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Experimental results on the nonlinear ∞ control via quasi-LPV representation and game theory for wheeled mobile robots

Published online by Cambridge University Press:  01 July 2009

Roberto S. Inoue ,
Adriano A. G. Siqueira  and
Marco H. Terra
Roberto S. Inoue
Affiliation:
Department of Electrical Engineering, University of São Paulo, São Carlos, C.P. 359, São Carlos, SP, 13560-970, Brazil.
Adriano A. G. Siqueira
Affiliation:
Department of Mechanical Engineering, University of São Paulo, São Carlos, Brazil.
Marco H. Terra*
Affiliation:
Department of Electrical Engineering, University of São Paulo, São Carlos, C.P. 359, São Carlos, SP, 13560-970, Brazil.
*
*Corresponding author. terra@sel.eesc.usp.br
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Summary

In this paper, nonlinear dynamic equations of a wheeled mobile robot are described in the state-space form where the parameters are part of the state (angular velocities of the wheels). This representation, known as quasi-linear parameter varying, is useful for control designs based on nonlinear ∞ approaches. Two nonlinear ∞ controllers that guarantee induced 2-norm, between input (disturbances) and output signals, bounded by an attenuation level γ, are used to control a wheeled mobile robot. These controllers are solved via linear matrix inequalities and algebraic Riccati equation. Experimental results are presented, with a comparative study among these robust control strategies and the standard computed torque, plus proportional-derivative, controller.

Keywords

Nonlinear H∞ controlLinear parameter varying systemsMobile robots
Type
Article
Information
Robotica , Volume 27 , Issue 4 , July 2009 , pp. 547 - 553
Copyright
Copyright © Cambridge University Press 2008

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References

1.Brockett, R. W., “Asymptotic stability and feedback stabilization,” in Differential Geometric Control Theory (Brockett, R. W., Millman, R. S. and Sussmann, H. J., eds.) (Birkhäuser, Boston, MA, 1983) pp. 181–191.Google Scholar
2.Samson, C. and Ait-Abderrahim, K., “Feedback Control of a Nonholonomic Wheeled Cart in Cartesian Space,” Proceedings of the International Conference on Robotics and Automation, Sacramento, California. vol. 2 (1991) pp. 1136–1141.Google Scholar
3.Dixon, W. E., Dawson, D. M., Zergeroglu, E. and Zhang, F., “Robust Tracking and Regulation Control for Mobile Robots,” Proceedings of the International Conference on Control Applications, Kohala Coast-Island of Hawaii, Hawaii, USA, vol. 2 (1999) pp. 1015–1020.Google Scholar
4.Dixon, W. E., Dawson, D. M., Zergeroglu, E. and Behal, A., “Adaptive tracking control of a wheele mobile robot via an uncalibrated camera system,” IEEE Trans. Syst. Man, Cybernet.-Part B: Cybernet., vol. 31, pp. 341–352 (2001).CrossRefGoogle Scholar
5.Duleba, I. and Khefifi, W., “Velocity space approach to motion planning of nonholonomic systems,” Robotica 25, 359–366 (2007).CrossRefGoogle Scholar
6.Fazli, S. and Kleeman, L., “Simultaneous landmark classification, localization and map building for an advanced sonar ring,” Robotica 25, 283–296 (2006).CrossRefGoogle Scholar
7.Padois, V., Fourquet, J.-Y. and Chiron, P., “Kinematic and dynamic model-based control of wheeled mobile manipulators: A unified framework for reactive approaches,” Robotica 25, 157–173 (2007).CrossRefGoogle Scholar
8.Kanayama, Y., Kimura, Y., Miyazaki, F. and Noguchi, T., “A Stable Tracking Control Method for an Autonomous Mobile Robot,” Proceedings of the IEEE International Conference on Robotics and Automation, Cincinnati, Ohio (May 1990) pp. 384–389.Google Scholar
9.Hwang, C. K., Chen, B. S., and Chang, Y. T., “Combination of Kinematical and Robust Dynamical Controllers for Mobile Robotics Tracking Control: (i) Optimal ∞ Control,” Proceedings of IEEE International Conference on Control Applications, Taipei, Taiwan (Sept. 2004) 1205–1210.Google Scholar
10.Chen, B. S., Lee, T. S. and Feng, J. H., “A nonlinear ∞ control design in robotic systems under parameter perturbation and external disturbance,” Int. J. Control 59 (2), 439–461 (1994).CrossRefGoogle Scholar
11.Siqueira, A. A. G. and Terra, M. H., “Nonlinear and Markovian ∞ controls of underactuated manipulators,” IEEE Trans. Control Syst. Technol. 12 (6), 811–826 (2004).CrossRefGoogle Scholar
12.Wu, F., Yang, X. H., Packard, A. and Becker, G., “Induced 2-norm control for LPV systems with bounded parameter variation rates,” Int. J. Robust and Nonlinear Control 6 (9–10), 983–998 (1996).3.0.CO;2-C>CrossRefGoogle Scholar
13.Coelho, P. and Nunes, U., “Lie algebra application to mobile robot control: A tutorial,” Robotica 21, 483–493 (2003).CrossRefGoogle Scholar
14.Bloch, A. M., Reyhanoglu, M. and McClamroch, N. H., “Control and stabilization of nonholonomic dynamic systems,” IEEE Trans. Automat. Control 37 (11), 1746–1757 (1992).CrossRefGoogle Scholar
15.Huang, Y. and Jadbabaie, A., “Nonlinear ∞ control: An enhanced Quasi-LPV approach,” in Workshop in ∞ nonlinear control by J. C. Doyle, Proceedings of the IEEE International Conference on Decision and Control, Tampa, FL (1998).Google Scholar
16.Wu, F., Control of linear parameter-varying systems. Ph.D. Thesis (Department of Mechanical Engineering, University of California, Berkeley, 1995).Google Scholar
17.Basar, T. and Bernhard, P., ∞-Optimal Control and Related Minimax Problems, (Birkhauser, Berlin, 1990).CrossRefGoogle Scholar
18.Basar, T. and Olsder, J., Dynamic Noncooperative Game Theory, (Academic Press, New York, 1982).Google Scholar
19.Johansson, R., “Quadratic optimization of motion coordination and control,” IEEE Trans. Automat. Control 35 (11), 1197–1208 (Nov. 1990).CrossRefGoogle Scholar
20.Gahinet, P., Nemiroviski, A., Laub, A. J. and Chilali, M., LMI Control Toolbox. (The MathWorks Inc., Natick, Massachusetts, 1995).Google Scholar