Efficient multi-robot task allocation (MRTA) is fundamental to various time-sensitive applications such as disaster response, warehouse operations, and construction. This paper tackles a particular class of these problems that we call MRTA-collective transport or MRTA-CT -- here tasks present varying workloads and deadlines, and robots are subject to flight range, communication range, and payload constraints. For large instances of these problems involving 100s-1000's of tasks and 10s-100s of robots, traditional non-learning solvers are often time-inefficient, and emerging learning-based policies do not scale well to larger-sized problems without costly retraining. To address this gap, we use a recently proposed encoder-decoder graph neural network involving Capsule networks and multi-head attention mechanism, and innovatively add topological descriptors (TD) as new features to improve transferability to unseen problems of similar and larger size. Persistent homology is used to derive the TD, and proximal policy optimization is used to train our TD-augmented graph neural network. The resulting policy model compares favorably to state-of-the-art non-learning baselines while being much faster. The benefit of using TD is readily evident when scaling to test problems of size larger than those used in training.

翻译：高效的多机器人任务分配（MRTA）是灾害响应、仓库运营和建筑施工等各类时间敏感型应用的基础。本文针对此类问题中的特定类别——我们称之为MRTA集体运输（MRTA-CT），其中任务具有可变工作负载和截止期限，机器人需满足飞行范围、通信范围和有效载荷限制。对于涉及数百至数千个任务及数十至数百个机器人的大规模问题实例，传统非学习求解器往往时间效率低下，而新兴的基于学习的策略在扩展到更大规模问题时，若不进行代价高昂的重新训练则难以实现良好扩展。为弥补这一不足，我们采用近期提出的编码器-解码器图神经网络（包含胶囊网络与多头注意力机制），并创新性地引入拓扑描述符作为新特征，以提升模型对未见问题（规模相似或更大）的泛化能力。通过持续同调计算拓扑描述符，并采用近端策略优化训练拓扑描述符增强型图神经网络。最终策略模型在保持显著速度优势的同时，性能优于当前最先进非学习基线方法。当扩展至训练集更大规模的测试问题时，拓扑描述符的效用尤为明显。