Adaptive SP-D control of a robotic manipulator in the presence of modeling error in a gravity regressor matrix: theory and experiment

Many controllers have been developed for setpoint control of robotic manipulators. An adaptive proportional and derivative (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 the stability analysis of such problem. As a byproduct of the result, we also show that existing setpoint controllers such as an adaptive saturated proportional-derivative (SP-D) and saturated proportional-integral and derivative (SP-ID) in the literature can be analyzed and designed in a unifying way as special cases of the proposed controller.