Hide-and-Seek with Directional Sensing

Details Hide-and-Seek with Directional Sensing Hide-and-Seek with Directional Sensing

2011-04-07

arxiv.org/abs/1104.1268v1

Computer Science

Computer Science and Game Theory

A short version of this paper (without proofs) will be presented at the 18th IFAC World Congress (IFAC 2011), Milan (Italy), A

Scientific paper

We consider a game played between a hider, who hides a static object in one of several possible positions in a bounded planar region, and a searcher, who wishes to reach the object by querying sensors placed in the plane. The searcher is a mobile agent, and whenever it physically visits a sensor, the sensor returns a random direction, corresponding to a half-plane in which the hidden object is located. We first present a novel search heuristic and characterize bounds on the expected distance covered before reaching the object. Next, we model this game as a large-dimensional zero-sum dynamic game and we apply a recently introduced randomized sampling technique that provides a probabilistic level of security to the hider. We observe that, when the randomized sampling approach is only allowed to select a very small number of samples, the cost of the heuristic is comparable to the security level provided by the randomized procedure. However, as we allow the number of samples to increase, the randomized procedure provides a higher probabilistic security level.

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