Synchronization of multiple autonomous underwater vehicles without velocity measurements

In this paper, we investigate the synchronization control of multiple autonomous underwater vehicles （AUVs）, considering both state feedback and output feedback cases. Treating multiple AUVs as a graph, we define the tracking error of each AUV with both its own tracking error and the relative position errors with respect to its neighbors taken into account. Lyapunov analysis is used to derive the control law for each AUV. For the output feedback case, a passive filter is used to compensate for the unknown relative velocity errors among AUVs, and an observer is employed to estimate the velocity of the AUV itself. Rigid mathematical proof is provided for the proposed algorithms for both state feedback and output feedback cases. Simulations are provided to demonstrate the effectiveness of the proposed approach. It is shown that, the synchronization error is smaller in the case of considering the relative errors between AUVs than in the case of considering the tracking error of the single AUV only.