Volume 26 Issue 3 - Publication Date: 1 March 2007
Surveillance Strategies for a Pursuer with Finite Sensor Range
R. Murrieta-Cid Centro de Investigación en Matemáticas CIMAT, Guanajuato México T. Muppirala, A. Sarmiento, S. Bhattacharya and S. Hutchinson University of Illinois at Urbana-Champaign Urbana, IL 61801 USA
The following motion coordination problem is studied: given n mobile vehicles and n source-destination pairs in the plane, what is the minimum time needed to transfer each vehicle from its source to its destination, avoiding conflicts with other vehicles? In the proposed model, vehicles do not explicitly communicate their intentions, and only have sensory information about the current position and velocity of their neighbors to ensure no conflicts. The environment is free of obstacles and a conflict occurs when the distance between any two vehicles is smaller than a velocity-dependent safety distance. The situation analyzed in which the vehicle size is such that at least a constant fraction of the n vehicles can be fitted inside the environment simultaneously. In the "best" case in which the source and destination points can be chosen ideally to maximize the transfer efficiency, it is shown that the transfer takes time to complete, where is the average distance between the source and destination points. It is shown that there exist a "worst" case distribution of the source and destination points, for which the transfer of vehicles takes at least time. The case is also analyzed in which source and destination points are generated randomly according to a uniform distribution, and an algorithm is presented providing a constructive upper bound on the time needed to transfer vehicles from sources to their corresponding destinations, proving that the transfer takes time, with high probability, thus recovering the best case performance.
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