Application of LQR in nonlinear control of manipulators

 

 

WEI Lai, YUN Chao, YANG Xuebing

 

(School of Mechanical Engineering and Automation, Beijing University of 

Aeronautics and Astronautics, Beijing 100191, China)

 

 

Abstract: 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.

 

Key words: manipulator; nonlinear control; computedtorque method; Markov decision process (MDPs); linear quadratic regulator (LQR); accuracy