“Terrain-adaptive bipedal locomotion control” by Wu and Popovic

  • ©Jia-chi Wu and Zoran Popovic




    Terrain-adaptive bipedal locomotion control



    We describe a framework for the automatic synthesis of biped locomotion controllers that adapt to uneven terrain at run-time. The framework consists of two components: a per-footstep end-effector path planner and a per-timestep generalized-force solver. At the start of each footstep, the planner performs short-term planning in the space of end-effector trajectories. These trajectories adapt to the interactive task goals and the features of the surrounding uneven terrain at run-time. We solve for the parameters of the planner for different tasks in offline optimizations. Using the per-footstep plan, the generalized-force solver takes ground contacts into consideration and solves a quadratic program at each simulation timestep to obtain joint torques that drive the biped. We demonstrate the capabilities of the controllers in complex navigation tasks where they perform gradual or sharp turns and transition between moving forwards, backwards, and sideways on uneven terrain (including hurdles and stairs) according to the interactive task goals. We also show that the resulting controllers are capable of handling morphology changes to the character.


    1. Abe, Y., da Silva, M., and Popović, J. 2007. Multiobjective control with frictional contacts. In SCA ’07: Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation, Eurographics Association, 249–258. Google ScholarDigital Library
    2. Abend, W., Bizzi, E., and Morasso, P. 1982. Human Arm Trajectory Formation. Brain 105, 2, 331–348.Google ScholarCross Ref
    3. Atkeson, C., and Morimoto, J. 2002. Nonparametric representation of policies and value functions: A trajectory-based approach. In Neural Information Processing Systems 2002.Google Scholar
    4. Bernstein, N. 1967. The Co-ordination and Regulation of Movements. Oxford: Pergamon Press.Google Scholar
    5. Bullock, D., and Grossberg, S. 1988. Neural dynamics of planned arm movements: Emergent invariants and speed-accuracy properties during trajectory formation. Psychological Review 95, 1, 49–90.Google ScholarCross Ref
    6. Carey, T. S., and Crompton, R. H. 2005. The metabolic costs of ‘bent-hip, bent-knee’ walking in humans. Journal of Human Evolution 48, 1, 25–44.Google ScholarCross Ref
    7. Chestnutt, J., Kuffner, J., Nishiwaki, K., and Kagami, S. 2003. Planning biped navigation strategies in complex environments. In Proceedings of the 2003 International Conference on Humanoid Robots.Google Scholar
    8. Coros, S., Beaudoin, P., Yin, K. K., and van de Pann, M. 2008. Synthesis of constrained walking skills. ACM Transactions on Graphics 27, 5 (Dec.), 113:1–113:9. Google ScholarDigital Library
    9. Coros, S., Beaudoin, P., and van de Panne, M. 2009. Robust task-based control policies for physics-based characters. ACM Transactions on Graphics 28, 5 (Dec.), 170:1–170:9. Google ScholarDigital Library
    10. Craig, J. J. 1989. Introduction to Robotics: Mechanics and Control. Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA. Google ScholarDigital Library
    11. da Silva, M., Abe, Y., and Popović, J. 2008. Simulation of human motion data using short-horizon model-predictive control. Computer Graphics Forum 27, 2, 371–380.Google ScholarCross Ref
    12. Farley, C. T., and Gonzlez, O. 1996. Leg stiffness and stride frequency in human running. Journal of Biomechanics 29, 2, 181–186.Google ScholarCross Ref
    13. Hansen, N. 2006. The CMA evolution strategy: a comparing review. In Towards a new evolutionary computation. Advances on estimation of distribution algorithms, J. Lozano, P. Larranaga, I. Inza, and E. Bengoetxea, Eds. Springer, 75–102.Google Scholar
    14. Hauser, K., Bretl, T., Latombe, J.-C., Harada, K., and Wilcox, B. 2008. Motion Planning for Legged Robots on Varied Terrain. The International Journal of Robotics Research 27, 11–12, 1325–1349.Google ScholarCross Ref
    15. Hodgins, J. K., Wooten, W. L., Brogan, D. C., and O’Brien, J. F. 1995. Animating human athletics. In Proceedings of SIGGRAPH 95, ACM, Computer Graphics Proceedings, Annual Conference Series, 71–78. Google ScholarDigital Library
    16. Khatib, O. 1987. A unified approach for motion and force control of robot manipulators: The operational space formulation. Robotics and Automation, IEEE Journal of 3, 1 (Feb.), 43–53.Google Scholar
    17. Kuffner, J. J., J., Nishiwaki, K., Kagami, S., Inaba, M., and Inoue, H. 2001. Footstep planning among obstacles for biped robots. In Intelligent Robots and Systems, 2001. Proceedings. 2001 IEEE/RSJ International Conference on, vol. 1, 500–505.Google Scholar
    18. Laszlo, J., van de Panne, M., and Fiume, E. 1996. Limit cycle control and its application to the animation of balancing and walking. In Proceedings of SIGGRAPH 96, ACM, Computer Graphics Proceedings, Annual Conference Series, 155–162. Google ScholarDigital Library
    19. Liu, C. K., Hertzmann, A., and Popović, Z. 2005. Learning physics-based motion style with nonlinear inverse optimization. ACM Transactions on Graphics 24, 3 (Jul.), 1071–1081. Google ScholarDigital Library
    20. Mosek ApS, 2009. The mosek optimization software version 6.0. http://www.mosek.com/.Google Scholar
    21. Muico, U., Lee, Y., Popović, J., and Popović, Z. 2009. Contact-aware nonlinear control of dynamic characters. ACM Transactions on Graphics 28, 3 (Aug.), 81:1–81:9. Google ScholarDigital Library
    22. Nocedal, J., and Wright, S. J. 2006. Numerical Optimization, 2nd ed. Springer.Google Scholar
    23. NVIDIA Corporation, 2008. NVIDIA PhysX SDK version 2.8.1. http://developer.nvidia.com/object/physx.html.Google Scholar
    24. Pratt, J., Dilworth, P., and Pratt, G. 1997. Virtual model control of a bipedal walking robot. In IEEE Conference on Robotics and Automation, 193–198.Google Scholar
    25. Raibert, M. H., and Hodgins, J. K. 1991. Animation of dynamic legged locomotion. In Computer Graphics (Proceedings SIGGRAPH 91), ACM, 349–358. Google ScholarDigital Library
    26. Rose, C., Guenter, B., Bodenheimer, B., and Cohen, M. F. 1996. Efficient generation of motion transitions using spacetime constraints. In Proceedings of SIGGRAPH 96, ACM, Computer Graphics Proceedings, Annual Conference Series, 147–154. Google ScholarDigital Library
    27. Safonova, A., Hodgins, J. K., and Pollard, N. S. 2004. Synthesizing physically realistic human motion in low-dimensional, behavior-specific spaces. ACM Transactions on Graphics 23, 3 (Aug.), 514–521. Google ScholarDigital Library
    28. Stewart, A. J., and Cremer, J. F. 1992. Animation of 3d human locomotion: climbing stairs and descending stairs. In Eurographics Workshop on Animation and Simulation, 152–168.Google Scholar
    29. Sun, H. C., and Metaxas, D. N. 2001. Automating gait generation. In Proceedings of SIGGRAPH 2001, ACM, Computer Graphics Proceedings, Annual Conference Series, 261–270. Google ScholarDigital Library
    30. Todorov, E. 2004. Optimality principles in sensorimotor control. Nature Neuroscience 7, 9 (Sep.), 907–915.Google ScholarCross Ref
    31. van de Panne, M., and Lamouret, A. 1995. Guided optimization for balanced locomotion. In 6th Eurographics Workshop on Animation and Simulation, Computer Animation and Simulation, September, 1995, Springer, Maastricht, Pays-Bas, D. Terzopoulos and D. Thalmann, Eds., Eurographics, 165–177.Google ScholarCross Ref
    32. van de Panne, M., Fiume, E., and Vranesic, Z. 1992. A controller for the dynamic walk of a biped across variable terrain. In Decision and Control, 1992., Proceedings of the 31st IEEE Conference on, 2668–2673 vol.3.Google Scholar
    33. Wampler, K., and Popović, Z. 2009. Optimal gait and form for animal locomotion. ACM Transactions on Graphics 28, 3 (Aug.), 60:1–60:8. Google ScholarDigital Library
    34. Wang, J. M., Fleet, D. J., and Hertzmann, A. 2009. Optimizing walking controllers. ACM Transactions on Graphics 28, 5 (Dec.), 168:1–168:8. Google ScholarDigital Library
    35. Yin, K., Loken, K., and van de Panne, M. 2007. SIMBICON: simple biped locomotion control. ACM Transactions on Graphics 26, 3 (Jul.), 105:1–105:10. Google ScholarDigital Library
    36. Yin, K., Coros, S., Beaudoin, P., and van de Panne, M. 2008. Continuation methods for adapting simulated skills. ACM Transactions on Graphics 27, 3 (Aug.), 81:1–81:7. Google ScholarDigital Library
    37. Zhang, L., Pan, J., and Manocha, D. 2009. Motion planning of human-like robots using constrained coordination. In Humanoid Robots, 2009. Humanoids 2009. 9th IEEE-RAS International Conference on, 188–195.Google Scholar

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