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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.
Aiming at the under-actuated three-link robot with the second joint as the passive joint, a hybrid control method is proposed. The kinematic space of underactuated three-link robot is divided into three stages: degenerating stage, swinging stage and balance stage.Firstly, In the degenerate phase, the Lyapunov function is constructed for the third joint, and the control law is designed for this function so that the connecting rod naturally extends relative to the previous connecting rod to degenerate the system into Pendubot-like robots. Meanwhile, the first joint is designed based on the idea of increasing energy Control law to save energy control time in the later stage.Secondly, in the swing-up phase, the third joint control law is kept in the same form. The first joint control law is designed by controlling the system energy and controlling the system energy and angular velocity simultaneously , The system enters the balance zone.Finally, the linearized control of the degraded system is used to stabilize it in the vertical upward unstable equilibrium point.Numerical simulation results show that the proposed method has the advantages of short control time and small required torque.