Robust Torque Control of Wheeled Mobile Robots with Kinematic Disturbances

Document Type : Research Article

Authors

Abstract

In this paper, robust control of the wheeled mobile robots in presence of external disturbances and parameter uncertainties of the dynamical system violating the nonholonomic kinematic constraint of non-slipping is presented. Despite to the previous works focused on the kinematic control design, a robust torque control developed as a unified approach for both of the tracking and regulation problems based on the tunable dynamic oscillator. The proposed controller guarantees that the tracking error converges exponentially to an arbitrarily small neighborhood of the origin. To demonstrate the performance of the proposed controller, simulation results for typical differential drive and skid steer mobile robots presented.

Keywords

References

[1] Brockett, R.W.; “Asymptotic Stability and Feedback Stabilization”, Differential Geometric Control Theory, R.W. Brockett, R.S. Millman, and H.J. Sussmann (Editors), Birkhauser, Boston, pp. 181-191, 1983.
[2] Bloch, A. M.; Reyhanoglu, M.; McClamroch, and N. H.; “Control and Stabilization of Nonholonomic Dynamic Systems”, IEEE Trans. on Automat Control, Vol. 37, p.p.1746-1757, 1992.
[3] Samson, C.; “Time-varying Feedback Stabilization Control of a Car-Like Wheeled Mobile Robot”, Int.J. of Robotics Research, Vol. 12, p.p. 55-66, 1993.
[4]Samson, C.; “Control of Chained Systems Application to Path Following and Time-Varying Point-Stabilization of Mobile Robots”, IEEE Trans.on Automat Control, Vol. 40, p.p. 64-77, 1995.
[5] Bloch, A. M.; McClamroch, N. H.; and Reyhanoglu, M.; “Controllability and Stabilizability Properties of a Nonholonomic Control System”, Proc. of 29th IEEE Int. Conf. on Decision and Control, Hawaii,p.p. 1312-1314, 1990.
[6] Canudas de Wit, C.; and Sørdalen, O. J.; “Exponential Stabilization of Mobile Robots with Nonholonomic Constraints”, IEEE Trans. On Automatic Control, Vol. 37, p.p. 1791-1797, 1992.
[7] Guldner, J.; and Utkin, V. I.; “Stabilization of Nonholonomic Mobile Robots Using Lyapunov Function for Navigation and Sliding Mode Control”,Proc. of 33rd IEEE Int. Conf. on Decision and Control, p.p. 2967-2972, 1994.
[8] Astolfi, A.; “Discontinuous Control of Nonholonomic Systems”, System & Control Letters, Vol. 27, p.p. 37-45, 1996.
[9] Pourboghrat, F.; “Exponential Stabilization of Nonholonomic Mobile Robots”, Computers and Electrical Engineering, Vol. 28, p.p. 349–359, 2002.
[10] Dong, W.; Liang Xu, W.; and Huo, W.; “Trajectory Tracking Control of Dynamic Nonholonomic Systems with Unknown Dynamics”, Int. J. of Robust and Nonlinear Control Vol. 9, p.p. 905-922,1999.
[11] Ge, S. S.; Wang, J.; Lee, T. H.; and Zhou, G. Y.; “Adaptive Robust Stabilization of Dynamic Nonholonomic Chained Systems”, J. of Robotic Systems, Vol. 18, p.p. 119-133, 2000.
[12] Kim, M. S.; Shin, J. H.; Hong, S. G.; and Lee, J. J.; “Designing a Robust Adaptive Dynamic Controller for Nonholonomic Mobile Robots Under Modeling Uncertainty and Disturbances”, Mechatronics, Vol.13, p.p. 507-519, 2003.
[13] Dong, W.; and Kuhnert, K. D.; “Robust Adaptive Control of Nonholonomic Mobile Robot with Parameter and Nonparameter Uncertainties”, IEEE Trans. on Robotics, vo. 21, p.p. 261-266, 2005.
[14] Ma, B. L.; and Tso, S. K.; “Robust Discontinuous Exponential Regulation of Dynamic Nonholonomic Wheeled Mobile Robots with Parameter Uncertainties”, Int. J. of Robust and Nonlinear Control, Vol. 18, p.p. 960-974, 2007.
[15] Mauder, M.; “Robust Tracking Control of Nonholonomic Dynamic Systems with Application to The Bi-Steerable Mobile Robot”, Automatica Vol. 44, p.p. 2588–2592, 2008.
[16] Chen, C. Y.; Li, T. S.; Yeh, Y. C.; and Chang, C. C.; “Design and Implementation of an Adaptive Sliding-Mode Dynamic Controller for Wheeled Mobile Robots”, Mechatronics, Vol. 19, p.p. 156-166, 2009.
[17] Corradini, M. L.; Leo, T.; and Orlando, G.; “Robust Stabilization of Mobile Robot Violating The Nonholonomic Constraint Via Quasi-Sliding Modes”, Proc. of American Control Conference,San Diego, California, p.p. 3935-3939, 1999.
[18] Dixon, W. E.; Dawson, D. M.; Zergeroglu, E.; and Behal, A.; Nonlinear Control of Wheeled Mobile Robots, 1st Edition, Springer-Verlag, 2001.
[19] Kozlowski, K.; and Pazderski, D.; “Practical Stabilization of a Skid-Steering Mobile Robot- A Kinematic-Based Approach”, IEEE 3rd Int. Conference on Mechatronics, Budapest, p.p. 519-524, 2006.
[20] Pazderski, D.; and Kozłowski, K.; “Trajectory Tracking of Underactuated Skid-Steering Robot”, American Control Conference, Washington, USA, p.p. 3506-3511, 2008.
[21] Leroquais, W.; and d'Andrea-Novel, B.; “Modeling and Control of Wheeled Mobile Robots Not Satisfying Ideal Velocity Constraints: The Unicycle Case”, Proc. of 35th Conf. on Decision and Control, Kobe, Japan, p.p. 1437-1442, 1996.
[22] Motte, I.; and Campion, G.; “A Slow Manifold Approach for The Control of Mobile Robots Not Satisfying The Kinematic Constraints”, IEEE Trans. on Robotics and Automation, Vol. 16, p.p. 875-880, 2000.
[23] Wang, Z. P.; Su, C. Y.; Lee, T. H.; and Ge, S. S.; “Robust Adaptive Control of a Wheeled Mobile Robot Violating The Pure Nonholonomic Constraint”, 8th Int. Conf. on Control, Automation, Robotics and Vision, Kumming, China, p.p. 987-992, 2004.
[24] Lewis, F.; Abdallah, C.; and Dawson, D.; Control of Robot Manipulators, 1st Edition, MacMillan Publishing Co., 1993.
[25] Ward, C. C.; and Iagnemma, K.; “A Dynamic-Model-Based Wheel Slip Detector for Mobile Robots on Outdoor Terrain”, IEEE Trans. on Robotics, Vol. 24, p.p. 821-831, 2008.
[26] Dawson, D. M.; Hu, J.; and Burg, T. C.; Nonlinear Control of Electric Machinery, 1st Edition, Marcel Dekker Inc., 1998.

Files

Share

How to cite

Statistics