PCT-Based Trajectory Tracking for Underactuated Marine Vessels

Abstract

This paper investigates the trajectory tracking problem of underactuated marine vessels within a polar coordinate framework. By introducing two polar coordinate transformations (PCTs), the original two-input-three-output second-order tracking model expressed in the Cartesian frame is reduced to a two-input-two-output feedback system. However, the resulting model does not necessarily satisfy the strict-feedback condition required by conventional backstepping approaches. To circumvent potential singularities arising in the controller design, a novel concept termed exponential modification of orientation (EMO) is proposed. While the PCTs yield substantial structural simplification, they also introduce inherent limitations, most notably singularities associated with angular coordinates. Addressing these singularities constitutes another key focus of this paper. Numerical simulation results are presented to demonstrate the effectiveness of the proposed control strategy.

Figures (6)

• Figure 1: Illustration of two polar coordinate systems and related variables.
• Figure 2: Reference trajectory and its tracking by two methods with $u_{ld}=10m/s$, $\forall t\geq0$.
• Figure 3: Tracking performance comparison with $u_{ld}=10m/s$, $\forall t\geq0$.
• Figure 4: Corresponding control efforts comparison with $u_{ld}=10m/s$, $\forall t\geq0$.
• Figure 5: Trajectory tracking results in both methods with $u_{ld}=1.3m/s$, $\forall t\geq0$.