Robust time-varying formation control for underactuated autonomous underwater vehicles with disturbances under input saturation

In this paper, a robust control scheme is developed for time-varying formation of multiple underactuated autonomous underwater vehicles (AUVs) with disturbances under input saturation. Firstly, the reference trajectory of the follower is defined using a body-fixed coordinate transformation based on the leader position and predetermined time-varying formation. Next, three new additional control terms are proposed to handle the input saturation and underactuation problems of AUVs, respectively. On the basis of the above, the robust formation control law is designed incorporating a disturbance observer into the dynamic surface control (DSC) method, where the disturbance observer is constructed to online estimate unknown time-varying disturbances. The designed formation control law does not depend on the leader's acceleration due to using DSC and the mass matrix in the dynamic model of AUVs is non-diagonal, which is more realistic. Strict stability analysis indicates that the designed robust formation control law can make AUVs achieve the predefined time-varying formation, while guaranteeing uniform ultimate boundedness of all signals of the AUV formation closed-loop control systems. Simulation results on three AUVs demonstrate the effectiveness of the proposed formation control scheme.