On time-optimal behavior scheduling of robotic swarms for achieving multiple goals

Robotic swarms are multi-robot systems whose global behaviors emerge from local interactions between individual robots. Each robot obeys a local control law that can be activated depending on an operator's choice of global swarm behavior. Real missions occur in uncontrolled environments with dynamically arising objectives and require combinations of behaviors. Given a library of swarm behaviors, a supervisory operator commanding the swarm must choose a sequence of behaviors to execute and their execution durations in order to accomplish a particular task during a mission composed of many tasks. In this paper, we address the following problem: given a library of swarm behaviors, the swarm initial state, the final goal and an unordered set of intermediate goals the operator wants to achieve, the objective is to identify a behavior schedule comprised of selected behaviors and associated time intervals of application of the behavior so that the total time to reach the final goal is minimized. Our contributions are as follows: (a) formalization of the problem of behavior scheduling to achieve multiple unordered goals with a robotic swarm, (b) an algorithm that produces a behavior schedule to achieve all intermediate goals and the final goal in minimum time such that the behavior durations are locally optimal and given which the goal sequence has bounded suboptimality and (c) application of this algorithm to configuration control of robot swarms.