线性二次调节器在机械臂非线性控制中的应用研究

Application of LQR in nonlinear control of manipulators

针对应用计算力矩法对机械臂进行非线性控制时动力学模型参数误差会引起伺服误差增大以及系统稳定性下降等问题,将线性二次型调节技术应用到机械臂非线性控制中,开展对机械臂线性化解耦控制律中闭环误差特性微分方程的分析,建立了伺服误差与动力学模型参数误差之间的关系,提出了在控制系统中加入误差补偿项的方法,误差补偿过程考虑为有限阶段马尔可夫决策的过程,利用线性二次调节器(LQR),通过收集先前动作中的伺服误差信息计算得出了补偿项,该方法适用于做重复工作的机械臂。在ADAMS动力学分析软件中的二连杆机械臂模型,以及单关节实验平台上对该方法抑制伺服误差的能力进行了评价,并进行了轨迹跟随试验。研究结果表明,该方法能够有效地补偿动力学模型的误差,减小机械臂伺服误差,提高轨迹精度。

Aiming at solving the problems of servo errors and instability caused by the mismatch between actual and modelled dynamic parameters in nonlinear control of manipulators using computed-torque method, the approach of linear quadratic regulation was investigated. After the analysis of closed-loop equation for the decoupling and linearizing manipulator-control system, the relationship between servo errors and the mismatch of dynamic parameters was established. A method was presented to add error-correction terms, which can be treat as a finite-horizon Markov decision process （ MDPs）, in the control system. A linear quadratic regulator （LQR） is employed to calculate the error- correction terms using the data collected in the process of motion, and it is well suited to manipulators performing repetitive tasks. The ability of the algorithm to suppress servo errors was evaluated on the two-link planar manipulator based on ADAMS and an experiment platform of a robot joint, the trajectory-following control were tested. The results indicate that this scheme helps to compensate modeling errors, suppress servo errors and improve the accuracy of the trajectory.