Velocity-Obstacle and COLREGs-Based Safety Control for Underactuated USVs with a Fixed-Time Fuzzy Observer: Theory and Experiment

Technical Summary: Velocity-Obstacle and COLREGs-Based Safety Control for Underactuated USVs

Problem Statement
The paper addresses the challenge of safe waypoint-following for underactuated Unmanned Surface Vehicles (USVs) operating in dynamic marine environments. These vehicles, typically lacking lateral thrusters, must navigate while encountering moving obstacle vessels and external environmental disturbances (wind, waves, currents). The core difficulty lies in designing a control system that simultaneously ensures trajectory tracking accuracy, adheres to the International Regulations for Preventing Collisions at Sea (COLREGs), and maintains stability despite model uncertainties and unknown disturbances. Existing methods often struggle with command continuity, computational complexity, or the explicit integration of COLREGs into analytical guidance laws.

Methodology
The proposed solution integrates a guidance layer and a control layer:

1. VOBCG Guidance Strategy:

   • The authors propose a Velocity-Obstacle Boundary and COLREGs-based Guidance (VOBCG) method. Unlike optimization-based approaches that search or sample the admissible velocity space, this method derives commanded headings directly from analytical Velocity-Obstacle (VO) boundary information.
   • The approach defines a safety domain based on the sum of the own ship's radius, the target ship's radius, and a buffer. When a target enters this domain, the guidance switches from Line-of-Sight (LOS) tracking to VO-based avoidance.
   • Collision cones are mapped to the absolute velocity space to define avoidance boundaries. The system classifies encounters into three scenarios—head-on, overtaking, and crossing—and applies specific COLREGs-compliant steering rules (e.g., turning starboard for head-on and crossing scenarios) to select the commanded heading ($\psi_d$) directly from the VO boundary angles ($\lambda^{\pm}_{VO}$).

2. Fixed-Time Fuzzy Observer (FT-FO) Controller:

   • To handle external disturbances and lumped uncertainties, a Fixed-Time Fuzzy Observer is integrated into the control framework. This observer utilizes fuzzy logic systems to approximate unknown nonlinear dynamics and external disturbances.
   • The control law employs fixed-time stability theory, utilizing fractional-order exponents in the error dynamics to ensure that the observation and tracking errors converge within a fixed time, independent of initial conditions.
   • A Lyapunov-based stability analysis is provided to prove that the closed-loop system achieves practical fixed-time stability.

3. Experimental Validation:

   • Simulation: A Simulink environment was used with a 4.9-m USV model ("Lanxin") to test the algorithm against four moving target ships simulating various encounter scenarios.
   • Sea Trials: Real-world experiments were conducted on a 4.9-m USV platform. Due to hardware limitations (lack of rotational-speed data for thrusters required for the full dynamic model), the sea trials utilized a T-S fuzzy controller for the physical execution, while the FT-FO was validated via simulation. Virtual target ships were introduced to simulate obstacle encounters in open waters.

Key Contributions
The paper highlights three primary contributions:

1. Analytical VOBCG Method: Unlike the Proactive Velocity Obstacle (PVO) method which relies on discrete sampling and optimization, the proposed VOBCG derives continuous commands from analytical boundaries. This eliminates command oscillations and chattering, resulting in smoother heading and surge-speed guidance that is more suitable for engineering implementation.
2. Fixed-Time Fuzzy Observer: The development of an FT-FO-based controller that offers faster disturbance-estimation convergence compared to conventional fixed-time observers. Theoretical analysis confirms the practical fixed-time stability of the closed-loop system.
3. Comprehensive Experimental Validation: The study establishes a marine experimental platform to validate the collision-avoidance scheme. It successfully demonstrates the system's ability to handle head-on, overtaking, and crossing scenarios in real marine environments while maintaining waypoint tracking.

Results

• Simulation: The VOBCG method demonstrated superior trajectory tracking precision and command smoothness compared to the PVO method. The USV successfully avoided all four dynamic obstacles while strictly adhering to COLREGs (e.g., passing astern of crossing targets and executing starboard turns for head-on encounters). Position errors increased during avoidance maneuvers but converged rapidly once the threat cleared.
• Sea Trials: The field experiments confirmed the feasibility of the strategy. The USV maintained relative distances strictly above the 10-meter safety threshold during interactions with virtual obstacles. The system demonstrated fast dynamic response and high-precision tracking of the desired heading.
• Observer Performance: Simulation results showed the proposed FT-FO could reconstruct disturbances more rapidly and with lower error than standard fixed-time observers.

Significance and Claims
The paper claims that the proposed strategy effectively bridges the gap between theoretical collision avoidance and practical engineering deployment. By deriving commands analytically rather than through optimization, the method ensures command continuity, which is critical for physical propulsion systems. The integration of COLREGs directly into the guidance law ensures legal compliance in maritime operations.

The authors modestly note a limitation in the experimental validation: while the FT-FO controller was theoretically designed and simulated, the physical sea trials utilized a T-S fuzzy controller due to the lack of rotational-speed feedback data required to model the specific low-cost thrusters on the experimental platform. Consequently, the full experimental validation of the FT-FO is reserved for future work, pending the acquisition of rotational-speed data to refine the USV dynamic model. Future research directions include investigating event-triggered and fault-tolerant control mechanisms to further enhance robustness.