×

Tracking control of mobile robots: A case study in backstepping. (English) Zbl 0882.93057

The paper considers the controlled system \[ \dot x=\nu\cos\theta,\quad\dot y=\nu\sin\theta,\quad\dot\theta= \omega, \] where \(\nu\) and \(\omega\) are control variables. Feedback stabilization and tracking are considered using a suitable quadratic Lyapunov function.

MSC:

93C85 Automated systems (robots, etc.) in control theory
93D15 Stabilization of systems by feedback
70Q05 Control of mechanical systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] d’Andreá-Novel, B.; Campion, G.; Bastin, G., Control of wheeled mobile robots not satisfying ideal velocity constraints: a singular perturbation approach, Int. J. Robust Nonlinear Control, 5, 243-267 (1995) · Zbl 0837.93046
[2] Bloch, A. and Drakunov, S. (1994) Stabilization of a nonholonomic system via sliding modes. In Proc.rd IEEE Conf. on Decision and Control; Bloch, A. and Drakunov, S. (1994) Stabilization of a nonholonomic system via sliding modes. In Proc.rd IEEE Conf. on Decision and Control
[3] Brockett, R.W. (1983) Asymptotic stability and feedback stabilization. In Differential Geometric Control Theory, ed. R.W. Brockett, R.S. Milman and H.J. Sussman, pp. 181-191. Birkhäuser, Boston.; Brockett, R.W. (1983) Asymptotic stability and feedback stabilization. In Differential Geometric Control Theory, ed. R.W. Brockett, R.S. Milman and H.J. Sussman, pp. 181-191. Birkhäuser, Boston. · Zbl 0528.93051
[4] Byrnes, C. I.; Isidori, A., New results and examples in nonlinear feedback stabilization, Syst. Control Lett., 12, 437-442 (1989) · Zbl 0684.93059
[5] Canudas de Wit, C., Berghuis, H. and Nijmeijer, H. (1994) Practical stabilization of nonlinear systems in chained form. In Proc.rd IEEE Conf. on Decision and Control; Canudas de Wit, C., Berghuis, H. and Nijmeijer, H. (1994) Practical stabilization of nonlinear systems in chained form. In Proc.rd IEEE Conf. on Decision and Control
[6] Canudas de Wit, C., Siciliano, B. and Bastin, G., eds (1996). Theory of Robot Control; Canudas de Wit, C., Siciliano, B. and Bastin, G., eds (1996). Theory of Robot Control · Zbl 0854.70001
[7] Fierro, R. and Lewis, F.L. (1995) Control of a nonholonomic mobile robot: backstepping kinematics into dynamics. In Proc.th IEEE Conf. on Decision and Control; Fierro, R. and Lewis, F.L. (1995) Control of a nonholonomic mobile robot: backstepping kinematics into dynamics. In Proc.th IEEE Conf. on Decision and Control
[8] Fliess, M.; Levine, J.; Martin, P.; Rouchon, P., Flatness and defect of non-linear systems: introductory theory and examples, Int. J. Control, 61, 1327-1361 (1995) · Zbl 0838.93022
[9] Fliess, M., Levine, J., Martin, P. and Rouchon, P. (1995b) Design of trajectory stabilizing feedback for driftless flat systems. In Proc.rd European Control Conf.; Fliess, M., Levine, J., Martin, P. and Rouchon, P. (1995b) Design of trajectory stabilizing feedback for driftless flat systems. In Proc.rd European Control Conf.
[10] Jiang, Z. P., Iterative design of time-varying stabilizers for multi-input systems in chained form, Syst. Control Lett., 28, 255-262 (1996) · Zbl 0866.93084
[11] Jiang, Z.P. and Nijmeijer, H. (1996) Tracking control of mobile robots: a case study in backstepping, memorandum 1321, University of Twente.; Jiang, Z.P. and Nijmeijer, H. (1996) Tracking control of mobile robots: a case study in backstepping, memorandum 1321, University of Twente.
[12] Jiang, Z.P. and Nijmeijer, H. (1997) Backstepping-based tracking control of nonholonomic chained systems. Submitted to European Control Conf.; Jiang, Z.P. and Nijmeijer, H. (1997) Backstepping-based tracking control of nonholonomic chained systems. Submitted to European Control Conf.
[13] Jiang, Z.P. and Pomet, J.-B. (1994) Combining backstepping and time-varying techniques for a new set of adaptive controllers. In Proc.rd IEEE Conf. on Decision and ControlInt. J. Adaptive Control Sig. Process; Jiang, Z.P. and Pomet, J.-B. (1994) Combining backstepping and time-varying techniques for a new set of adaptive controllers. In Proc.rd IEEE Conf. on Decision and ControlInt. J. Adaptive Control Sig. Process
[14] Jiang, Z.P. and Pomet, J.-B. (1995) Backstepping-based adaptive controllers for uncertain nonholonomic systems. In Proc.th IEEE Conf. on Decision and Control; Jiang, Z.P. and Pomet, J.-B. (1995) Backstepping-based adaptive controllers for uncertain nonholonomic systems. In Proc.th IEEE Conf. on Decision and Control
[15] Kanayama, Y., Kimura, Y., Miyazaki, F. and Noguchi, T. (1990) A stable tracking control scheme for an autonomous mobile robot. In Proc. IEEE International Conf. on Robotics and Automation; Kanayama, Y., Kimura, Y., Miyazaki, F. and Noguchi, T. (1990) A stable tracking control scheme for an autonomous mobile robot. In Proc. IEEE International Conf. on Robotics and Automation
[16] Khalil, H.K. (1992) Nonlinear Systems; Khalil, H.K. (1992) Nonlinear Systems · Zbl 0969.34001
[17] Koditschek, D.E. (1987) Adaptive techniques for mechanical systems. In Proc.th Yale Workshop on Adaptive Systems; Koditschek, D.E. (1987) Adaptive techniques for mechanical systems. In Proc.th Yale Workshop on Adaptive Systems
[18] Kolmanovsky, H.; McClamroch, N. H., Developments in nonholonomic control systems, IEEE Control Syst. Magazine, 15, 6, 20-36 (1995)
[19] Krstić, M., Kanellakopoulos, I. and Kokotović, P.V. (1995) Nonlinear and Adaptive Control Design; Krstić, M., Kanellakopoulos, I. and Kokotović, P.V. (1995) Nonlinear and Adaptive Control Design
[20] McCloskey, R.T. and Murray, R.M. (1994) Exponential stabilization of driftless nonlinear control systems via time-varying, homogeneous feedback. In Proc.rd IEEE Conf. on Decision and Control; McCloskey, R.T. and Murray, R.M. (1994) Exponential stabilization of driftless nonlinear control systems via time-varying, homogeneous feedback. In Proc.rd IEEE Conf. on Decision and Control
[21] Micaelli, A. and Samson, C. (1993) Trajectory tracking for unicycle-type and two-steering-wheels mobile robots. INRIA Technical Report No. 2097.; Micaelli, A. and Samson, C. (1993) Trajectory tracking for unicycle-type and two-steering-wheels mobile robots. INRIA Technical Report No. 2097.
[22] Murray, R. M.; Sastry, S. S., Nonholonomic motion planning: steering using sinusoids, IEEE Trans. Autom. Control, AC-38, 700-716 (1993) · Zbl 0800.93840
[23] Murray, R.M., Walsh, G. and Sastry, S.S. (1992) Stabilization and tracking for nonholonomic control systems using time-varying state feedback. In IFAC Nonlinear Control Systems Design; Murray, R.M., Walsh, G. and Sastry, S.S. (1992) Stabilization and tracking for nonholonomic control systems using time-varying state feedback. In IFAC Nonlinear Control Systems Design
[24] Oelen, W.; van Amerongen, J., Robust tracking control of two-degrees-of-freedom mobile robots, Control Engng Practice, 2, 333-340 (1994)
[25] Oelen, W.; Berghuis, H.; Nijmeijer, H.; Canudas de Wit, C., Hybrid stabilizing control on a real mobile robot, IEEE Robotics Automation Magazine, 2, 16-23 (1995)
[26] Pomet, J.-B., Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift, Syst. Control Lett., 18, 147-158 (1992) · Zbl 0744.93084
[27] Popov, V.M. (1973) Hyperstability of Control Systems. Springer-Verlag, Berlin.; Popov, V.M. (1973) Hyperstability of Control Systems. Springer-Verlag, Berlin. · Zbl 0276.93033
[28] Samson, C. (1991) Velocity and torque feedback control of a nonholonomic cart. In Proc. Advanced Robot Control; Samson, C. (1991) Velocity and torque feedback control of a nonholonomic cart. In Proc. Advanced Robot Control · Zbl 0800.93910
[29] Samson, C. and Ait-Abderrahim, K. (1991) Feedback control of a nonholonomic wheeled cart in Cartesian space. In Proc. IEEE International Conf. on Robotics and Automation; Samson, C. and Ait-Abderrahim, K. (1991) Feedback control of a nonholonomic wheeled cart in Cartesian space. In Proc. IEEE International Conf. on Robotics and Automation
[30] Tsinias, J., Sufficient Lyapunov-like conditions for stabilization, Math. Control Sig. Syst., 2, 343-357 (1989) · Zbl 0688.93048
[31] Vidyasagar, M. (1993) Nonlinear Systems Analysis; Vidyasagar, M. (1993) Nonlinear Systems Analysis · Zbl 0900.93132
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.