Tracking Control of Unmanned Surface Vehicles With Abkowitz Steering Model

Abstract

This paper is concerned with the tracking control of unmanned surface vehicles. Steering dynamics is modeled using nonlinear equations with three degrees of freedom following Abkowitz. Tracking control of this nonlinear system leads to the need to derive a control algorithm for linear error equations which have time-varying coefficients. Next, a control algorithm has been derived for this set of linear time-varying equations. Lyapunov transformations have been applied to transform the error equation into a canonical form. A desired closed-loop PD-spectrum and the desired right PD-modal matrix have been chosen and the resulting Sylvester equation has been solved to obtain a matrix of time-varying controller gains. This leads to the closed loop equations for controlling the ship steering of an unmanned ship. The controller algorithm is applied to the motion control of ships with parametric values from published reports. Several tracking trajectories have been generated with and without obstacles, and time-varying control has been investigated and presented. The control algorithm is shown to be quite effective for tracking of unmanned surface vehicles. Stability conditions are derived to ensure convergence. Present work in experimental verification is outlined.