基于力矩变换的PAA型欠驱动机器人鲁棒镇定控制

针对在第2 关节和第3 关节仅有两个驱动器的PAA（passive-active-active）型欠驱动三连杆机器人，提出一种基于力矩变换的鲁棒镇定控制方法. 首先对第3 关节的控制输入引入一种与第2 关节控制输入和机器人状态相关的力矩变换，以消除第3 关节控制输入对系统的影响，将机器人动力学方程化为更简单的形式，然后基于能量进行摇起控制设计. 在平衡区，将机器人第1 连杆和第2 连杆的角速度看成一种不确定性，得到机器人在不稳定平衡点附近的不确定模型；然后基于线性矩阵不等式推导鲁棒镇定状态反馈控制律，达到较大范围的平衡控制. 仿真结果表明，该控制方法具有稳定时间短和控制力矩小等优点.

Robust Stabilization Control of Underactuated PAA Robot Based on Torque Transformation

Robust stabilization control based on torque transform is proposed for an underactuated three-link manipulator, named a passive-active-active (PAA) robot. It is equipped with only two actuators on the second and third joints. A torque transform,as a function of control input of the second joint and state of the robot,is used for the control input of the third joint. The robot dynamics is transformed to a simpler form,where the influence of control input of the third joint is explicitly eliminated. An energy-based swingup control law is then designed. In the balancing area,an uncertain model is obtained by treating velocities of the first and second links around the unstable equilibrium as uncertainties. A robust stabilizing state feedback control law is derived to reach a large balancing region based on a technique of linear matrix inequality (LMI). Simulation results show that the proposed approach has advantages of short settling time and small control torques.