基于模型降阶的平面三连杆欠驱动机械系统位置控制

摘要

This paper presents a position control method based on model reduction for a planar three-link passive-active-active (PAA) under-actuated mechanical system with a passive first joint. Firstly, a mathematical model of the system is built, and its integral characteristic is analyzed. Next, the partially integrable three-link system is reduced to two completely integrable two-link systems by the method of piecewise degree reduction, and the state constraint relationships of the system between the active link and the passive link can be obtained based on the two subsystems. Then, the target angles of the active links are calculated by particle swarm optimization (PSO) algorithm according to the target position of the end of the system. Finally, the controllers of the two link subsystems are designed respectively to achieve the system control objective from any initial position to any target position. Simulation results demonstrate the validity of the proposed control method.%针对第一关节为被动的平面三连杆欠驱动机械系统，提出一种基于模型降阶的位置控制方法。首先，建立平面三连杆欠驱动系统数学模型，并分析其积分特性；其次，将部分可积的三连杆系统分段降阶为两个完全可积的两连杆子系统，并基于两子系统获得系统驱动杆与欠驱动杆之间的状态约束关系；然后，利用粒子群优化算法，根据系统末端点目标位置计算驱动杆目标角度；最后，分别设计两连杆子系统控制器，实现系统从任意初始位置到任意目标位置的控制目标。仿真结果验证所提控制策略的有效性。