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Beyond 1D and oversimplified kinematics: A generic analytical framework for surrogate safety measures

Sixu Li, Mohammad Anis, Dominique Lord, Hao Zhang, Yang Zhou, Xinyue Ye

TL;DR

The paper addresses the limitations of traditional 1D surrogate safety measures by introducing a generic analytical framework capable of deriving SSMs across highway geometries and vehicle dynamics with varying dimensionality and fidelity. By grounding the framework in a universal vehicle movement model and generic collision boundaries, it unifies time-based, deceleration-based, and energy-based safety indicators, and shows how classical TTC, RCRI, and DeltaV measures emerge as special cases. The authors demonstrate the framework's validity through analytical and numerical comparisons, revealing substantial accuracy and highlighting the necessity of higher-dimensional SSMs in complex driving scenarios. The work enables more realistic, real-time safety assessments and paves the way for integration with digital twins and safety evaluations across mixed traffic environments.

Abstract

This paper presents a generic analytical framework tailored for surrogate safety measures (SSMs) that is versatile across various highway geometries, capable of encompassing vehicle dynamics of differing dimensionality and fidelity, and suitable for dynamic, real-world environments. The framework incorporates a generic vehicle movement model, accommodating a spectrum of scenarios with varying degrees of complexity and dimensionality, facilitating the prediction of future vehicle trajectories. It establishes a generic mathematical criterion to denote potential collisions, characterized by the spatial overlap between a vehicle and any other entity. A collision risk is present if the collision criterion is met at any non-negative time point, with the minimum threshold representing the remaining time to collision. The framework's proficiency spans from conventional one-dimensional (1D) SSMs to extended multi-dimensional, high-fidelity SSMs. Its validity is corroborated through simulation experiments that assess the precision of the framework when linearization is performed on the vehicle movement model. The outcomes showcase remarkable accuracy in predicting vehicle trajectories and the time remaining before potential collisions occur. The necessity of higher-dimensional and higher-fidelity SSMs is highlighted through a comparison of conventional 1D SSMs and extended three-dimensional (3D) SSMs. The results showed that using 1D SSMs over 3D SSMs could be off by 300% for non-critical Time-to-Collision (TTC) values and about 20% for critical TTC values (below 1.5 seconds). Furthermore, the framework's practical application is demonstrated through a case study that actively evaluates all potential conflicts, underscoring its effectiveness in dynamic, real-world traffic situations.

Beyond 1D and oversimplified kinematics: A generic analytical framework for surrogate safety measures

TL;DR

The paper addresses the limitations of traditional 1D surrogate safety measures by introducing a generic analytical framework capable of deriving SSMs across highway geometries and vehicle dynamics with varying dimensionality and fidelity. By grounding the framework in a universal vehicle movement model and generic collision boundaries, it unifies time-based, deceleration-based, and energy-based safety indicators, and shows how classical TTC, RCRI, and DeltaV measures emerge as special cases. The authors demonstrate the framework's validity through analytical and numerical comparisons, revealing substantial accuracy and highlighting the necessity of higher-dimensional SSMs in complex driving scenarios. The work enables more realistic, real-time safety assessments and paves the way for integration with digital twins and safety evaluations across mixed traffic environments.

Abstract

This paper presents a generic analytical framework tailored for surrogate safety measures (SSMs) that is versatile across various highway geometries, capable of encompassing vehicle dynamics of differing dimensionality and fidelity, and suitable for dynamic, real-world environments. The framework incorporates a generic vehicle movement model, accommodating a spectrum of scenarios with varying degrees of complexity and dimensionality, facilitating the prediction of future vehicle trajectories. It establishes a generic mathematical criterion to denote potential collisions, characterized by the spatial overlap between a vehicle and any other entity. A collision risk is present if the collision criterion is met at any non-negative time point, with the minimum threshold representing the remaining time to collision. The framework's proficiency spans from conventional one-dimensional (1D) SSMs to extended multi-dimensional, high-fidelity SSMs. Its validity is corroborated through simulation experiments that assess the precision of the framework when linearization is performed on the vehicle movement model. The outcomes showcase remarkable accuracy in predicting vehicle trajectories and the time remaining before potential collisions occur. The necessity of higher-dimensional and higher-fidelity SSMs is highlighted through a comparison of conventional 1D SSMs and extended three-dimensional (3D) SSMs. The results showed that using 1D SSMs over 3D SSMs could be off by 300% for non-critical Time-to-Collision (TTC) values and about 20% for critical TTC values (below 1.5 seconds). Furthermore, the framework's practical application is demonstrated through a case study that actively evaluates all potential conflicts, underscoring its effectiveness in dynamic, real-world traffic situations.
Paper Structure (20 sections, 69 equations, 18 figures, 4 tables)

This paper contains 20 sections, 69 equations, 18 figures, 4 tables.

Table of Contents

  1. Introduction
  2. The generic analytical framework
  3. Formulation
  4. Time-Invariant Linearization Approximation
  5. Instances equivalent to conventional SSMs
  6. Conventional time-based SSM
  7. Conventional deceleration-based SSM
  8. Extended higher-dimensional and higher-fidelity SSMs
  9. 2-D kinematic model in the Cartesian coordinate system
  10. 2-D motion and 3-D dynamics model in the path coordinate system
  11. Discussion of cases beyond analytical trajectory solutions
  12. Tradeoffs between analytical and numerical solutions
  13. Simulation experiments
  14. 2-D kinematic Cartesian coordinate model experiment
  15. 2-D motion and 3-D dynamics path coordinate model experiment
  16. ...and 5 more sections

Figures (18)

  • Figure 1: Examples of index $i$ and $k$: (a) intersection scenario; (b) curved road scenario with obstacle
  • Figure 2: Direction and measure points of position and velocity
  • Figure 3: 2-D kinematic model
  • Figure 4: Visualization of bounding circles being tangential in 2-D space
  • Figure 5: Longitudinal forces acting on a vehicle moving on an inclined road
  • ...and 13 more figures