Email this article On linear and nonlinear trajectory tracking control for nonholonomic integrator
- Authors: 1, 2, 1, 3
-
Affiliations:
- UFABC, Santo André, SP, Brazil
- UNICAMP, Campinas, SP, Brazil
- Samara State Aerospace University
- Issue: Vol 1, No 1 (2014)
- Pages: 43-48
- Section: Articles
- URL: https://dynvibro.ru/dynvibro/article/view/1653
- DOI: https://doi.org/10.18287/2409-4579-2014-1-1-43-48
- ID: 1653
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Abstract
This paper presents two different kinds of trajectory tracking control strategies for the nonholonomic integrator known in literature as Brockett system. The first strategy presents a time-varying linear feedback control law and the second strategy is based on State Dependent Ricatti Equation (SDRE) method. Numerical simulation results indicated that both methods can be successfully used for control of the nonholomic integrator.
Keywords: Brockett integrator, Hamilton – Jacobi – Bellman equation, SDRE method.
About the authors
UFABC, Santo André, SP, Brazil
Author for correspondence.
Email: elvira.rafikova@ufabc.edu.br
Russian Federation
UNICAMP, Campinas, SP, Brazil
Email: kurka@fem.unicamp.br
Russian Federation
UFABC, Santo André, SP, Brazil
Email: marat.rafikov@ufabc.edu.br
Russian Federation
Samara State Aerospace University
Email: gafurov@ssau.ru
Russian Federation
References
- Li, Z., Canny, J. (1993) Nonholonomic motion planning, Kluwer Academic Publisher.
- Murray, R., Sastry, S. (1993) Nonholonomic motion planning: Steering using sinusoids, IEEE Trans Aut Cont, 38(5), p. 700.
- Dahleh, M., Peirce, A., Rabitz, H., Ramakrishna, V. (1996) Control of molecular motion, Proc of the IEEE, 84(1), pp. 7-15.
- Neimark, J., Fufaev, N. (1972) Dynamics of Nonholonomic Systems, American Mathematical Society, Providence, RI.
- Brockett, R. (1983) Asymptotic stability and feedback stabilization. In Differential Geometric Control Theory, Birkhäuser, Boston, MA, pp. 181-191.
- Bloch, A. (2003) Nonholonomic Mechanics and Control, Springer-Verlag, Berlin.
- Kolmanovsky, I., McClamroch, N. (1995) Developments in nonholonomic control problems, IEEE Control Systems Magazine, 15, pp. 20-36.
- Astolfi, A. (1998) Discontinuous control of the brockett integrator, Eur J Control, 4(1), pp. 49–63.
- Astolfi, A. (1997) Discontinuous control of the Brockett integrator, Proceedings of the 36th Conference on Decision & Control, San Diego, California USA.
- Canudas de Wit, C., Sordalen, O. (1992) Exponential stabilization of mobile robots with nonholonomic constraints, IEEE Transactions on Automatic Control, 37(11), pp. 1791-1797.
- Morgansen, K., Brockett, R. (200) Optimal regulation and reinforcement learning for the nonholonomic integrator, Proceedings of the 2000 American Control Conference, 1(6), pp. 462-6.
- Bloch, A., Drakunov, S. (1996) Stabilization and tracking in the nonholonomic integrator via sliding modes, Sys Control Lett, 29, pp. 91-9.
- Samson, C. (1990) Velocity and torque feedback control of a nonholonomic cart, Proceedings of the international workshop in adaptive and nonlinear control: Issues in robotics.
- Teel, A., Murray, R., Walsh, C. (1995) Non-holonomic control systems: From steering to stabilization with sinusoids, International Journal Control, 62(4), pp. 849-870.
- Pomet, J., (1992) Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift, Systems and Control Letters, 18(2), pp.147-158.
- Walsh, G., Tilbury, D., Sastry, S., Murray, R. Laumond, J. (1994) Stabilization of trajectories for systems with nonholonomic constraints, IEEE Trans Auto. Control, 39(1), pp. 216–222.
- Jiang, Z., Nijmeijer, H. (1999) A recursive technique for tracking control of nonholonomic systems in chained form, IEEE Trans. Autom.Control, 44(2), pp. 265–279.
- Jiang, Z. (2000) Lyapunov design of global state and output feedback trackers for nonholonomic control systems, Int. J. Control, 73, pp. 744–761.
- Qu, Z., Wang, J., Plaisted, C., Hull R. (2006) Global-stabilizing near-optimal control design for nonholonomic chained systems, IEEE Trans Aut Cont, 51(9), pp. 1440-56.
- Rafikov, M., Balthazar, J. (2008) On control and synchronization in chaotic and hyperchaotic systems via linear feedback control, Commun. Nonlinear. Sci. Numer. Simul, pp. 1246–1255.
- Cloutier, J., (1997) State-dependent Riccati equation techniques, An overview, presented at the American Control Conf., Albuquerque, NM.
- Cloutier, J., Mracek, C., Ridgely, D., Hammett, K. (1998) State dependent Riccati equation techniques: Theory and applications, presented at the Workshop Notes: Amer. Control Conf., Philadelphia, PA.
- Oriolo, G., Luca, A. de, Vendittelli, M. (2002) WMR Control via Dynamic Feedback Linearization: Design, Implementation, and Experimental Validation, IEEE Transaction on Control System Tecnology, 10 (6).
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