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32
EnergyEfficient Algorithms for . . .
, 2007
"... We study scheduling problems in batteryoperated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadlinebased settings, in this article we are interested in schedules that guarantee good respons ..."
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Cited by 62 (2 self)
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We study scheduling problems in batteryoperated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadlinebased settings, in this article we are interested in schedules that guarantee good response times. More specifically, our goal is to schedule a sequence of jobs on a variablespeed processor so as to minimize the total cost consisting of the energy consumption and the total flow time of all jobs. We first show that when the amount of work, for any job, may take an arbitrary value, then no online algorithm can achieve a constant competitive ratio. Therefore, most of the article is concerned with unitsize jobs. We devise a deterministic constant competitive online algorithm and show that
Searching for the Kernel of a Polygon: A Competitive Strategy Using SelfApproaching Curves
 In Proc. 11th Annu. ACM Sympos. Comput. Geom
, 1995
"... We present a competitive strategy for walking into the kernel of an initially unknown starshaped polygon. From an arbitrary start point, s, within the polygon, our strategy finds a path to the closest kernel point, k, whose length does not exceed 5.3331 ...times the distance from s to k. This is ..."
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Cited by 28 (11 self)
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We present a competitive strategy for walking into the kernel of an initially unknown starshaped polygon. From an arbitrary start point, s, within the polygon, our strategy finds a path to the closest kernel point, k, whose length does not exceed 5.3331 ...times the distance from s to k. This is complemented by a general lower bound of # 2. Our analysis relies on a result about a new and interesting class of curves which are selfapproaching in the following sense.
Distanceoptimal navigation in an unknown environment without sensing distances
 IEEE Transactions on Robotics
, 2007
"... Abstract — This paper considers what can be accomplished using a mobile robot that has limited sensing. For navigation and mapping, the robot has only one sensor, which tracks the directions of depth discontinuities. There are no coordinates, and the robot is given a motion primitive that allows it ..."
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Cited by 25 (13 self)
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Abstract — This paper considers what can be accomplished using a mobile robot that has limited sensing. For navigation and mapping, the robot has only one sensor, which tracks the directions of depth discontinuities. There are no coordinates, and the robot is given a motion primitive that allows it to move toward discontinuities. The robot is incapable of performing localization or measuring any distances or angles. Nevertheless, when dropped into an unknown planar environment, the robot builds a data structure, called the Gap Navigation Tree, which enables it to navigate optimally in terms of Euclidean distance traveled. In a sense, the robot is able to learn the critical information contained in the classical shortestpath roadmap, although surprisingly it is unable to extract metric information. We prove these results for the case of a point robot placed into a simply connected, piecewiseanalytic planar environment. The case of multiply connected environments is also addressed, in which it is shown that further sensing assumptions are needed. Due to the limited sensor given to the robot, globally optimal navigation is impossible; however, our approach achieves locally optimal (within a homotopy class) navigation, which is the best that is theoretically possible under this robot model. Index Terms — Visibility, navigation, optimality, map building, minimal sensing, shortest paths, information spaces, sensorbased
Gap navigation trees: Minimal representation for visibilitybased tasks
 In Proc. Workshop on the Algorithmic Foundations of Robotics
, 2004
"... Abstract. In this paper we present our advances in a data structure, the Gap Navigation Tree (GNT), useful for solving different visibilitybased robotic tasks in unknown planar environments. We present its use for optimal robot navigation in simplyconnected environments, locally optimal navigation ..."
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Cited by 22 (10 self)
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Abstract. In this paper we present our advances in a data structure, the Gap Navigation Tree (GNT), useful for solving different visibilitybased robotic tasks in unknown planar environments. We present its use for optimal robot navigation in simplyconnected environments, locally optimal navigation in multiplyconnected environments, pursuitevasion, and robot localization. The guiding philosophy of this work is to avoid traditional problems such as complete map building and exact localization by constructing a minimal representation based entirely on critical events in online sensor measurements made by the robot. The data structure is introduced from an information space perspective, in which the information used among the different visibilitybased tasks is essentially the same, and it is up to the robot strategy to use it accordingly for the completion of the particular task. This is done through a simple sensor abstraction that reports the discontinuities in depth information of the environment from the robot’s perspective (gaps), and without any kind of geometric measurements. The GNT framework was successfully implemented on a real robot platform. 1
Randomized algorithms for minimum distance localization
 In Proc. Workshop on Algorithmic Foundations of Robotics
, 2004
"... Abstract. We address the problem of minimum distance localization in environments that may contain selfsimilarities. A mobile robot is placed at an unknown location inside a ¢¤£ selfsimilar polygonal environment ¥. The robot has a map of ¥ and can compute visibility data through sensing. However, ..."
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Cited by 13 (1 self)
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Abstract. We address the problem of minimum distance localization in environments that may contain selfsimilarities. A mobile robot is placed at an unknown location inside a ¢¤£ selfsimilar polygonal environment ¥. The robot has a map of ¥ and can compute visibility data through sensing. However, the selfsimilarities in the environment mean that the same visibility data may correspond to several different locations. The goal, therefore, is to determine the robot’s true initial location while minimizing the distance traveled by the robot. We present two randomized approximation algorithms that solve the problem of minimum distance localization. The performance of our algorithms is evaluated empirically. 1
Competitive Searching in a Generalized Street
 In Proc. 10th Annu. ACM Sympos. Comput. Geom
, 1999
"... We consider the problem of a robot which has to find a target in an unknown simple polygon, based only on what it has seen so far. A street is a polygon for which the two boundary chains from start to target are mutually weakly visible. A target inside a street can be found by walking a path that is ..."
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Cited by 13 (4 self)
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We consider the problem of a robot which has to find a target in an unknown simple polygon, based only on what it has seen so far. A street is a polygon for which the two boundary chains from start to target are mutually weakly visible. A target inside a street can be found by walking a path that is at most a constant times longer than the shortest path in the street from start to target. We define a strictly larger class of polygons, called generalized streets or Gstreets, which are characterized by the property that every point on the boundary of a Gstreet is visible from a point on a horizontal line segment connecting the two boundary chains. We present an online strategy for a robot to find the target in an unknown rectilinear Gstreet; the length of its path is at most 9 times the length of the shortest path in the L 1 metric, and 9.06 times the length of the L 2 shortest path. These bounds are optimal. Key words: Simple polygon, street, searching, doubling, competitive...
Optimal Robot Localization in Trees
"... The problem of localization, i.e. of a robot finding its position on a map, is an important task for autonomous mobile robots. It has applications in numerous areas of robotics ranging from aerial photography to autonomous vehicle exploration. In this paper we present a new strategy for a robot to f ..."
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Cited by 11 (0 self)
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The problem of localization, i.e. of a robot finding its position on a map, is an important task for autonomous mobile robots. It has applications in numerous areas of robotics ranging from aerial photography to autonomous vehicle exploration. In this paper we present a new strategy for a robot to find its position on a map where the map is represented as a geometric tree. Our strategy exploits to a high degree the selfsimilarities that may occur in the environment. We use the framework of competitive analysis to analyze the performance of our strategy. In particular, we show that the distance traveled by the robot is at most O(pn) times longer than the shortest possible route to localize the robot, where n is the number of vertices of the tree. This is a significant improvement over the best known previous bound of O(n2=3). Moreover, since there is a lower bound of \Omega (pn), our strategy is optimal up to a constant factor. Using the same approach we can also show that the problem of searching for a target in a geometric tree, where the robot is given a map of the tree and the location of the target but does not know its own position, can be solved by a strategy with a competitive ratio of O(pn), which is again optimal up to a constant factor.
On comparing the power of robots
 International Journal of Robotics Research. Under review
"... Robots must complete their tasks in spite of unreliable actuators and limited, noisy sensing. In this paper, we consider the information requirements of such tasks. What sensing and actuation abilities are needed to complete a given task? Are some robot systems provably “more powerful, ” in terms of ..."
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Cited by 11 (3 self)
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Robots must complete their tasks in spite of unreliable actuators and limited, noisy sensing. In this paper, we consider the information requirements of such tasks. What sensing and actuation abilities are needed to complete a given task? Are some robot systems provably “more powerful, ” in terms of the tasks they can complete, than others? Can we find meaningful equivalence classes of robot systems? This line of research is inspired by the theory of computation, which has produced similar results for abstract computing machines. The basic idea is a dominance relation over robot systems that formalizes the idea that some robots are stronger than others. This comparison, which is based on the how the robots progress through their information spaces, induces a partial order over the set of robot systems. We prove some basic properties of this partial order and show that it is directly related to the robots’ ability to complete tasks. We give examples to demonstrate the theory, including a detailed analysis of a limitedsensing global localization problem. 1
Robot localization without depth perception
 In Scandinavian Workshop on Algorithm Theory
, 2002
"... Abstract. Consider the problem of placing reflectors in a 2D environment in such a way that a robot equipped with a basic laser can always determine its current location. The robot is allowed to swivel at its current location, using the laser to detect at what angles some reflectors are visible, bu ..."
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Cited by 9 (0 self)
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Abstract. Consider the problem of placing reflectors in a 2D environment in such a way that a robot equipped with a basic laser can always determine its current location. The robot is allowed to swivel at its current location, using the laser to detect at what angles some reflectors are visible, but no distance information is obtained. A polygonal map of the environment and reflectors is available to the robot. We show that there is always a placement of reflectors that allows the robot to localize itself from any point in the environment, and that such a reflector placement can be computed in polynomial time on a real RAM. This result improves over previous techniques which have up to a quadratic number of ambiguous points at which the robot cannot determine its location [1, 9]. Further, we show that the problem of optimal reflector placement is equivalent to an artgallery problem within a constant factor. 1
Efficient Robot SelfLocalization in Simple Polygons
 Intelligent RobotsSensing, Modelling and Planning
, 1997
"... Introduction One of the basic tasks faced by an autonomous mobile robot is the problem of selflocalization, that is determining its position in its environment; this is also sometimes called the "where am I?" problem. There are many variations of this problem depending on the environment and the ..."
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Cited by 8 (1 self)
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Introduction One of the basic tasks faced by an autonomous mobile robot is the problem of selflocalization, that is determining its position in its environment; this is also sometimes called the "where am I?" problem. There are many variations of this problem depending on the environment and the sensor data and apriori information available to the robot. Here, we consider a robot that is given a map of its environment but has no knowledge of its location on the map. Often, it is assumed that this problem can be solved by only using sensor data and allowing the robot to make a small local pertubation of its current position. But if there are selfsimilar parts in the environment, then this approach may not suffice to distinguish between the possible locations of the robot. This issue has been addressed in numerous contexts, ranging from aerial photography to autonomous vehicles for the exploration of landscapes. We consider an idealized version of the problem