一类多体系统非完整运动最优规划的拟牛顿算法

研究带有非完整约束的一类多体系统运动规划问题。多体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。在系统动量和动量矩守恒情况下,动力学方程降阶为非完整形式约束方程,系统的控制问题可转化为无漂移系统的非完整运动规划问题。文中首先导出具有多体开链系统的非完整运动模型。利用最优控制理论和最优化技术,采用输入参数化的方法将连续的最优控制问题转化为离散的最优控制问题,提出一种非完整多体系统运动规划的拟牛顿算法。最后将该方法用于自由漂浮的空间三连杆机构,仿真结果验证了该方法的有效性。

Quasi-newton method to nonholonomic motion planning of a sort of multi-body systems

The motion planning problem of a nonholonomic multi-body system is investigated in this paper.Nonholonomicity arises in many multi-body systems subject to nonintegrable velocity constraints or nonintegrable conservation laws.When the total angular momentum is zero,the control problem of system can be converted to the motion planning problem for a driftless control system.The equation of dynamics of multi-body chain system with free floating is obtained by using the momentum theorem.Based on the input parameterization,the continuous optimal control problem is transformed into the discrete one.The quasi-Newton method of motion planning for nonholonomic multi-body system is proposed.The effectiveness of the numerical algorithm is demonstrated by numerical simulation.