Physics-Driven Collision Risk Evaluation of Autonomous Surface Vehicles Using Quaternion Ship Domain and Geometric-Temporal Indicators

With the rapid advancement of artificial intelligence and computational technologies, collision risk assessment remains a key challenge for Autonomous Surface Vehicles (ASVs). Traditional approaches typically based on five indicators including distance, Distance/Time to Closest Point of Approach (DCPA/TCPA), relative heading, and speed ratio often suffer from redundancy, weak indicator independence, and limited correspondence to the physical characteristics of dynamic encounters. To overcome these limitations, this study proposes a physics-driven collision risk evaluation framework grounded in the Quaternion Ship Domain (QSD). The model simplifies the indicator system to three physically interpretable metrics: inter-ship distance, the coupled DCPA-TCPA index, and the coupled Bow Crossing Range-Bow Crossing Time (BCR-BCT) index. A logarithmic and sigmoid function is introduced as the factor collision risk normalization function, in contrast to a traditional Min–Max scaling function, thereby enhancing the smoothness and interpretability of risk evolution. Python-based simulations involving overtaking, head-on, and crossing scenarios were conducted to validate the proposed approach. The results demonstrate that the framework accurately captures both the magnitude and temporal evolution of collision risk, significantly improving interpretability, robustness, and practical applicability. The proposed QSD-based model provides a physics-consistent and computationally efficient solution for real-time collision risk assessment of ASVs.