Trajectory tracking for vessels with the kinematic model using complex networks

In this work, the trajectory synchronization in ship networks is proposed applying the theory of complex dynamic networks. The network nodes were modeled by the kinematic equation in the horizontal plane, without considering environmental disturbances. To solve the trajectory synchronization problem, the error synchronization is calculated as the difference between the ships trajectories, and then this error must be converged to zero. The error convergence is proven by the Lyapunov analysis proposed in the present work. The control law design for this method is determined by the structural properties of the network, as well as the dynamic characteristics in the nodes, and the simple choice of a coupling constant. To keep the separation distance between the ships trajectories a repulsion coefficient is added into the control law. Numerical simulations were carried out using Matlab, showing a fast error convergence for network synchronization. The obtained results in this work suggest the use of this method to solve the trajectory tracking problem in coordinated motion between ships, where the nodes in the network include the dynamic equation for ships.