LAUSR

Abstract We address the persistent monitoring problem in a 2D mission space where agents are restricted to move on a graph topology consisting of multiple intersecting 1D line segments (subspaces) on such a graph. The objective is to control the movement of multiple cooperating agents allocated over these line segments in order to minimize an uncertainty metric associated with a finite set of data sources/targets. Previously, we have shown that in 1D the optimal control solution is for each agent to move at maximum speed and switch directions at a sequence of locations, possibly waiting for some time at a target. We show that this optimal control structure can be extended to the 2D setting considered here and that we can parameterize the optimal solution to determine each agent’s switching points and dwell times in each linear segment over a given finite time horizon. We use Infinitesimal Perturbation Analysis (IPA) to obtain a complete on-line solution through an event-driven gradient-based algorithm. We also solve the optimal assignment problem of agents over subspaces. Simulation examples are included to demonstrate the combined optimal agent allocation and trajectory design.