Connectivity Maintenance and Recovery for Multi-Robot Motion Planning

Connectivity is crucial in many multi-robot applications, yet balancing between maintaining it and the fleet's traversability in obstacle-rich environments remains a challenge. Reactive controllers, such as control barrier functions, while providing connectivity guarantees, often struggle to traverse obstacle-rich environments due to deadlocks. We propose a real-time B\'ezier-based constrained motion planning algorithm, namely, MPC--CLF--CBF, that produces trajectory and control concurrently, under high-order control barrier functions and control Lyapunov functions conditions. Our motion planner significantly improves the navigation success rate of connected fleets in a cluttered workspace and recovers after inevitable connection loss by bypassing obstacles or from an initially disconnected fleet configuration. In addition, our predictive motion planner, owing to its B\'ezier curve solution, can easily obtain continuous-time arbitrary orders of derivatives, making it suitable for agile differentially flat systems, such as quadrotors. We validate the proposed algorithm through simulations and a physical experiment with $8$ Crazyflie nano-quadrotors.