Formation Trajectory Tracking of Discrete-Time Distributed Multi-AUVs with Nonconvex Control Inputs and Weak Communication

Abstract

This paper considers the formation trajectory tracking problem of discrete-time distributed multi-AUVs (multiple autonomous underwater vehicles) with control input in a nonconvex set and weak communication. Firstly, a linear model of a single AUV is obtained by the feedback linearization of a single AUV model using the Lie derivative theory. Then, a linear equation of multi-AUV formation is obtained, and the formation coordinated control system of multi-AUVs based on the feedback linearization model is given. Secondly, the formation trajectory tracking problem of multi-AUVs is transformed into the coordination control problem of leader–followers formation. The coordination controller of the leader–followers formation under a weak communication environment is designed, and the controller satisfies the nonconvex constraints. Next, the coordination control problem of leader–followers formation is transformed into the stability of the error of leader and followers at zero by coordinate transformation. By establishing an appropriate Lyapunov–Krasovskii function, the corresponding linear matrix inequalities are obtained, and the condition of zero stability is obtained by solving the linear matrix inequalities of the leader–followers formation. Under this condition, stable trajectory tracking can be achieved in the multi-AUV formation. Finally, the stability of the designed coordination controller is verified by simulation experiments.