Practical Formation Control of Multiple Underactuated Ships with Limited Sensing Ranges

This paper presents a constructive method to design cooperative controllers that force a group of N underactuated ships with limited sensing ranges to perform a desired formation, and guarantee no collisions between the ships. These ships do not have an independent actuator in the sway axis. The desired formation is stabilized at any sufficiently smooth reference trajectories, including fixed points and nonadmissible trajectories for the ships. The formation control design is based on several nonlinear coordinate changes, the transverse function approach, the backstepping technique, the Lyapunov direct method, and smooth and p-times differentiable step functions. These functions are introduced and incorporated into novel potential functions to solve the collision avoidance problem without the need of switchings despite the ships’ limited sensing ranges. Simulations illustrate the results.