Constrained coordinated path-following control for underactuated surface vessels with the disturbance rejection mechanism

This note proposed a practical coordinated path-following algorithm for a group of underactuated surface vessels to achieve and maintain the desired formation pattern. The developed scheme consists of two envelopes. One is to stabilize the individual vessel to the virtual vessel moving along with the predefined path. The other is to synchronize the surge speed of virtual vehicles to guarantee the desired geometric formation. Within the design framework, a nonlinear disturbance observer (DOB) is constructed to estimate the lumped disturbance which includes the model uncertainty and the unknown disturbance. By virtue of the auxiliary system and the novel tan-type barrier Lyapunov function (BLF), the observer based control law is designed to eliminate the effect of the input and velocity constraints. Furthermore, on the basis of the undirected graph, the speed agreement is presented to ensure the motion synchronization of networked underactuated vessels. Compared with the existing results, the proposed algorithm is more applicable to the marine practice, e.g. the collaborative search and rescue scene. Through the Lyapunov analysis, it is proved that all the variables of the closed-loop system are with the uniform ultimate bounded stability. Finally, the scaling formation example and comparison simulation are conducted to illustrate the effective of the proposed algorithm.