Attitude Stabilization of a Rigid Body with Communication Time Delay

A predictor augmented with a geometric controller is proposed to stabilize the attitude of a rigid body with both states as well as input time delay, possibly encountered while operating over a network. The predictor, as well as the controller, are proposed on SO(3) to remove the singularities and ambiguities associated with local representation. The predictor predicts the future states of the rigid body and the output of the predictor is used as input to the geometric controller. It is proved with the help of the Lyapunov Razumikhin theorem that the predictor is asymptotically stable. The controller is also shown to be asymptotically stable. Numerical simulation, as well as comparison results, are given to show the superiority of the proposed approach.