Global asymptotic full state formation control of underactuated surface ships with non-diagonal inertia/damping matrices

In this work, we investigate the full state formation control problem of multiple underactuated surface ships with non-diagonal inertia and damping matrices. By combining the input/state transformations and the nonlinear time-varying tools, a formation controller is derived guaranteeing that the position and orientation states of all the ships globally asymptotically converge to the desired stationary geometric formation pattern under the scenarios of fixed communication graph with a spanning tree, and the velocities of ships tend to zero. Simulation examples are given to illustrate the effectiveness of the proposed control scheme.