Evaluating Trajectory Collision Probability through Adaptive Importance Sampling for Safe Motion Planning

TL;DR

This paper introduces an adaptive importance sampling Monte Carlo method to accurately evaluate the safety of robot trajectories under uncertainty, providing confidence intervals for collision probability estimates in complex, nonlinear systems.

Contribution

It develops a novel adaptive importance sampling framework for probabilistic collision checking that offers accuracy guarantees and is suitable for complex robot dynamics.

Findings

Effective in estimating collision probabilities with confidence intervals

Applicable to nonlinear robot dynamics and various noise models

Parallelizable for computational efficiency

Abstract

This paper presents a tool for addressing a key component in many algorithms for planning robot trajectories under uncertainty: evaluation of the safety of a robot whose actions are governed by a closed-loop feedback policy near a nominal planned trajectory. We describe an adaptive importance sampling Monte Carlo framework that enables the evaluation of a given control policy for satisfaction of a probabilistic collision avoidance constraint which also provides an associated certificate of accuracy (in the form of a confidence interval). In particular this adaptive technique is well-suited to addressing the complexities of rigid-body collision checking applied to non-linear robot dynamics. As a Monte Carlo method it is amenable to parallelization for computational tractability, and is generally applicable to a wide gamut of simulatable systems, including alternative noise models. Numerical experiments demonstrating the effectiveness of the adaptive importance sampling procedure are presented and discussed.