Convexified Graph Neural Networks for Distributed Control in Robotic Swarms

A network of robots can be viewed as a signal graph, describing the underlying network topology with naturally distributed architectures, whose nodes are assigned to data values associated with each robot. Graph neural networks (GNNs) learn representations from signal graphs, thus making them well-suited candidates for learning distributed controllers. Oftentimes, existing GNN architectures assume ideal scenarios, while ignoring the possibility that this distributed graph may change along time due to link failures or topology variations, which can be found in dynamic settings. A mismatch between the graphs on which GNNs were trained and the ones on which they are tested is thus formed. Utilizing online learning, GNNs can be retrained at testing time, overcoming this issue. However, most online algorithms are centralized and work on convex problems (which GNNs scarcely lead to). This paper introduces novel architectures which solve the convexity restriction and can be easily updated in a distributed, online manner. Finally, we provide experiments, showing how these models can be applied to optimizing formation control in a swarm of flocking robots.