A kinematic hybrid feedback controller on the unit circle suitable for orientation control of ships

Abstract

This paper presents a hybrid feedback controller suitable for orientation control of ships. A hybrid kinematic controller on the unit circle is constructed from the gradient of a synergistic potential function, which globally asymptotically stabilizes a desired orientation, with yaw rate viewed as control input. While this idea is not new, the potential function is novel and possesses some desired properties. The kinematic controller generates smooth reference signals for the desired velocity and acceleration, except at instances when the controller switches. Continuity of velocity and acceleration is achieved by controlling the yaw rate through a double integrator. Moreover, the velocity and acceleration converge to their desired values exponentially. The resulting closed-loop system is stable, provided the controller gains satisfy mild constraints. This is shown using a hybrid Lyapunov function.