Adaptive SP-D control of robots with structural uncertainty in gravity regressor matrix: theory and experiment

Many controllers have been developed for setpoint control of robotic manipulators. Adaptive PD controller is one of the simplest and most effective setpoint controller in the presence of uncertainty in gravitational force. However, an exact model of gravity regressor is required in the adaptive PD control. In this paper we propose an adaptive setpoint controller with modeling error in the gravity regressor, and show that convergence can be guaranteed even when the gravity regressor is uncertain. A new Lyapunov function is presented for convergence analysis of such problem. As a by-product of the result we also show that existing setpoint controllers, such as the adaptive SP-D and SP-ID in the literature, can be analyzed and designed in an unifying way as special cases of the proposed controller