We study the problem of mobile robots with distinct visibility ranges patrolling a curve. Assume a set of k mobile robots (patrolmen) a 1, a 2,⋯, a k walking along a unit-length curve in any of the two directions, not exceeding their maximal speeds. Every robot a i has a range of visibility r i, representing the distance from its current position at which the robot can see in each direction along the curve. The goal of the patrolling problem is to find the perpetual movement of the robots minimizing the maximal time when a point of the curve remains unseen by any robot. We give the optimal patrolling algorithms for the case of close curve environment (known as the boundary patrolling problem in the robotics literature) and open curve (fence patrolling), when all robots have the same maximal speed. We briefly discuss the case of distinct speeds, showing that the boundary patrolling problem for robots with distinct visibility ranges is essentially different than the case of point visibility robots. We also give the optimal algorithm for fence patrolling by two robots with distinct speeds and visibility ranges. For the case when the environment in which the robots operate is a general graph, we show that the patrolling problem for robots with distinct visibility ranges is NP-hard, while it is known that the same problem for point-visibility robots has been known to have a polynomial-time solution.

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Keywords Cycle, Graph, Mobile Robots, Patrolling, Segment, Speed, Visibility
Persistent URL dx.doi.org/10.1007/978-3-319-09620-9_18
Czyzowicz, J. (Jurek), Kranakis, E, Pajak, D. (Dominik), & Taleb, N. (Najmeh). (2014). Patrolling by robots equipped with visibility. doi:10.1007/978-3-319-09620-9_18