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

arXiv: https://arxiv.org/abs/1609.05399 · HTML: https://mlsanity.com/paper/1609.05399/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2016.

## Built on by (most cited first, 10 of 10)

- [LEADER: Learning Attention over Driving Behaviors for Planning under Uncertainty](https://mlsanity.com/paper/2209.11422/) (2022)
- [Risk Conditioned Neural Motion Planning](https://mlsanity.com/paper/2108.01851/) (2021)
- [Exact and Bounded Collision Probability for Motion Planning under Gaussian Uncertainty](https://mlsanity.com/paper/2110.06348/) (2021)
- [Probabilistic Uncertainty-Aware Risk Spot Detector for Naturalistic Driving](https://mlsanity.com/paper/2303.07181/) (2023)
- [CoachNet: An Adversarial Sampling Approach for Reinforcement Learning](https://mlsanity.com/paper/2101.02649/) (2021)
- [Fast nonlinear risk assessment for autonomous vehicles using learned conditional probabilistic models of agent futures](https://mlsanity.com/paper/2109.09975/) (2021)
- [Safe and Efficient Path Planning under Uncertainty via Deep Collision Probability Fields](https://mlsanity.com/paper/2409.04306/) (2024)
- [REACT: Runtime-Enabled Active Collision-avoidance Technique for Autonomous Driving](https://mlsanity.com/paper/2505.11474/) (2025)
- [Learned Risk Metric Maps for Kinodynamic Systems](https://mlsanity.com/paper/2302.14803/) (2023)
- [Adaptive Splitting of Reusable Temporal Monitors for Rare Traffic Violations](https://mlsanity.com/paper/2405.15771/) (2024)

## Abstract (arXiv)

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.