Communication topology for AUV formation consensus based on optimal cost control under time-varying communication and input delays

This study investigates the optimal communication topology for consensus in autonomous underwater vehicle (AUV) formations, considering both leader-following and leaderless scenarios. Initially, a second-order dynamic model of the AUV is established using the feedback linearization method. To address time-varying delays, a universal predictor-based consensus protocol is introduced, capable of operation with or without a designated leader. Subsequently, two global quadratic cost functions are formulated based on distinct consensus errors. Utilizing linear quadratic regulator (LQR) theory and matrix theory, the optimal communication topologies and associated gain matrices are deduced. Specifically, for leader-following AUV formations, the optimal communication topology is identified as an unevenly weighted star-shaped directed spanning tree. Conversely, for leaderless formations, the optimal topology adopts a complete digraph, which indicates high interaction requirements. To accommodate practical constraints, a suboptimal topology is devised, featuring a directed spanning tree. These findings offer a theoretical framework for selecting communication topologies in AUV formations, with numerical examples provided to validate the proposed approaches.