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Stable running of a planar underactuated biped robot

Published online by Cambridge University Press:  01 September 2010

Yong Hu ,
Gangfeng Yan  and
Zhiyun Lin
Yong Hu
Affiliation:
College of Electrical Engineering, Zhejiang University, 38 Zheda Road, Hangzhou, 310027P. R. China
Gangfeng Yan
Affiliation:
College of Electrical Engineering, Zhejiang University, 38 Zheda Road, Hangzhou, 310027P. R. China
Zhiyun Lin*
Affiliation:
College of Electrical Engineering, Zhejiang University, 38 Zheda Road, Hangzhou, 310027P. R. China
*
*Corresponding author. E-mail: [email protected]
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Summary

This paper investigates the stable-running problem of a planar underactuated biped robot, which has two springy telescopic legs and one actuated joint in the hip. After modeling the robot as a hybrid system with multiple continuous state spaces, a natural passive limit cycle, which preserves the system energy at touchdown, is found using the method of Poincaré shooting. It is then checked that the passive limit cycle is not stable. To stabilize the passive limit cycle, an event-based feedback control law is proposed, and also to enlarge the basin of attraction, an additive passivity-based control term is introduced only in the stance phase. The validity of our control strategies is illustrated by a series of numerical simulations.

Keywords

Biped robotPassive runningUnderactuated system
Type
Articles
Information
Robotica , Volume 29 , Issue 5 , September 2011 , pp. 657 - 665
Copyright
Copyright © Cambridge University Press 2010

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References

1.Ames, A. D., Gregg, R. D., Wendel, E. D. B. and Sastry, S., “On the geometric reduction of controlled three-dimensional bipedal robotic walkers,” Lecture Notes Control Inf. Sci. 366, 183–196 (2007).Google Scholar
2.Borzova, E. and Hurmuzlu, Y., “Passively walking of five-link robot,” Automatica 40 (4), 621–629 (2004).Google Scholar
3.Buehler, M. and Koditschek, D. E., “Analysis of a simplified hopping robot,” Int. J. Robot. Res. 10, 587–605 (1991).Google Scholar
4.Chevallereau, C., Abba, G., Aoustin, Y., Plestan, F., Westervelt, E. R., Canudas-de Wit, C. and Grizzle, J. W., “Rabbit: a testbed for advanced control theory,” IEEE Control Syst. Mag. 23, 57–79 (2003).Google Scholar
5.Chevallereau, C. and Aoustin, Y., “Optimal reference trajectories for walking and running of a biped robot,” Robotica 19, 557–569 (2001).Google Scholar
6.Chevallereau, C., Grizzle, J. W. and Shih, C., “Asymptotically stable walking of a five-link underactuated 3d bipedal robot,” IEEE Trans. Robot. Autom. 25, 37–50 (2008).CrossRefGoogle Scholar
7.Chevallereau, C. and Sardain, P., “Design and Actuation Optimization of a 4 Axes Biped Robot for Walking and Running.” Proceedings of IEEE International Conference on Robotics and Automation, San Francisco, USA (2000) pp. 3365–3370.Google Scholar
8.Chevallereau, C., Westervelt, E. R. and Grizzle, J. W., “Asymptotic Stabilization of a Five-Link, Four-Actuator, Planar Bipedal Runner,” Proceedings of 43rd IEEE Conference on Decision and Control, Nassau, Bahamas (2004) pp. 303–310.Google Scholar
9.Chevallereau, C., Westervelt, E. R. and Grizzle, J. W., “Asymptotically stable running for a five-link, four-actuator, planar bipedal robot,” Int. J. Robot. Res. 24, 431–464 (2005).CrossRefGoogle Scholar
10.Chu, B., Hong, D., Park, J. and Chung, J. H., “Passive dynamic walker controller design employing an RLS-based natural actor–critic learning algorithm,” Eng. Appl Artif. Intell. 21, 1027–1034 (2008).CrossRefGoogle Scholar
11.Collins, S., Ruina, A., Tedrake, R. and Wisse, M., “Efficient bipedal robots based on passive-dynamic walkers,” Science 307, 1082–1085 (2005).CrossRefGoogle ScholarPubMed
12.Garcia, M., Chatterjee, A., Ruina, A. and Coleman, M., “The simplest walking model: Stability, complexity and scaling,” J. Biomech. Eng. 120, 281–288 (1998).Google Scholar
13.Geppert, L., “QRIO, the robot that could.” IEEE Spectr. 41, 34–37 (2004).Google Scholar
14.Goswami, A., Thuilot, B. and Espiau, B., “A study of the passive gait of a compass-like biped robot: symmetry and chaos,” Int. J. Robot. Res. 17, 1282–1311 (1998).Google Scholar
15.Hirose, R. and Takenaka, T., “Development of the humanoid robot ASIMO,” Honda R&D Tech. Rev. 13, 1–6 (2001).Google Scholar
16.Hyon, S. H. and Emura, T., “Running Control of a Planar Biped Robot Based on Energy-Preserving Strategy,” Proceedings of IEEE International Conference on Robotics and Automation, New Orleans, USA (2004) pp. 3791–3796.Google Scholar
17.Ishida, T., “Development of a Small Biped Entertainment Robot QRIO,” Proceedings of the 2004 International Symposium on Micro-NanoMechatronics and Human Science, Nagoya, Japan (2004), pp. 23–28.Google Scholar
18.Kaneko, K., Kanehiro, F., Kajita, S., Hirukawa, H., Kawasaki, T., Hirata, M., Akachi, K. and Isozumi, T., “Humanoid Robot HRP-2,” Proceedings of 2004 IEEE International Conference on Robotics and Automation, New Orleans, USA (2004) pp. 1083–1090.Google Scholar
19.McGeer, T., “Passive Bipedal Running,” Proceedings of the Royal Society of London. Series B, Biological Sciences, The Royal Society (1990) pp. 107–134.Google Scholar
20.McGeer, T., “Passive dynamic walking,” Int. J. Robot. Res. 9, 62–82 (1990).Google Scholar
21.Morris, B., Westervelt, E. R., Chevallereau, C., Buche, G. and Grizzle, J. W., “Achieving bipedal running with RABBIT: six steps toward infinity,” Lecture Notes Control Inf. Sci. 340, 277–297 (2006).Google Scholar
22.Owaki, D. and Ishiguro, A., “Enhancing Stability of a Passive Dynamic Running Biped by Exploiting a Nonlinear Spring. IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, China (2006) pp. 4923–4928.Google Scholar
23.Owaki, D., Osuka, K. and Ishiguro, A., “On the Embodiment that Enables Passive Dynamic Bipedal Running,” Proceedings of 2008 IEEE International Conference on Robotics and Automation, Psadena, USA (2008).Google Scholar
24.Parker, T. S. and Chua, L. O., Practical Numerical Algorithms for Chaotic Systems (Springer-Verlag, 1989).CrossRefGoogle Scholar
25.Poulakakis, I., Papadopoulos, E. and Buehler, M., “On the stability of the passive dynamics of quadrupedal running with a bounding gait,” Int. J. Robot. Res. 25, 669–687 (2006).CrossRefGoogle Scholar
26.Raibert, M. H., Legged Robots That Balance (The MIT Press, 1986).Google Scholar
27.Raibert, M. H. and Tello, E. R., “Legged robots that balance,” IEEE Expert [see also IEEE Intelligent Systems and Their Applications] 1, 89–89 (1986).Google Scholar
28.Sato, A. and Buehler, M., “A Planar Hopping Robot with one Actuator: Design, Simulation and Experimental Results. Proceedings of 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems, Sendai, Japan (2004) pp. 3540–3545.Google Scholar
29.Satoshi, S., Katsuhisa, F. and Shoshiro, H., “Passive walking towards running,” Math. Comput. Modelling Dyn. Syst. 11, 371–395 (2005).Google Scholar
30.Spong, M. W., Holm, J. K. and Lee, D., “Passivity-based control of bipedal locomotion,” IEEE Robot. Autom. Mag. 14, 30–40 (2007).CrossRefGoogle Scholar
31.Tedrake, R., Zhang, T. W., Fong, M. and Seung, H. S., “Actuating a Simple 3D Passive Dynamic Walker,” Proceedings of 2004 IEEE International Conference on Robotics and Automation, New Orleans, USA (2004) pp. 4656–4661.Google Scholar
32.Vakakis, A. F. and Burdick, J. W., “Chaotic Motions in the Dynamics of a Hopping Robot,” Proceedings of 1990 IEEE International Conference on Robotics and Automation, Tsukuba, Japan (1990) pp. 1464–1469.Google Scholar
33.Westervelt, E. R., Grizzle, J. W., Chevallereau, C., Choi, J. H. and Morris, B., Feedback Control of Dynamic Bipedal Robot Locomotion (CRC Press, 2007).Google Scholar
34.Wisse, M., Feliksdal, G., Van Frankkenhuyzen, J. and Moyer, B., “Passive-based walking robot,” IEEE Robot. Autom. Mag. 14, 52–62 (2007).Google Scholar