  In this paper, we present a learning method to solve the unlabelled motion
problem with motion constraints and space constraints in 2D space for a large
number of robots. To solve the problem of arbitrary dynamics and constraints we
propose formulating the problem as a multi-agent problem. In contrast to
previous works that propose using learning solutions for unlabelled motion
planning with constraints, we are able to demonstrate the scalability of our
methods for a large number of robots. The curse of dimensionality one
encounters when working with a large number of robots is mitigated by employing
a graph convolutional neural (GCN) network to parametrize policies for the
robots. The GCN reduces the dimensionality of the problem by learning filters
that aggregate information among robots locally, similar to how a convolutional
neural network is able to learn local features in an image. Additionally, by
employing a GCN we are also able to overcome the computational overhead of
training policies for a large number of robots by first training graph filters
for a small number of robots followed by zero-shot policy transfer to a larger
number of robots. We demonstrate the effectiveness of our framework through
various simulations.
