On cooperative patrolling: Optimal trajectories, complexity analysis, and approximation algorithms

Fabio Pasqualetti*, Antonio Franchi, Francesco Bullo

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

108 Citations (Scopus)


The subject of this paper is the patrolling of an environment with the aid of a team of autonomous agents. We consider both the design of open-loop trajectories with optimal properties and of distributed control laws converging to optimal trajectories. As performance criteria, the refresh time and the latency are considered, i.e., respectively, time gap between any two visits of the same region and the time necessary to inform every agent about an event occurred in the environment. We associate a graph with the environment, and we study separately the case of a chain, tree, and cyclic graph. For the case of chain graph, we first describe a minimum refresh time and latency team trajectory and propose a polynomial time algorithm for its computation. Then, we describe a distributed procedure that steers the robots toward an optimal trajectory. For the case of tree graph, a polynomial time algorithm is developed for the minimum refresh time problem, under the technical assumption of a constant number of robots involved in the patrolling task. Finally, we show that the design of a minimum refresh time trajectory for a cyclic graph is NP-hard, and we develop a constant factor approximation algorithm.

Original languageEnglish
Article number6122514
Pages (from-to)592-606
Number of pages15
JournalIEEE transactions on robotics
Issue number3
Publication statusPublished - 2012
Externally publishedYes


  • Algorithm design and analysis
  • Combinatorial mathematics
  • Distributed algorithm
  • Graph partitioning
  • Mobile agents
  • Multirobot systems
  • network theory (graphs)
  • Patrol

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