Study On Several Control Problems Of Nonholonomic System

Nonholonomic constraints exist in wheeled mobile robots, flexible manipulators, artificial satellites, aircrafts etc. These systems are often controlled difficultly with nonholonomic constraints. However, its controllability makes it challenging that the research and realization to the control problem of these nonholonomic systems. As the results, it is important in both theory and engineering that the control of nonholonomic system is studied deeply.Aimed at three control problems of nonholonomic system, such as motion planning, stabilization and trajectory tracking, it was studied deeply and broadly. And it mainly includes as following:1. Aimed at the nonholonomic chained system, the motion planning problem is studied. Firstly, a method based on Bang-Bang control is proposed to design a switching strategy. The strategy, which is obtained through the proposed method, can make every state of the single chained system move from the initial value to the terminal value after the finite time and the finite switches. And then, aimed at the acute change between the control inputs in the traditional Bang-Bang control, a method based on the smooth Bang-Bang is proposed. The scope of control inputs is decreased using this method. Finally, the method based on smooth Bang-Bang control is extended to m-chained system with m+1 control inputs, and the motion planning of this class of nonholonomic system is realized.2. Aimed at nonholonomic chained systems and a kind of nonholonomic systems, which can't be transformed into chained system, the stabilization problem is studied. Firstly, an iterative method based on invariant maniform is proposed to design a feedback stabilization controller. And through this method, a discontinuous time-invariant control law and the analytic results of the chained system are obtained. And then this method is extended to multi-chained system with m+1 control inputs and m chains, and the local stabilization of the class of systems is solved. Finally, aimed at a class of nonholonomic system, which can't be transformed into chained form, the discontinuous time-invariant feedback control law and the continuous time-variant feedback control law are proposed to solve the local and global stabilization of this class of systems. And aimed at the system with the uncertain parameters, using the adaptive method, two kinds of adaptive control law are designed, that is adaptive discontinuous time-invariant control law and adaptive continuous control law. And the stabilization of this system with the uncertain parameters is realized.