A Multi-Robot Cooperative Patrolling Algorithm with Sharing Multiple Cycles

In this paper, a multiple Cycle Sharing Algorithm (CSA) is proposed to solve the Multi-Robot Patrolling Problem (MRPP). In the MRPP, robots visit vertices in a graph continuously. The evaluation metric of the idleness of vertices is considered to evaluate the performance of an algorithm. Minimizing average graph idleness and the graph idleness standard deviation is covered because smaller average idleness means robots visit vertices more often, and smaller standard deviation of the graph idleness means robots visit vertices more regularly. The most effective way to minimize standard deviation is finding a Hamiltonian cycle in a graph. A Hamiltonian cycle visits each vertex exactly once, except for the vertex in which it starts and ends, thus visiting it twice. The solution to the Traveling Salesman Problem is known to minimize the cost of the corresponding Hamiltonian cycle. It is an NP-complete problem. If graph size becomes larger the longer time required for finding the minimum cost cycle; however, by partitioning the graph correctly into multiple sections with cooperative robots, the calculation time can be reduced remarkably.