Multi-Agent Intermittent Interaction Planning via Sequential Greedy Selections Over Position Samples

In this work, we propose a method to solve the interaction planning problem for a set of mobile agents with obstacles and agent collisions via a core path planner and constrained random position sampling approach. The interaction constraint is posed in the form of an arbitrary number of discretized times in which we enforce a desired topological condition. The general objective function, to be maximized subject to the interaction constraint, is coverage of an environmental process here modeled as a Gaussian mixture model. The main tool we use to select positions and the times of interaction is the greedy algorithm, along with a submodular objective function and matroid constraint. Through this we guarantee strong theoretical lower bounds on sub-optimality. Simulations, including several Monte Carlo trials, are presented to corroborate our proposed methods.