An Optical Rangefinder For Autonomous Robot Cart Navigation

Miller, G. L.; Wagner, E. R.

doi:10.1117/12.968241

Cited by 30 publications

(13 citation statements)

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“…We assume that the robot is in an environment such as an o ce or factory, with at vertical walls and a at oor | thus the problem we address is for polygonal workspaces in two dimensions. The subject of this paper is localization using a range nder 19], a device commonly used in real robots 8,9,10,19]. A range nder is a device that emanates a beam (laser or sonic), and determines the distance to the rst point of contact with any object in that direction.…”

Section: Introductionmentioning

confidence: 99%

The Robot Localization Problem

Guibas¹,

Motwani²,

Raghavan³

1997

SIAM J. Comput.

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We consider the following problem: given a simple polygon P and a star-shaped polygon V, nd a point (or the set of points) in P from which the portion of P that is visible is translation-congruent to V. The problem arises in the localization of robots equipped with a range-nder and a compass | P is a map of a known environment, V is the portion visible from the robot's position, and the robot must use this information to determine its position in the map. We give a scheme that preprocesses P so that any subsequent query V is answered in optimal time O(m + log n + A), where m and n are the number of vertices in V and P, and A is the number of points in P that are valid answers (the output size). Our technique uses O(n 5 ) space and preprocessing in the worst case; within certain limits, we can trade o smoothly between the query time and the preprocessing time and space. In the process of solving this problem, we also devise a data structure for output-sensitive determination of the visibility polygon of a query point inside a polygon P. We then consider a variant of the localization problem in which there is a maximum distance to which the robot can \see" | this is motivated by practical considerations, and we outline a similar solution for this case. We nally show that a single localization query V can be answered in time O(mn) with no preprocessing.

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Section: Introductionmentioning

confidence: 99%

The Robot Localization Problem

Guibas¹,

Motwani²,

Raghavan³

1997

SIAM J. Comput.

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“…A full imaging system has not been built. Miller and Wagner [1987] have built an AM radar unit using a modulated infrared LED. The system scans 360 degrees in azimuth, digitizing about 1,000 points in a second.…”

Section: Amplitude Modulationmentioning

confidence: 99%

Active Optical Range Imaging Sensors

Besl¹

1989

Springer Series in Perception Engineering

129

117

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Active, optical range imaging systems collect three-dimensional coordinate data from object surfaces. These systems can be useful in a wide variety of automation applications, including shape acquisition, bin picking, assembly, inspection, gauging, robot navigation, medical diagnosis, cartography, and military tasks. The range-imaging sensors in such systems are unique imaging devices in that the image data points explicitly represent scene surface geometry in a sampled form. At least six different optical principles have been used to actively obtain range images: (1) radar, (2) triangulation, (3) moire, (4) holographic interferometry, (5) lens focusing, and (6) diffraction. The relative capabilities of different sensors and sensing methods are evaluated using a figure of merit based on range accuracy, depth of field, and image acquisition time.

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“…Practical sensors have a limited range, D, beyond which the noise levels are too high to give reliable measurements [31]. Our algorithm for grids already assumes limited range of visibility, since we assume that the robot senses only the immediate neighboring grid cell; this can readily be extended to allow the robot to sense all cells within grid graph distance D. Our algorithm for localization in polygons can also be extended to the limited-range case, as we now describe.…”

Section: The Limited-range Versionmentioning

confidence: 99%

A Near-Tight Approximation Algorithm for the Robot Localization Problem

Koenig¹,

Mitchell²,

Mudgal³

et al. 2009

SIAM J. Comput.

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Abstract. Localization is a fundamental problem in robotics. The "kidnapped robot" possesses a compass and map of its environment; it must determine its location at a minimum cost of travel distance. The problem is NP-hard [G. Dudek, K. Romanik, and S. Whitesides, SIAM J. Comput., 27 (1998), pp. 583-604] even to minimize within factor c log n [C. Tovey and S. Koenig, Proceedings of the National Conference on Artificial Intelligence, Austin, TX, 2000, pp. 819-824], where n is the map size. No approximation algorithm has been known. We give an O(log 3 n)-factor algorithm. The key idea is to plan travel in a "majority-rule" map, which eliminates uncertainty and permits a link to the 1 2 -Group Steiner (not Group Steiner) problem. The approximation factor is not far from optimal: we prove a c log 2− n lower bound, assuming NP ⊆ ZT IME(n polylog(n) ), for the grid graphs commonly used in practice. We also extend the algorithm to polygonal maps by discretizing the problem using novel geometric techniques.

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An Optical Rangefinder For Autonomous Robot Cart Navigation

Cited by 30 publications

References 0 publications

The Robot Localization Problem

The Robot Localization Problem

Active Optical Range Imaging Sensors

A Near-Tight Approximation Algorithm for the Robot Localization Problem

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