Sensor Beams, Obstacles, and Possible Paths

Tovar, Benjamín; Cohen, Fred; LaValle, Steven M.

doi:10.1007/978-3-642-00312-7_20

Cited by 40 publications

(51 citation statements)

References 22 publications

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“…Motivation: Homotopy Invariant in (R 2 − O) We are interested in constructing computable homotopy invariants for trajectories in a configuration space that are amenable to graph search-based path planning. To that end there is a very simple construction for configuration spaces of the form R 2 − O (Euclidean plane punctured by obstacles) (Grigoriev and Slissenko 1998;Hershberger and Snoeyink 1991;Tovar et al 2008;Bhattacharya et al 2015;Kim et al 2014): We start by placing representative points, ζ i , inside the i th connected component of the obstacles, O i ⊂ O. We then construct non-intersecting rays, r 1 , r 2 , · · · , r m , emanating from the representative points (this is always possible, for example, by choosing the rays to be parallel to each other).…”

Section: Configuration Spaces With Free Fundamental Groupsmentioning

confidence: 99%

Path Homotopy Invariants and their Application to Optimal Trajectory Planning

Bhattacharya

2015

Proceedings of the IMA Conference on Mathematics of Robotics

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We consider the problem of optimal path planning in different homotopy classes in a given environment. Though important in robotics applications, path-planning with reasoning about homotopy classes of trajectories has typically focused on subsets of the Euclidean plane in the robotics literature. The problem of finding optimal trajectories in different homotopy classes in more general configuration spaces (or even characterizing the homotopy classes of such trajectories) can be difficult. In this paper we propose automated solutions to this problem in several general classes of configuration spaces by constructing presentations of fundamental groups and giving algorithms for solving the word problem in such groups. We present explicit results that apply to knot and link complements in 3-space, and also discuss how to extend to cylindricallydeleted coordination spaces of arbitrary dimension.

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Section: Configuration Spaces With Free Fundamental Groupsmentioning

confidence: 99%

Path Homotopy Invariants and their Application to Optimal Trajectory Planning

Bhattacharya

2015

Proceedings of the IMA Conference on Mathematics of Robotics

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“…Filter 19 (Gap Navigation Tree) We describe a filter over an I-space I trees of rooted trees [51]. Each tree captures some critical structure of the environment and is combinatorially equivalent to the notion of a shortest path tree that arises in visibility algorithms [?].…”

Section: Gap Navigation Treesmentioning

confidence: 99%

“…If there are no subtrees labeled g ′ and g ′′ , then new child nodes corresponding to g ′ and g ′′ are attached to the root. More details appear in [37,51].…”

Section: Gap Navigation Treesmentioning

confidence: 99%

Sensing and Filtering: A Fresh Perspective Based on Preimages and Information Spaces

LaValle

2010

FNT in Robotics

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This paper presents an unusual perspective on sensing uncertainty and filtering with the intention of understanding what information is minimally needed to achieve a specified task. Information itself is modeled using information space concepts, which originated from dynamic game theory (rather than information theory, which was developed mainly for communication). The guiding principle in this paper is avoid sensing, representing, and encoding more than is necessary. The concepts and tools are motivated by many tasks of current interest, such as tracking, monitoring, navigation, pursuit-evasion, exploration, and mapping. First, an overview of sensors that appear in numerous systems is presented. Following this, the notion of a virtual sensor is explained, which provides a mathematical way to model numerous sensors while abstracting away their particular physical implementation. Dozens of useful models are given, each as a mapping from the physical world to the set of possible sensor outputs. Preimages with respect to this mapping represent a fundamental source of uncertainty: These are equivalence classes of physical states that would produce the same sensor output. Pursuing this idea further, the powerful notion of a sensor lattice is introduced, in which all possible virtual sensors can be rigorously compared. The next part introduces filters that aggregate information from multiple sensor readings. The integration of information over space and time is considered. In the spatial setting, classical triangulation methods are expressed in terms of preimages. In the temporal setting, an information-space framework is introduced that encompasses familiar Kalman and Bayesian filters, but also introduces a novel family called combinatorial filters. Finally, the planning problem is presented in terms of filters and information spaces. The paper concludes with some discussion about connections to many related research fields and numerous open problems and future research directions.

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“…Recently, in [23] the problem in which one agent travels among obstacles and binary detection beams was considered. Algorithms were proposed to determine possible paths followed by an agent based only on binary sensor data from a set of sensor beams.…”

Section: Introductionmentioning

confidence: 99%

Minimalist multiple target tracking using directional sensor beams

Bobadilla

Sánchez

Czarnowski

et al. 2011

2011 IEEE/RSJ International Conference on Intelligent Robots and Systems

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Abstract-We consider the problem of determining the paths of multiple, unpredictable moving bodies in a cluttered environment using weak detection sensors that provide simple crossing information. Each sensor is a beam that, when broken, provides the direction of the crossing (one bit) and nothing else. Using a simple network of beams, the individual paths are separated and reconstructed as well as possible, up to combinatorial information about the route taken. In this setup, simple filtering algorithms are introduced, and a low-cost hardware implementation that demonstrates the practicality of the approach is shown. The results may apply in settings such as verification of multirobot system execution, surveillance and security, and unobtrusive behavioral monitoring for wildlife and the elderly.

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Sensor Beams, Obstacles, and Possible Paths

Cited by 40 publications

References 22 publications

Path Homotopy Invariants and their Application to Optimal Trajectory Planning

Path Homotopy Invariants and their Application to Optimal Trajectory Planning

Sensing and Filtering: A Fresh Perspective Based on Preimages and Information Spaces

Minimalist multiple target tracking using directional sensor beams

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