Abstract: Based on the Lagrange equation, the multi-joint robotic manipulator dynamical model is transformed into a linear state equation. And then, corresponding to the linear state equation, by solving a linear quadratic regulator (LQR) problem, the robust optimal control law is obtained, which guarantee that the joint variables converge into the given point asymptotically in global sense. Finally, an example of two-joint robot is illustrated. Simulation results show that the proposed control law is very effective and indeed has robust performance.

Key words: algebraic Riccati equation, robot, robust optimal control, LQR

摘要： 基于拉格朗日方程，把多关节机器人机械臂动力学模型转化成一线性状态方程。然后，针对此线性状态方程，通过解一线性二次型优化问题，得到鲁棒最优控制律，保证了关节变量全局渐近收敛。最后，以两关节机器人为例，仿真结果表明我们所设计的控制律的有效性和鲁棒性。

关键词: 代数里卡蒂方程, 机器人, 鲁棒最优控制, 线性二次型优化