Upper Bounds for Continuous-Time End-to-End Risks in Stochastic Robot Navigation

TL;DR

This paper introduces an analytical approach to estimate upper bounds on continuous-time collision risks in stochastic robot navigation, improving safety assessment efficiency over traditional Monte Carlo methods.

Contribution

It provides a novel analytical method leveraging Brownian motion properties and probability inequalities to estimate continuous-time risks in robot navigation.

Findings

Method is significantly faster than Monte Carlo sampling.

Proposed bounds outperform discrete-time risk bounds.

Effective for real-world ground robot navigation scenarios.

Abstract

We present an analytical method to estimate the continuous-time collision probability of motion plans for autonomous agents with linear controlled Ito dynamics. Motion plans generated by planning algorithms cannot be perfectly executed by autonomous agents in reality due to the inherent uncertainties in the real world. Estimating end-to-end risk is crucial to characterize the safety of trajectories and plan risk optimal trajectories. In this paper, we derive upper bounds for the continuous-time risk in stochastic robot navigation using the properties of Brownian motion as well as Boole and Hunter's inequalities from probability theory. Using a ground robot navigation example, we numerically demonstrate that our method is considerably faster than the naive Monte Carlo sampling method and the proposed bounds perform better than the discrete-time risk bounds.