Precise and Efficient Collision Prediction under Uncertainty in Autonomous Driving
Marc Kaufeld, Johannes Betz
AI summary
Problem
Deterministic collision checks become inaccurate or overly conservative due to noisy sensor data, localization errors, and unpredictable traffic behavior, hindering safe real-time motion planning.
Approach
The authors derive two semi-analytic formulations to calculate collision probability: one integrates spatial overlap between the ego vehicle and obstacles, while the other computes stochastic boundary crossing rates. Both methods incorporate full position, orientation, and velocity uncertainties and use efficient numerical integration.
Key results
- Matches Monte Carlo simulation accuracy without sampling overhead
- Handles arbitrary convex obstacle shapes with full state uncertainties
- Achieves real-time computational speeds suitable for online planning
- Enables explicit risk-performance trade-offs in trajectory evaluation
Why it matters
Provides autonomous vehicles with a computationally efficient, mathematically rigorous way to quantify collision risk, enabling safer and less conservative decision-making in dynamic traffic.
Abstract
This research introduces two efficient methods to estimate the collision risk of planned trajectories in autonomous driving under uncertain driving conditions. Deterministic col- lision 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 obsta- cles. The first approach evaluates the probability of spatial over- lap 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 meth- ods are available as open-source software: https://github. com/TUM-AVS/Collision-Probability-Estimation