Trajectory Tracking Controller Based on Linear Algebra: a case study in underactuated surface vessels.

Abstract

The main difficulty in the control of underactuated system is that the system has more degrees of outputs to be controlled than the number of independent inputs. In order to solve the problem of the trajectory-tracking of underactuated vessels and let the controlled vessel track a reference trajectory quickly. A novel trajectory-tracking controller designed originally for robotic systems is applied for underactuated surface ships. A simple approach is proposed to track trajectories, knowing the desired state, a value for the control action needed to force the system to go from its current state to a desired one can be 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. In addition, the convergence to zero of tracking errors and simulation results are included in this article.