CBF Based Quadratic Program for Trajectory Tracking of Underatuated Marine Vessels

TL;DR

This paper introduces a control barrier function-based quadratic programming approach to improve trajectory tracking of underactuated marine vessels, effectively handling singularities caused by coordinate transformations.

Contribution

It develops a novel CBF-based quadratic program method that addresses singularity issues in vessel trajectory tracking control.

Findings

Successfully reduces singularities in the control design.

Demonstrates improved trajectory tracking in simulations.

Provides a robust control framework for underactuated marine vessels.

Abstract

By introducing two polar coordinates transformations, the marine vessel's original two-input-three-output second-order tracking model can be reduced to a two-input-two-output feedback form. However, the resulting system does not confirm to the strict-feedback structure, leading to potential singularity when designing the stabilizing function for the virtual input in the recursive controller design. Moreover, the polar coordinate transformation itself inherently introduces singularities. To address these singularity issues, this paper employs a control barrier function (CBF) based approach and formulates the trajectory tracking problem as a quadratic program (QP) solved via a QP optimizer. Numerical simulations are carried out to demonstrate the effectiveness of the proposed method.