Adaptive control of a rigid body vehicle on exponential coordinates with guaranteed performance

Adaptive control systems are widely used for compensating the effect of disturbances, system uncertainties, unmodeled dynamics, and changes in systemdynamics. In this paper, the problemof controlling an uncertain rigid body vehicle is investigated for tracking a desired trajectory, where the relative configuration is described in terms of exponential coordinates on the Lie group of rigid body motions. First, one of the existing nominal controllers, which provides coupled translational and rotational maneuvers, is augmented with an adaptive controller to suppress the effects of systemuncertainties. Second, in order to achieve a prescribed user-defined performance guarantee, nominal controller is augmented with set-theoretic adaptive controller to enforce the systemstate trajectory to evolve inside a-priori user-defined compact set. Finally, the efficacy of the presented theoretical results are demonstrated through an illustrative numerical example.