Min-Max Vertex Cycle Covers With Connectivity Constraints for Multi-Robot Patrolling

We consider a multi-robot patrolling scenario with intermittent connectivity constraints, ensuring that robots' data finally arrive at a base station. In particular, each robot traverses a closed tour periodically and meets with the robots on neighboring tours to exchange data. We model the problem as a variant of the min-max vertex cycle cover problem (MMCCP), which is the problem of covering all vertices with a given number of disjoint tours such that the longest tour length is minimal. In this work, we introduce the minimum idleness connectivity-constrained multi-robot patrolling problem, show that it is NP-hard, and model it as a mixed-integer linear program (MILP). The computational complexity of exactly solving this problem restrains practical applications, and therefore we develop approximate algorithms taking a solution for MMCCP as input. Our simulation experiments on 10 vertices and up to 3 robots compare the results of different solution approaches (including solving the MILP formulation) and show that our greedy algorithm can obtain an objective value close to the one of the MILP formulations but requires much less computation time. Experiments on instances with up to 100 vertices and 10 robots indicate that the greedy approximation algorithm tries to keep the length of the longest tour small by extending smaller tours for data exchange.