基于小波逼近的机械系统非完整运动规划数值方法

WAVELET APPROXIMATION BASEDNUMERICAL ALGORITHM FORNONHOLONOMIC MOTION PLANNINGOF MECHANICAL SYSTEM

机械系统中的非完整约束通常是由不可积的速度约束或不可积的守恒律引起。由于非完整约束的存在,系统的运动控制和规划问题比一般的机械系统要困难得多。机械系统在动量和动量矩守恒且为零的情况下,系统动力学方程可降阶为非完整形式约束方程。基于这样的方程,将系统的控制问题转化为无漂移系统的非完整运动规划问题。针对带有非完整约束的机械系统,导出自由漂浮的空间机器人系统非完整运动模型。利用最优控制技术和小波分析方法,在控制输入中引入小波函数逼近,提出一种非完整机械系统运动规划数值方法。将该方法用于自由漂浮空间双臂机器人系统,仿真结果验证了方法的有效性。

Nonholonomicity arises in many mechanical systems subject to nonintegrable velocity constraints or nonintegrable conservation laws. Due to nonholonomic constraints, the mo-tion planning and control of a nonholonomic mechanical system is much more difficult than that of a conventional system. When the total angular momentum is zero, the dynamics of a me-chanical system is described in the form of differential equa-tions of first order. According to such equations, the control problem of system can be converted to the motion planning problem for a driftless control system. The equation of dynam-ics of space robot with free floating is obtained by using the momentum theorem. The control technique and wavelet analy-sis method are made use of and an numerical algorithm for nonholonomic motion planning is proposed. The wavelet ap-proximation is used to optimal control and to generate a feasible trajectory for a nonholonomic system. The effectiveness of the numerical algorithm is demonstrated by numerical simulation.