On Robust Adaptive PD Control of Robot Manipulators

In this study, an adaptive proportional-derivative (PD) control scheme is proposed for trajectory tracking of multidegree- of-freedom robot manipulators in the presence of model uncertainties and external disturbances whose upper bounds are unknown but bounded. The developed controller takes the advantages of linear control in the sense of simplicity and easy design, but simultaneously possesses high robustness against model uncertainties and disturbances while avoiding the necessity of precise knowledge of the system dynamics. Due to the linear feature of the proposed method, both the transient and steady-state responses are easily controlled to meet desired specifications. Also, an adaptive law for control gains using only position and velocity measurements is introduced so that parameter uncertainties and disturbances are successfully compensated, where the prior knowledge about their upper bounds is not required. Stability analysis is conducted using the Lyapunov’s direct method and brief guidelines on how to select control parameters are also provided. Simulation results corroborate that the adaptive PD control law proposed in this paper can achieve a fast convergence rate, small tracking errors, low control effort, and small computational cost and its performance is compared with that of an existing nonlinear sliding mode control method.