欠驱动三连杆机器人的混杂控制方法

Hybrid control strategy for an underactuated three-link manipulator

针对第二关节为被动关节的欠驱动三连杆机器人,提出一种混杂控制方法.欠驱动三连杆机器人的运动空间分为3个阶段:退化阶段、摇起阶段和平衡阶段.首先,在退化阶段,对第三关节构造Lyapunov函数,并针对此函数设计控制律使其连杆相对于前一连杆自然伸展,使系统退化为类Pendubot机器人;同时基于能量不断增加的思想设计第一关节控制律,以节省后阶段的能量控制时间.其次,在摇起阶段,保持第三关节控制律形式不变;通过仅控制系统能量和同时控制系统能量、角速度两种方法设计第一关节控制律,使系统进入平衡区.最后,对退化后的系统采用线性控制将其稳定在竖直向上不稳定平衡点上.数值仿真结果表明文中所提方法具有控制时间短,所需力矩小等优点.

This paper presents a hybrid control strategy for an underactuated three-link manipulator with its second joint being passive. The motion space of the manipulator is divided into three stages： order-reduced stage, swing-up stage and balancing stage. Firstly, in the order-reduced stage, a Lyapunov function is constructed for the third joint, and a control law is designed to force the third link to stretch out toward the second one in a natural way. Meanwhile, another control law is designed for the first joint based on the idea of increasing tile system energy continuously. Consequently, the manipulator is reduced to a Pendubot-like system. Then, in the swing-up stage, by retaining the designed control law for the third joint, two different control law design methods are proposed for the first joint to force the manipulator to enter into the balancing stage. One method is only based on the system energy, while another one is based on both the energy and the angular velocity of the first joint. Finally, a linear control is employed for the reduced Pendubot-like system, which stabilizes the manipulator at the straight-up unstable equilibrium position. Numerical simulations show that the proposed strategy has the advantages of short settling time and small control torques.