Backstepping-based cooperative and adaptive tracking control design for a group of underactuated AUVs in horizontal plan

In this paper, we investigate new implementable cooperative adaptive backstepping controllers for a group of underactuated autonomous vehicles that are communicating with their local neighbours to track a time-varying virtual leader of which the relative position may only be available to a portion of the team members. At the kinematic cooperative control level of the autonomous underwater vehicle, the virtual cooperative controller is basically designed on a proportional and derivative consensus algorithm presented in Ren (2010), which involves velocity information from local neighbours. In this paper, we propose a new design algorithm based on singular perturbation theory that precludes the use of the neighbours' velocity information in the cooperative design. At the dynamic cooperative control level, calculation of the partial derivatives of some stabilising functions which in turn will contain velocity information from the local neighbours is required. To facilitate the implementation of the cooperative controllers, we propose a command filter approach technique to avoid analytic differentiation of the virtual cooperative control laws. We show how Lyapunov-based techniques and graph theory can be combined together to yield a robust cooperative controller where the uncertain dynamics of the cooperating vehicles and the constraints on the communication topology which contains a directed spanning tree are explicitly taken into account. Simulation results with a dynamic model of underactuated autonomous underwater vehicles moving on the horizontal plane are presented and discussed.