Algebraic-Connectivity-Based Multi-USV Distributed Formation Method via Adding a Reverse Edge

This paper concerns the formation problem in multi-USV cluster formation containment tracking tasks with a special topology. A topology reconstruction method was proposed that enables the followers' formation to be dispersed while achieving the fastest convergence rate for the system. This topology structure is based on tree topology and DAG (directed acyclic graph) local structure stem as prototypes, using the principle of adding reverse edges on the stem to reduce algebraic connectivity. By adding a reverse edge to obtain a more dispersed formation, a method for selecting appropriate reverse edges was achieved. Through relevant theoretical quantitative and qualitative analysis, it was demonstrated that adding this reverse edge can enable the system to achieve the fastest convergence rate. Finally, through simulation experiments, it was verified that the selected reverse edge can optimize the formation of followers and achieve the fastest convergence rate.