Spatio-Temporal Reconnection for Multi-Robot Networks using Adaptive Prescribed-Time CBFs^*

In multi-robot systems, maintaining persistent communication graph connectivity is often overly restrictive, especially when robots have limited communication ranges but operate in large environments. Allowing robots to temporarily disconnect and later reconnect can improve task efficiency while still ensuring timely information sharing across the team. We propose an adaptive prescribed-time control barrier function (adaptive PT-CBF) framework that enables robots to temporarily disconnect and re-enter communication range within an adjustable and feasible prescribed time. We introduce a reconnection triggering mechanism that jointly considers task execution and reconnection urgency, providing a principled way to decide when reconnection should occur. Theoretical analysis establishes convergence to satisfying reconnection within a prescribed finite time. Experimental results validate the performance of the adaptive PT-CBF with improved task efficiency and reconnection behavior.