Breaking Symmetries and Constraints: Transitions from 2D to 3D in Passive Walkers
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The inherent dynamics of bipedal, passive mechanisms are studiedto investigate the relation between motions constrained to two-dimensional (2D)planes and those free to move in a three-dimensional (3D) environment. Inparticular, we develop numerical and analytical techniques usingdynamical-systems methodology to address the persistence and stabilitychanges of periodic, gait-like motions due to the relaxation ofconfiguration constraints and the breaking of problem symmetries. Theresults indicate the limitations of a 2D analysis to predictthe dynamics in the 3D environment. For example, it is shownhow the loss of constraints may introduce characteristically non-2Dinstability mechanisms, and how small symmetry-breaking terms may result inthe termination of solution branches.
- Pratt, J.E., ‘Virtual model control of a biped walking robot’, Master's Thesis, MIT, Department of Electrical Engineering and Computer Science, 1995.
- Pratt, J.E. and Pratt, G.A., ‘Exploiting natural dynamics in the control of a 3D bipedal walking simulation’, in International Conference on Climbing and Walking Robots (CLAWAR99), Portsmouth, U.K., 1999.
- Formal'sky, A.M., Ballistic Locomotion of a Biped. Design and Control of Two Biped Machines, CISM Advanced School on Modelling and Simulation of Human and Walking Robots Locomotion, Udine, 1996.
- Howell, G.W. and Baillieul, J., ‘Simple controllable walking mechanism which exhibit bifurcations’, in Proceedings of the 37th IEEE Conference on Decision and Control, IEEE, New York, 1998, 3027–3032.
- Berbuyk, V.E. and Boström, A.E. and Lytwyn, B.A. and Peterson, B., ‘Optimization of control laws of the bipedal locomotion systems’, Advances in Computational Multibody Dynamics 37 1999, 703–728.
- McGeer, T., ‘Passive dynamic walking’, International Journal of Robotics Research 9, 1990, 62–82.
- Garcia, M., Chatterjee, A. and Ruina, A., ‘Efficiency, speed, and scaling of passive dynamical bipedal walking’, Dynamics and Stability of Systems 15(2), 2000, 75–99.
- Adolfsson, J., Dankowicz, H. and Nordmark, A., ‘3-D stable gait in passive bipedal mechanisms’, in Proceedings of European Mechanics Colloquium, Euromech 372, J.A.C. Ambrósio and W.O. Schiehlen (eds), 1999, 253–259.
- Garcia, M., Chatterjee, A., Ruina, A. and Coleman, M., ‘Passive-dynamic models of human gait’, in Proceedings of the Conference on Biomechanics and Neural Control of Human Movement, 1998, 32–33.
- Dankowicz, H.J., Adolfsson, J. and Nordmark, A.B., ‘Repetetive gait of passive bipedal mechanisms in a three-dimensional environment’, Journal of Biomechanical Engineering 123(1), 2001, 40–46.
- Adolfsson, J., Dankowicz, H. and Nordmark, A., ‘3D passive walkers: Finding periodic gaits in the presence of discontinuities’, Nonlinear Dynamics 24, 2001, 205–229.
- Garcia, M., Chatterjee, A., Ruina, A. and Coleman, M., ‘The simplest walking model: Stability, complexity, and scaling’, ASME Journal of Biomechanical Engineering 120, 1998, 281–288.
- McGeer, T., ‘Passive walking with knees’, in Proceedings of the IEEE Conference on Robotics and Automation, Vol. 2, IEEE, New York, 1990, 1640–1645.
- Piiroinen, P.T., Dankowicz, H.J. and Nordmark, A.B., ‘On a normal-formal analysis for a class of passive bipedal walkers’, International Journal of Bifurcation and Chaos 11(9), 2001, 2411–2425.
- Collins, S., Wisse, M. and Ruina, A., ‘A 3-D passive-dynamic walking robot with two legs and knees’, International Journal of Robotics Research 20(7), 2001, 607–615.
- Coleman, M. and Ruina, A., ‘An uncontrolled toy that can walk but cannot stand still’, Physical Review Letters 80(16), 1998, 3658–3661.
- Adolfsson, J., ‘Passive control of mechanical systems — Bipedal walking and autobalancing’, Ph.D. Thesis, Royal Institute of Technology, Department of Mechanics, Sweden, 2001.
- Parker, T.S. and Chua, L.O., Practical Numerical Algorithms for Chaotic Systems, Springer-Verlag, New York, 1989.
- Leine, R., ‘Bifurcations in discontinuous mechanical systems of Filippov-type’, Ph.D. Thesis, Technische Universiteit Eindhoven, The Netherlands, 2000.
- Guckenheimer, J. and Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, Berlin, 1983.
- Breaking Symmetries and Constraints: Transitions from 2D to 3D in Passive Walkers
Multibody System Dynamics
Volume 10, Issue 2 , pp 147-176
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- passive bipedal mechanisms
- periodic motion
- center manifold
- nonlinear dynamics
- multibody modeling
- dynamical systems
- Industry Sectors
- Author Affiliations
- 1. Department of Engineering Mathematics, University of Bristol, Bristol, BS2 1TR, U.K.
- 2. Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, U.S.A
- 3. Department of Mechanics, Royal Institute of Technology, SE-100 44, Stockholm, Sweden