成对近似可能选出错误的多机器人计划
Pairwise Approximation Can Select the Wrong Multi-Robot Plan
- National University of Singapore（新加坡国立大学）
- Singapore Technologies Engineering（新加坡科技工程有限公司）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对多机器人计划评分中忽略高阶项的问题，本文通过对比成对近似与实际覆盖函数，发现成对近似常导致错误选择，且低重建误差不保证低选择遗憾。
AI中文摘要：
多机器人协调方法通常仅根据单体和成对项对联合计划进行评分，而忽略了涉及三个或更多机器人的项。我们利用冻结的多机器人轨迹，测量了两种成对近似相对于实际覆盖范围的计划选择遗憾。在一个室内探索基准上，对于每个四机器人计划，重放所有16个机器人子集可得到精确的交付覆盖集函数$F$。从相同的子集值中，我们计算两个成对分数：精确的2阶Möbius截断$F_2$（仅依赖于单体和成对值）以及等权重最小二乘两加性拟合$G$。在15米候选生成范围内，在两个候选家族中，按$F_2$而非$F$排序会在七个地图中的六个上改变所选计划，遗憾值最高达地图覆盖率的0.337。改用$G$会减少遗憾，但在每个家族中仍会在七个地图中的三个上改变选择。仅保留单体项的加性分数$F_1$，在一个家族的七个地图中的六个上选出精确获胜者，在另一个家族中为七个中的四个，而$F_2$仅为七个中的一个。我们还发现，较低的平均重建误差并不能保证较低的选择遗憾。
英文摘要：
Multi-robot coordination methods often score a joint plan from singleton and pairwise terms, leaving out the terms that involve three or more robots. We measure the plan-selection regret of two pairwise approximations to delivered coverage using frozen multi-robot trajectories. For each four-robot plan on an indoor exploration benchmark, replaying all 16 robot subsets gives the exact delivered-coverage set function $F$. From the same subset values we compute two pairwise scores: the exact order-2 Möbius truncation $F_2$, which depends only on the singleton and pair values, and an equal-weight least-squares two-additive fit $G$. Ranking by $F_2$ instead of $F$ changes the selected plan on six of seven maps at the 15 m candidate-generation range in each of two candidate families, with regret up to 0.337 of map coverage. Switching to $G$ reduces the regret but still changes the selection on three of seven maps in each family. The additive score $F_1$, which keeps only the singleton terms, selects the exact winner on six of seven maps in one family and four of seven in the other, against one of seven for $F_2$. We also find that lower average reconstruction error does not guarantee lower selection regret.
