G. Dudek, K. Romanik, and S. Whitesides. Localizing a robot with minimum travel. In ACM-SIAM Symposium on Discrete Algorithms, pages 437--446, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....wrong hypotheses in the second stage and determines exactly where it is by traveling around in its environment. This is a typical on line problem, because the robot has to process the information on line to nd a path for eliminating the wrong hypotheses, which is as short as possible. Dudek et al. [4] have already shown that nding an optimal path (with minimum length) is NP hard, and described a competitive greedy strategy, which was recently improved by Schuierer [8] This paper concentrates on the rst stage of the localization process, that is, on generating the possible robot locations. ....

G. Dudek, K. Romanik, and S. Whitesides. Localizing a Robot with Minimum Travel. In Proceedings of the 6th Annual ACMSIAM Symposium on Discrete Algorithms, pages 437446, 1995.

....however, we are able to show a competitive ratio of O(n log n ) o(n) In contrast, the strongest lower bound we can show is Omega Gamma n) in both types of environments. Closing this gap remains an interesting open question. In independent work, Dudek, Romanik, and Whitesides [DRW] give a geometric implementation of the shortest distinguishing paths algorithm which appears as Step 3 in the main algorithm of this chapter when the environment is a simple polygon. Their algorithm is O(k) competitive when the robot initially cannot distinguish among k possible ....

G. Dudek, K. Romanik, S. Whitesides, "Localizing a robot with minimum travel," Proc. 6th ACM-SIAM Symposium on Discrete Algorithms.

....of these plans, with some walls being misplaced by over a meter This certainly highlights the need for robots that can construct their own models, a topic we hope to address in the near future. 7 Related Work An algorithm for explicitly re localising a robot is described by Dudek et al. [5]. This is a theoretical analysis that describes how a robot at some unknown 21 location in a polygonal environment can determine its location with the least possible e ort. That is, it describes an algorithm for obtaining the shortest path the robot can take to unambiguously determine its ....

Gregory Dudek, Kathleen Romanik, and Sue Whitesides. Localizing a robot with minimum travel. In Proceedings of the 6th ACM-SIAM Symposium on Discrete Algorithms, 1995.

....that the robot s initial location is known. Unfortunately, in practice, robots tend to get lost, usually as a result of sensor noise. Under these circumstances, the robot may have to execute a complex series of actions in order to re localise itself. Although relocalisation algorithms do exist [ Dudek et al. 1995 ] we have chosen instead to restate the navigation problem. Our version is as follows: given a robot that is at some unknown initial location, plan and execute a series of actions that will take the robot to the goal . That is, we attempt to develop an single algorithm that can be used for both ....

Gregory Dudek, Kathleen Romanik, and Sue Whitesides. Localizing a robot with minimum travel. In Proceedings of the 6th ACM-SIAM Symposium on Discrete Algorithms, 1995.

....for long periods of time, these robots must have some technique that enables them to determine that they are lost and to take steps towards recovery. Conventional approaches, which are based on localisation and path planning, do not address this problem well. With a few notable exceptions [1], most attempts at making systems more robust have concentrated on increasing the reliability of the localisation process, either by physically altering the environment [2] by using sophisticated sensor fusion and map registration techniques [3] 4] 5] or by using planning techniques that ....

Gregory Dudek, Kathleen Romanik, and Sue Whitesides, "Localizing a robot with minimum travel", in Proceedings of the 6th ACM-SIAM Symposium on Discrete Algorithms, 1995.

.... et al. 16] and, independently, by Schuierer et al. 33] Other interesting geometric applications for competitive strategies are e.g. the search for the kernel of a polygon [15,24,28,22] exploration or path planning in unknown environments [7,11,12,1,6] or localization in known environments [8,10,14,19,32]. It has been posed as a challenging open problem whether more general classes 2 of polygons admit competitive searching. In this paper, we introduce such a class of polygons, namely the generalized streets,orG streets for short. We give a strategy for searching in the rectilinear case which is ....

G. Dudek, K. Romanik, and S. Whitesides. Localizing a robot with minimum travel. SIAM J. Comput., 27(2):583--604, 1998.

....is of complexity O(n 3 ) Next, we turn to subproblem (2) the design of an exploration tour which enables the robot to determine its current position p among all candidates found in step (1) The solution we are going to present has been recently discovered by Dudek et al. see ref. [6]. Figure 14 shows an example of a floor plan where the points indicated by dots have identical visibility polygons. Let us assume that the vertical segments of the main corridor are much longer than its horizontal segments and the other vertical corridors. Then the robot should stay on its ....

....An optimal solution to subproblem (2) would consist of precomputing a decision tree whose weighted height, i.e. the maximum sum of edge weights along all root toleaf paths, is a minimum. This, however, is not feasible, due to a strong connection to the NP complete problem Abstract Decision Tree [6]. In the latter, a collection of subsets A i , 1 # i # k, of some universe of size c and a number h are given. The question is if there exists a decision tree of height # h that uniquely identifies each element p of the universe by tests of the type p # A i contained in the nodes. One ....

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G. Dudek, K. Romanik, and S. Whitesides. Localizing a robot with minimum travel. In Proc. 6th ACM-SIAM Sympos. Discrete Algorithms, 1995.

....V consists of m vertices [2] If more than one placement exists, then the robot has to follow a path that allows it to distinguish between the different placements. Dudek, Romanik, and Whitesides consider a setting in which the environment can be modeled as a simple polygon P as described above [1]. They propose a simple strategy where the robot repeatedly travels to the closest point that eliminates at least one of the possible placements. Unfortunately, the algorithm presented by Dudek et al. has a time and space complexity of O(k 2 n 4 ) which is prohibitively large, even for a small ....

....Distance Localization A mentioned before a simple strategy for robot localization is to repeatedly go to the closest point from the wake up position of the robot at which at least one of the initial placements can be eliminated. The idea for this strategy was first proposed by Dudek et al. [1]. The following is one key observation. Lemma 3.1 If q is the closest point to the origin at which at least one placement can be eliminated , then there is a placement p in and a vertex v of P such that p q is located on the window of vis(v) that is the closest to p. In fact, p q ....

G. Dudek, K. Romanik, and S. Whitesides. Localizing a robot with minimum travel. In Proc. 6th ACM-SIAM Symp. on Discrete Algorithms, pages 437--446, 1995.

....approach using polygon metrics [KW99] In this paper we use our feature based localization to generate the hypotheses set but other approachs can be used as well. KS99] All solutions generate a set of hypotheses, but they do not reduce this set to the true position. In past, Dudek et al. [DRW95] gave a theoretical solution using overlayarrangements. But this solution was very expensive concerning time complexity of O(k 2 n 4 ) Therein k ist the number of hypotheses and n is the number of vertices of the map polygon. The approach was improved 1996 by Schuierer who uses windows on ....

....by the localization strategy L and the decision strategy N in a worst case map on worst case positions and the optimum path for this worst case scenario. 3 The approach of Schuierer and adaptations The second part of the self localization problem was first introduced and solved by Dudek et. al [DRW95]. They showed that the problem is NP complete by reducing it on the minimum decision tree problem. They gave an approximative solution by using overlay arrangements of visibility decompositions. Their algorithm has a time complexity of O(k 2 n 4 ) whereas k denotes the number of hypotheses and ....

Gregory Dudek, Kathleen Romanik and Sue Whitesides. Localizing a Robot with Minimum Travel. In Proceedings of the 6th Annual ACM--SIAM Symposium on Discrete Algorithms, pp. 437--446, 1995.

....it is by travelling around in its environment. This is a typical on line problem, because the robot has to consider the new information that arrives while the robot is exploring its environment to nd a path as eOEcient (i.e. short) as possible for eliminating the wrong hypotheses. Dudek et al. [4] have already shown that nding an optimal localization strategy is NP hard, and described a competitive greedy strategy, the running time of which was recently improved by Schuierer [9] This paper concentrates on the rst stage of the localization process, that is, on generating the possible ....

G. Dudek, K. Romanik, and S. Whitesides. Localizing a Robot with Minimum Travel. In Proceedings of the 6th Annual ACMSIAM Symposium on Discrete Algorithms, pages 437446, 1995.

....the same visibility polygon, they cannot be distinguished by a non moving robot. In those cases, the robot eliminates the wrong hypotheses and determines its position exactly by moving around in its environment (as little as possible) in the second stage. For this, Dudek, Romanik, and Whitesides [1] describe a simple competitive greedy strategy with time and space complexity O(k 2 n 4 ) which was recently improved by Schuierer [5] to a running time of O(kn log n) and space complexity of O(kn) In this talk we concentrate on generating the possible robot locations in the framework of ....

G. Dudek, K. Romanik, and S. Whitesides. Localizing a Robot with Minimum Travel. In Proceedings of the 6th Annual ACMSIAM Symposium on Discrete Algorithms, pages 437446, 1995.

....niches in Fig. 2 cannot be distinguished using only their visibility polygons. If there is more than one hypothetical position, the robot eliminates the wrong hypotheses in the second stage and determines exactly where it is by traveling around in its environment. For this problem, Dudek et al. [3] have already shown that finding an optimal localization strategy is NP hard, and described a competitive greedy strategy, the running time of which was recently improved by Schuierer [8] This paper only investigates the first stage of the localization process, that is, the generation of the ....

G. Dudek, K. Romanik, and S. Whitesides. Localizing a Robot with Minimum Travel. In Proceedings of the 6th Annual ACM--SIAM Symposium on Discrete Algorithms, pages 437--446, 1995.

....The robot has a map of the environment. It wakes up at a position s and has to uniquely determine its initial position using a short path. In the following we concentrate on the robot navigation problem. We refer the reader to [4, 35, 36, 44] for literature on the exploration problem, and to [37, 43, 51, 63] for literature on the localization problem. Many robot navigation problems were introduced by Baeza Yates et al. 13] and Papadimitriou and Yannakakis [59] We call an robot navigation A strategy c competitive, if the length of the path used by A is at most c times the length of the shortest ....

G. Dudek, K. Romanik and S. Whitesides. Localizing a robot with minimum travel. In Proc. 6th ACM-SIAM Symp. on Discrete Algorithms, 437-- 446, 1995.

....if the length of the path traveled by a robot using strategy S is at most c times L(p; P ) for all possible polygons P and points p 2 P . The value c is called the competitive ratio of S. There have been two approaches to the localization problem. The first by Dudek, Romanik, and Whitesides [6] considers the full complexity of the problem and utilizes a decomposition of the polygon P into visibility cells such that the same set of vertices of P is visible b q 1 q 2 d s t p n n=2 n=2 Figure 1: A geometric tree for which every on line localization strategy is no better ....

....that eliminates at least one of the possible placements. It is easy to show that if there are k possible placements, then the strategy is k competitive. Furthermore, if k p n, where n is the number of vertices of the polygon, then it can be shown that k is the best competitive ratio possible [6]. The second approach, proposed by Kleinberg, leaves aside all concerns raised by the visibility structure of P and abstracts the combinatorial nature of the problem [9] In this context two types of environments are considered: bounded degree trees embedded in IE d (called geometric trees) and ....

G. Dudek, K. Romanik, and S. Whitesides. Localizing a robot with minimum travel. In Proc. 6th ACM-SIAM Symp. on Discrete Algos., pp. 437-- 446, 1995.

No context found.

G. Dudek, K. Romanik, and S. Whitesides. Localizing a robot with minimum travel. In ACM-SIAM Symposium on Discrete Algorithms, pages 437--446, 1995.

No context found.

Dudek, Romanik and Whitesides, Localizing a Robot with Minimum Travel, SIAM Journal on Computing 27 (1998), pp. 583-604.

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Gregory Dudek, Kathleen Romanik, and Sue Whitesides. Localizing a robot with minimum travel. SIAM Journal on Computing, 27(2):583--604, March 1998.

No context found.

G. Dudek, K. Romanik, and S. Whitesides, \Localizing a robot with minimum travel," in Proc. of the 6th annual ACM-SIAM Symposium on Discrete Algorithms, pp. 437-446, 1995.

No context found.

G. Dudek, K. Romanik, and S. Whitesides. Localizing a robot with minimum travel. SIAM J. Comput, 27(2):583--604, 1998.

No context found.

G. Dudek, K. Romanik, and S. Whitesides. Localizing a robot with minimum travel. In Proceedings of the Annual ACM-SIAM Sympsosium on Discrete Algorithms, pages 437--446, 1995.

No context found.

G. Dudek, K. Romanik, and S. Whitesides. Localizing a robot with minimum travel. In Proc. 6th ACM-SIAM Sympos. Discrete Algorithms, pages 437--446, 1995.

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