  Recently a line of researches has delved the use of graph neural networks
(GNNs) for decentralized control in swarm robotics. However, it has been
observed that relying solely on the states of immediate neighbors is
insufficient to imitate a centralized control policy. To address this
limitation, prior studies proposed incorporating $L$-hop delayed states into
the computation. While this approach shows promise, it can lead to a lack of
consensus among distant flock members and the formation of small clusters,
consequently resulting in the failure of cohesive flocking behaviors. Instead,
our approach leverages spatiotemporal GNN, named STGNN that encompasses both
spatial and temporal expansions. The spatial expansion collects delayed states
from distant neighbors, while the temporal expansion incorporates previous
states from immediate neighbors. The broader and more comprehensive information
gathered from both expansions results in more effective and accurate
predictions. We develop an expert algorithm for controlling a swarm of robots
and employ imitation learning to train our decentralized STGNN model based on
the expert algorithm. We simulate the proposed STGNN approach in various
settings, demonstrating its decentralized capacity to emulate the global expert
algorithm. Further, we implemented our approach to achieve cohesive flocking,
leader following and obstacle avoidance by a group of Crazyflie drones. The
performance of STGNN underscores its potential as an effective and reliable
approach for achieving cohesive flocking, leader following and obstacle
avoidance tasks.
