二阶非完整平面欠驱动机械系统的位置控制

Position Control of Second-Order Nonholonomic Planar Underactuated Mechanical System

针对中间关节为欠驱动的二阶非完整平面三连杆机械系统提出一种基于模型降阶的分段控制策略。首先,控制欠驱动关节到达目标位置,并控制第三连杆角度和角速度为零,将系统降阶为平面虚拟Pendubot系统;其次,依据平面Pendubot系统的幂零近似特性,设计一个周期开环迭代镇定控制器,使平面虚拟Pendubot系统两连杆的角速度都收敛为零的同时,欠驱动关节又回到目标位置,从而使平面三连杆系统降阶为初始速度为零的平面虚拟Acrobot系统。然后,根据平面虚拟Acrobot系统的运动状态约束关系,利用在线粒子群优化算法求取两连杆的目标角度;接着,针对第三连杆设计控制器实现平面虚拟Acrobot系统的控制目标,从而实现整个系统的控制目标,仿真结果验证所提出控制策略的有效性。

This paper presents a control strategy based on model reduction for a second-order nonholonomic planar three-link underactuated mechanical system with passive middle joints.Firstly,the system was reduced to a planar virtual Pendubot by moving the underactuated joint to the target position.Additionally,the angle and angular velocity of third joint lever were tuned to zero.Next,according to the nilpotent approximation property of the planar virtual Pendubot,an open-loop iterative stabilization controller was designed,which is able to make the angular velocity of the planar virtual Pendubot's joint levers converge to zero.Furthermore,the controller drove the underactuated joints to target positions.As a result,a planar three-link underactuated mechanical system was reduced to a planar virtual Acrobot system.Then,according to constraints of motion states of the Acrobot system,the target angles of two joint levels were calculated by the online particle swarm optimization algorithm.Finally,the controllers of the third joint levels were designed to achieve the controlling goal of the planar virtual Acrobot system as well as the whole system.Simulation results demonstrate the validity of the proposed control method.