An Adaptive Control Approach with Automatic Gain Blending for Robot Manipulators under Dynamic Uncertainties

Abstract

To ensure convergence of the tracking errors despite uncertainties in the inertial parameters of a robot manipulator, adaptive tracking controllers can be applied, which adapt a parameter estimate on-line. The common adaptive robot controllers feature a proportional-derivative (PD) feedback of the tracking errors. Tuning the PD gains can be challenging due to tradeoffs between desired control performance and the risk of exceeding feasible limits of actuators. Far from the desired equilibria, small gains are beneficial in order to avoid actuator saturation. However, low gains usually come at the cost of a degraded tracking performance, especially in the presence of model uncertainties. The thesis addresses the problem in proposing a combined adaptive tracking controller for robot manipulators. It adapts a parameter estimate utilizing a natural adaptation law. Moreover, nominal high gains and global low gains are adaptively blended depending on the current tracking errors and the estimated uncertainties. In general, the blended gains decrease with growing tracking errors. However, they are shifted towards the nominal high gains if the errors remain large or if model uncertainties are estimated to affect the control performance. Consequently, the current weighting between ensuring a desired control performance and avoiding large actuation effort is automatically adapted. A recently proposed adaptation mechanism that can blend two control actions depending on the current tracking errors is taken as a starting point for the controller development. The thesis extends the approach such that the current estimated uncertainties can be included and unifies it with a parameter adaptation law to obtain a combined adaptive controller. A mathematical proof for the global uniform convergence of the tracking errors and the boundedness of the parameter estimation error is provided. Simulative and experimental results with a lightweight robot manipulator with seven degrees of freedom validate the theoretic results.