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Stochastic COLREGs Evaluation for Safe Navigation under Uncertainty

Peter Nicholas Hansen, Dimitrios Papageorgiou, Roberto Galeazzi, Mogens Blanke

TL;DR

The paper tackles uncertainty in COLREGs interpretation for encounters between vessels by introducing two probabilistic, explainable decision frameworks: a Kernel Density Estimation (KDE) based stochastic model and a Discrete Event System (DES) based automata model. Both approaches propagate estimation uncertainty through $X_{TCPA}$, $X_{DCPA}$, and $X_{\beta}$ using Monte-Carlo sampling and non-parametric density estimation to yield probabilities of risk and give-way across rule sets, enabling risk-aware automation for MASS and decision-support on manned bridges. The methods are demonstrated across three scenarios, showing comparable results and highlighting the trade-offs between bandwidth selection, memory footprint, and sample efficiency. The work advances practical, uncertainty-aware safety assessment and provides a pathway to robust COLREGs-compliant decision-making under real-world sensor noise and environmental disturbances. It highlights the potential for integrating these probabilistic tools into existing situation-awareness architectures for autonomous navigation while acknowledging limitations and future directions for conditioning on historical data and scaling to larger multi-vessel scenes.

Abstract

The encounter situation between marine vessels determines how they should navigate to obey COLREGs, but time-varying and stochastic uncertainty in estimation of angles of encounter, and of closest point of approach, easily give rise to different assessment of situation at two approaching vessels. This may lead to high-risk conditions and could cause collision. This article considers decision making under uncertainty and suggests a novel method for probabilistic interpretation of vessel encounters that is explainable and provides a measure of uncertainty in the evaluation. The method is equally useful for decision support on a manned bridge as on Marine Autonomous Surface Ships (MASS) where it provides input for automated navigation. The method makes formal safety assessment and validation feasible. We obtain a resilient algorithm for machine interpretation of COLREGs under uncertainty and show its efficacy by simulations.

Stochastic COLREGs Evaluation for Safe Navigation under Uncertainty

TL;DR

The paper tackles uncertainty in COLREGs interpretation for encounters between vessels by introducing two probabilistic, explainable decision frameworks: a Kernel Density Estimation (KDE) based stochastic model and a Discrete Event System (DES) based automata model. Both approaches propagate estimation uncertainty through , , and using Monte-Carlo sampling and non-parametric density estimation to yield probabilities of risk and give-way across rule sets, enabling risk-aware automation for MASS and decision-support on manned bridges. The methods are demonstrated across three scenarios, showing comparable results and highlighting the trade-offs between bandwidth selection, memory footprint, and sample efficiency. The work advances practical, uncertainty-aware safety assessment and provides a pathway to robust COLREGs-compliant decision-making under real-world sensor noise and environmental disturbances. It highlights the potential for integrating these probabilistic tools into existing situation-awareness architectures for autonomous navigation while acknowledging limitations and future directions for conditioning on historical data and scaling to larger multi-vessel scenes.

Abstract

The encounter situation between marine vessels determines how they should navigate to obey COLREGs, but time-varying and stochastic uncertainty in estimation of angles of encounter, and of closest point of approach, easily give rise to different assessment of situation at two approaching vessels. This may lead to high-risk conditions and could cause collision. This article considers decision making under uncertainty and suggests a novel method for probabilistic interpretation of vessel encounters that is explainable and provides a measure of uncertainty in the evaluation. The method is equally useful for decision support on a manned bridge as on Marine Autonomous Surface Ships (MASS) where it provides input for automated navigation. The method makes formal safety assessment and validation feasible. We obtain a resilient algorithm for machine interpretation of COLREGs under uncertainty and show its efficacy by simulations.
Paper Structure (16 sections, 49 equations, 7 figures, 4 tables, 2 algorithms)

This paper contains 16 sections, 49 equations, 7 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Motivation
  3. Background
  4. Behavioural Model
  5. Method
  6. Stochastic Behaviour Model
  7. Analysis of Uncertainty Propagation
  8. Kernel Density Estimation
  9. Discrete Event Systems
  10. Experiments
  11. Starboard Crossing
  12. Port Crossing/Head-on scenario
  13. Overtaking/Port Crossing scenario
  14. Discussion
  15. Conclusion
  16. ...and 1 more sections

Figures (7)

  • Figure 1: An ambiguous situtation where the target vessel (black dot) with uncertainty ellipse (shown in red) can result in the situation being interpreted as; 1) in a head-on (blue), 2) a port-side crossing (red) or 3) a starboard crossing (green).
  • Figure 2: A visualisation of how $g_1$ maps a bearing $\beta$ into the different regions: head-on (HO), starboard (SB), overtaking (OT) and port (PS)
  • Figure 3: Histograms of the Calculated and values for the 7 different scenarios. Note that the values are truncated in the histograms, such that the count in the lowest and highest bins are "artificially" high.
  • Figure 4: of , and bearing values for the 7 different scenarios.
  • Figure 5: estimates of $n=10^5$ samples of using three different methods for estimating the bandwidth: , Silverman's rule of thumb and lastly a grid-search based method using cross-validation.
  • ...and 2 more figures

Theorems & Definitions (6)

  • Definition 1
  • Remark 1
  • Definition 2
  • Remark 2
  • Remark 3
  • Remark