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Sensing and filtering: A tutorial based on preimages and information spaces. Foundations and Trends in Robotics
"... This tutorial presents a fresh perspective on sensing uncertainty and filtering with the intention of understanding what information is minimally needed to achieve a specified task. The guiding principle is not to sense, represent, and encode more than is necessary. The concepts and tools are motiv ..."
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This tutorial presents a fresh perspective on sensing uncertainty and filtering with the intention of understanding what information is minimally needed to achieve a specified task. The guiding principle is not to sense, represent, and encode more than is necessary. The concepts and tools are motivated by many tasks of current interest, such as tracking, monitoring, navigation, pursuitevasion, 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 informationspace 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 tutorial concludes with some discussion about connections to many related research fields and numerous open problems and future research directions. 1 1
How many landmark colors are needed to avoid confusion in a polygon?
"... Abstract — Suppose that two members of a finite point guard set S within a polygon P must be given different colors if their visible regions overlap, and that every point in P is visible from some point in S. The chromatic art gallery problem, introduced in [7], asks for the minimum number of colors ..."
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Abstract — Suppose that two members of a finite point guard set S within a polygon P must be given different colors if their visible regions overlap, and that every point in P is visible from some point in S. The chromatic art gallery problem, introduced in [7], asks for the minimum number of colors required to color any guard set (not necessarily a minimal guard set) of P. We study two related problems. First, given a polygon P and a guard set S of P, can the members of S be efficiently and optimally colored so that no two members of S that have overlapping visibility regions have the same color? Second, given a polygon P and a set of candidate guard locations N, is it possible to efficiently and optimally choose the guard set S ⊆ N that requires the minimum number of colors? We provide an algorithm that solves the first question in polynomial time, and demonstrate the NPhardness of the second question.
Sensing and Filtering: A Fresh Perspective Based on Preimages and Information Spaces
"... 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 ..."
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Cited by 3 (2 self)
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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, pursuitevasion, 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 informationspace 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. 1 1
Algorithms Group
"... Searching for radio beacons among geometric obstacles with mobile agents ..."
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Reconnecting with the Ideal Tree: An Alternative to Heuristic Learning in RealTime Search
"... In this paper, we present a conceptually simple, easytoimplement realtime search algorithm suitable for a priori partially known environments. Instead of performing a series of searches towards the goal, like most RealTime Heuristic Search Algorithms do, our algorithm follows the arcs of a tree ..."
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In this paper, we present a conceptually simple, easytoimplement realtime search algorithm suitable for a priori partially known environments. Instead of performing a series of searches towards the goal, like most RealTime Heuristic Search Algorithms do, our algorithm follows the arcs of a tree T rooted in the goal state that is built initially using the heuristic h. When the agent observes that an arc in the tree cannot be traversed in the actual environment, it removes such an arc from T and our algorithm carries out a reconnection search whose objective is to find a path between the current state and any node in T. The reconnection search need not be guided by h, since the search objective is not to encounter the goal. Furthermore, h need not be updated. We implemented versions of our algorithm that utilize various blind search algorithms for reconnection. We show experimentally that these implementations significantly outperform stateoftheart realtime heuristic search algorithms for the task of pathfinding in grids. In grids, our algorithms, which do not incorporate any geometrical knowledge, naturally behaves similarly to a bug algorithm, moving around obstacles, and never returning to areas that have been visited in the past. In addition, we prove theoretical properties of the algorithm.
GPSOptimal Micro Air Vehicle Navigation in Degraded Environments*
"... Abstract — We investigate a computationally and memory efficient algorithm for radio frequency (RF) sourceseeking with a singlewing rotating micro air vehicle (MAV) operating in an urban canyon environment. We present an algorithm that overcomes two significant difficulties of operating in an urba ..."
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Abstract — We investigate a computationally and memory efficient algorithm for radio frequency (RF) sourceseeking with a singlewing rotating micro air vehicle (MAV) operating in an urban canyon environment. We present an algorithm that overcomes two significant difficulties of operating in an urban canyon environment. First, Global Positioning System (GPS) localization quality can be degraded due to the lack of clear line of sight to a sufficient number of GPS satellites. Second, the spatial RF field is complex due to multipath reflections leading to multiple maxima and minima in received signal strength (RSS). High quality GPS localization is maintained by observing the GPS signal to noise ratio (SNR) to each satellite and making inferences about directions of high GPS visibility (allowable) and directions of low GPS visibility (forbidden). To avoid local maxima in RSS due to multipath reflections we exploit the rotation of the MAV and the directionality of its RF antenna to derive estimates of the angle of arrival (AOA) at each rotation. Under mild assumptions on the noise associated with the AOA measurements, a greedy algorithm is shown to exhibit a global recurrence property. Simulations supplied with actual GPS SNR measurements indicate that this algorithm reliably finds the RF source while maintaining an acceptable level of GPS visibility. Additionally, outdoor experiments using Lockheed Martin’s Samarai MAV demonstrate the efficacy of this approach for static sourceseeking in an urban canyon environment. I.