Minimally disruptive connectivity enhancement for resilient multi-robot teams

In this work, we focus on developing algorithms to maintain and enhance the connectivity of a multi-robot system with minimal disruption to the primary tasks that the robots are performing. Such algorithms are useful for collaborating robots to be resilient to reduction in connectivity of the communication graph of the robot team when robots can arrive or leave. These algorithms are also useful in a supervisory control setting when an operator wants to enhance the connectivity of the robot team. In contrast to many existing works that can only maintain the current connectivity of the multi-robot graph, we propose a generalized connectivity control framework that allows for reconfiguration of the multi-robot system to provably satisfy any connectivity demand, while minimally disrupting the execution of their original tasks. In particular, we propose a novel k-Connected Minimum Resilient Graph (k-CMRG) algorithm to compute an optimal k-connectivity graph that minimally constrains the robots' original task-related motion, and employ the Finite-Time Convergence Control Barrier Function (FCBF) to enforce the pairwise robot motion constraints defined by the edges of the graph. The original controllers are minimally modified to drive the robots and form the k-CMRG. We demonstrate the effectiveness of our approach via simulations in the presence of multiple tasks and robot failures.