Optimal Routing of Multi-Agent Swarms Via Low-Dimensional Approximation
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Swarming models can demonstrate patterns similar to those seen in schools of fish or flocks of birds, human crowds, and swarms of robots moving together. Here we assume agents in the swarm know about the locations and velocities of nearby agents but may not have a complete picture of the geometry and dynamics of the swarm as a whole. A key question we investigate is how can one navigate the swarm through a landscape with obstacles. We present a method for approximating a swarm of agents macroscopically and navigating this macroscopic swarm through a landscape using optimal control. Then we present how one may add dynamics to the microscopic swarming model to allow the swarm to follow the computed path well attempting to minimize the deformation done to the swarm at a large scale.