PCT-Based Trajectory Tracking for Underactuated Marine Vessels

TL;DR

This paper introduces a novel control strategy for underactuated marine vessels using polar coordinate transformations and exponential modifications to address singularities, with simulations validating its effectiveness.

Contribution

The paper proposes a new PCT-based control method with EMO to handle singularities in trajectory tracking of underactuated marine vessels.

Findings

Effective trajectory tracking demonstrated through simulations.

Structural simplification achieved via polar coordinate transformations.

Singularity issues addressed with exponential modification of orientation.

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.