Study for Control System Design of Nonholonomic System

非完整系统不能用光滑的静态反馈控制律镇定。为了稳定非完整系统的原点，人们提出了许多控制律。然而，这些控制律是分段解析或时变函数。因此，这些控制律中的许多不能应用于真实系统，因为这些控制律关于时间的一阶导数不存在。为了克服这些困难，本研究提出了非完整链式系统和非完整Caplygin系统的控制律。所提出的链式系统控制律是光滑的静态反馈，它能指数稳定除某些初始状态外的平衡点。所提出的Caplygin系统的控制律是分段解析的时变状态反馈。可以计算出这些提出的控制律对时间的一阶导数。因此，它可以应用于Planor空间机器人。在此基础上，开发了自由飞行空间机器人卫星本体运动与末端执行器运动解耦的控制系统。大量的数值仿真证明了所提出的控制系统的有效性。

Nonholonomic systems cannot be stabilized by smooth static state feedback controllaws. In order to stabilize the origin of the nonholonomic systems many control laws have been proposed. However, these control laws are piecewise analytic or time varying functions. Therefore many of these control laws cannot be applied to real systems because the first derivative of these control laws with respect to time does not exist. In this study to overcome these difficulties, control laws for nonholonomic chained systems and nonholonomic Caplygin systems have been proposed. Proposed control law for chained systems is smooth and static state feedback which exponentially stabilizes the equilibrium point except some initial states. Proposed control law for Caplygin systems is piecewise analytic and time-variant state feedback. The first derivative of these proposed control laws with respect to time can be calculated. Therefore it can be applied to planor space robot. Furthermore we develop the control system which decouples motions of satellite base body with end-effector movement for free-flying space robot. Many numerical simulations demonstrate the usefulness of these proposed contorl systems.