Robust adaptive multi-task tracking control of redundant manipulators with dynamic and kinematic uncertainties and unknown disturbances

Abstract In this paper, a novel adaptive multi-priority controller for redundant manipulators is proposed to accomplish the multi-task tracking when kinematic/dynamic uncertainties and unknown disturbances exist. Prioritized redundancy resolution in kinematic level is incorporated into this passivity-based control framework. The kinematic and dynamic parameter adaptations are driven by both tracking error and prediction error. Moreover, the tracking information from both primary and subtasks are all utilized to accelerate the parameter estimation when the tasks are independent, whereas the inevitable tracking error of the subtasks due to algorithmic singularities is properly eliminated in the adaptation laws when the tasks are dependent. Potential ill-conditioned solution of the pseudoinverse is avoided using an improved singularity-robust inverse of the projected Jacobian. Along with the improvement of the multi-task tracking performance, smoothness of the commanded torques is still guaranteed for easy application. Measurements of the noisy joint acceleration and task velocity are avoided. The controller is mathematically derived based on Lyapunov stability analysis. Simulation results of the two cases are presented to verify the effectiveness and superiority of the proposed controller.