Abstract
Special purpose numerical optimal control algorithms can be used to create biped multibody systems and open loop joint torque histories that create periodic motions that are asymptotically stable without any feedback. In this context, we have produced open-loop stable biped walking, running, hopping, somersaults and flip-flops. In this paper, we specifically investigate the stabilizing role of springs and dampers added to a biped walking system by including the spring and damper constants in the stability optimization. It is shown that stability and robustness to state disturbances of the asymptotically stable open loop gaits can be very substantially increased by an optimization-based selection of spring and damper components and that springs and dampers help to induce a more natural appearing solution.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
M. Ahmadi and M. Buehler. Stable control of a simulated one-legged running robot with hip and leg compliance. IEEE Transactions on Robotics and Automation, 13(1):96–104, Feb. 1997.
R. McNeill Alexander. Principles of Animal Locomotion. Princeton University Press, 2002.
H. G. Bock. Randwertproblemmethoden zur Parameteridentifizierung in Systemen nichtlinearer Differentialgleichungen. In Bonner Mathematische Schriften 183. Universität Bonn, 1987.
H. G. Bock and K.-J. Plitt. A multiple shooting algorithm for direct solution of optimal control problems. In Proceedings of the 9th IFAC World Congress, Budapest, 242–247. International Federation of Automatic Control, 1984.
S. H. Collins, A. L. Ruina, R. Tedrake, and M. Wisse. Efficient bipedal robots based on passive-dynamic walkers. Science, 307:1082 – 1085, 2005.
J. C. Hsu and A. U. Meyer. Modern Control Principles and Applications. McGraw-Hill, 1968.
D. B. Leineweber, I. Bauer, H. G. Bock, and J. P. Schlöder. An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization - part I: theoretical aspects. Comput. Chem. Engng, 27:157 – 166, 2003.
D. B. Leineweber, A. Schäfer, H. G. Bock, and J. P. Schlöder. An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization - part II: software aspects and applications. Comput. Chem. Engng, 27:167 – 174, 2003.
T. McGeer. Passive dynamic walking. International Journal of Robotics Research, 9:62–82, 1990.
S. Mochon and T. S. McMahon. Ballistic walking. Biomechanics, 13:49 – 57, 1980.
K. D. Mombaur. Performing open-loop stable flip-flops - an example for stability optimization and robustness analysis of fast periodic motions. In Fast Motions in Robotics and Biomechanics - Optimization and Feedback Control, Lecture Notes in Control and Information Science. Springer, 2006.
K. D. Mombaur, H. G. Bock, J. P. Schlöder, and R. W. Longman. Open-loop stability – a new paradigm for periodic optimal control and analysis of walking mechanisms. In Proceedings of IEEE CIS-RAM 04, Singapore, 2004.
K. D. Mombaur, H. G. Bock, J. P. Schlöder, and R. W. Longman. Open-loop stable solution of periodic optimal control problems in robotics. ZAMM - Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 85(7):499 – 515, July 2005.
K. D. Mombaur, H. G. Bock, J. P. Schlöder, and R. W. Longman. Self-stabilizing somersaults. IEEE Transactions on Robotics, 21(6), Dec. 2005.
D. Papadopoulos and M. Buehler. Stable running in a quadruped robot with compliant legs. In Proceedings of IEEE International Conference on Robotics and Automation, 444–449, San Francisco, USA, April 2000.
G. A. Pratt, M. M. Williamson, P. Dillworth, J. Pratt, K. Uhland, and A. Wright. Stiffness isn’t everything. In Proceedings of International Symposium of Experimental Robotics ISER, Stanford, 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mombaur, K.D., Longman, R.W., Bock, H.G., Schiöder, J.P. (2008). Optimizing Spring-Damper Design in Human Like Walking that is Asymptotically Stable Without Feedback. In: Bock, H.G., Kostina, E., Phu, H.X., Rannacher, R. (eds) Modeling, Simulation and Optimization of Complex Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79409-7_28
Download citation
DOI: https://doi.org/10.1007/978-3-540-79409-7_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79408-0
Online ISBN: 978-3-540-79409-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)