On Cooperative Patrolling: Optimal Trajectories, Complexity Analysis, and Approximation Algorithms

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 t...

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Bibliographic Details
Published in:IEEE transactions on robotics Vol. 28; no. 3; pp. 592 - 606
Main Authors: Pasqualetti, F., Franchi, A., Bullo, F.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.06.2012
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithm design and analysis
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Approximation
Approximation algorithms
Collision avoidance
combinatorial mathematics
Computer science; control theory; systems
Computer systems and distributed systems. User interface
Control system synthesis
Control theory. Systems
distributed algorithms
Exact sciences and technology
graph partition
mobile agents
multirobot systems
network theory (graphs)
Optimization
patrol
Polynomials
Robot sensing systems
Robotics
Robots
Software
Theoretical computing
Trajectory
Algorithm design and analysis
Tree(graph)
Control program
Control synthesis
network theory (graphs)
Approximation algorithm
Delay
Robotics
Minimum time
Graph chain
Cooperation
mobile agents
Mobile agent
multirobot systems
patrol
graph partition
Graph theory
Computational complexity
Combinatorial mathematics
Latency
Polynomial time
Multiagent system
distributed algorithms
Optimal trajectory
Distributed algorithm
NP hard problem
Open loop
Distributed control
Algorithm analysis
ISSN:1552-3098, 1941-0468
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Summary: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.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:1552-3098
1941-0468
DOI:10.1109/TRO.2011.2179580