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16
Minimum-cost coverage of point sets by disks
"... We consider a class of geometric facility location problems in which the goal is to determine a set X of disks given bytheir centers (t j) and radii (r j) that cover a given set of demand points Y ae R2 at the smallest possible cost. We consider costfunctions of the form a* j f (r j), where f (r) ..."
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Cited by 28 (5 self)
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We consider a class of geometric facility location problems in which the goal is to determine a set X of disks given bytheir centers (t j) and radii (r j) that cover a given set of demand points Y ae R2 at the smallest possible cost. We consider costfunctions of the form a* j f (r j), where f (r) = ra is the cost of transmission to radius r. Special cases arise for a = 1 (sum ofradii) and a = 2 (total area); power consumption models in wireless network design often use an exponent a> 2. Different scenarios arise according to possible restrictions on the transmission centers t j, which may be constrained to belong to a givendiscrete set or to lie on a line, etc. We obtain several new results, including (a) exact and approximation algorithms for selecting transmission points t j on agiven line in order to cover demand points Y ae R2; (b) approximation algorithms (and an algebraic intractability result) for selecting an optimal line on which to place transmission points to cover Y; (c) a proof of NP-hardness for a discrete set oftransmission points in R2 and any fixed a> 1; and (d) a polynomial-time approximation scheme for the problem of computinga minimum cost covering tour (MCCT), in which the total cost is a linear combination of the transmission cost for the set of
Online searching with turn cost
, 2004
"... We consider the problem of searching for an object on a line at an unknown distance OPT from the original position of the searcher, in the presence of a cost of d for each time the searcher changes direction. This is a generalization of the well-studied linear-search problem. We describe a strategy ..."
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We consider the problem of searching for an object on a line at an unknown distance OPT from the original position of the searcher, in the presence of a cost of d for each time the searcher changes direction. This is a generalization of the well-studied linear-search problem. We describe a strategy that is guaranteed to find the object at a cost of at most 9 · OPT + 2d, which has the optimal competitive ratio 9 with respect to OPT plus the minimum corresponding additive term. Our argument for upper and lower bound uses an infinite linear program, which we solve by experimental solution of an infinite series of approximating finite linear programs, estimating the limits, and solving the resulting recurrences for an explicit proof of optimality. We feel that this technique is interesting in its own right and should help solve other searching problems. In particular, we consider the star search or cow-path problem with turn cost, where the hidden object is placed on one of m rays emanating from the original position of the searcher. For this problem we give a tight bound of 1 + 2 m m (m−1) m−1 OPT+m
Automated intruder tracking using particle filtering and a network of binary motion sensors
- in IEEE International Conference on Automation Science and Engineering (CASE’06
, 2006
"... Abstract — Our objective is to automatically track and capture photos of an intruder using a robotic pan-tiltzoom camera. In this paper, we consider the problem of automated position estimation using a wireless network of inexpensive binary motion sensors. The challenge is to incorporate data from a ..."
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Abstract — Our objective is to automatically track and capture photos of an intruder using a robotic pan-tiltzoom camera. In this paper, we consider the problem of automated position estimation using a wireless network of inexpensive binary motion sensors. The challenge is to incorporate data from a network of noisy sensors that suffer from refractory periods during which they may be unresponsive. We propose an estimation method based on Particle Filtering, a numerical sequential Monte Carlo technique. We model sensors with conditional probability density functions and incorporate a probabilistic model of an intruder’s state that utilizes velocity. We present simulation and experiments with passive infrared (PIR) motion sensors that suggest that our estimator is effective and degrades gracefully with increasing sensor refractory periods.
View planning problem with combined view and traveling costs: Problem formulation, hardness of approximation, and approximation algorithms
, 2006
"... AbstractIn this paper, we introduce the problem of view planning with combined view and traveling cost, denoted by Traveling VPP. It refers to planning a sequence of sensing actions with minimum total cost by a robot-sensor system to completely inspect the surfaces of objects in a known workspace. T ..."
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AbstractIn this paper, we introduce the problem of view planning with combined view and traveling cost, denoted by Traveling VPP. It refers to planning a sequence of sensing actions with minimum total cost by a robot-sensor system to completely inspect the surfaces of objects in a known workspace. The cost to minimize is a combination of the view cost, proportional to the number of viewpoints planned, and the traveling cost for the robot to realize them. First, we formulate Traveling VPP as an integer linear program (ILP). The focus of this paper is to design an approximation algorithm that guarantees worst-case performance (w.r.t. the optimal solution cost). We propose a linear program based rounding algorithm that achieves an approximation ratio of the order of view frequency, dened to be the maximum number of viewpoints that see a single surface patch of the object. Together with the result we showed in [22], the best approximation ratio for Traveling VPP is either the order of view frequency or a poly-log function of the input size, whichever is smaller. Motivated from the robot motion planning techniques, where the graph built for robot traveling is a tree, we then consider the corresponding special case of Traveling VPP, and give a polynomial sized LP formulation. We conclude with a discussion of realistic issues and constraints towards implementing our algorithm on real robot-sensor systems. I.
Generalized Watchman Route Problem with Discrete View Cost
"... In this paper, we introduce a generalized version of the Watchman Route Problem (WRP) where the objective is to plan a continuous closed route in a polygon (possibly with holes) and a set of discrete viewpoints on the planned route such that every point on the polygon boundary is visible from at lea ..."
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In this paper, we introduce a generalized version of the Watchman Route Problem (WRP) where the objective is to plan a continuous closed route in a polygon (possibly with holes) and a set of discrete viewpoints on the planned route such that every point on the polygon boundary is visible from at least one viewpoint. The total cost to minimize is a weighted sum of the view cost, proportional to the number of viewpoints, and the travel cost, the total length of the route. We call this problem the Watchman Route Problem with Discrete View Cost or the Generalized Watchman Route Problem (GWRP). In this paper, we consider a restricted version of GWRP that arises naturally in inspection tasks in robotic applications, where each polygon edge is entirely visible from at least one planned viewpoint. We call it Whole Edge Covering GWRP. This whole edge covering restriction is not trivial in that WEC-GWRP has the same NPhardness and inapproximability as GWRP. The algorithm we propose first constructs a graph that connects O(n 12) number of sample viewpoints in the polygon, where n is the number of polygon vertices; and then solves the corresponding View Planning Problem with Combined View and Traveling Cost, using an LP-relaxation based algorithm we introduced in [19]. We show that our algorithm has an approximation ratio in the order of either the view frequency, defined as the maximum number of sample viewpoints that cover a polygon edge, or a polynomial of log n, whichever is smaller. 1
Mapping and Pursuit-Evasion Strategies For a Simple Wall-Following Robot
, 2010
"... This paper defines and analyzes a simple robot with local sensors that moves in an unknown polygonal environment. The robot can execute wall-following motions and can traverse the interior of the environment only when following parallel to an edge. The robot has no global sensors that would allow pr ..."
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Cited by 4 (1 self)
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This paper defines and analyzes a simple robot with local sensors that moves in an unknown polygonal environment. The robot can execute wall-following motions and can traverse the interior of the environment only when following parallel to an edge. The robot has no global sensors that would allow precise mapping or localization. Special information spaces are introduced for this particular model. Using these, strategies are presented for solving several tasks: 1) counting vertices, 2) computing the path winding number, 3) learning a combinatorial map, called the cut ordering, that encodes partial geometric information, and 4) solving pursuit-evasion problems.
Mapping and Pursuit-Evasion Strategies For a Simple Wall-Following Robot
"... This paper defines and analyzes a simple robot with local sensors that moves in an unknown polygonal environment. The robot can execute wall-following motions and can traverse the interior of the environment only when following parallel to an edge. The robot has no global sensors that would allow pr ..."
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Cited by 1 (1 self)
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This paper defines and analyzes a simple robot with local sensors that moves in an unknown polygonal environment. The robot can execute wall-following motions and can traverse the interior of the environment only when following parallel to an edge. The robot has no global sensors that would allow precise mapping or localization. Special information spaces are introduced for this particular model. Using these, strategies are presented for solving several tasks: 1) counting vertices, 2) computing the path winding number, 3) learning a combinatorial map, called the cut ordering, that encodes partial geometric information, and 4) solving pursuit-evasion problems.
A Competitive Online Algorithm for Exploring a Solar Map
"... Abstract — In this paper, we study the problem of quickly building the 3D model of an outdoor environment from mea-surements obtained by a robot equipped with a solar panel. The robot knows the angle of the sun and the locations of the objects in the environment. It does not know, however, the heigh ..."
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Abstract — In this paper, we study the problem of quickly building the 3D model of an outdoor environment from mea-surements obtained by a robot equipped with a solar panel. The robot knows the angle of the sun and the locations of the objects in the environment. It does not know, however, the height of the objects. For example, it might be possible to use satellite images to obtain locations of trees in a field but not their heights. In order to compute the height of an object, the robot must find the projection of the object’s highest point. This is where the shadow of the object ends. The robot can find it by tracing the shadow (moving parallel to the sun) until the measurement switches from shadow to sun or vice versa. The robot’s goal is to compute the height of every object as quickly as possible using only solar measurements. We formulate this as an online optimization problem. The optimal offline algorithm is given by the Traveling Salesman path of the transition points. The robot does not know these locations a priori. It must search for each of them. We present an algorithm with the property that for n objects, our distance traveled is guaranteed to be within a factor O(log n) of this optimal offline tour. In addition to analytical proofs, we demonstrate the algorithm with simulations using solar data collected from field experiments, and examine its performance for uniformly distributed sites. I.
Optimal strategies for maintaining a chain of relays between an explorer and a base camp
- THEORETICAL COMPUTER SCIENCE
, 2009
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