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18
Distributed control of robotic networks: a mathematical approach to motion coordination algorithms
, 2009
"... (i) You are allowed to freely download, share, print, or photocopy this document. (ii) You are not allowed to modify, sell, or claim authorship of any part of this document. (iii) We thank you for any feedback information, including errors, suggestions, evaluations, and teaching or research uses. 2 ..."
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Cited by 41 (1 self)
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(i) You are allowed to freely download, share, print, or photocopy this document. (ii) You are not allowed to modify, sell, or claim authorship of any part of this document. (iii) We thank you for any feedback information, including errors, suggestions, evaluations, and teaching or research uses. 2 “Distributed Control of Robotic Networks ” by F. Bullo, J. Cortés and S. Martínez
Largest bounding box, smallest diameter, and related problems on imprecise points
 In Proc. 10th Workshop on Algorithms and Data Structures, LNCS 4619
, 2007
"... We model imprecise points as regions in which one point must be located. We study computing the largest and smallest possible values of various basic geometric measures on sets of imprecise points, such as the diameter, width, closest pair, smallest enclosing circle, and smallest enclosing bounding ..."
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Cited by 18 (6 self)
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We model imprecise points as regions in which one point must be located. We study computing the largest and smallest possible values of various basic geometric measures on sets of imprecise points, such as the diameter, width, closest pair, smallest enclosing circle, and smallest enclosing bounding box. We give efficient algorithms for most of these problems, and identify the hardness of others. 1
Improving Connectivity of Wireless AdHoc Networks
"... A fully connected topology is critical to many fundamental network operations in wireless adhoc networks. In this paper, we consider the problem of deploying additional wireless nodes to improve the connectivity of an existing wireless network. Specifically, given a disconnected wireless network, w ..."
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Cited by 16 (1 self)
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A fully connected topology is critical to many fundamental network operations in wireless adhoc networks. In this paper, we consider the problem of deploying additional wireless nodes to improve the connectivity of an existing wireless network. Specifically, given a disconnected wireless network, we investigate how to deploy as few additional nodes as possible so that the augmented network can be connected. The problem is termed as the Connectivity Improvement (CI) problem. We first prove that CI is NPcomplete, and then present a Delaunay Triangulationbased algorithm, Connectivity Improvement using Delaunay Triangulation (CIDT). Depending on the priority based on which the components in a disconnected network should be chosen to connect, we devise several different versions of CIDT. We also present two additional optimization techniques to further improve the performance of CIDT. Finally, we verify the effectiveness of CIDT, and compare the performance of its variations via JSim simulation.
Minmaxmin Geometric Facility Location Problems
, 2006
"... We propose algorithms for a special type of geometric facility location problem in which customers may choose not to use the facility. We minimize the maximum cost incurred to a customer, where the cost itself is a minimum between two costs, according to whether the facility is used or not. We there ..."
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Cited by 12 (2 self)
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We propose algorithms for a special type of geometric facility location problem in which customers may choose not to use the facility. We minimize the maximum cost incurred to a customer, where the cost itself is a minimum between two costs, according to whether the facility is used or not. We therefore call this type of location problem a minmaxmin geometric facility location problem. As a first example, we describe the Closer Post Office problem, a generalization of the minimum spanning circle problem. We show that this problem can be solved in O(n) randomized expected time. We also show that the proposed algorithm solves two other minmaxmin geometric facility location problems. One, which we call the Moving Walkway problem, seems to be the first instance of a facility location problem using time metrics.
Some constrained minimax and maximin location problems
 STUDIES IN LOCATIONAL ANALYSIS
, 2000
"... In this paper we consider constrained versions of the Euclidean minimax facility location problem. We provide an O(n+m) time algorithm for the problem of constructing the minimum enclosing circle of a set of n points with center constrained to satisfy m linear constraints. As a corollary, we obtain ..."
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Cited by 5 (2 self)
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In this paper we consider constrained versions of the Euclidean minimax facility location problem. We provide an O(n+m) time algorithm for the problem of constructing the minimum enclosing circle of a set of n points with center constrained to satisfy m linear constraints. As a corollary, we obtain a linear time algorithm for the problem when the center is constrained to lie in an mvertex convex polygon, which improves the best known solution of O((n + m) log(n + m)) time. We also consider some constrained versions of the maximin problem, namely an obnoxious facility location problem in which we are given a set of n linear constraints, each representing a halfplane where some population may live, and the goal is to locate a point such that the minimum distance to the inhabited region is maximized. We provide optimal (n) time algorithms for this problem in the plane, as well as on the sphere.
NONSMOOTH COORDINATION AND GEOMETRIC OPTIMIZATION VIA DISTRIBUTED DYNAMICAL SYSTEMS
, 2009
"... Emerging applications for networked and cooperative robots motivate the study of motion coordination for groups of agents. For example, it is envisioned that groups of agents will perform a variety of useful tasks including surveillance, exploration, and environmental monitoring. This paper deals w ..."
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Cited by 4 (1 self)
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Emerging applications for networked and cooperative robots motivate the study of motion coordination for groups of agents. For example, it is envisioned that groups of agents will perform a variety of useful tasks including surveillance, exploration, and environmental monitoring. This paper deals with basic interactions among mobile agents such as “move away from the closest other agent” or “move toward the furthest vertex of your own Voronoi polygon.” These simple interactions amount to distributed dynamical systems because their implementation requires only minimal information about neighboring agents. We characterize the close relationship between these distributed dynamical systems and the diskcovering and spherepacking cost functions from geometric optimization. Our main results are: (i) we characterize the smoothness properties of these geometric cost functions, (ii) we show that the interaction laws are variations of the nonsmooth gradient of the cost functions, and (iii) we establish various asymptotic convergence properties of the laws. The technical approach relies on concepts from computational geometry, nonsmooth analysis, and nonsmooth stability theory.
Automatic Assembly Feature Recognition and Disassembly Sequence Generation
, 2001
"... This thesis is concerned not with geometric features on a single component but rather with those that arise from the spatial adjacency of two, or more, components in an assembly. From a review of the literature on the nature and use of assembly features, it is concluded that the majority of assembly ..."
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Cited by 4 (1 self)
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This thesis is concerned not with geometric features on a single component but rather with those that arise from the spatial adjacency of two, or more, components in an assembly. From a review of the literature on the nature and use of assembly features, it is concluded that the majority of assembly features involve sets of spatially adjacent faces. Three principle types of adjacency relationships proposed in CHAPTER 3.1 are identified and an algorithm is presented for identifying assembly features which arise from "external spatial", "internal spatial" and "contact" face adjacency relationships (known as esadjacency , isadjacency and cadjacency respectively).
Optimal Location of Transportation Devices
, 2007
"... We consider algorithms for finding the optimal location of a simple transportation device, that we call a moving walkway, consisting of a pair of points in the plane between which the travel speed is high. More specifically, one can travel from one endpoint of the walkway to the other at speed v> ..."
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Cited by 3 (1 self)
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We consider algorithms for finding the optimal location of a simple transportation device, that we call a moving walkway, consisting of a pair of points in the plane between which the travel speed is high. More specifically, one can travel from one endpoint of the walkway to the other at speed v> 1, but can only travel at unit speed between any other pair of points. The travel time between any two points in the plane is the minimum between the actual geometric distance, and the time needed to go from one point to the other using the walkway. A location for a walkway is said to be optimal with respect to a given finite set of points if it minimizes the maximum travel time between any two points of the set. We give a simple lineartime algorithm for finding an optimal location in the case where the points are on a line. We also give an Ω(n log n) lower bound for the problem of computing the travel time diameter of a set of n points on a line with respect to a given walkway. Then we describe an O(n log n) algorithm for locating a walkway with the additional restriction that the walkway must be horizontal. This algorithm is based on a recent generic method for solving quasiconvex programs with implicitly defined constraints. It is used in a (1+ε)approximation algorithm for optimal location of a walkway of arbitrary orientation.
Moving walkways, escalators, and elevators
 CoRR
"... Abstract. We study a simple geometric model of transportation facility that consists of two points between which the travel speed is high. This elementary definition can model shuttle services, tunnels, bridges, teleportation devices, escalators or moving walkways. The travel time between a pair of ..."
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Cited by 1 (0 self)
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Abstract. We study a simple geometric model of transportation facility that consists of two points between which the travel speed is high. This elementary definition can model shuttle services, tunnels, bridges, teleportation devices, escalators or moving walkways. The travel time between a pair of points is defined as a time distance, in such a way that a customer uses the transportation facility only if it is helpful. We give algorithms for finding the optimal location of such a transportation facility, where optimality is defined with respect to the maximum travel time between two points in a given set. 1