  We introduce a method called MASCOT (Multi-Agent Shape Control with Optimal
Transport) to compute optimal control solutions of agents with
shape/formation/density constraints. For example, we might want to apply shape
constraints on the agents -- perhaps we desire the agents to hold a particular
shape along the path, or we want agents to spread out in order to minimize
collisions. We might also want a proportion of agents to move to one
destination, while the other agents move to another, and to do this in the
optimal way, i.e. the source-destination assignments should be optimal. In
order to achieve this, we utilize the Earth Mover's Distance from Optimal
Transport to distribute the agents into their proper positions so that certain
shapes can be satisfied. This cost is both introduced in the terminal cost and
in the running cost of the optimal control problem.
