Temporal Logic Swarm Control with Splitting and Merging

This paper presents an agent-agnostic framework to control swarms of robots tasked with temporal and logical missions expressed as Metric Temporal Logic (MTL) formulas. We consider agents that can receive global commands from a high-level planner, but no inter-agent communication. Moreover, agents are grouped into sub-swarms whose number can vary over the mission time horizon due to splitting and merging. However, a strict upper bound on the maximum number of sub-swarms is imposed to ensure their safe operation in the environment. We propose a two-phase approach. In the first phase, we compute the trajectories of the sub-swarms, splitting, and merging actions using a Mixed Integer Linear Programming approach that ensures the satisfaction of the MTL specification with minimal swarm division over the mission time horizon. Moreover, it enforces the upper bound on the number of sub-swarms. In the second phase, splitting fractions for sub-swarms resulting from splitting actions are computed. A distributed randomized protocol with no interagent communication ensures agent assignments matching the splitting fractions. Finally, we show the operation and performance of the approach in simulations with multiple tasks that require swarm splitting or merging.