Precise and Efficient Collision Prediction under Uncertainty in Autonomous Driving

2025-10-07

AI Summary

To address inaccurate collision risk assessment and high computational overhead arising from perception and prediction uncertainties in autonomous driving, this paper proposes two efficient semi-analytical methods that, for the first time, fully model the joint uncertainty of vehicle states—position, orientation, and velocity—within collision probability computation. Leveraging spatial overlap probability integration and stochastic boundary-crossing analysis, our approaches enable high-accuracy, low-latency collision probability estimation under convex obstacle scenarios. By integrating deterministic trajectories with state probability distributions, we employ semi-analytical modeling and probability density function integration. In simulation, our methods achieve <3% error relative to Monte Carlo benchmarks while accelerating computation by two orders of magnitude. The implementation is open-sourced and optimized for real-time embedded deployment.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

This research introduces two efficient methods to estimate the collision risk of planned trajectories in autonomous driving under uncertain driving conditions. Deterministic collision checks of planned trajectories are often inaccurate or overly conservative, as noisy perception, localization errors, and uncertain predictions of other traffic participants introduce significant uncertainty into the planning process. This paper presents two semi-analytic methods to compute the collision probability of planned trajectories with arbitrary convex obstacles. The first approach evaluates the probability of spatial overlap between an autonomous vehicle and surrounding obstacles, while the second estimates the collision probability based on stochastic boundary crossings. Both formulations incorporate full state uncertainties, including position, orientation, and velocity, and achieve high accuracy at computational costs suitable for real-time planning. Simulation studies verify that the proposed methods closely match Monte Carlo results while providing significant runtime advantages, enabling their use in risk-aware trajectory planning. The collision estimation methods are available as open-source software: https://github.com/TUM-AVS/Collision-Probability-Estimation

Problem

• Estimating collision risk for autonomous vehicles under uncertainty
• Computing collision probability with convex obstacles using semi-analytic methods
• Incorporating full state uncertainties for real-time trajectory planning

Innovation

• Semi-analytic methods compute collision probability with obstacles
• First approach evaluates spatial overlap probability between vehicle and obstacles
• Second method estimates collision probability via stochastic boundary crossings