A Novel Finite-Time Controller for the Tracking Problem on the Heisenberg System

https://doi.org/10.58571/CNCA.AMCA.2022.066

Resumen: In this paper, a novel second-order sliding-mode controller for the tracking problem on the Heisenberg system is proposed. The controller design takes into account a nonlinear change of coordinates and the selection of some particular sliding variables. These, ensure the tracking error convergence to zero in a finite time. One important characteristic of this design is the simplicity of the controller structure and the ease of tunning the gains and parameters. Additionally, the implementability of the approach is illustrated through some simulation results.

¿Cómo citar?

Manuel Mera, Héctor Ríos & Andrey Polyakov. A Novel Finite-Time Controller for the Tracking Problem on the Heisenberg System Memorias del Congreso Nacional de Control Automático, pp. 256-261, 2022. https://doi.org/10.58571/CNCA.AMCA.2022.066

Palabras clave

Control de Sistemas No Lineales; Control Discontinuo (modos deslizantes); Robótica y Mecatrónica

• Bloch, A. and Drakunov, S. (1996). Stabilization and tracking in the nonholonomic integrator via sliding modes. Systems & Control Letters, 29(2), 91–99.
• Bloch, A.M. (2003). Nonholonomic mechanics. In Nonholonomic mechanics and control, 207–276. Springer.
• Brockett, R.W. (1982). Control theory and singular riemannian geometry. In New directions in applied mathematics, 11–27. Springer.
• Defoort, M. and Djema¨ı, M. (2010). Finite-time controller design for nonholonomic mobile robot using the Heisenberg form. In 2010 IEEE International Conference on Control Applications, 1269–1274. IEEE.
• Defoort, M. and Djema¨ı, M. (2013). A Lyapunov-based design of a modified super-twisting algorithm for the heisenberg system. IMA Journal of Mathematical Control and Information, 30(2), 185–204.
• Defoort, M., Floquet, T., Perruquetti, W., and Drakunov, S.V. (2009). Integral sliding mode control of an extended heisenberg system. IET control theory & applications, 3(10), 1409–1424.
• Filippov, A.F. (1988). Differential equations with discontinuous righthand sides. Kluwer Academic Publishers.
• Floquet, T., Drakunov, S.V., and Perruquetti, W. (2004). Sliding mode control of extended heisenberg systems. IFAC Proceedings Volumes, 37(13), 609–614.
• Ghommam, J., Mnif, F., and Derbel, N. (2010). Global stabilisation and tracking control of underactuated Surface vessels. IET control theory & applications, 4(1), 71–88.
• Lambert, N.O., Schindler, C.B., Drew, D.S., and Pister, K.S. (2020). Nonholonomic yaw control of an underactuated flying robot with model-based reinforcement learning. IEEE Robotics and Automation Letters, 6(2), 455–461.
• Li, L., d’Andrea-Novel, B., and Quadrat, A. (2020). Longitudinal and lateral control for four wheel steering vehicles. IFAC-PapersOnLine, 53(2), 15713–15718.
• Marchand, N. and Alamir, M. (2003). Discontinuous exponential stabilization of chained form systems. Automatica, 39(2), 343–348.
• Mera, M., R´ıos, H., and Mart´ınez, E.A. (2020). A slidingmode based controller for trajectory tracking of perturbed unicycle mobile robots. Control Engineering Practice, 102, 104548.
• Murray, R.M., Li, Z., and Sastry, S.S. (1994). A mathematical introduction to robotic manipulation. CRC press.
• Orlov, Y. (2004). Finite time stability and robust control synthesis of uncertain switched systems. SIAM Journal on Control and Optimization, 43(4), 1253–1271.
• Ortega, R., Perez, J.A.L., Nicklasson, P.J., and Sira-Ramirez, H.J. (1998). Passivity-based control of Euler- Lagrange systems: mechanical, electrical and electromechanical applications. Springer Science & Business Media.
• Rehan, M., Reyhanoglu, M., and van Steen, J. (2019). Trajectory tracking of a knife-edge on a flat surface. In 2019 18th European Control Conference (ECC), 1648–1652. IEEE.
• Rocha, E., Casta˜nos, F., and Moreno, J.A. (2022). Robust finite-time stabilisation of an arbitrary-order nonholonomic system in chained form. Automatica, 135, 109956.
• Rochel, P., R´ıos, H., Mera, M., and Dzul, A. (2022). Trajectory tracking for uncertain unicycle mobile robots: A super-twisting approach. Control Engineering Practice, 122, 105078.
• Shi, S., Xu, S., Yu, X., Li, Y., and Zhang, Z. (2018). Finite-time tracking control of uncertain nonholonomic systems by state and output feedback. International Journal of Robust and Nonlinear Control, 28(6), 1942–1959.
• Takahashi, Y., Sakamoto, H., and Sakai, S. (2022). Kinematics control of electromagnetic formation flight using angular-momentum conservation constraint. Journal of Guidance, Control, and Dynamics, 45(2), 280–295.
• Thomas,M., Bandyopadhyay, B., and Vachhani, L. (2018). A finite-time sliding mode observer for a class of perturbed nonholonomic systems. In IECON 2018-44th Annual Conference of the IEEE Industrial Electronics Society, 2165–2170. IEEE.
• Vershik, A. and Gershkovich, V.Y. (1988). Nonholonomic problems and the theory of distributions. Acta Applicandae Mathematica, 12(2), 181–209.
• Zimenko, K., Polyakov, A., and Efimov, D. (2018). On finite-time robust stabilization via nonlinear state feedback. International Journal of Robust and Nonlinear Control, 28(16), 4951–4965.