Abstract
In this paper we present some ideas on the control of underactuated mechanical systems using switching and saturation. We focus on the swingup control problem for a class of “gymnast” robots and also for the classical cart-pole system. The design methodology is based on partial feedback linearization in a first stage to linearize the actuated degrees of freedom followed by the control of the transfer of energy from the actuated to the unactuated degrees of freedom in a second stage. In a typical swingup control the desired equilibrium is unstable in the closed loop system as a consequence of the non-minimum phase behavior of the system. For this reason it is necessary to switch controllers at the appropriate time to a controller which renders the equilibrium stable. The successful implementation of the switching control has proved to be nontrivial, both in simulation and in experiment. We discuss both local and global design methods and present some simulation results.
The research of the first author is partially supported by the National Science Foundation under grants CMS-9402229, and INT-9415757
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Saito, F., Fukuda, T., and Arai, F., “Swing and Locomotion Control for Two-Link Brachiation Robot,” Proc. 1993 IEEE Int. Conf. on Robotics and Automation, pp. 719–724, Atlanta, GA, 1993.
Bortoff, S.A., Pseudolinearization using Spline Functions with Application to the Acrobot, Ph.D. Thesis, Dept. of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, 1992.
Spong, M.W., “Modeling and Control of Elastic Joint Robots”, ASME J. Dyn. Systems, Mean. and Control, Vol. 109, pp. 310–319, December, 1987.
Spong, M. W., and Vidyasagar, M., Robot Dynamics and Control, John Wiley & Sons, Inc., New York, 1989.
Teel, A.R., “Using saturation to stabilize a class of single-input partially linear composite systems,” IFAC NOLCOS'92 Symposium, Bordeaux, June 1992. See also: “A Nonlinear Small Gain Theorem for the Analysis of Control Systems with Saturation,” IEEE Trans. on Automatic Control, submitted, 1994.
Mazenc, F., and Praly, L., “Adding an Integration and Global Asymptotic Stabilization of Feedforward Systems,” IEEE Trans. on Automatic Control, submitted, 1994. See also: Proceed. 33rd IEEE Conference on Decision and Control, December 1994.
Janković, M., Sepulchre, R., and Kokotović, P.V., “Global Stabilization of an Enlarged Class of Cascade Nonlinear Systems,” preprint, 1995.
Spong, M.W., “The Swing Up Control Problem for the Acrobot,” IEEE Control Systems Magazine, Vol. 15, No. 1, pp. 49–55, Feb. 1995.
Chung, C.C. and Hauser, J., “Nonlinear Control of a Swinging Pendulum,” Automatica, Vol. 31, No. 6, pp. 851–862, 1995.
Jurdjevic, V., and Quinn, J.P., “Controllability and Stability,” Journal of Differential Equations, Vol. 4, pp. 381–389, 1978.
Bacciotti, A., “Local Stabilizability of Nonlinear Control Systems,” Series on Advances in Mathematics for Applied Sciences, Vol. 8, World Scientific, 1992.
Wiklund, M., Kristenson, A., and Astrom, K.J., “A New Strategy for Swinging up an Inverted Pendulum,” Proc. IFAC Symposium, Sydney, Australia, 1993.
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© 1997 Springer-Verlag London Limited
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Spong, M.W., Praly, L. (1997). Control of underactuated mechanical systems using switching and saturation. In: Stephen Morse, A. (eds) Control Using Logic-Based Switching. Lecture Notes in Control and Information Sciences, vol 222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036093
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DOI: https://doi.org/10.1007/BFb0036093
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