368
        DOI:10.1145/3386569
        Issue’s Table of Contents

        Copyright © 2020 ACM

        Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

        Publisher

        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 12 August 2020
        Published in tog Volume 39, Issue 4

        Permissions

        Request permissions about this article.

        Request Permissions

        Check for updates

        Qualifiers

        • research-article

      PDF Format

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader