TY - JOUR

T1 - Multirobot tree and graph exploration

AU - Brass, Peter

AU - Cabrera-Mora, Flavio

AU - Gasparri, Andrea

AU - Xiao, Jizhong

N1 - Funding Information:
Manuscript received October 12, 2010; accepted February 23, 2011. Date of publication March 28, 2011; date of current version August 10, 2011. This paper was recommended for publication by Associate Editor K. Kyriakopoulos and Editor D. Fox upon evaluation of the reviewers’ comments. This work was supported in part by the National Science Foundation of the U.S. under Grant IIS-0644127. This paper was presented in part at the IEEE International Conference on Robotics and Automation, Kobe, Japan, 2009.

PY - 2011/8

Y1 - 2011/8

N2 - In this paper, we present an algorithm for the exploration of an unknown graph by multiple robots, which is never worse than depth-first search with a single robot. On trees, we prove that the algorithm is optimal for two robots. For k robots, the algorithm has an optimal dependence on the size of the tree but not on its radius. We believe that the algorithm performs well on any tree, and this is substantiated by simulations. For trees with e edges and radius r, the exploration time is less than 2e/k + (1 + (k/r))k-1 (2/k!)r k-1 = (2e/k) + O((k + r)k-1 ) (for r > k, = (2e/k) + 2rk-1 ), thereby improving a recent method with time O((e/log k) + r) [2], and almost reaching the lower bound max((2e/k), 2r). The model underlying undirected-graph exploration is a set of rooms connected by opaque passages; thus, the algorithm is appropriate for scenarios like indoor navigation or cave exploration. In this framework, communication can be realized by bookkeeping devices being dropped by the robots at explored vertices, the states of which are read and changed by further visiting robots. Simulations have been performed in both tree and graph explorations to corroborate the mathematical results.

AB - In this paper, we present an algorithm for the exploration of an unknown graph by multiple robots, which is never worse than depth-first search with a single robot. On trees, we prove that the algorithm is optimal for two robots. For k robots, the algorithm has an optimal dependence on the size of the tree but not on its radius. We believe that the algorithm performs well on any tree, and this is substantiated by simulations. For trees with e edges and radius r, the exploration time is less than 2e/k + (1 + (k/r))k-1 (2/k!)r k-1 = (2e/k) + O((k + r)k-1 ) (for r > k, = (2e/k) + 2rk-1 ), thereby improving a recent method with time O((e/log k) + r) [2], and almost reaching the lower bound max((2e/k), 2r). The model underlying undirected-graph exploration is a set of rooms connected by opaque passages; thus, the algorithm is appropriate for scenarios like indoor navigation or cave exploration. In this framework, communication can be realized by bookkeeping devices being dropped by the robots at explored vertices, the states of which are read and changed by further visiting robots. Simulations have been performed in both tree and graph explorations to corroborate the mathematical results.

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U2 - 10.1109/TRO.2011.2121170

DO - 10.1109/TRO.2011.2121170

M3 - Article

AN - SCOPUS:80051695871

SN - 1552-3098

VL - 27

SP - 707

EP - 717

JO - IEEE Transactions on Robotics

JF - IEEE Transactions on Robotics

IS - 4

M1 - 5739538

ER -