Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-25T09:26:06.816Z Has data issue: false hasContentIssue false
  • English
  • Français

Rotational Stability Index (RSI) point: postural stability in planar bipeds

Published online by Cambridge University Press:  12 October 2010

Goswami Dip  and
Vadakkepat Prahlad
Goswami Dip*
Affiliation:
Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore117576. E-mail: [email protected]
Vadakkepat Prahlad
Affiliation:
Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore117576. E-mail: [email protected]
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

The postural stability of bipedal robots is investigated in perspective of foot-rotation during locomotion. With foot already rotated, the biped is modeled as an underactuated kinematic structure. The stability of such biped robots is analyzed by introducing the concept of rotational stability. The rotational stability investigates whether a biped would lead to a flat-foot posture or the biped would topple over. The rotational stability is quantified as a ground reference point named “rotational stability index (RSI)” point. Conditions are established to achieve rotational stability during biped locomotion using the concept of the RSI point. The applicability of the RSI point is illustrated through experimentation for the landing stability analysis of the bipedal jumping gaits.

The traditional stability criteria such as zero-moment point (ZMP) [M. Vukobratovic and B. Borovac, “Zero-moment point – thirty five years of its life,” Int. J. Humanoid Robot. 1(1), 157–173 (2004)] and foot-rotation indicator (FRI) [A. Goswami, “Postural stability of biped robots and the foot-rotation indicator (FRI) point,” Int. J. Robot. Res. 18(6), 523–533 (1999)] are not applicable to analyze biped's postural stability when foot is already rotated. The RSI point is established as a stability criteria for planar bipedal locomotion in presence of foot rotation.

Keywords

Internal dynamicsRotational stabilityRotational-stability index (RSI) point
Type
Articles
Information
Robotica , Volume 29 , Issue 5 , September 2011 , pp. 705 - 715
Copyright
Copyright © Cambridge University Press 2010

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.Goswami, A., “Postural stability of biped robots and the foot-rotation indicator (FRI) point,” Int. J. Robot. Res. 18 (6), 523–533 (1999).CrossRefGoogle Scholar
2.Vukobratovic, M. and Borovac, B., “Zero-moment point—thirty five years of its life,” Int. J. Humanoid Robot. 1 (1), 157–173 (2004).CrossRefGoogle Scholar
3.Goswami, D. and Vadakkepat, P., “Planar bipedal jumping gaits with stable landing,” IEEE Trans. Robot. 25 (5), 1030–1046 (2009).CrossRefGoogle Scholar
4.Popovic, M. B., Goswami, A. and Herr, H., “Ground reference points in legged locomotion: Definitions, biological trajectories and control implications,” Int. J. Robot. Res. 24 (12), 1013–1032 (2005).CrossRefGoogle Scholar
5.Westervelt, E. R., Grizzle, J. W., Chevallereau, C., Choi, J. and Morris, B., Feedback Control of Dynamic Bipedal Robot Locomotion (CRC Press, Boca Raton, 2007).Google Scholar
6.Arakawa, T. and Fukuda, T., “Natural Motion Generation of Biped Locomotion Robot Using Hierarchical Trajectory Generation Method Consisting of GA, EP Layers,” IEEE International Conference on Robotics and Automation, vol. 1, (1997) pp. 211–216.Google Scholar
7.Craig, J. J., Introduction to Robotics: Mechanics and Control (Addison-Wesley Longman Publishing Co., Inc. Boston, MA, 1989).Google Scholar
8.Isidori, A., Nonlinear Control Systems (Springer-Verlag, New York, 1995).CrossRefGoogle Scholar
9.Slotine, J. E. and Li, W., Applied Nonlinear Control (Prentice Hall, Englewood Cliffs, New Jersey, 1991).Google Scholar
10.Spong, M. W. and Vidyasagar, M., Robot Dynamic and Control (John Wiley and Sons, New York, 1989).Google Scholar
11.Khalil, H. K., Nonlinear Systems (Prentice Hall, Portland, OR, 2001).Google Scholar
12.Vukobratović, M., Biped Locomotion: Dynamics, Stability, Control and Application (Springer-Verlag, Berlin and New York, 1990). [Online]. Available: http://www.getcited.org/inst/144229CrossRefGoogle Scholar
13.Nagasaka, K., Kuroki, Y., Suzuki, S., Itoh, Y. and Yamaguchi, J., “Integrated Motion Control for Walking, Jumping and Running on a Small Bipedal Entertainment Robot,” IEEE International Conference on Robotics and Automation, (Apr. 26–May 1, 2004) pp. 3189–3194.CrossRefGoogle Scholar
14.Vadakkepat, P., Goswami, D. and Hwee, C. M., “Disturbance rejection by online ZMP compensation,” Robotica 26, 9–17 (2007).Google Scholar
15.Napoleon, S. N. and Sampei, M., “Balance Control Analysis of Humanoid Robot Based on ZMP Feedback Control,” IEEE International Conference on Intelligent Robots and System, (2002) pp. 2437–2442.Google Scholar
16.Nikkhah, M., Ashrafiuon, H. and Fahimi, F., “Robust control of underactuated bipeds using sliding modes,” Robotica 25 (3), 367–374 (May 2007).CrossRefGoogle Scholar
17.Berkemeier, M. D. and Fearing, R. S., “Tracking fast inverted trajectories of the underactuated acrobot,” IEEE Trans. Robot. Autom. 15, 740–750 (1999).CrossRefGoogle Scholar
18.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 (6), 431–464 (2005).CrossRefGoogle Scholar
19.Westervelt, E. R., Grizzle, J. W. and Koditschek, D. E., “Hybrid zero dynamics of planar biped walkers,” IEEE Trans. Autom. Control 48 (1), 42–56 (Jan. 2003).CrossRefGoogle Scholar
20.Raibert, M. H., Brown, H. B. Jr., and Chepponis, M., “Experiments in balance with a 3D one-legged hopping-machine,” Int. J. Robot. Res. 3 (2), 75–92 (1984).CrossRefGoogle Scholar
21.Hurmuzlu, Y. and Marghitu, D. B., “Rigid body collisions of planar kinematic chains with multiple contact points,” Int. J. Robot. Res. 13 (1), 82–92 (1994).CrossRefGoogle Scholar
22.Goswami, D., Vadakkepat, P. and Kien, P. D., “Genetic algorithm-based optimal bipedal walking gait synthesis considering tradeoff between stability margin and speed,” Robotica 27, 355–365 (2009).Google Scholar
23.Bertsekas, D. P. and Rhodes, I. B., “On the minimax reachability of target sets and target tubes,” Automatica 7, 233–247 (1971).CrossRefGoogle Scholar