Multirobot Reconnection on Graphs: Problem, Complexity, and Algorithms

In several multirobot applications in which communication is limited, the mission could require the robots to iteratively take coordinated joint decisions on how to spread out in the environment and on how to reconnect with each other to share data and compute plans. Exploration and surveillance are examples of these applications. In this paper, we consider the problem of computing robots' paths on a graph-represented environment for restoring connections at minimum traveling cost. We call it the multirobot reconnection problem, we show its NP-hardness and hardness of approximation on some important classes of graphs, and we provide optimal and heuristic algorithms to solve it in practical settings. The techniques we propose are then exploited to derive a new efficient planning algorithm for a relevant connectivity-constrained multirobot planning problem addressed in the literature, the multirobot informative path planning with periodic connectivity problem.