Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-25T12:03:49.280Z Has data issue: false hasContentIssue false

Parametric-based dynamic synthesis of 3D-gait

Published online by Cambridge University Press:  07 July 2009

Guy Bessonnet*
Affiliation:
Laboratoire de Mécanique des Solides, CNRS-UMR6610, Université de Poitiers, SP2MI, Bd. M. & P. Curie, BP 30179, 86962 Futuroscope Chasseneuil cedex, France
Jérôme Marot
Affiliation:
Laboratoire de Mécanique des Solides, CNRS-UMR6610, Université de Poitiers, SP2MI, Bd. M. & P. Curie, BP 30179, 86962 Futuroscope Chasseneuil cedex, France
Pascal Seguin
Affiliation:
Laboratoire de Mécanique des Solides, CNRS-UMR6610, Université de Poitiers, SP2MI, Bd. M. & P. Curie, BP 30179, 86962 Futuroscope Chasseneuil cedex, France
Philippe Sardain
Affiliation:
Laboratoire de Mécanique des Solides, CNRS-UMR6610, Université de Poitiers, SP2MI, Bd. M. & P. Curie, BP 30179, 86962 Futuroscope Chasseneuil cedex, France
*
*Corresponding author. E-mail: [email protected]

Summary

This paper describes a dynamic synthesis method for generating optimal walking patterns of biped robots having a human-like locomotion system. The generating principle of gait is based on the minimisation of driving torques. A parametric optimisation technique is used to solve the underlying optimal control problem. Special attention is devoted to foot-ground interactions in order to ensure a steady dynamic balance of the biped. Transition states between step sub-phases are fully optimised together with step length and sub-phase lengths with respect to a given walking velocity. The data needed to generate purely cyclic steps can be reduced to the forward velocity.

Type
Article
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Collins, S. H., Wisse, M. and Ruina, A., “A three-dimensional passive-dynamic walking robot with two legs and knees,” Int. J. Robot. Res. 20, 607615(2001).CrossRefGoogle Scholar
2.Collins, S. H. and Ruina, A., “A Bipedal Walking Robot with Efficient and Human-Like Gait,” Proceedings of the IEEE International Conference on Robotics and Automation, Barcelona, Spain (2005) pp. 19831988.Google Scholar
3.Collins, S. H., Ruina, A., Wisse, M. and Tedrake, R., “Efficient bipedal robots based on passive-dynamic walkers,” Science 307, 10821085(2005).CrossRefGoogle ScholarPubMed
4.McGeer, T., “Passive dynamic walking,” Int. J. Robot. Res. 9, 6282(1990).Google Scholar
5.McGeer, T., “Passive Walking with Knees,” Proceedings of IEEE International Conference on Robotics and Automation, Cincinnati, Ohio (1990) pp. 16401645.CrossRefGoogle Scholar
6.Goswami, A., Espiau, B. and Keramane, A., “Limit cycles in a passive compass gait biped and passivity-mimicking control laws,” J. Auton. Robots 4 (3), 273286(1997).CrossRefGoogle Scholar
7.Garcia, M., Chatterjee, A. and Ruina, A., “Speed, Efficiency, and Stability of Small-Slope 2-D Passive Dynamic Bipedal Walking,” Proceedings of IEEE International Conference on Robotics and Automation, Leuven, Belgium (1998) pp. 23512356.Google Scholar
8.Garcia, M., Ruina, A. and Coleman, M., “Some Results in Passive-Dynamic Walking,” Proceedings of the Euromech Conference on Biology and Technology of Walking”, Prague, Czech Republic (1998) pp. 268275.Google Scholar
9.Holm, J. K., Lee, D. and Spong, M. W., “Time-Scaling Trajectories of Passive-Dynamic Bipedal Robots,” Proceedings of IEEE International Conference on Robotics and Automation, Roma, Italy (2007) pp. 36033608.CrossRefGoogle Scholar
10.Wisse, M., Essentials of dynamic walking; analysis and design of two-legged robots Ph. D. Thesis (Delf, The Netherlands: Technische Universiteit, 2004).Google Scholar
11.Collins, S. H. and Ruina, A., “A Bipedal Walking Robot with Efficient and Human-Like Gait,” Proceedings of IEEE International Conference on Robotics and Automation, Barcelona, Spain (2005) pp. 19831988.Google Scholar
12.Leboeuf, F., Bessonnet, G., Seguin, P. and Lacouture, P., “Energetic versus sthenic optimality criteria for gymnastic movement synthesisMultibody Syst. Dyn. 16, 213236(2006).CrossRefGoogle Scholar
13.Gienger, M., Löffler, K. and Pfeiffer, F., “A Biped Robot that Jogs,” Proceedings of IEEE International Conference on Robotics and Automation, San Francisco, CA (2000) pp. 33343339.Google Scholar
14.Hirose, M., Haikawa, Y., Takenaka, T. and Hirai, K., “Development of Honda Humanoid Robot ASIMO,” Proceedings of IEEE/RSJ International Conference on Intelligent Robotic and Systems (Seoul, South Korea, 2001).Google Scholar
15.Yokoi, K., Kanehiro, F., Kaneko, K., Kajita, S., Fujiwara, K. and Hirukawa, H., “Experimental Study of Humanoid Robot HRP-1S,” Int. J. Robot. Res. 23, 351362(2004).Google Scholar
16.Ogura, Y., Aikawa, H., Shimomura, K., Kondo, H., Morishima, A., Lim, H. and Takanishi, A., “Development of a New Humanoid Robot WABIAN-2,” Proceedings of IEEE International Conference on Robotics and Automation, Orlando, Florida (2006) pp. 7681.Google Scholar
17.Akashi, K., Kaneko, K., Kanehira, N., Ota, S., Miyamori, G., Hirata, M., Kajita, S. and Kanehiro, K., “Development of Humanoid Robot HRP-3P” Proceedings of the IEEE-RAS International Conference on Humanoid Robots, Tsukuba, Japan (2005) pp. 5055.Google Scholar
18.Vukobratovic, M. and Stepanenko, J., “On the stability of anthropomorphic systems,” Math. Biosci. 15 (1), 137(1972).CrossRefGoogle Scholar
19.Vukobratovic, M., Borovac, B., Surla, D. and Stokic, D., Biped Locomotion: Dynamics, Stability, Control and Applications (Springer-Verlag, Berlin, 1990).CrossRefGoogle Scholar
20.Vukobratovic, M. and Borovac, B., “Zero-moment point – Thirty five years of its life,” Int. J. Human. Robot. 1 (1), 157173(2004).CrossRefGoogle Scholar
21.Hirai, K., Hirose, M., Haikawa, Y. and Takenaka, T., “The Development of Honda Humanoid Robot,” Proceedings of IEEE International Conference on Robotics and Automation, Leuven, Belgium (1998) pp. 160165.Google Scholar
22.Mitobe, K., Capi, G. and Nasu, Y., “Control of walking robots based on manipulation of the zero moment point,” Robotica 18, 651657(2000).CrossRefGoogle Scholar
23.Huang, Q., Yokoi, K., Kajita, S., Kaneko, K., Arai, H., Koyachi, N. and Tanie, K., “Planning walking patterns for a biped robot,” IEEE Trans. Robot. Autom. 17 (3), 280289(2001).Google Scholar
24.Pfeiffer, F., Löffler, K. and Gienger, M., “Humanoid robots,” Proceedings of the 6th International Conference on Climbing and Walking Robots (2003) pp. 505–516.Google Scholar
25.Löffler, K., Gienger, M. and Pfeiffer, F., “Sensors and control concept of walking «Johnnie»,” Int. J. Robot. Res. 22 (3–4), 229239(2003).Google Scholar
26.Kanehiro, F., Hirukawa, H. and Kajita, S., “Open HRP: Open architecture humanoid robotics platform,” Int. J. Robot. Res. 23 (2), 155165(2004).CrossRefGoogle Scholar
27.Pratt, J.-E. and Pratt, G.-A., “Exploiting Natural Dynamics in the Control of a 3D Bipedal Walking Simulation,” Proceedings of International Conference on Climbing and Walking Robots, Portsmouth, UK (1999) pp. 797807.Google Scholar
28.Kajita, S., Matsumoto, O. and Saigo, M., “Real-Time 3D Walking Pattern Generation for a Biped Robot with Telescopic Legs,” Proceedings of IEEE International Conference on Robotics and Automation (2001) pp. 2299–2306.Google Scholar
29.Chew, C.-M. and Pratt, G.-A., “Frontal Plane Algorithms for Dynamic Bipedal Walking,” Proceedings of IEEE International Conference on Robotics and Automation, Taipei, Taiwan (2003) pp. 45–50.Google Scholar
30.Hirukawa, H., Kanehiro, F., Kajita, S., Fujiwara, K., Yokoi, K., Kaneko, K. and Harada, K., “Experimental Evaluation of the Dynamics Simulation of Biped Walking of Humanoid Robots,” Proceedings of IEEE International Conference on Robotics and Automation, Taipei, Taiwan (2003) pp. 16401645.Google Scholar
31.Löffler, K., Gienger, M. and Pfeiffer, F., “Sensors and control concept of walking «Johnnie»,” Int. J. Robot. Res. 22 (3–4), 229239(2003).Google Scholar
32.Takanishi, A., Lim, H., Tsuda, M. and Kato, I., “Realization of Biped Dynamic Walking Stabilized by Trunk Motion on a Sagittally Uneven Surface,” Proceedings of IEEE International Workshop on Intelligent Robots and Systems, IROS'90, Ibaraki, Japan (1990) pp. 323330.Google Scholar
33.Li, Q., Takanishi, A. and Kato, I., “Learning Control for a Biped Walking Robot with a Trunk,” Proceedings IEEE/RSJ International Conference on Intelligent Robots and Systems, Yokohama, Japan (1993) pp. 17711777.Google Scholar
34.Chow, C. K. and Jacobson, D. H., “Studies of human locomotion via optimal programming,” Math. Biosci. 10, 239306(1971).CrossRefGoogle Scholar
35.Bessonnet, G., Chessé, S. and Sardain, P., “Optimal motion synthesis – Dynamic modelling and numerical solving aspects,” Multibody Syst. Dyn. 8, 257278(2002).CrossRefGoogle Scholar
36.Bessonnet, G., Chessé, S. and Sardain, P., “Optimal gait synthesis of a seven-Link planar biped,” Int. J. Robot. Res. 33, 10591073(2004).Google Scholar
37.Bessonnet, G. and Chessé, S., “Optimal dynamics of actuated kinematic chains – Part 2: Problem statements and computational aspects,” Eur. J. Mech. A/Solids 24, 472490(2005).CrossRefGoogle Scholar
38.Beletskii, V. V. and Chudinov, P. S., “Parametric optimisation in the problem of biped locomotion,” Mech. Solids 12 (1), 2535(1977).Google Scholar
39.Channon, P. H., Hopkins, S. H. and Pham, D. T., “Derivation of optimal walking motions for bipedal walking robot,” Robotica 10, 165172(1992).CrossRefGoogle Scholar
40.Chevallereau, C. and Aoustin, Y., “Optimal reference trajectories for walking and running of a biped robot,” Robotica 19, 557569(2001).CrossRefGoogle Scholar
41.Muraro, A., Chevallereau, C. and Aoustin, Y., “Optimal trajectories for a quadruped robot with trot, amble and curvet gaits for two energetic criteria,” Multibody Syst. Dyn. 9, 3962(2003).CrossRefGoogle Scholar
42.Saidouni, T. and Bessonnet, G., “Generating globally optimised sagittal gait cycles of a biped robot,” Robotica 21, 199210(2003).Google Scholar
43.Seguin, P. and Bessonnet, G., “Generating optimal walking cycles using spline-based state-parameterization,” Int. J. Human. Robot. 2, 4780(2005).Google Scholar
44.Bessonnet, G., Seguin, P. and Sardain, P., “A parametric optimization approach to walking pattern synthesis,” Int. J. Robot. Res. 24, 523536(2005).CrossRefGoogle Scholar
45.Denk, J. and Schmidt, G., “Synthesis of Walking Primitive Databases for Bipeds in 3D-Environments,” Proceedings of IEEE International Conference on Robotics and Automation, Taipei, Taiwan (2003) pp. 13431349.Google Scholar
46.Plestan, F., Grizzle, J. W., Vestervelt, E. R. and Abba, G., “Stable walking of a 7-DOF biped robot,” IEEE Trans. Robot. Autom. 19 (4), 653668(2003).CrossRefGoogle Scholar
47.Djoudi, D., Chevallereau, C. and Grizzle, J. W., “A Path-Following Approach to Stable Bipedal Walking and Zero Moment Point Regulation,” Proceedings of IEEE International Conference on Robotics and Automation, Roma, Italy (2007) pp. 35973602.Google Scholar
48.Hirukawa, H., Kanehiro, F., Kajita, S., Fujiwara, K., Yokoi, K., Kaneko, K. and Harada, K., “Experimental Evaluation of the Dynamics Simulation of Biped Walking of Humanoid Robots,” Proceedings of IEEE International Conference on Robotics and Automation, Taipei, Taiwan (2003) pp. 16401645.Google Scholar
49.Kajita, S., Kaneko, K., Morisawa, M., Nakaoka, S. and Hirukawa, H., “ZMP-Based Biped Running Enhanced by Toe Springs,” Proceedings of IEEE International Conference on Robotics and Automation, Taipei, Taiwan (2003) pp. 39633969.Google Scholar
50.Marot, J., Contribution à la synthèse dynamique optimale de la marche PhD Thesis (Poitiers, France: University of Poitiers, 2007) (in French).Google Scholar
51.Khalil, W. and Dombre, E., Modelling, Identification and Control of Robots (Butterworth Heinemann, Oxford, UK, 2004).Google Scholar
52.Blajer, W. and Schiehlen, W., “Walking without impacts as a motion/force control problem,” ASME J. Dyn. Syst. Meas. Control 114, 660665(1992).CrossRefGoogle Scholar
53.Chevallereau, C., Bessonnet, G., Abba, G. and Aoustin, Y., “Les robots marcheurs bipèdes – modélisation, conception, synthèse de la marche, commande,” Hermès, Paris (2007).Google Scholar
54.Miossec, S. and Aoustin, Y., “A Simplified Stability Study for a Biped Walk with Underactuared and Overactuated Phases,” Int. J. Robot. Res. 24 (7), 537551(2005).Google Scholar
55.Hull, D. G., “Conversion of Optimal Control Problems into Parameter Optimization Problems,” J. Guid. Control Dyn. 20, 5760(1997).CrossRefGoogle Scholar
56.Betts, J. T., “Practical methods for optimal control using nonlinear programming,” SIAM (2001).Google Scholar
57.Scilab-4.0, Consortium Scilab (INRIA, ENPC, Copyright@1989–2006(2006).Google Scholar
58.Lawrence, C. T., Zhou, J. L. and Titts, A. L., “User's Guide for CFSQP Version 2.3: A C Code for Solving (Large Scale) Constrained Nonlinear (Minimax) Optimization Problems, Generating Iterates Satisfying all Inequality Constrained,” Institute for Systems Research (College Park, Maryland, 1995).Google Scholar
59.Rose, J. and Gamble, G. J., Human Walking, 2nd ed. (William & Wilkins, Baltimore, 1994).Google Scholar