Autonomous Multi-agent Cycle Based Patrolling

Abstract

We introduce a novel multi-agent patrolling strategy. By assumption, the swarm of agents performing the task consists of very low capability ant-like agents. The agents have little memory, they can not communicate and their sensing abilities are local. Furthermore, the agents do not possess any knowledge regarding the graph or the swarm size. However, the agents may mark the graph vertices with pheromone stamps which can later be sensed. These markings are used as a primitive form of distributed memory and communication. The proposed strategy is a bundle of two algorithms. A single agent (the “leader”) is responsible of finding a short cycle which covers the graph, and this is achieved using a “cycle finding” algorithm. All other agents follow that cycle while maintaining even gaps between them using a “spreading algorithm”. We prove that the algorithms converge within a finite expected time. After convergence, the maximum time lag between two successive visits to any vertex using the proposed strategy is at most $4\frac{k}{k-1}\frac{l_{max}}{l_{min}}$ times the optimal, where the optimal time is bounded from below by $\frac{n\cdot l_{min}}{k}$, and where l _max (l _min ) is the longest (shortest) edge in the graph and k is the swarm size.

The “cycle finding” algorithm is robust i.e. in case the graph changes, the leader autonomously finds a new patrolling route. The “spreading algorithm” is scalable and robust. In case the patrolling cycle or the number of agents change during run (e.g. as a result of an agent break down) the agents autonomously redeploy uniformly over the patrolling cycle.