提出两种高效方法，在不确定性下精准预测自动驾驶轨迹碰撞风险。
Precise and Efficient Collision Prediction under Uncertainty in Autonomous Driving
- 基于空间重叠与随机边界穿越，半解析计算碰撞概率。
- 融合位置、朝向、速度全状态不确定性，精度接近蒙特卡洛模拟。
- 实时性能优越，适合用于风险感知的轨迹规划，开源可用。
本研究提出两种高效方法，用于在不确定驾驶环境下估计自动驾驶规划轨迹的碰撞风险。传统确定性碰撞检测常因感知噪声、定位误差及交通参与者预测不确定性而产生不准确或过度保守的结果。本文提出的两种半解析方法可计算规划轨迹与任意凸障碍物之间的碰撞概率：第一种评估自车与周围障碍物的空间重叠概率，第二种基于随机边界穿越估算碰撞概率。两种方法均纳入位置、朝向和速度的完整状态不确定性，在保证高精度的同时，计算开销适合实时规划。仿真结果表明，所提方法与蒙特卡洛模拟结果高度吻合，且显著提升运行效率，支持在风险感知轨迹规划中应用。相关代码已开源：https://github.com/TUM-AVS/Collision-Probability-Estimation。
原文摘要 · Abstract (English)
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
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