发表机构
Iowa State University; Technion - Israel Institute of Technology（爱荷华州立大学; 以色列理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对机器人规划中规则手册下多目标最优解计算成本高的问题，提出RA*pex算法，结合降维与规则层次处理，大幅提升计算效率。
AI 中文摘要
机器人规划通常涉及具有复杂优先级关系的多个目标，例如安全性、效率和合规性。规则手册将这些关系形式化，允许对目标进行偏序，该偏序概括了帕累托优势和词典序优势。然而，计算完整的规则手册最优解集的计算成本很高。为应对这一挑战，我们引入了ε-规则优势的概念，这是规则手册下的一种原则性近似优势概念，并提出了RA*pex，这是一种最佳优先搜索算法，可高效计算紧凑的ε-近似规则手册最优解集。RA*pex利用降维技术（该技术用于加速现有多目标搜索算法），同时通过维护独立的闭集并对截断和残差规则集执行优势检查来尊重规则层次结构。我们对RA*pex进行了形式化分析，证明每个规则手册最优解都被返回集中至少一个解ε-规则优势（我们引入的近似优势的概括）。实验结果表明，我们的方法实现的计算时间比现有方法快两个数量级以上。
英文摘要
Robotic planning often involves multiple objectives with complex priority relationships, such as safety, efficiency, and regulatory compliance. Rulebooks formalize these relationships, allowing partial ordering of objectives that generalizes both Pareto and lexicographic dominance. Computing the full set of rulebook-optimal solutions, however, is computationally expensive. To address this challenge, we introduce the concept of epsilon-rule-dominance, a principled notion of approximate dominance under rulebooks, and propose RA*pex, a best-first search algorithm that efficiently computes a compact set of epsilon-approximate rulebook-optimal solutions. RA*pex leverages dimensionality reduction, a technique used to speed up existing multi-objective search algorithms, while respecting rule hierarchies by maintaining separate closed sets and performing dominance checks over truncated and residual rule sets. We provide a formal analysis of RA*pex, proving that every rulebook-optimal solution is epsilon-rule-dominated (a generalization of approximate dominance we introduce) by at least one solution in the returned set. Empirical results demonstrate that our approach achieves computation times over two orders of magnitude faster than existing methods.
