发表机构
Czech Technical University in Prague（布拉格捷克理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种闭式传播高程图接触最大值不确定性的方法，通过Clark递归和精确高斯二次型恒等式，将均值误差中位数从2.3%降至0.19%，并在GPU上实现5.5微秒的快速规划。
AI 中文摘要
风险感知规划器使用路径代价的均值和标准差，在不确定的高程图上对路径进行评分。然而，建模刚性接触需要对多个不确定单元计算最大值。一阶传播在此处因仅在单个单元处微分而失去准确性，而蒙特卡洛采样则每次抽取都需要完整的路径评估。我们使用Clark的成对递归以闭式形式计算该接触最大值的矩。通过跟踪每个接触与共享地图单元的协方差，我们使用精确的高斯二次型恒等式传播平滑余项。一次竞赛深度校准，仅在两条设计穿越上拟合一次，弥补了剩余的聚合标准差不足。在317条留出的漫游车路径段上，与来自相同信念的蒙特卡洛参考进行评分，所有预注册标准均得到满足。校正后的Clark折叠将均值的误差中位数从线性化的2.3%降至0.19%，并在所有测试方法的90%水平上实现了条件风险价值（CVaR）的最低误差。一个基准计划在GPU上仅需5.5微秒。这些精度提升集中在有争议的接触上。虽然它们很少改变在此地形上选择的路径，但该折叠在98%的决策中仍选择了参考最佳路径，而线性化为93%至96%。在第二个数据集上，均值可迁移，但风险数值则不然。
英文摘要
Risk-aware planners score paths on uncertain elevation maps using the path cost's mean and standard deviation. Modeling rigid contact, however, requires computing a maximum over several uncertain cells. First-order propagation loses accuracy here by differentiating at only a single cell, while Monte Carlo sampling requires a full path evaluation per draw. We compute the moments of that contact maximum in closed form using Clark's pairwise recursion. By tracking each contact's covariance against the shared map cells, we propagate the smooth remainder using exact Gaussian quadratic-form identities. A contest-depth calibration, fitted once on two design traverses, closes the aggregate standard-deviation shortfall that remains. On 317 held-out rover path segments, scored against a Monte Carlo reference from the same belief, every pre-registered criterion was met. The corrected Clark fold cuts the median error of the mean from linearization's 2.3% to 0.19% and attains the lowest error in the conditional value at risk (CVaR) at the 90% level of every method tested. A benchmark plan costs just 5.5 microseconds on a GPU. These accuracy gains concentrate at contested contacts. While they seldom change which path is chosen on this terrain, the fold still selects the reference-best path in 98% of decisions against linearization's 93 to 96%. On a second dataset the mean transfers, though the risk number does not.
Comments8 pages, 4 figures, 2 tables. Submitted to the 2027 IEEE International Conference on Robotics and Automation (ICRA)
