# On The Evaluation of Collision Probability along a Path

arXiv: https://arxiv.org/abs/2311.08204 · HTML: https://mlsanity.com/paper/2311.08204/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2023.

## Built on by (most cited first, 1 of 1)

- [Error Bounds for Physics-Informed Neural Networks in Fokker-Planck PDEs](https://mlsanity.com/paper/2410.22371/) (2024)

## Abstract (arXiv)

Characterizing the risk of operations is a fundamental requirement in robotics, and a crucial ingredient of safe planning. The problem is multifaceted, with multiple definitions arising in the vast recent literature fitting different application scenarios and leading to different computational approaches. A basic element shared by most frameworks is the definition and evaluation of the probability of collision for a mobile object in an environment with obstacles. We observe that, even in basic cases, different interpretations are possible. This paper proposes an index we call "Risk Density", which offers a theoretical link between conceptually distant assumptions about the interplay of single collision events along a continuous path. We show how this index can be used to approximate the collision probability in the case where the robot evolves along a nominal continuous curve from random initial conditions. Indeed, under this hypothesis the proposed approximation outperforms some well-established methods either in accuracy or computational cost.