B. Awerbuch, M. Betke, R. L. Rivest, and M. Singh. Piecemeal graph exploration by a mobile robot. In Proc. 8th Annual ACM Conference on Computational Learning Theory, pages 321-328, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....we call Greedy Mapping. Then we explain how to model it as a graph search problem and use D Lite to solve it. 3 Greedy Mapping Mapping is an important task for mobile robots and a large number of mapping methods have been developed for them, both in robotics and in theoretical computer science [9, 20, 13, 18, 3, 8, 12, 21, 23, 29, 2, 10, 11, 19, 30, 27, 6, 24, 25]. A good overview is given in [31] In this paper, we study Greedy Mapping, a simple sensor based planning method that discretizes terrain into cells and then always moves the robot from its current cell to the closest cell with unknown blockage status, that is, to the closest unobserved cell, ....

B. Awerbuch, M. Betke, R. Rivest, and M. Singh. Piecemeal graph exploration by a mobile robot. Information and Computation, 152(2):155 --172, 1999.

....of prior knowledge about parts of the terrain (if available) and can be used by several robots cooperatively. 1 Introduction Mapping is an important task for mobile robots and a large number of mapping methods have been developed for them, both in robotics and in theoretical computer science [7, 18, 11, 15, 3, 6, 10, 19, 20, 24, 2, 8, 9, 16, 25, 23, 4, 21, 22]. A good overview is given in [26] In this paper, we show that greedy mapping methods are easy to implement and easy to integrate into complete robot architectures. At the same time, planning is efficient and results in short travel distances of the robot. We study Greedy Mapping, a simple ....

B. Awerbuch, M. Betke, R. Rivest, and M. Singh. Piecemeal graph exploration by a mobile robot. Information and Computation, 152(2):155 --172, 1999.

....mapping an unknown environment is a fundamental problem with applications ranging from robot navigation to searching the World Wide Web. As such, a large body of work has focused on nding ecient solutions to variants of the problem, with restrictive assumptions on the form of the environment (cf. [16, 15, 22, 31, 17, 35, 10, 6, 2]) In this paper, we consider a model that makes very limited assumptions about the environment, and give ecient algorithms to solve the mapping problem in this general setting. A natural way to model the problem is by a robot exploring a graph G = V; E) The case in which the graph has both ....

....for this problem. These works study exploration from the perspective of competitive analysis. The results are stated in terms of the de ciency of the graph (i.e. the minimum number of edges to be added to make the graph Eulerian) Betke, Rivest, and Singh [12] and together with Awerbuch [6] study the problem of piecemeal learning undirected labeled graphs. In the piecemeal learning problem the robot is required to return to its starting position periodically. Rivest and Schapire [35, 34] study the problem of learning environments modeled by nite automata. Here, an environment is ....

B. Awerbuch, M. Betke, R. L. Rivest, and M. Singh. Piecemeal graph exploration by a mobile robot. In Proceedings of the Eighth Annual ACM Conference on Computational Learning Theory, pages 321-328, 1995.

.... postmansetsofi beforeflndingtheoptimalCPT solution.The selectingCPP canalsobeused forsolvingtheproblemofcheckinga web sitewhere some linkshave beenmechanicallyconstructed(e.g. fromtemplatesandarethereforeknown tobe correct) but others,theonesto be checked,werecreatedby hand.The piecemealproblem[8]istoperforma tour, whileoccasionally returningtothestartingpoint (for instance,torefuela robot,ortoresetthemobilephone tostandby say,ifithastimeoutsthatforcea reset) Ifwebpagescannotbeaccessedfromthehome page ofa site,then theyarehardlypartofthesite,butthere isno needforeverypagetobe ....

B. Awerbuch, M. Betke, R. L.Rivest& M. Singh,\PiecemealGraph Explorationby a Mobile Robot," Informationand Computation, 152(2):155-172,1999.

....the room. The algorithm they present achieves a competitive ratio of O(k) Kalyanasundaram and Pruhs [8] show a lower bound of Omega Gamma 17 (k; p kff) for terrain acquisition in the presence of convex obstacles, where ff is the average aspect ratio of the k obstacles. Finally, Awerbuch et al. [1] consider terrain acquisition with the restriction that the robot must occasionally return to some home base for refueling. Representing the domain as graph G = V; E) they give an algorithm that traverses O(jEj jV j 1 o(1) edges, achieving nearly linear time. We chose a modified ....

Baruch Awerbuch, Margrit Betke, Ron Rivest, and Monah Singh. Piecemeal graph exploration by a mobile robot. In Proc. 8th Annu. Workshop on Comput. Learning Theory, pages 321--328. ACM Press, New York, NY, 1995.

....many infinite recursive branches, and we only want to learn one of them. Recently, there has been extensive theoretical research on the problem of navigating a robot in unknown environments. It has been studied whether it is possible to efficiently learn a complete model of the environment (e.g. [1, 18]) or a path to a target point in the environment (e.g. 2, 17] Learning infinite branches in trees models the task of learning a path in unknown infinite environments. Hereby, the target point is the point 1 and the environment is represented by a computable function. In other words, learning a ....

B. Awerbuch, M. Betke, R. L. Rivest, and M. Singh. Piecemeal graph exploration by a mobile robot. In Proceedings of the Eighth Annual Conference on Computational Learning Theory, pages 321--328, 1995.

....and partially by DARPA grant DABT63 96 C 0018. Laboratory for Computer Science, MIT, 545 Technology Square, Cambridge, MA 02139. Email: salil math.mit.edu. Supported by a DOD NDSEG doctoral fellowship and partially by DARPA grant DABT63 96 C 0018. tions on the form of the environment (cf. [13, 12, 16, 23, 14, 27, 7, 4, 1]. In this paper, we consider a model that makes very limited assumptions about the environment, and give efficient algorithms to solve the mapping problem in this general setting. A natural way to model the problem is by a robot exploring a graph G = V;E) The case in which the graph has both ....

....gorithms for this problem. These works study exploration from the perspective of competitive analysis. The results are stated in terms of the deficiency of the graph (i.e. the minimum number of edges to be added to make the graph Eulerian) Betke, Rivest, and Singh [9] and together with Awerbuch [4] study the problem of piecemeal learning undirected labeled graphs. In the piecemeal learning problem the robot is required to return to its starting position periodically. Rivest and Schapire [27, 26] study the problem of learning environments modeled by finite automata. Here, an environment is ....

B. Awerbuch, M. Betke, R. L. Rivest, and M. Singh. Piecemeal graph exploration by a mobile robot. In Proceedings of the Eighth Annual ACM Conference on Computational Learning Theory, pages 321--328, 1995.

....an unknown environment is a fundamental problem with applications ranging from robot navigation to searching the World Wide Web. As such, a large body of work has focused on finding efficient solutions to variants of the problem, with restrictive assumptions on the form of the environment (cf. [13, 12, 16, 22, 14, 26, 7, 4, 1]. In this paper, we consider a model that makes very limited assumptions about the environment, and give efficient algorithms to solve the mapping problem in this general setting. A natural way to model the problem is by a robot exploring a graph. The case where the graph has both undirected ....

....for this problem. These works study exploration from the perspective of competitive analysis. The results are stated in terms of the deficiency of the graph (i.e. the minimum number of edges to be added to make the graph Eulerian) Betke, Rivest, and Singh [9] and together with Awerbuch [4] study the problem of piecemeal learning undirected labeled graphs. In the piecemeal learning problem the robot is required to return to its starting position periodically. Rivest and Schapire [26, 25] study the problem of learning environments modeled by finite automata. Here, an environment is ....

B. Awerbuch, M. Betke, R. L. Rivest, and M. Singh. Piecemeal graph exploration by a mobile robot. In Proceedings of the Eighth Annual ACM Conference on ComputationalLearning Theory, pages 321-- 328, 1995.

....of undirected graphs with labeled nodes. In piecemeal learning, the learner must return to a fixed starting point from time to time during the learning process. Betke, Rivest, and Singh provide linear algorithms for learning grid graphs with rectangular obstacles [BRS93] and with Awerbuch [ABRS95] extend this work to show nearly linear algorithms for general graphs. Rivest and Schapire [RS87, RS93] explore the problem of learning deterministic finite automata whose nodes are not distinguishable except by the observed output. We rely heavily on their results in this paper. Their work has ....

Baruch Awerbuch, Margrit Betke, Ronald L.Rivest, and Mona Singh. Piecemeal graph exploration by a mobile robot. In Proceedings of the 1995 ACM Conference on Computational Learning Theory, pages 321--328, Santa Cruz, CA, July 1995.

....to minimize the total distance traveled. Recently, Berman et al. BBF 96] investigated the case where the obstacles are oriented rectangles. Other work relating to exploring geometric domain are be found in [LS86, LS87, EBEY92, LT94, TK94, AWZ96] Betke et al. BRS95] and Awerbuch et al. ABRS95] investigated the problem with the additional constraints that the robot is required to return to its starting point for refueling periodically. Bender and Slonim [BS94] illustrated how two robots can collaborate in exploring directed graph with regular degree and indistinguishable vertices. ....

B. Awerbuch, M. Betke, R. Rivest, and M. Singh. Piecemeal graph exploration by a mobile robot. In Proc. 8th Annu. Conf. on Comput. Learning Theory, pages 321--328. ACM Press, New York, NY, 1995. 3 In fact, the deficiency of the family of graphs constructed in [AH97] seems to be bounded by o(log n).

....my joint work with Ronald L. Rivest, Mona Singh, and Baruch Awerbuch. An extended abstract will be published in the Proceedings of the 1995 Conference on Computational Learning Theory [3] It is also published as an MIT Laboratory for Computer Science technical memo MIT LCS TM 516 in January 1995 [4]. Chapter 3 presents my joint work with Leonid Gurvits [16] The work was accepted as a regular journal paper at the IEEE Transactions on Robotics and Automation in February 1995. An extended abstract of this paper is published in the Proceedings of the IEEE RSJ GI International Conference on ....

.... of ratio 4 [15] distinguishable nodes 2 cooperating learners, algorithm with expected [14] indistinguishable nodes time polynomial in number of nodes undirected piecemeal learning graphs grid graphs with linear algorithms [19] rectangular obstacles arbitrary graphs almost linear algorithms [4] geometric interior exterior of competitive algorithm [39] model rectilinear polygons of ratio 2 [39] of ratio 5 4 [66] interior of rectilinear O(k) competitive [39] polygon with k obstacles algorithm polygons of arbitrary shape, competitive algorithm [39] bounded number of obstacles ....

Baruch Awerbuch, Margrit Betke, Ronald L. Rivest, and Mona Singh. Piecemeal graph exploration by a mobile robot. Technical Report MIT/LCS/TM516, MIT, January 1995.

....on Computational Learning Theory and as an MIT AI Memo 1474, CBCL Memo 93 [19] Chapter 2 also describes my joint work with Ronald L. Rivest, Mona Singh, and Baruch Awerbuch. An extended abstract will be published in the Proceedings of the 1995 Conference on Computational Learning Theory [3]. It is also published as an MIT Laboratory for Computer Science technical memo MIT LCS TM 516 in January 1995 [4] Chapter 3 presents my joint work with Leonid Gurvits [16] The work was accepted as a regular journal paper at the IEEE Transactions on Robotics and Automation in February 1995. An ....

Baruch Awerbuch, Margrit Betke, Ronald L. Rivest, and Mona Singh. Piecemeal graph exploration by a mobile robot. In Proceedings of the 1995.

....Proceedings of the Sixth Conference on Computational Learning Theory [17] The second part of this chapter is joint work with Baruch Awerbuch, Margrit Betke and Ron Rivest. An extended abstract describing this work appeared in Proceedings of the Eighth Conference on Computational Learning Theory [5]. Chapter 4 is joint work with Bonnie Berger, and a paper describing this work is to appear in the First Annual Conference on Computational Molecular Biology. Table of Contents 1 Introduction 11 2 Learning functions on k terms 19 2.2 Notation and definitions : ....

Baruch Awerbuch, Margrit Betke, Ronald L. Rivest, and Mona Singh. Piecemeal graph exploration by a mobile robot. In Proceedings of the Eighth Conference on Computational Learning Theory, Santa Cruz, CA, July 1995.

....a time) They achieve linear time on special graphs such as grid graphs with non convex obstacles, triangular tesselations with triangular obstacles, and planar graphs in general. Further studies in this area resulted in algorithms for general graphs, for which Awerbuch, Betke, Rivest, and Singh [3] have achieved O(n 1 ffl m) running time. In this paper we introduce a novel search technique along with a new algorithm for the piecemeal graph exploration problem. Our recursive piecemeal search (RPS) relies on the sparse neighborhood covers of Awerbuch, Berger, Cowen, and Peleg [2] By ....

....BFS will successfully explore the graph. In the context of physical exploration, where continuity is necessary, BFS is inefficient as it has to traverse O(m 2 ) edges in the worst case (Fig. 1 b) 2. 3 Recursive Exploration To deal with the above problems Awerbuch, Betke, Rivest, and Singh [3] use recursion. A BFS tree of small depth r is constructed directly with small overhead cost. For a large depth 4 2 3 n Source . Source 2 3 4 5 n 1 n (b) a) Figure 1: a) The radius of the graph is 1 but for any Max 2(n Gamma 1) DFS fails to explore the graph. b) All nodes lie on ....

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Baruch Awerbuch, Margit Betke, Ronald Rivest, and Mona Singh. Piecemeal graph exploration by a mobile robot. In 8'th Conference on Computational Learning Theory, pages 321--328, July 1995.

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B. Awerbuch, M. Betke, R. L. Rivest, and M. Singh. Piecemeal graph exploration by a mobile robot. In Proc. 8th Annual ACM Conference on Computational Learning Theory, pages 321-328, 1995.

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B. Awerbuch, M. Betke, R. L. Rivest, and M. Singh. Piecemeal graph exploration by a mobile robot. In Proceedings of the Eighth Annual ACM Conference on Computational Learning Theory, pages 321--328, 1995.

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