Nonlinear optimal control for multi‐DOF robotic manipulators with flexible joints

Abstract

AbstractA main problem in the control of flexible‐joint robots and in the precise positioning of their end‐effector, is synchronization between the turn angles of the robots' joints and the turn angles of the motors that provide actuation to these joints. In this article, a nonlinear optimal (H‐infinity) control method is proposed for multi‐DOF robotic manipulators with flexible joints. The dynamic model of these robotic manipulators is shown to be underactuated and to satisfy differential flatness properties. The state‐space description of these robots undergoes approximate linearization around a temporary operating point which is recomputed at each iteration of the control method. The linearization procedure makes use of first‐order Taylor‐series expansion and relies on the computation of Jacobian matrices. For the approximately linearized model of these multi‐DOF robotic systems an H‐infinity feedback controller is designed. This controller stands for the solution of the robots' optimal control problem under model uncertainty and external disturbances. The computation of the controller's feedback gain requires the solution of an algebraic Riccati equation, which is performed again at each time‐step of the control algorithm. The stability properties of the control scheme are proven trough Lyapunov analysis. First, it is confirmed that the controller satisfies the H‐infinity tracking performance criterion which ascertains its robustness. Moreover, it is proven that the control loop is globally asymptotically stable. Finally, to implement sensorless control for such robotic systems the H‐infinity Kalman Filter is used as a robust state estimator. The proposed control method for multi‐DOF robotic manipulators with flexible joints retains the advantages of linear optimal control, that is fast and accurate tracking of its reference setpoints under moderate variations of the control inputs.