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.

翻译：我们提出了一种名为MASCOT（基于最优传输的多智能体形状控制）的方法，用于计算具有形状/编队/密度约束的智能体的最优控制解。例如，我们可能希望对智能体施加形状约束——也许期望智能体在路径上保持特定形状，或希望智能体分散以最小化碰撞。我们可能还希望让一部分智能体以最优方式前往一个目的地，而其余智能体前往另一个目的地，即源-目的地分配需达到最优。为实现这一目标，我们利用最优传输中的推土机距离将智能体分配到恰当位置，从而满足特定形状要求。该代价同时引入最优控制问题的终端代价和运行代价中。