AI 中文总结
针对部分已知环境中异构多机器人系统任务分配难题，提出基于最小-最大遗憾优化的框架，用区域绑定原子命题捕获资源不确定性，借助扩展规划决策树及新型分支定界策略，实现近线性可扩展性，性能优于基线方法。
AI 中文摘要
大规模异构多机器人系统（HMRS）的高效任务分配至关重要，但在部分已知环境（PKE）中处理复杂的时态逻辑任务仍是计算瓶颈。现有方法难以平衡探索不确定区域和利用已知资源，且计算复杂度呈指数增长。本文提出一个健壮的规划框架，它能同时处理高级逻辑约束和环境不确定性且不牺牲可扩展性。将问题表述为最小-最大遗憾优化，提出区域绑定原子命题（RbAP）在自动机结构内捕获资源不确定性。为此，提出配备新型基于遗憾的分支定界（BnB）策略的扩展规划决策树（E-PDT）。与传统方法不同，该方法动态修剪次优策略，有效平衡信息收集（探索）和任务完成（利用）的需求。理论分析证实了方法的可行性和完备性。大量数值和物理实验表明，所提框架在机器人数量和类型方面实现了近线性可扩展性，在解决方案质量和计算效率上显著优于基于混合整数线性规划（MILP）的基线方法。
英文摘要
Efficient task allocation for large-scale Heterogeneous Multi-Robot Systems (HMRS) is critical, yet dealing with complex temporal logic tasks in partially known environment (PKE) remains a computational bottleneck. Existing approaches often struggle to balance exploring uncertain regions and exploiting known resources, while also suffering from exponential computational complexity. To address these issues, this paper presents a robust planning framework that simultaneously handles high-level logical constraints and environmental uncertainty without sacrificing scalability. We formulate the problem as a min-max regret optimization, proposing a Region-Binding Atomic Proposition (RbAP) to capture resource uncertainty within the automaton structure. To solve this, we propose the Extended Planning Decision Tree (E-PDT) equipped with a novel Regret-based Branch-and-Bound (BnB) strategy. Unlike traditional methods that rely on prior probabilities or worst-case analysis, our approach dynamically prunes suboptimal policies, effectively balancing the need for information gathering (exploration) and task completion (exploitation). Theoretical analysis confirms the feasibility and completeness of our approach. Extensive numerical and physical experiments demonstrate that the proposed framework achieves near-linear scalability with respect to the number of robots and types, significantly outperforming MILP-based baselines in both solution quality and computational efficiency.
