  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.
