Bearing-based formation tracking control of AUVs with optimal gains tuning

This paper investigates the bearing-based formation tracking control problem of multiple autonomous underwater vehicles (AUVs), where the linear velocity and actuator constraints are considered. Different from the existing control methods for AUVs, position or relative position measurements are not required in our work. A leader-follower structure is adopted, where the leaders move with a time-varying and unknown linear velocity in the earth-fixed frame. We propose a consensus-based orientation estimator and an adaptation law for estimating the leaders' linear velocity in the leaders' common body-fixed frame, respectively. Then, a bearing-based formation tracking controller is designed for the followers to track the leaders and achieve the desired formation shape. Using cascade system theories, the global asymptotic stability of the overall system is rigorously analyzed. Furthermore, the estimator gains and controller gains are determined by the proposed optimal gains tuning method such that the prescribed performance criteria are optimized while satisfying the linear velocity and actuator constraints. Hence, stability, optimality, and feasibility are all achieved. Some simulation results are also given to demonstrate the effectiveness of our method.