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:我们引入了一种叫做MASCOT(Multi-Agent shape Control with 最佳运输方式)的方法,以计算形状/形状/密度限制的物剂的最佳控制方法。例如,我们也许想对物剂施加形状限制 -- -- 也许我们希望物剂沿路径保持某种形状,或者想分散物剂,以尽量减少碰撞。我们也许也希望一定比例的物剂转移到一个目的地,而其他物剂转移到另一个目的地,并且以最佳的方式做到这一点,即源-目的地分配应该是最佳的。为了实现这一目标,我们利用地球移动者从最优运输方式的距离将物剂分配到其适当的位置,以便某些形状能够得到满足。这种成本既引入终端成本,也引入于最佳控制问题的运行成本。