Objectives In order to achieve the cooperative formation control of underactuated autonomous underwater vehicle (AUVs) with external environmental disturbances and model uncertainties, a bio-inspired terminal sliding mode control method is proposed.

Methods Firstly, the bow angle of the leader AUV is smoothed by differential tracker and the desired trajectory for the follower AUVs are generated based on the leader–follower formation control strategy. Then, the virtual control laws of the velocity are designed in a backstepping approach and the AUVs' position errors are stabilized. At the same time, aiming at smoothing the virtual control law, alleviating the system oscillation and reducing the computational complexity of the controller, a bio-inspired model is designed. In addition, a fixed-time nonsingular terminal sliding mode is proposed for convergence faster. Finally, a radial basis function neural network (RBFNN) with minimal learning parameter (MLP) is adopted for approximating the environmental disturbances and model uncertainties.

Results Compared with integral sliding mode control, the proposed control method can enable the AUV formation system to track the desired trajectory faster and more accurately.

Conclusions The designed formation control algorithm can achieve the trajectory tracking of AUVs.