Multi-Agent Shape Control with Optimal Transport

Optimal control seeks to find the best policy for an agent that optimizes a certain criterion. This general formulation allows optimal control theory to be applied in numerous areas such as robotics, finance, aeronautics, and many other fields. Inherently, optimal control optimizes the control of a single agent, but in recent years, extending optimal control problems to the realm of multi-agents has been a popular trend. Indeed, there are numerous cases where we want to model not just a single agent, but many, e.g. a fleet of drones. Here we introduce MASCOT: Multi-Agent Shape Control with Optimal Transport, a method to compute solutions to multi-agent optimal control problems that involve shape, formation, or density constraints among the agents. These constraints can be formulated in the running cost of the agents, or as a terminal cost, or even both. We first introduce the reader to optimal control and its multi-agent version. We then review the idea of optimal transport and Earth Mover's Distance. Finally, we demonstrate the method on some examples.