Correct-by-construction control synthesis for multi-robot mixing

This paper considers the problem of controlling a team of heterogeneous agents to conform to high-level interaction (coordination, sensing, and communication) missions. We consider interactions that can be specified via symbolic inputs from the braid group. We define a novel specification language, called Braid Temporal Logic (BTL), that allows us to specify rich, temporally-layered tasks involving agents' locations in an environment, their relative positions to each other, and frequency of location swaps and information exchanges between agents. We use techniques from formal methods to generate symbolic inputs that conform to a given BTL specification and use recently developed hybrid optimal control synthesis techniques to enact the synthesized pattern. The generated trajectories are provably guaranteed to be collision-free, respect physical boundaries of the agents' mission space, and to satisfy the high-level mission. Results are validated via implementation on a team of wheeled robots.