Immersion and invariance‐based adaptive pose tracking control under disturbances and input saturation

Abstract

This paper addresses the simultaneous attitude and position tracking of a rigid body subject to general bounded disturbances and input saturation in the framework of dual quaternions, which provide a compact and integrated description of the coupled rotation and translation. Treating disturbances as unknown parameters, a modular adaptive saturated pose tracking control scheme is then derived which consists of two separately designed parts. One part is the noncertainty equivalent disturbance estimator designed via the immersion and invariance method. Most existing adaptive pose controllers are based on the certainty equivalence principle. Since its parameter adaption process is unpredictable and acts like a forcing disturbance imposed on the deterministic system, it can cause arbitrary degradation of the closed-loop performance. Instead of invoking the certainty equivalence principle, the adaption law designed based on the novel immersion and invariance method counters the effects of the uncertain parameters from a robustness perspective and eliminates the performance degradation by introducing a stable attracting manifold in the adaption process. For both constant and time-varying disturbances, the proposed estimator can effectively attenuate their effects on the closed-loop performance. The other part is the saturated pose tracking controller where the estimated disturbances are directly used. Based on two useful lemmas, it is proved that the saturation constraints can be removed in finite time, which enables the Lyapunov stability analysis of the closed-loop system. Simulation results demonstrate improvements of the proposed control scheme in closed-loop performance and control precision when compared with a certainty equivalent controller and a sliding mode controller.