Joint Formation Control with Obstacle Avoidance of Towfish and Multiple Autonomous Underwater Vehicles Based on Graph Theory and the Null-Space-Based Method

In this study, a new joint formation combined with a two-part underwater towed vehicle (towfish) with multiple autonomous underwater vehicles (AUVs) was investigated. A triangular structure formation was established based on graph theory, in which the main point is the secondary towed vehicle acting as the “leader,” and the other two points are AUVs acting as “followers.” The excellent real-time performance and high flexibility of the towfish is highlighted, and the communication delay and fixed routine of AUVs can be avoided simultaneously. As to the obstacle avoidance, the null-space-based behavioral approach is proposed. On the basis of this approach, the formation task moving to the target is decomposed into different subtasks, and the obstacle avoidance subtask is set as the highest priority. The vector of the low-level task is projected to the null space of the high-level task vector, and the integrated task output is used as the final output function. The low-level task is partially or completely accomplished while handling the higher task; therefore, the mutual conflict between different level targets can be avoided. Moreover, the corresponding task functions are designed in accordance with different subtask priorities. The comprehensive output function of formation motion is deduced and established to ensure that obstacles can be avoided effectively. Furthermore, simulation results demonstrate the effectiveness and feasibility of the proposed method in a complex underwater environment with obstacles.