Abstract
This paper considers the problem of stabilizing nonholonomic robotic systems in the presence of uncertainty regarding the system dynamic model. It is proposed that a simple and effective solution to this problem can be obtained by combining ideas from homogeneous system theory and adaptive control theory. Thus each of the proposed control systems consists of two subsystems: a (homogeneous) kinematic stabilization strategy which generates a desired velocity trajectory for the nonholonomic system, and an adaptive control scheme which ensures that this velocity trajectory is accurately tracked. This approach is shown to provide arbitrarily accurate stabilization to any desired configuration and can be implemented without knowledge of the system dynamic model. Moreover, it is demonstrated that exponential rates of convergence can be achieved with this methodology. The efficacy of the proposed stabilization strategies is illustrated through extensive computer simulations with nonholonomic robotic systems arising from explicit constraints on the system kinematics and from symmetries of the system dynamics.
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References
Kolmanovsky, I. and McClamroch, N.: Developments in nonholonomic control problems, IEEE Control Systems 15(6) (1995), 20–36.
Gorinevsky, D., Kapitanovsky, A., and Goldenberg, A.: Intelligent control of nonholonomic space systems using radial basis function network, in: Proc. ASME Winter Annual Meeting, New Orleans, LA, USA, December 1993.
Nader, S.: Nodal link perceptron network with applications to control of a nonholonomic system, IEEE Trans. Neural Networks 6(6) (1995), 1516–1523.
Fierro, R. and Lewis, F.: Control of a nonholonomic mobile robot using neural networks, IEEE Trans. Neural Networks 9(4) (1998), 589–600.
Hespanha, J., Liberzon, D., and Morse, A.: Towards the supervisory control of uncertain nonholonomic systems, preprint, May 1998.
Su, C. and Stepanenko, Y.: Robust motion/force control of mechanical systems with classical nonholonomic constraints, IEEE Trans. Automat. Control 39(3) (1994), 609–614.
Jiang, Z. and Pomet, J.: Backstepping-based adaptive controllers for uncertain nonholonomic systems, in: Proc. of 34th IEEE Conf. on Decision and Control, New Orleans, LA, USA, December 1995.
Chang, Y. and Chen, B.: Adaptive tracking control design of nonholonomic mechanical systems, in: Proc. of 35th IEEE Conf. on Decision and Control, Kobe, Japan, December 1996.
Colbaugh, R., Barany, E., and Glass, K.: Adaptive control of nonholonomic mechanical systems, in: Proc. of 35th IEEE Conf. on Decision and Control, Kobe, Japan, December 1996, and J. Robotic Systems 15(7) (1998), 365–393.
Dong, W. and Huo, W.: Adaptive stabilization of dynamic nonholonomic chained systems with uncertainty, in: Proc. of 36th IEEE Conf. on Decision and Control, San Diego, CA, USA, December 1997.
Colbaugh, R., Barany, E., and Glass, K.: Adaptive stabilization of uncertain nonholonomic mechanical systems, in: Proc. of 36th IEEE Conf. on Decision and Control, San Diego, CA, USA, December 1997, and Robotica 16(2) (1998), 181–192.
M'Closkey, R.: Exponential stabilization of driftless nonlinear control systems, PhD Dissertation, Department of Mechanical Engineering, California Institute of Technology, 1995.
M'Closkey, R. and Murray, R.: Exponential stabilization of driftless nonlinear control systems using homogeneous feedback, IEEE Trans. Automat. Control 42(5) (1997), 614–628.
Morin, P. and Samson, C.: Application of backstepping techniques to the time-varying exponential stabilization of chained form systems, European J. Control 3 (1997), 15–36.
Morin, P. and Samson, C.: Time-varying exponential stabilization of a rigid space-craft with two control torques, IEEE Trans. Automat. Control 42(4) (1997), 528–534.
Godhavn, J. and Egeland, O.: A Lyapunov approach to exponential stabilization of nonholonomic systems in power form, IEEE Trans. Automat. Control 42(7) (1997), 1028–1032.
Colbaugh, R., Seraji, H., and Glass, K.: Adaptive compliant motion control for dexterous manipulators, Internat. J. Robotics Res. 14(3) (1995), 270–280.
Colbaugh, R., Glass, K., and Barany, E.: Adaptive regulation of manipulators using only position measurements, Internat. J. Robotics Res. 16(5) (1997), 703–713.
Brockett, R.: Asymptotic stability and feedback stabilization, Differential Geometric Control Theory, Birkhauser, Boston, 1983.
Nijmeijer, H. and van der Schaft, A.: Nonlinear Dynamical Control Systems, Springer, New York, 1990.
Teel, A., Murray, R., and Walsh, G.: Nonholonomic control systems: From steering to stabilization with sinusoids, in: Proc. of 31st IEEE Conf. on Decision and Control, Tucson, AZ, USA, December 1992.
Lin, Y. and Sontag, E.: On control-Lyapunov functions under input constraints, in: Proc. of 33rd IEEE Conf. on Decision and Control, Orlando, FL, USA, December 1994.
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Colbaugh, R., Glass, K. Stabilization of Nonholonomic Robotic Systems Using Adaptation and Homogeneous Feedback. Journal of Intelligent and Robotic Systems 26, 1–27 (1999). https://doi.org/10.1023/A:1008011519198
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DOI: https://doi.org/10.1023/A:1008011519198