Complex multi-robot missions often require heterogeneous teams to jointly optimize task allocation, scheduling, and path planning to improve team performance under strict constraints. We formalize these complexities into a new class of problems, dubbed Spatio-Temporal Efficacy-optimized Allocation for Multi-robot systems (STEAM). STEAM builds upon trait-based frameworks that model robots using their capabilities (e.g., payload and speed), but goes beyond the typical binary success-failure model by explicitly modeling the efficacy of allocations as trait-efficacy maps. These maps encode how the aggregated capabilities assigned to a task determine performance. Further, STEAM accommodates spatio-temporal constraints, including a user-specified time budget (i.e., maximum makespan). To solve STEAM problems, we contribute a novel algorithm named Efficacy-optimized Incremental Task Allocation Graph Search (E-ITAGS) that simultaneously optimizes task performance and respects time budgets by interleaving task allocation, scheduling, and path planning. Motivated by the fact that trait-efficacy maps are difficult, if not impossible, to specify, E-ITAGS efficiently learns them using a realizability-aware active learning module. Our approach is realizability-aware since it explicitly accounts for the fact that not all combinations of traits are realizable by the robots available during learning. Further, we derive experimentally-validated bounds on E-ITAGS' suboptimality with respect to efficacy. Detailed numerical simulations and experiments using an emergency response domain demonstrate that E-ITAGS generates allocations of higher efficacy compared to baselines, while respecting resource and spatio-temporal constraints. We also show that our active learning approach is sample efficient and establishes a principled tradeoff between data and computational efficiency.

翻译：复杂多机器人任务通常需要异构团队在严格约束下联合优化任务分配、调度与路径规划，以提升团队性能。我们将此类复杂问题形式化为一类新问题——多机器人系统时空效能优化分配（STEAM）。STEAM建立在基于特征的框架之上，该框架通过机器人的能力（如负载与速度）对其建模，但突破了典型的二元成败模型，通过特征-效能映射显式建模分配效能。这些映射编码了分配给任务的聚合能力如何决定性能。此外，STEAM兼容时空约束，包括用户指定的时间预算（即最大完工时间）。为求解STEAM问题，我们提出一种名为效能优化增量任务分配图搜索（E-ITAGS）的新算法，该算法通过交错执行任务分配、调度与路径规划，在优化任务性能的同时遵守时间预算。鉴于特征-效能映射难以（甚至无法）人工指定，E-ITAGS通过可实现性感知的主动学习模块高效学习这些映射。我们的方法具有可实现性感知能力，因为它显式考虑了在学习过程中并非所有特征组合都能由可用机器人实现。此外，我们通过实验验证推导了E-ITAGS在效能方面的次优性边界。基于应急响应领域的详细数值仿真与实验表明，E-ITAGS在遵守资源与时空约束的同时，能生成比基线方法更高效能的分配方案。我们还证明所提出的主动学习方法具有样本高效性，并在数据效率与计算效率之间建立了理论权衡。