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Control Policies for a Large Region of Attraction for Dynamically Balancing Legged Robots: A Sampling-Based Approach

Published online by Cambridge University Press:  05 May 2020

Pranav A. Bhounsule Open the ORCID record for Pranav A. Bhounsule [Opens in a new window] ,
Ali Zamani ,
Jeremy Krause ,
Steven Farra  and
Jason Pusey
Pranav A. Bhounsule*
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 W Taylor St, Chicago, IL60607, USA. E-mails: [email protected], [email protected], [email protected]
Ali Zamani
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 W Taylor St, Chicago, IL60607, USA. E-mails: [email protected], [email protected], [email protected]
Jeremy Krause
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 W Taylor St, Chicago, IL60607, USA. E-mails: [email protected], [email protected], [email protected]
Steven Farra
Affiliation:
Department of Mechanical Engineering, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX78249, USA. E-mail: [email protected]
Jason Pusey
Affiliation:
Vehicle Technology Directorate, U.S. Army Research Laboratory, Aberdeen Proving Grounds, Aberdeen, MD21001, USA. E-mail: [email protected]
*
*Corresponding author. E-mail: [email protected]
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Summary

The popular approach of assuming a control policy and then finding the largest region of attraction (ROA) (e.g., sum-of-squares optimization) may lead to conservative estimates of the ROA, especially for highly nonlinear systems. We present a sampling-based approach that starts by assuming an ROA and then finds the necessary control policy by performing trajectory optimization on sampled initial conditions. Our method works with black-box models, produces a relatively large ROA, and ensures exponential convergence of the initial conditions to the periodic motion. We demonstrate the approach on a model of hopping and include extensive verification and robustness checks.

Keywords

Region of attractionOrbital Lyapunov functionPoincaré mapPeriodic motionDynamically balancing legged robotsDeep learning neural nets
Type
Articles
Information
Robotica , Volume 39 , Issue 1 , January 2021 , pp. 107 - 122
Copyright
Copyright © Cambridge University Press 2020

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References

Hobbelen, D. and Wisse, M., “Limit Cycle Walking,” In: Humanoid Robots Human-Like Machines (Hackel, M., ed.) (IntechOpen, 2007) pp. 277–294.Google Scholar
Tedrake, R., “LQR-Trees: Feedback Motion Planning on Sparse Randomized Trees,” Papers of the Fifth Annual Robotics: Science and Systems Conference, June 28-July 1, 2009, University of Washington, Seattle, USA.10.15607/RSS.2009.V.003CrossRefGoogle Scholar
Prajna, S., Papachristodoulou, A. and Parrilo, P. A., “Introducing Sostools: A General Purpose Sum of Squares Programming Solver,” Proceedings of the the 41st IEEE Conference on Decision and Control (2002) pp. 741–746.Google Scholar
Bhounsule, P. A., Zamani, A. and Pusey, J., “Switching Between Limit Cycles in a Model of Running Using Exponentially Stabilizing Discrete Control Lyapunov Function,” Proceedings of the Annual American Control Conference (2018) pp. 3714–3719.Google Scholar
Zamani, A., Galloway, J. D. II and Bhounsule, P. A., “Feedback Motion Planning of Legged Robots by Composing Orbital Lyapunov Functions Using Rapidly-Exploring Random Trees,” Proceedings of the IEEE International Conference on Robotics and Automation (IEEE, 2019).CrossRefGoogle Scholar
McGeer, T., “Passive dynamic walking,” Int. J. Robot. Res. 9(2), 62–82 (1990).CrossRefGoogle Scholar
McGeer, T., “Passive Dynamic Biped Catalogue,” Proceedings of the 2nd International Symposium on Experimental Robotics (1991) pp. 465–490.Google Scholar
Garcia, M., Chatterjee, A., Ruina, A. and Coleman, M., “The simplest walking model: stability, complexity, and scaling,” ASME J. Biomech. Eng. 120(2), 281–288 (1998).CrossRefGoogle Scholar
Strogatz, S., Nonlinear Dynamics and Chaos (Addison-Wesley Reading, Boston, MA, 1994).Google Scholar
Schwab, A. and Wisse, M., “Basin of Attraction of the Simplest Walking Model,” Proceedings of the ASME Design Engineering Technical Conference (2001) pp. 531–539.Google Scholar
Hsu, C. S., Cell-to-Cell Mapping: A Method of Global Analysis for Nonlinear Systems (Springer-Verlag, New York, NY, 1987).CrossRefGoogle Scholar
Heim, S. and Spröwitz, A., “Beyond Basins of Attraction: Evaluating Robustness of Natural Dynamics,” arXiv preprint arXiv:1806.08081 (2018).Google Scholar
Wieber, P.-B., “Viability and Predictive Control for Safe Locomotion,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (2008) pp. 1103–1108.Google Scholar
Pratt, J., Carff, J., Drakunov, S. and Goswami, A., “Capture Point: A Step Toward Humanoid Push Recovery,” Proceedings of the 6th IEEE-RAS International Conference on Humanoid Robots (2006) pp. 200–207.Google Scholar
Pratt, J., Koolen, T., Boer, T. D., Rebula, J., Cotton, S., Carff, J., Johnson, M. and Neuhaus, P., “Capturability-based analysis and control of legged locomotion. Part 2: Application to M2V2, a lower-body humanoid,” Int. J. Robot. Res. 31(10), 1117–1133 (2012).CrossRefGoogle Scholar
Zaytsev, P., Wolfslag, W. and Ruina, A., “The boundaries of walking stability: Viability and controllability of simple models,” IEEE Trans. Robot. 34(2), 336–352 (2018).CrossRefGoogle Scholar
Koditschek, D. and Robert, J., “Templates and anchors: Neuromechanical hypotheses of legged locomotion on land,” J. Exp. Biol. 202(23), 3325–3332 (1999).Google Scholar
Whitman, E. C., Coordination of Multiple Dynamic Programming Policies for Control of BipedalWalking Ph.D. Thesis (Carnegie Mellon University, 2013).Google Scholar
Mandersloot, T., Wisse, M. and Atkeson, C. G., “Controlling Velocity in Bipedal Walking: A Dynamic Programming Approach,” Proceedings of the 6th IEEE-RAS International Conference on Humanoid Robots (2006) pp. 124–130.Google Scholar
Raibert, M. H. and Wimberly, F. C., “Tabular control of balance in a dynamic legged system,” IEEE Trans. Syst., Man, Cybern. 1(2), 334–339 (1984).CrossRefGoogle Scholar
Da, X., Hartley, R. and Grizzle, J. W., “Supervised Learning for Stabilizing Underactuated Bipedal Robot Locomotion, with Outdoor Experiments on the Wave Field,” Proceedings of the IEEE International Conference on Robotics and Automation (2017) pp. 3476–3483.Google Scholar
Manchester, I. R., Tobenkin, M. M., Levashov, M. and Tedrake, R., “Regions of Attraction for Hybrid Limit Cycles of Walking Robots,” Proceedings of the 18th World Congress The International Federation of Automatic Control (2011) pp. 5801–5806.Google Scholar
Bhounsule, P. A. and Zamani, A., “A discrete control lyapunov function for exponential orbital stabilization of the simplest walker,” J. Mech. Robot. 9(5), 051011–8 (2017).CrossRefGoogle Scholar
Betts, J., “Survey of numerical methods for trajectory optimization,” J. Guid. Control Dyn. 21(2), 193–207 (1198).CrossRefGoogle Scholar
Srinivasan, M., Why Walk and Run: Energetic Costs and Energetic Optimality in Simple Mechanics-based Models of a Bipedal Animal Ph.D. Thesis (Cornell University, 2006).Google Scholar
Gill, P., Murray, W. and Saunders, M., “SNOPT: An SQP algorithm for large-scale constrained optimization,” SIAM J. Optim. 12(4), 979–1006 (2002).10.1137/S1052623499350013CrossRefGoogle Scholar
Zamani, A. and Bhounsule, P., “Control synergies for rapid stabilization and enlarged region of attraction for a model of hopping,” Biomimetics 3(3), 1–13 (2018).CrossRefGoogle Scholar
Grizzle, J., Abba, G. and Plestan, F., “Asymptotically stable walking for biped robots: Analysis via systems with impulse effects,” IEEE Trans. Autom. Control 46(1), 51–64 (2001).CrossRefGoogle Scholar
Zaytsev, P., Hasaneini, S. J., and Ruina, A., “Two Steps is Enough: No Need to Plan Far Ahead for Walking Balance,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) (IEEE, 2015) pp. 6295–6300.CrossRefGoogle Scholar