Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-18T15:53:46.307Z Has data issue: false hasContentIssue false
  • English
  • Français

Globally stable control of a dynamic bipedal walker using adaptive frequency oscillators

Published online by Cambridge University Press:  15 January 2014

Gabriel Aguirre-Ollinger
Gabriel Aguirre-Ollinger*
Affiliation:
School of Electrical, Mechanical and Mechatronic Systems, University of Technology, Sydney, Broadway, NSW 2007, Australia
*
*Corresponding author. E-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Summary

We present a control method for a simple limit-cycle bipedal walker that uses adaptive frequency oscillators (AFOs) to generate stable gaits. Existence of stable limit cycles is demonstrated with an inverted-pendulum model. This model predicts a proportional relationship between hip torque amplitude and stride frequency. The closed-loop walking control incorporates adaptive Fourier analysis to generate a uniform oscillator phase. Gait solutions (fixed points) are predicted via linearization of the walker model, and employed as initial conditions to generate exact solutions via simulation. Global stability is determined via a recursive algorithm that generates the approximate basin of attraction of a fixed point. We also present an initial study on the implementation of AFO-based control on a bipedal walker with realistic mass distribution and articulated knee joints.

Keywords

BipedsGait stabilityLimit-cycle walkersNonlinear oscillatorsBasin of attraction
Type
Articles
Information
Robotica , Volume 32 , Issue 7 , October 2014 , pp. 1039 - 1063
Copyright
Copyright © Cambridge University Press 2014 

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.Pinto, C. and Golubitsky, M., “Central pattern generators for bipedal locomotion,” J. Math. Biol. 53, 474–489 (2006).Google Scholar
2.Nakamura, Y., Mori, T., Sato, M. and Ishii, S., “Reinforcement learning for a biped robot based on a CPG-actor-critic method,” Neural Netw. 20, 723–735 (2007).CrossRefGoogle ScholarPubMed
3.Verdaasdonk, B. W., Koopman, H. F. J. M. and van der Helm, F. C. T., “Energy efficient walking with central pattern generators: From passive dynamic walking to biologically inspired control,” Biol. Cybern. 101, 49–61 (2009).Google Scholar
4.Nakanishi, J., Morimoto, J., Endo, G., Cheng, G., Schaal, S. and Kawato, M., “Learning from demonstration and adaptation of biped locomotion,” Robot. Auton. Syst. 47, 79–91 (2004).Google Scholar
5.Fu, C., Tan, F. and Chen, K., “A simple walking strategy for biped walking based on an intermittent sinusoidal oscillator,” Robotica 28, 869–884 (2010).CrossRefGoogle Scholar
6.Righetti, L. and Ijspeert, A., “Programmable Central Pattern Generators: An Application to Biped Locomotion Control,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Orlando, FL (May 15–19, 2006) pp. 1585–1590.Google Scholar
7.Righetti, L., Buchli, J. and Ijspeert, A., “Dynamic Hebbian learning in adaptive frequency oscillators,” Physica 216 (2), 269–281 (2006).Google Scholar
8.Ijspeert, A., Nakanishi, J. and Schaal, S., “Trajectory Formation for Imitation with Nonlinear Dynamical Systems,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), vol. 2, Maui, HI (Oct. 29–Nov. 3, 2001) pp. 752–757.Google Scholar
9.Degallier, S., Righetti, L., Gay, S. and Ijspeert, A., “Toward simple control for complex, autonomous robotic applications: Combining discrete and rhythmic motor primitives,” Auton. Robots, 31 (2–3), 155–181 (2011).Google Scholar
10.Gams, A., Ijspeert, A., Schaal, S. and Lenarcic, J., “On-line learning and modulation of periodic movements with nonlinear dynamical systems,” Auton. Robots 27 (1), 3–23 (2009).Google Scholar
11.Petric, T., Gams, A., Ijspeert, A. and Zlajpah, L., “On-line frequency adaptation and movement imitation for rhythmic robotic tasks,” Int. J. Robot. Res. 30 (14), 1775–1788 (2011).Google Scholar
12.Hobbelen, D. and Wisse, M., “Limit Cycle Walking,” In: Humanoid Robots, Human-Like Machines (Hackel, M., ed.) (Vienna: InTech, 2007).Google Scholar
13.Kuo, A. D., “Energetics of actively powered locomotion using the simplest walking model,” J. Biomech. Eng. 124, 113–120 (2002).Google Scholar
14.Kuo, A., Donelan, J. and Ruina, A., “Energetic consequences of walking like an inverted pendulum: Step-to-step transitions,” Exerc. Sport Sci. Rev. 33 (2), 88–97 (2005).CrossRefGoogle Scholar
15.Vukobratovic, M. and Rodic, A., “Contribution to the integrated control of biped locomotion mechanisms,” Int. J. Humanoid Robot. 4 (1), 49–95 (2007).CrossRefGoogle Scholar
16.Garcia, M., Chatterjee, A., Ruina, A. and Coleman, M., “The simplest walking model: Stability, complexity and scaling,” ASME J. Biomech. Eng. 120, 281–288 (1998).Google Scholar
17.Schwab, A. and Wisse, M., “Basin of Attraction of the Simplest Walking Model,” Proceedings of DETC01/ASME 2001 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Pittsburgh, PA (Sep. 9–12, 2001).Google Scholar
18.Wisse, M., Schwab, A., van der Linde, R. and van der Helm, F., “How to keep from falling forward: Elementary swing leg action for passive dynamic walkers,” IEEE Trans. Robot. 21 (3), 393–401 (2005).CrossRefGoogle Scholar
19.Hobbelen, D. and Wisse, M., “Swing-leg retraction for limit cycle walkers improves disturbance rejection,” IEEE Trans. Robot. 24 (2), 377–389 (2008).Google Scholar
20.Ijspeert, A., “Central pattern generators for locomotion control in animals and robots: A review,” Neural Netw. 21, 642–653 (2008).Google Scholar
21.Buchli, J. and Ijspeert, A., “Self-organized adaptive legged locomotion in a compliant quadruped robot,” Auton. Robots 25 (4), 331–347 (2008).CrossRefGoogle Scholar
22.Nagrath, I. and Gopal, M., Control Systems Engineering, 5th ed. (Anshan Ltd., Tunbridge Wells, UK, 2008).Google Scholar
23.Neptune, R., Sasaki, K. and Kautz, S., “The effect of walking speed on muscle function and mechanical energetics,” Gait Posture 28 (1), 135–143 (2008).Google Scholar
24.Xu, J., Guttalu, R. and Hsu, C., “Domains of attraction for multiple limit cycles of coupled Van der Pol equations by simple cell mapping,” Int. J. Non-Linear Mech. 20 (5–6), 507–517 (1985).Google Scholar
25.Jain, R., Kasturi, R. and Schunck, B., Machine Vision, 1st ed. (McGraw-Hill, New York, 1995).Google Scholar
26.Ronsse, R., van den Kieboom, J. and Ijspeert, A. J., “Automatic Resonance Tuning and Feedforward Learning of Biped Walking Using Adaptive Oscillators,” Proceedings of the Conference in Multibody Dynamics 2011, ECCOMAS Thematic Conference, Brussels, Belgium (Jul. 4–7, 2011).Google Scholar
27.Garofalo, G., Ott, C. and Albu-Schaffer, A., “Walking Control of Fully Actuated Robots Based on the Bipedal Slip Model,” IEEE International Conference on Robotics and Automation (ICRA), St. Paul, MN (May 14–18, 2012), pp. 1456–1463.Google Scholar