Trajectory Tracking of Underactuated Surface Vessels: A Linear Algebra Approach

This brief presents the design of a controller that allows an underactuated vessel to track a reference trajectory in the x-y plane. A trajectory tracking controller designed originally for robotic systems is applied for underactuated surface ships. Such a model is represented by numerical methods and, from this approach, the control actions for an optimal operation of the system are obtained. Its main advantage is that the condition for the tracking error tends to zero, and the calculation of control actions are obtained solving a system of linear equations. The proofs of convergence to zero of the tracking error are presented here and complete the previous work of the authors. Simulation results show the good performance of the proposed control system.