research-article

Locomotion skills for simulated quadrupeds

Authors:

Andrej Karpathy,

Lionel Reveret,

Michiel van de PanneAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 30, Issue 4

Article No.: 59, Pages 1 - 12

https://doi.org/10.1145/2010324.1964954

Published: 25 July 2011 Publication History

Abstract

We develop an integrated set of gaits and skills for a physics-based simulation of a quadruped. The motion repertoire for our simulated dog includes walk, trot, pace, canter, transverse gallop, rotary gallop, leaps capable of jumping on-and-off platforms and over obstacles, sitting, lying down, standing up, and getting up from a fall. The controllers use a representation based on gait graphs, a dual leg frame model, a flexible spine model, and the extensive use of internal virtual forces applied via the Jacobian transpose. Optimizations are applied to these control abstractions in order to achieve robust gaits and leaps with desired motion styles. The resulting gaits are evaluated for robustness with respect to push disturbances and the traversal of variable terrain. The simulated motions are also compared to motion data captured from a filmed dog.

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References

[1]

Abourachid, A., Herbin, M., Hackert, R., Maes, L., and Martin, V. 2007. Experimental study of coordination patterns during unsteady locomotion in mammals. J. Experimental Biology 210, 366--372.

[2]

Alexander, R. 1984. The gaits of bipedal and quadrupedal animals. The International Journal of Robotics Research 3, 2, 49--59.

[3]

Blumberg, B., and Galyean, T. 1995. Multi-level direction of autonomous creatures for real-time virtual environments. In Proc. ACM SIGGRAPH, ACM, 47--54.

[4]

Buehler, M., Playter, R., and Raibert, M. 2005. Robots step outside. In Int. Symp. Adaptive Motion of Animals and Machines (AMAM), Ilmenau, Germany, 1--4.

[5]

Coros, S., Beaudoin, P., and van de Panne, M. 2010. Generalized biped walking control. ACM Transctions on Graphics 29, 4, Article 130.

[6]

de Lasa, M., Mordatch, I., and Hertzmann, A. 2010. Feature-based locomotion controllers. ACM Transactions on Graphics (TOG) 29, 4, Article 131.

Digital Library

[7]

Faloutsos, P., van de Panne, M., and Terzopoulos, D. 2001. Composable controllers for physics-based character animation. In Proc. ACM SIGGRAPH, 251--260.

[8]

Furusho, J., Sano, A., Sakaguchi, M., and Koizumi, E. 2002. Realization of bounce gait in a quadruped robot with articular-joint-type legs. In Proc. IEEE Intl Conf on Robotics and Automation, vol. 1, 697--702.

[9]

Gillette, R. L., and Angle, T. C. 2008. Recent developments in canine locomotor analysis: A review. The Veterinary Journal 178, 165--176.

[10]

Girard, M., and Maciejewski, A. 1985. Computational modeling for the computer animation of legged figures. ACM SIGGRAPH Computer Graphics 19, 3, 263--270.

Digital Library

[11]

Hecker, C., Raabe, B., Enslow, R. W., DeWeese, J., Maynard, J., and van Prooijen, K. 2008. Real-time motion retargeting to highly varied user-created morphologies. ACM Trans. on Graphics (Proc. SIGGRAPH) 27, 3.

Digital Library

[12]

Herr, H., and McMahon, T. 2001. A galloping horse model. Intl Journal of Robotics Research 20, 1, 26.

[13]

Hodgins, J., Wooten, W., Brogan, D., and O'Brien, J. 1995. Animating human athletics. In Proc. ACM SIGGRAPH, 71--78.

[14]

Kimura, H., Fukuoka, Y., and Cohen, A. 2007. Adaptive dynamic walking of a quadruped robot on natural ground based on biological concepts. Intl Journal of Robotics Research 26, 5, 475.

Digital Library

[15]

Kohl, N., and Stone, P. 2004. Policy gradient reinforcement learning for fast quadrupedal locomotion. In Proc. IEEE Intl Conf. on Robotics and Automation, vol. 3, 2619--2624.

[16]

Kokkevis, E., Metaxas, D., and Badler, N. 1995. Autonomous Animation and Control of Four-Legged Animals. In Proc. Graphics Interface, 10--17.

[17]

Kolter, J., Rodgers, M., and Ng, A. 2008. A control architecture for quadruped locomotion over rough terrain. In Proc. IEEE Intl Conf. on Robotics and Automation, 811--818.

[18]

Krasny, D. P., and Orin, D. E. 2004. Generating high-speed dynamic running gaits in a quadruped robot using an evolutionary search. IEEE Trans. on Systems, Man and Cybernetics 34, 4, 1685--1696.

Digital Library

[19]

Krasny, D., and Orin, D. 2006. A 3D galloping quadruped robot. Climbing and Walking Robots, 467--474.

[20]

Kry, P. G., Reveret, L., Faure, F., and Cani, M.-P. 2009. Modal locomotion: Animating virtual characters with natural vibrations. Computer Graphics Forum 28, 2.

[21]

Laszlo, J. F., van de Panne, M., and Fiume, E. 1996. Limit cycle control and its application to the animation of balancing and walking. In Proc. ACM SIGGRAPH, 155--162.

[22]

Lee, Y., Kim, S., and Lee, J. 2010. Data-driven biped control. ACM Transactions on Graphics (TOG) 29, 4, Article 129.

Digital Library

[23]

Marhefka, D., Orin, D., Schmiedeler, J., and Waldron, K. 2003. Intelligent control of quadruped gallops. IEEE/ASME Trans. on Mechatronics 8, 4, 446--456.

[24]

Muico, U., Lee, Y., Popović, J., and Popović, Z. 2009. Contact-aware nonlinear control of dynamic characters. ACM Transactions on Graphics (TOG) 28, 3, 1--9.

Digital Library

[25]

Paul, R. 1981. Robot manipulators: mathematics, programming, and control: the computer control of robot manipulators. The MIT Press.

[26]

Playter, R., Buehler, M., and Raibert, M. 2006. BigDog. In Proc. of SPIE, vol. 6230, 62302O.

[27]

Poulakakis, I., Smith, J., and Buehler, M. 2005. Modeling and experiments of untethered quadrupedal running with a bounding gait: The Scout II robot. Intl Journal of Robotics Research 24, 4, 239.

Digital Library

[28]

Pratt, J., Chew, C., Torres, A., Dilworth, P., and Pratt, G. 2001. Virtual model control: An intuitive approach for bipedal locomotion. Int'l J. Robotics Research 20, 2, 129.

[29]

Raibert, M. H., and Hodgins, J. K. 1991. Animation of dynamic legged locomotion. In Proc. ACM SIGGRAPH, 349--358.

[30]

Raibert, M. H. 1986. Legged Robots That Balance. MIT Press.

[31]

Ringrose, R. 1996. Self-stabilizing running. PhD thesis, MIT.

[32]

Skrba, L., Reveret, L., Hétroy, F., Cani, M., and O'Sullivan, C. 2008. Quadruped animation. Eurographics 2008-State of the Art Reports, 1--17.

[33]

Sok, K. W., Kim, M., and Lee, J. 2007. Simulating biped behaviors from human motion data. ACM Trans. on Graphics (Proc. SIGGRAPH) 26, 3, Article 107.

Digital Library

[34]

Sunada, C., Argaez, D., Dubowsky, S., and Mavroidis, C. 1994. A coordinated jacobian transpose control for mobile multi-limbed robotic systems. In Proc. IEEE Int'l Conf. on Robotics and Automation, 1910--1915.

[35]

Torkos, N., and van de Panne, M. 1998. Footprint-based quadruped motion synthesis. In Proc. Graphics Interface, 151--160.

[36]

TreT, 2011. Tret - parkour dog from ukraine, https://www.youtube.com/watch?v=pxelh_vm0uc. Accessed on January 9, 2011.

[37]

Tsujita, K., Tsuchiya, K., and Onat, A. 2001. Adaptive gait pattern control of a quadruped locomotion robot. In Proc. IEEE Intelligent Robots and Systems, vol. 4, 2318--2325.

[38]

van de Panne, M. 1996. Parameterized gait synthesis. IEEE Computer Graphics and Applications 16, 2 (March), 40--69.

Digital Library

[39]

Van Den Bogert, A., Schamhardt, H., and Crowe, A. 1989. Simulation of quadrupedal locomotion using a rigid body model. Journal of biomechanics 22, 1, 33--41.

[40]

Walter, R. M., and Carrier, D. R. 2007. Ground forces applied by galloping dogs. The Journal of Experimental Biology 210, 208--216.

[41]

Wampler, K., and Popović, Z. 2009. Optimal gait and form for animal locomotion. ACM Transactions on Graphics (TOG) 28, 3, 1--8.

Digital Library

[42]

Wong, H., and Orin, D. 1995. Control of a quadruped standing jump over irregular terrain obstacles. Autonomous Robots 1, 2, 111--129.

[43]

Wu, J., and Popović, Z. 2010. Terrain-adaptive bipedal locomotion control. ACM Transactions on Graphics (TOG) 29, 4, Article 72.

Digital Library

[44]

Ye, Y., and Liu, C. 2010. Optimal feedback control for character animation using an abstract model. ACM Transactions on Graphics (TOG) 29, 4, Article 74.

Digital Library

[45]

Yin, K., Loken, K., and van de Panne, M. 2007. SIMBICON: Simple biped locomotion control. ACM Trans. on Graphics (Proc. SIGGRAPH) 26, 3, Article 105.

Digital Library

[46]

Zucker, M., Bagnell, J., Atkeson, C., and Kuffner, J. 2010. An optimization approach to rough terrain locomotion. In Proc. IEEE Intl Conf. on Robotics and Automation, 3589--3595.

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Index Terms

Locomotion skills for simulated quadrupeds
1. Computing methodologies
  1. Computer graphics
    1. Animation
    2. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 30, Issue 4

July 2011

829 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2010324

Issue’s Table of Contents

Copyright © 2011 ACM.

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Publication History

Published: 25 July 2011

Published in TOG Volume 30, Issue 4

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Cited By

Mittal MRudin NKlemm VAllshire AHutter M(2024)Symmetry Considerations for Learning Task Symmetric Robot Policies2024 IEEE International Conference on Robotics and Automation (ICRA)10.1109/ICRA57147.2024.10611493(7433-7439)Online publication date: 13-May-2024
https://doi.org/10.1109/ICRA57147.2024.10611493
Grandia RFarshidian FKnoop ESchumacher CHutter MBächer M(2023)DOC: Differentiable Optimal Control for Retargeting Motions onto Legged RobotsACM Transactions on Graphics10.1145/359245442:4(1-14)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592454
Han SPark JChoi S(2023)Generating Haptic Motion Effects for Multiple Articulated Bodies for Improved 4D Experiences: A Camera Space ApproachProceedings of the 2023 CHI Conference on Human Factors in Computing Systems10.1145/3544548.3580727(1-17)Online publication date: 19-Apr-2023
https://dl.acm.org/doi/10.1145/3544548.3580727
Bing ZRohregger AWalter FHuang YLucas PMorin FHuang KKnoll A(2023)Lateral flexion of a compliant spine improves motor performance in a bioinspired mouse robotScience Robotics10.1126/scirobotics.adg71658:85Online publication date: 6-Dec-2023
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Li XGao WLi XZhang S(2023)Terrain-guided Symmetric Locomotion Generation for Quadrupedal Robots via Reinforcement Learning2023 IEEE International Conference on Robotics and Biomimetics (ROBIO)10.1109/ROBIO58561.2023.10354605(1-6)Online publication date: 4-Dec-2023
https://doi.org/10.1109/ROBIO58561.2023.10354605
Lin ZZhou SPan ZLiu SWang R(2023)Exploring the Effect of Pitching and Rolling Spine Angle for a Galloping Quadruped Robot via Trajectory Optimization2023 6th International Conference on Robotics, Control and Automation Engineering (RCAE)10.1109/RCAE59706.2023.10398751(56-62)Online publication date: 3-Nov-2023
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Zhao YWang JCao GYuan YYao XQi L(2023)Intelligent Control of Multilegged Robot Smooth Motion: A ReviewIEEE Access10.1109/ACCESS.2023.330499211(86645-86685)Online publication date: 2023
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