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Counting targets with mobile sensors in an unknown environment
 In Proceedings of the 3rd International Workshop in Algorithmic Aspects of Wireless Sensor Networks (ALGOSENSORS), Revised Selected Papers
, 2007
"... Abstract. We consider the problem of counting the number of indistinguishable targets using a simple binary sensing model. Our setting includes an unknown number of point targets in a (simple or multiplyconnected) polygonal workspace, and a moving pointrobot whose sensory input at any location is a ..."
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Cited by 19 (3 self)
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Abstract. We consider the problem of counting the number of indistinguishable targets using a simple binary sensing model. Our setting includes an unknown number of point targets in a (simple or multiplyconnected) polygonal workspace, and a moving pointrobot whose sensory input at any location is a binary vector representing the cyclic order of the polygon vertices and targets visible to the robot. In particular, the sensing model provides no coordinates, distance or angle measurements. We investigate this problem under two natural models of environment, friendly and hostile, which differ only in whether the robot can walk up to them or not, and under three different models of motion capability. In the friendly scenario we show that the robots can count the targets, whereas in the hostile scenario no (2 − ε)approximation is possible, for any ε> 0. Next we consider two, possibly minimally more powerful robots that can count the targets exactly. 1 The Problem and the Model
P.: Simple robots in polygonal environments: A hierarchy
 In: Proceedings of the Fourth International Workshop on Algorithmic Aspects of Wireless Sensor Networks
, 2008
"... Abstract. With the current progress in robot technology and related areas, sophisticated moving and sensing capabilities are at hand to design robots capable of solving seemingly complex tasks. With the aim of understanding the limitations of such capabilities, swarms of simple and cheap robots play ..."
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Cited by 8 (6 self)
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Abstract. With the current progress in robot technology and related areas, sophisticated moving and sensing capabilities are at hand to design robots capable of solving seemingly complex tasks. With the aim of understanding the limitations of such capabilities, swarms of simple and cheap robots play an increasingly important role. Their advantages are, among others, the cost, reusability, and faulttolerance. While it can be expected that for a variety of problems a wealth of robot models are proposed, it is rather unfortunate that almost all proposals fail to point out their assumptions explicitly and clearly. This is problematic because seemingly small changes in the models can lead to significant differences in the capabilities of the robots. Hence, a clean assessment of the “power of robot models ” is dearly needed, not only in absolute terms, but also relative to each other. We make a step in this direction by explaining for a set of elementary sensing devices which of these devices (alone and in combination) enable a robot to solve which problems. This not only leads to a natural relation (and hierarchy) of power between robot models that supports a more systematic design, but also exhibits surprising connections and equivalences. For example, one of the derived relations between the robot models implies that a very simple robot (that cannot measure distances) moving inside a simple polygon can find a shortest path between two vertices by means of a sensor that detects for an angle at a vertex of the polygon whether it is convex. We give an explicit algorithm which allows the robot to find a shortest path. 1
MultiAgent Deployment for Visibility Coverage in Polygonal Environments with Holes
, 2010
"... ..."
Mapping and PursuitEvasion Strategies For a Simple WallFollowing Robot
, 2010
"... This paper defines and analyzes a simple robot with local sensors that moves in an unknown polygonal environment. The robot can execute wallfollowing 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 wallfollowing 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 pursuitevasion problems.
Mapping Simple Polygons: How Robots Benefit from Looking Back
 ALGORITHMICA
"... We consider the problem of mapping an initially unknown polygon of size n with a simple robot that moves inside the polygon along straight lines between the vertices. The robot sees distant vertices in counterclockwise order and is able to recognize the vertex among them which it came from in its ..."
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Cited by 3 (3 self)
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We consider the problem of mapping an initially unknown polygon of size n with a simple robot that moves inside the polygon along straight lines between the vertices. The robot sees distant vertices in counterclockwise order and is able to recognize the vertex among them which it came from in its last move, i.e. the robot can look back. Other than that the robot has no means of distinguishing distant vertices. We assume that an upper bound on n is known to the robot beforehand and show that it can always uniquely reconstruct the visibility graph of the polygon. Additionally, we show that multiple identical and deterministic robots can always solve the weak rendezvous problem in which the robots need to position themselves such that all of them are mutually visible to each other. Our results are tight in the sense that the strong rendezvous problem, where robots need to gather at a vertex, cannot be solved in general, and, without knowing a bound beforehand, not even n can be determined. In terms
Telling convex from reflex allows to map a polygon
"... We consider the exploration of a simple polygon P by a robot that moves from vertex to vertex along edges of the visibility graph of P. The visibility graph has a vertex for every vertex of P and an edge between two vertices if they see each other, i.e. if the line segment connecting them lies insid ..."
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Cited by 2 (1 self)
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We consider the exploration of a simple polygon P by a robot that moves from vertex to vertex along edges of the visibility graph of P. The visibility graph has a vertex for every vertex of P and an edge between two vertices if they see each other, i.e. if the line segment connecting them lies inside P entirely. While located at a vertex, the robot is capable of ordering the vertices it sees in counterclockwise order as they appear on the boundary, and for every two such vertices, it can distinguish whether the angle between them is convex ( ≤ π) or reflex (> π). Other than that, distant vertices are indistinguishable to the robot. We assume that an upper bound on the number of vertices is known and show that the robot is always capable of reconstructing the visibility graph of P. We also show that multiple identical, indistinguishable and deterministic such robots can always position themselves such that they mutually see each other, i.e. such that they form a clique in the visibility graph.
How Simple Robots Benefit from Looking Back
 In: Proceedings of the 7th International Conference on Algorithms and Complexity
, 2010
"... Abstract. We study the sensor and movement capabilities that simple robots need in order to create a map of an unknown polygon of size n, and to meet. We consider robots that can move from vertex to vertex, can backtrack movements, and see distant vertices in counterclockwise order but have no mean ..."
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Cited by 2 (2 self)
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Abstract. We study the sensor and movement capabilities that simple robots need in order to create a map of an unknown polygon of size n, and to meet. We consider robots that can move from vertex to vertex, can backtrack movements, and see distant vertices in counterclockwise order but have no means of visibly identifying them. We show that such robots can always solve the weak rendezvous problem and reconstruct the visibility graph, given an upper bound on n. Our results are tight: The strong rendezvous problem, in which robots need to gather at a common location, cannot be solved in general, and without a bound on n, not even n can be determined. In terms of mobile agents exploring a graph, our result implies that they can reconstruct any graph that is the visibility graph of a simple polygon. This is in contrast to the known result that the reconstruction of arbitrary graphs is impossible in general, even if n is known. 1
Mapping and PursuitEvasion Strategies For a Simple WallFollowing Robot
"... This paper defines and analyzes a simple robot with local sensors that moves in an unknown polygonal environment. The robot can execute wallfollowing 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 wallfollowing 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 pursuitevasion problems.
Walking in Streets with Minimal Sensing
"... Abstract. We consider the problem of walking in an unknown street, starting from a point s, to reach a target t by a robot which has a minimal sensing capability. The goal is to decrease the traversed path as short as possible. The robot cannot infer any geometric properties of the environment such ..."
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Abstract. We consider the problem of walking in an unknown street, starting from a point s, to reach a target t by a robot which has a minimal sensing capability. The goal is to decrease the traversed path as short as possible. The robot cannot infer any geometric properties of the environment such as coordinates, angles or distances. The robot is equipped with a sensor that can only detect the discontinuities in the depth information (gaps) and can locate the target point as soon as it enters in its visibility region. In addition, a pebble as an identiable point is available to the robot to mark some position of the street. We oer a data structure similar to Gap Navigation Tree to maintain the essential sensed data to explore the street. We present an online strategy that guides such a robot to navigate the scene to reach the target, based only on what is sensed at each point and is saved in the data structure. Although the robot has a limited capability, we show that the detour from the shortest path can be restricted such that generated path by our strategy is at most 11 times as long as the shortest path to target. 1