This paper seeks to provide a solution for the formation control issue that arises when autonomous underwater vehicles (AUVs) are subjected to interference from obstacles and complex ocean currents.

To tackle the issue of AUV hysteresis resulting from an overly rapid predicted convergence speed during dynamic obstacle avoidance, a multi-AUV formation adaptive control method (NDP-ABS) based on brain dynamics model prediction is created. Active and inhibitory sources are created to solve the local optimization problem of potential field methods. When paired with optimal control, dynamic obstacle avoidance, formation control, and predicted tracking are accomplished. Second, a nonlinear adaptive backstepping method is used to design the AUV expected tracking controller, which resolves the interference of shallow ocean current disturbances and nonlinear factors on the AUV expected tracking control in consideration of unknown nonlinear factors and ocean current disturbances introduced in the control law of the NDP process. Finally, Lyapunov theory is used to demonstrate the system's stability.

The anti-interference and obstacle avoidance performance of the NDP-ABS system are tested in six sets of comparative simulation tests, and the results confirm its efficacy.

The NDP-ABS formation scheme offers several benefits, including cheap obstacle avoidance costs, robust resistance to interference from ocean currents, high stability, and clear advantages in the non-explicit formation control of multiple AUVs.