Second-Order Time to Collision With Non-Static Acceleration

TL;DR

This paper introduces a second-order time to collision (TTC) model that accounts for non-static acceleration and turning, providing more accurate collision predictions in dynamic scenarios.

Contribution

The paper develops a novel second-order TTC model considering non-static acceleration and turning, along with an efficient algorithm (STAR) for its computation.

Findings

Second-order TTC with non-static acceleration improves collision time accuracy.

The STAR algorithm efficiently computes the proposed TTC with reduced error.

Results demonstrate superior performance in real-world and simulated scenarios involving turning.

Abstract

We propose a second-order time to collision (TTC) considering non-static acceleration and turning with realistic assumptions. This is equivalent to considering that the steering wheel is held at a fixed angle with constant pressure on the gas or brake pedal and matches the well-known bicycle model. Past works that use acceleration to compute TTC consider only longitudinally aligned acceleration. We additionally develop and present the Second-Order Time-to-Collision Algorithm using Region-based search (STAR) to efficiently compute the proposed second-order TTC and overcome the current limitations of the existing built-in functions. The evaluation of the algorithm in terms of error and computation time is conducted through statistical analysis. Through numerical simulations and publicly accessible real-world trajectory datasets, we show that the proposed second-order TTC with non-static acceleration is superior at reflecting accurate collision times, especially when turning is involved.