THEORY AND IMPLEMENTATION OF A REPETITIVE ROBOT CONTROLLER WITH CARTESIAN TRAJECTORY DESCRIPTION

This paper presents a new repetitive learning controller for motion co ntrol of mechanical manipulators undergoing periodic tasks defined in Cartesian space. The controller does not require knowledge of the mani pulator 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 stabi lity of this algorithm is proven using the Lyapunov approach, and the nonlinear characteristics of the manipulator ave explicitly taken into account. The results of implementation of this new repetitive learnin g controller on an IBM 7545 robotic manipulator are presented Cartesia n feedback was obtained from optical joint position encoders using for ward kinematics, and velocity was estimated by simple numerical differ entiation of the Cartesian position signal in software. The performanc e of the algorithm was compared to that of a simple PD feedback system , and a modified ''Computed Torque'' controller using inverse kinemati cs on the Cartesian path. The learning algorithm outperformed both of these controllers by a significant margin, exhibited convergence withi n approximately three cycles, and did not require inverse kinematics t o execute the Cartesian path.