AI 中文总结
本文提出一种基于B样条和正则化的占据分布近似方法，用于自主车辆在移动障碍物环境中的轨迹规划，通过泊松随机场集成风险，支持可控风险接受，并减少求解器计算负载高达50%。
AI 中文摘要
本文提出了一种近似占据分布的方法，占据分布是自主车辆在不确定环境中进行轨迹规划时常用的一种概率表示。所提出的方法采用B样条曲面并结合正则化技术，以确保平滑性和可微性。将所得近似解释为泊松随机场的强度函数，能够将多个占据分布无缝集成到一个连贯的风险表示中，同时保持与概率分布语义的兼容性。该方法专为最优控制问题（OCPs）设计，其中求解器受益于梯度和高阶导数信息。它还保留了占据分布的空间和时间结构信息，这对于处理动态障碍物至关重要。我们在一个涉及自主车辆和具有时变不确定性的移动障碍物的轨迹规划场景中展示了该方法的可行性。通过实现可控的风险接受，我们的公式超越了保守的“无碰撞”策略，并允许原本会被排除的可行轨迹。在我们的应用场景中，通过适当调整正则化，我们报告求解器计算负载减少了高达50%。
英文摘要
This paper presents a method for approximating occupancy distributions, a common probabilistic representation used in trajectory planning for autonomous vehicles operating in uncertain environments. The proposed method employs B-spline surfaces in conjunction with regularization techniques to ensure smoothness and differentiability. Interpreting the resulting approximation as an intensity function of a Poisson random field enables seamless integration of multiple occupancy distributions into a coherent risk representation, while retaining compatibility with the semantics of probability distributions. The method is tailored to optimal control problems (OCPs), where solvers benefit from gradient and higher-order derivative information. It also preserves information about the spatial and temporal structure of occupancy distributions, which is critical for handling dynamic obstacles. We demonstrate the feasibility of the approach in a trajectory planning scenario involving autonomous vehicles and moving obstacles with time-varying uncertainty. By enabling controlled risk acceptance, our formulation extends beyond conservative "no-collision" strategies and allows for admissible trajectories that would otherwise be ruled out. In our application scenario, we report a reduction in solver computational load of up to 50\% through proper tuning of the regularization.
Comments27 pages, 15 figures, presented 2024 on IFIP TC7, Hamburg, Germany
