Fast Collision Probability Estimation for Automated Driving using Multi-circular Shape Approximations

TL;DR

This paper introduces a computationally efficient method for estimating collision probabilities in automated driving using multi-circular shape approximations under Gaussian uncertainties, reducing reliance on resource-intensive Monte Carlo sampling.

Contribution

The paper proposes a novel analytical approach for collision probability estimation with multi-circular shape approximations, offering efficiency and error bounds compared to Monte Carlo sampling.

Findings

The method is more efficient than Monte Carlo sampling.

Provides upper and lower bounds for estimation errors.

Applicable to Gaussian uncertainty scenarios.

Abstract

Many state-of-the-art methods for safety assessment and motion planning for automated driving require estimation of the probability of collision (POC). To estimate the POC, a shape approximation of the colliding actors and probability density functions of the associated uncertain kinematic variables are required. Even with such information available, the derivation of the POC is in general, i.e., for any shape and density, only possible with Monte Carlo sampling (MCS). Random sampling of the POC, however, is challenging as computational resources are limited in real-world applications. We present expressions for the POC in the presence of Gaussian uncertainties, based on multi-circular shape approximations. In addition, we show that the proposed approach is computationally more efficient than MCS. Lastly, we provide a method for upper and lower bounding the estimation error for the POC induced by the used shape approximations.