Repetitive and adaptive control of robot manipulators with velocity estimation

This paper presents repetitive and adaptive motion control schemes for rigid-link robot manipulators, when the manipulator's joint velocities cannot be measured by the control system. The control objective consists in tracking a prescribed desired trajectory. In the case of repetitive control, the desired trajectory is periodic and it is required that the robot achieve the control objective through repeated learning trials. We assume that the robot inverse dynamics are totally unknown, except that they can be represented by an integral of the product of known differentiable kernel and an unknown influence function. In the case of adaptive control, it is assumed that only the manipulator inertia parameters are unknown and that the desired trajectory jerks are available to the control system. In both control schemes, a velocity observer, which is formulated based on the desired input/output relation of the manipulator, is used to estimate the manipulator joint velocities. A stability analysis of the repetitive and adaptive control schemes with velocity estimation is presented. Simulation and experimental results show that the proposed repetitive control algorithm is successful in acheiving the control objective without direct measurement of the joint velocities.