Continuum Swarm Tracking Control: A Geometric Perspective in Wasserstein Space
Abstract
We consider a setting in which one swarm of agents is to service or track a second swarm, and formulate an optimal control problem which trades off between the competing objectives of servicing and motion costs. We consider the continuum limit where large-scale swarms are modeled in terms of their time-varying densities, and where the Wasserstein distance between two densities captures the servicing cost. We show how this non-linear infinite-dimensional optimal control problem is intimately related to the geometry of Wasserstein space, and provide new results in the case of absolutely continuous densities and constant-in-time references. Specifically, we show that optimal swarm trajectories follow Wasserstein geodesics, while the optimal control tradeoff determines the time-schedule of travel along these geodesics. We briefly describe how this solution provides a basis for a model-predictive control scheme for tracking time-varying and real-time reference trajectories as well.
Keywords
Cite
@article{arxiv.2303.15638,
title = {Continuum Swarm Tracking Control: A Geometric Perspective in Wasserstein Space},
author = {Max Emerick and Bassam Bamieh},
journal= {arXiv preprint arXiv:2303.15638},
year = {2023}
}
Comments
8 pages; accepted version; incorporates reviewer feedback, including additional motivation, visuals, and simplified notation; revised arguments in section 3, results unchanged