Capture bounds for visibility-based pursuit evasion

Klein, Kyle N.; Suri, Subhash

doi:10.1145/2493132.2462364

Cited by 3 publications

(3 citation statements)

References 11 publications

(16 reference statements)

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“…In game theory, the homicidal chauffeur is a pursuit evasion problem which pits a slowly moving but highly maneuverable runner against the driver of a vehicle, which is faster but less maneuverable, who is attempting to run him over [7], [28]. Capture bounds for a pursuit-evasion problem that require the pursuer to physically capture the evader suggests the number or pursuers required to satisfy this capture condition exceeds that needed for the visibilitybased pursuit-evasion problem [10].…”

Section: A Differential Gamesmentioning

confidence: 99%

Pursuit-evasion with fixed beams

Stiffler

O’Kane

2016

2016 IEEE International Conference on Robotics and Automation (ICRA)

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We introduce a complete algorithm for solving a pursuit-evasion problem in a simplyconnected two-dimensional environment, for the case of a single pursuer equipped with fixed beam sensors. The input for our algorithm is an environment and a collection of sensor directions, in which each is capable of line-of-sight detection in a fixed direction. The output is a pursuer motion strategy that ensures the detection of an evader that moves with unbounded speed, or a statement that no such strategy exists. The intuition of the algorithm is to decompose the environment into a collection of convex conservative regions, within which the evader cannot sneak between any pair of adjacent sensors. This decomposition induces a graph we call the pursuit-evasion graph (PEG), such that any correct solution strategy can be expressed as a path through the PEG. For an instance defined by m beams and an environment with n vertices, the algorithm runs in time O(2 m n 2 ). We implemented the algorithm in simulation and present some computed examples illustrating the algorithm's correctness.

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Section: A Differential Gamesmentioning

confidence: 99%

Pursuit-evasion with fixed beams

Stiffler

O’Kane

2016

2016 IEEE International Conference on Robotics and Automation (ICRA)

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“…The other variant is the so-called visibility based pursuer-evader games, where one or multiple pursuers wish to catch an intruder inside a polygonal environment. Here the objectives are-how many pursuers are needed to catch an intruder, and how quickly can they catch them; see [10] for some recent work and for a review of earlier work. The so-called localization problem [20] and art gallery problem [19,25] are also related.…”

Section: Related Workmentioning

confidence: 99%

Computing highly occluded paths on a terrain

Lebeck

Mølhave

Agarwal

2013

Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems

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Understanding the locations of highly occluded paths on a terrain is an important GIS problem. In this paper we present a model and a fast algorithm for computing highly occluded paths on a terrain. It does not assume the observer locations to be known and yields a path likely to be occluded under a rational observer strategy. We present experimental results that examine several different observer strategies. The repeated visibility map computations necessary for our model is expedited using a fast algorithm for calculating approximate visibility maps that models the decrease in observational fidelity as distance increases. The algorithm computes a multiresolution approximate visibility map and makes use of a graphics processing unit (GPU) to speed up computation. We present experimental results on terrrain data sets with up to 144 million points.

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“…Further work on the theme of determining complex geometric information with multiple relatively simple sensing devices can also be found in recent work on geometric pursuit-evasion games [9].…”

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confidence: 99%

Efficient Proximity Probing Algorithms for Metrology

Adler

Panahi

Stappen

et al. 2015

IEEE Trans. Automat. Sci. Eng.

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Abstract-Metrology, the theoretical and practical study of measurement, has applications in automated manufacturing, inspection, robotics, surveying, and healthcare. The geometric probing problem considers how to optimally use a probe to measure geometric properties. In this paper, we consider a proximity probe which, given a point, returns the distance to the boundary of the nearest object. When there is an unknown convex polygon P in the plane, the goal is to minimize the number of probe measurement needed to exactly determine the shape and location of P . We present an algorithm with upper bound of 3.5n + k + 2 probes, where n is the number of vertices and k ≤ 3 is the number of acute angles of P . The algorithm requires constant time per probe, and hence O(n) time to determine P . We also address the related problem where the unknown polygon is a member of a known finite set Γ and the goal is to efficiently determine which polygon is present. When m is the size of Γ and n is the maximum number of vertices of any member of Γ, we present an O(n m) algorithm with an upper bound of 2n + 2 probes.Note to Practitioners: Abstract-This paper was inspired by the problem of using a sensor with low-dimensional output, such as a range sensor, to determine the shape of an object, which is typically too complex for a single measurement to characterize. Existing approaches to shape measurement generally use sensors with high-dimensional output, such as cameras, or use lowdimensional sensors to measure fixed points, such as with Scanning Probe Microscopy (SPM). It is shown here that by employing an algorithm that uses the results of previous measurements to determine how the next measurement is taken, a non-directional range sensor can be used to efficiently and exactly determine the shape of a convex polygon. This suggests an alternative approach to obtaining information on the shape of an object in cases where low-dimensional sensors are more accurate, faster, or cheaper than their counterparts.

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Capture bounds for visibility-based pursuit evasion

Cited by 3 publications

References 11 publications

Pursuit-evasion with fixed beams

Pursuit-evasion with fixed beams

Computing highly occluded paths on a terrain

Efficient Proximity Probing Algorithms for Metrology

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