Global fixed-time trajectory tracking control of underactuated USV based on fixed-time extended state observer

Area of Science:

• Robotics
• Control Systems Engineering
• Marine Engineering

Background:

• Unmanned Surface Vehicles (USVs) face challenges in trajectory tracking due to unmeasurable velocities and unknown environmental disturbances.
• Existing control methods often struggle with slow convergence times and controller complexity.

Purpose of the Study:

• To develop a robust and efficient control strategy for USV trajectory tracking.
• To address limitations of unmeasurable states and external disturbances in USV control systems.
• To reduce the error convergence time for USV navigation.

Main Methods:

• A fixed-time sliding mode control (FTSMC) law is proposed, integrating a fixed-time extended state observer (FESO) and a fixed-time differentiator.
• A saturation function is incorporated to manage the terminal sliding mode surface, avoiding singularity.
• An auxiliary dynamic system is designed to handle actuator saturation issues.

Main Results:

• The proposed FTSMC law achieves fixed-time convergence for trajectory tracking errors.
• The FESO effectively estimates unmeasurable velocities and lumped disturbances.
• The auxiliary dynamic system successfully compensates for actuator saturation, ensuring system stability.
• Uniformly global fixed-time stability (UGFTS) of the closed-loop system is proven using Lyapunov's theory.

Conclusions:

• The developed control strategy offers enhanced performance for USV trajectory tracking.
• The integration of FESO and fixed-time differentiator simplifies controller design while improving accuracy.
• Numerical simulations validate the superiority of the proposed controller in handling complex USV operating conditions.