Tracking Control Of Nonholonomic Systems

Nonholonomic systems represent a wide class of mechanical systems. The research on nonholonomic control systems show high significance both in theory and application. Recently,the tracking problem of nonholonomic systems has been a hotspot of the research of mechanical control systems. Compared with convergence problem, we did't put much enthusiasm on it. In fact, the tracking problem is so similar to the convergence problem if you see tracking as the convergence of the given trajectory. The thesis gives a summary introduction to nonholonomic control systems, including relevant background knowledge, research status, current control approaches and results, etc. The tracking control problem of nonholonomic control systems consist the main theme of the thesis. The cascaded systems can be written aswherez₁∈Rⁿ,z₂∈R^m,f₁(t₁,z₁) is continuously differentiable in (t₁,z₁)and f₂(t₂,z₂), g(t,z₁,z₂) are continuous in their arguments, and locally Lipschitz in z₂ and (z₁,z₂)respectively To stabilize the systems, we did not use the cascade method, but at first step use the finite time convergence controller in order to simplify the system structure, which facilitated the following design.First of all, in the first chapter and the second chapter a summary introduction to nonholonomic control systems, including relevant background knowledge, research status, current control approaches and results, etc was given. In the third chapter, the tracking control for a class of simple nonholonomic system- nonholonomic system in chained form. In this chapter, the cascade structure and the finite time convergence controller were used to make the design process more concise and the design conditions more relaxed. In the fourth chapter, the tracking control problem for a class of nonholonomic systems with uncertainties was discussed. At the first step, we use the finite time convergence method to design controller to make the error system become simple after a finite time, which was contributed to the following design. And the method to stabilize the nonlinear systems with uncertainties can be used to solve the tracking problem for nonholonomic systems with uncertainties. At the same time, a detailed design process of output feedback controller was given. The simulation examples prove its effectiveness. On the application of nonholonomic systems, we use the same idea to study a kind of mobile robots in the fifth chapter , and the state feedback controller and the output feedback controller were given respectively.