Objective   Aiming at the cluster control problem of small underactuated autonomous underwater vehicles (AUVs), a formation control strategy based on an improved RRT* algorithm is designed.

  Method  Paths planned by the RRT* algorithm are steep and difficult to track, with slow convergence speed, so an improved method is proposed to solve the above problems. First, a deviation function is added to bring the random sampling points closer to the target point, then the sampling points are connected smoothly using a Dubins curve. By rerouting within the variable radius range and designing the cost function in relation to the curve length and obstacle avoidance, the best path is chosen. According to the cost and minimum value, multiple AUVs are assigned a rendezvous point, and the speed of multiple AUVs is coordinated to complete the minimum rendezvous time constraint. A segmented vector field construction method based on the Dubins path is then designed, enabling multiple AUVs to track the planned path and reach the target rendezvous point with the direction remaining the same.

  Results  The simulation results show that the average path length of multiple AUV formations is shortened by 26.6% and the average assembly time is shortened by 21.7%.

  Conclusion  The improved algorithm proposed herein has high path planning quality and can successfully complete formation assembly tasks.