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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 26 (14 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
Pursuitevasion in an unknown environment using gap navigation graphs
 In Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems
, 2004
"... In this paper we present an online algorithm for pursuitevasion in a unknown simply connected environment, for one pursuer that has minimal sensing and carries a set of stationary sentries that it can drop off and pick up during the pursuit. In our sensing model, the pursuer is only able to detect d ..."
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Cited by 14 (9 self)
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In this paper we present an online algorithm for pursuitevasion in a unknown simply connected environment, for one pursuer that has minimal sensing and carries a set of stationary sentries that it can drop off and pick up during the pursuit. In our sensing model, the pursuer is only able to detect discontinuities in depth information (gaps), and it is able to find all of the evaders without any explicit localization or geometric information, by using a Gap Navigation Tree. The strategy is based on growing an evaderfree region, by reading “exploration” schedules from the Gap Navigation Tree, that is constructed online. We prove that a pursuer with k +1 sentries can clear any environment that could be cleared by k pursuers using the algorithm in [7], which required a complete map and perfect sensing. I.
"Localization Space": a framework for localization and planning, for systems using a Sensor/Landmarks module
, 2001
"... One of the common ways of localization in robotics is the triangulation using a system composed of a sensor and some landmarks (which can be artificial or natural). This paper presents a framework, namely the Localization Space, in order to deal with problems such as the landmark placement and mo ..."
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Cited by 9 (2 self)
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One of the common ways of localization in robotics is the triangulation using a system composed of a sensor and some landmarks (which can be artificial or natural). This paper presents a framework, namely the Localization Space, in order to deal with problems such as the landmark placement and motion planning including the localization constraint. Based on this framework, we present general approaches to the optimal distribution of the landmarks or to the computation of reliable trajectories. The case
LocallyOptimal Navigation in MultiplyConnected Environments Without Geometric Maps
"... In this paper we present an algorithm to build a sensorbased, dynamic data structure useful for robot navigation in an unknown, multiplyconnected planar environment. This data structure offers a robust framework for robot navigation, avoiding the need of a complete geometric map or explicit locali ..."
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Cited by 8 (4 self)
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In this paper we present an algorithm to build a sensorbased, dynamic data structure useful for robot navigation in an unknown, multiplyconnected planar environment. This data structure offers a robust framework for robot navigation, avoiding the need of a complete geometric map or explicit localization, by building a minimal representation based entirely on critical events in online sensor measurements made by the robot. There are two sensing requirements for the robot: it must detect when it is close to the walls, to perform wallfollowing reliably, and it must be able to detect discontinuities in depth information. It is also assumed that the robot is able to drop, detect and recover a marker. The navigation paths generated are optimal up to the homotopy class to which the paths belong, even though no distance information is measured.
VisibilityBased PursuitEvasion with Bounded
"... Summary. This paper presents an algorithm for a visibilitybased pursuitevasion problem in which bounds on the speeds of the pursuer and evader are given. The pursuer tries to find the evader inside of a simplyconnected polygonal environment, and the evader in turn tries actively to avoid detectio ..."
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Cited by 6 (1 self)
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Summary. This paper presents an algorithm for a visibilitybased pursuitevasion problem in which bounds on the speeds of the pursuer and evader are given. The pursuer tries to find the evader inside of a simplyconnected polygonal environment, and the evader in turn tries actively to avoid detection. The algorithm is at least as powerful as the complete algorithm for the unbounded speed case, and with the knowledge of speed bounds, generates solutions for environments that were previously unsolvable. Furthermore, the paper develops a characterization of the set of possible evader positions as a function of time. This characterization is more complex than in the unboundspeed case, because it no longer depends only on the combinatorial changes in the visibility region of the pursuer. 1
New Visibility Partitions with Applications in Affine Pattern Matching
, 1999
"... Visibility partitions play an important role in computer vision and pattern matching. A visibility partition is formed by regions in which the combinatorial structure of the visibility is constant. This paper studies new types of visibility partitions with applications in affine pattern matching. Fi ..."
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Visibility partitions play an important role in computer vision and pattern matching. A visibility partition is formed by regions in which the combinatorial structure of the visibility is constant. This paper studies new types of visibility partitions with applications in affine pattern matching. First, we discuss the conventional visibility partition for finite line segment collections. The machinery from this analysis is then used to describe the two new partitions induced by alternative forms of visibility, namely transvisibility and reflectionvisibility. We present algorithms that compute each of the partitions in O((n + k) log(n) + v) randomised time, where k is the number of visibility edges (at most O(n )), and v is the number of vertices in the partition (at most O(n )). In addition, we show that each of the partitions has worstcase combinatorial complexity ). Our model of computation assumes that the absolute value of a quotient of polynomials of degree at most d can be integrated over a triangle in (d) time. We use reflectionvisibility partitions to compute the reection metric in O(r(nA + nB )) randomised time, for two line segment unions, with nA and nB line segments, separately, where r is the complexity of the overlay of two reflectionvisibility partitions (at most O(nA + nB )).
Studying Localization With Landmarks
"... Localization with landmarks is a recurrent problem in robotics. In order to perceive the environment, robots are often equipped with some exteroceptive sensors (such as camera, laser range finder, etc). One way of using these sensors for localization is to detect some features in the environment and ..."
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Localization with landmarks is a recurrent problem in robotics. In order to perceive the environment, robots are often equipped with some exteroceptive sensors (such as camera, laser range finder, etc). One way of using these sensors for localization is to detect some features in the environment and to use them as landmarks. In this paper, we present how we tackle the complete set up of a fast, reliable and e#cient localization system. We start by giving methods to optimize the landmark placement in our environment. Then, we show how a specific SLAM algorithm can be e#ciently associated with a robust data association method to make simultaneous matching, localization and mapping (SMLAM) in this environment. We also give a method to integrate the need for localization in a path planning algorithm, and we finish by presenting experimental results which show the relevance and the e#ciency of our method.