Adaptive and repetitive controller for robotic manipulators with slowly updating scheme using B-spline shape function

This paper studies the real-time adaptive and repetitive control problem using the Desired Compensation Learning Law (DCLL) that has the advantage of robustness under the presence of unknown parameters with low memory requirement. The control structure of DCLL consists of a feedforward compensator that is designed by a linear combination of shape functions that is adaptable to parameter variations; hence the selection of appropriate shape functions plays an important role in the adaptive ability and accuracy of DCLL. In this study, the B-spline shape function is proposed to be used under the slowly updating scheme and the obtained results show that the robustness and accuracy of the tracking can be greatly improved even under payload variation and torque limits.