Theory and Implementation of a Repetitive Robot Controller With Cartesian Trajectory Description

This paper presents a new repetitive learning controller for motion control of mechanical manipulators undergoing periodic tasks defined in Cartesian space. The controller does not require knowledge of the manipulator dynamic parameters beyond a simple geometric description. The desired task will be defined in Cartesian coordinates, and no inverse kinematics or inverse Jacobian will be calculated. The asymptotic stability of this algorithm is proven using the Lyapunov approach, and the nonlinear characteristics of the manipulator are explicitly taken into account. The results of implementation of this new repetitive learning controller on an IBM 7545 robotic manipulator are presented. Cartesian feedback was obtained from optical joint position encoders using forward kinematics, and velocity was estimated by simple numerical differentiation of the Cartesian position signal in software. The performance of the algorithm was compared to that of a simple PD feedback system, and a modified “Computed Torque” controller using inverse kinematics on the Cartesian path. The learning algorithm outperformed both of these controllers by a significant margin, exhibited convergence within approximately three cycles, and did not require inverse kinematics to execute the Cartesian path.