用高斯-勒让德积分和泊松过程精准估算赛车超车碰撞风险
Probabilistic Collision Risk Estimation through Gauss-Legendre Cubature and Non-Homogeneous Poisson Processes
- 结合高斯-勒让德积分与非齐次泊松过程，分两阶段计算碰撞风险
- 在446个场景中误差比最优基线低52%，每秒处理1000次
- 适用于高速自动驾驶运动规划，尤其适合极限超车场景
高速自动驾驶赛车中的超车行为需要精确、实时的碰撞风险估计，尤其在轮对轮场景中安全余量极小。现有方法要么依赖简化几何近似（如包围圆），要么采用蒙特卡洛采样，导致赛车速度下运动规划过于保守。本文提出高斯-勒让德矩形（GLR）算法，一种基于高斯-勒让德积分与非齐次泊松过程的两阶段积分方法，能准确评估考虑车辆几何形状与轨迹不确定性的碰撞风险。在高保真公式一赛车仿真环境中，针对446个超车场景的实验表明，GLR优于五种先进基线，平均误差降低77%，性能超越次优方法52%，且运行频率达1000 Hz。该框架具有通用性，可推广至更广泛的运动规划场景。
原文摘要 · Abstract (English)
Overtaking in high-speed autonomous racing demands precise, real-time estimation of collision risk; particularly in wheel-to-wheel scenarios where safety margins are minimal. Existing methods for collision risk estimation either rely on simplified geometric approximations, like bounding circles, or perform Monte Carlo sampling which leads to overly conservative motion planning behavior at racing speeds. We introduce the Gauss-Legendre Rectangle (GLR) algorithm, a principled two-stage integration method that estimates collision risk by combining Gauss-Legendre with a non-homogeneous Poisson process over time. GLR produces accurate risk estimates that account for vehicle geometry and trajectory uncertainty. In experiments across 446 overtaking scenarios in a high-fidelity Formula One racing simulation, GLR outperforms five state-of-the-art baselines achieving an average error reduction of 77% and surpassing the next-best method by 52%, all while running at 1000 Hz. The framework is general and applicable to broader motion planning contexts beyond autonomous racing.
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