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Coordinated Robot Navigation via Hierarchical Clustering

ESE Technical Report

July, 2015

OmurArslan, Dan P. Guralnik , D. E. Koditschek
Electrical and Systems Engineering, University of Pennsylvania
Full PDF | arXiv

Hierarchical Navigation of Disks
Hierarchical Navigation of Disks
Abstract
       We introduce the use of hierarchical clustering for relaxed, deterministic coordination and control of multiple robots. Traditionally an unsupervised learning method, hierarchical clustering offers a formalism for identifying and representing spatially cohesive and segregated robot groups at different resolutions by relating the continuous space of configurations to the combinatorial space of trees. We formalize and exploit this relation, developing computationally effective reactive algorithms for navigating through the combinatorial space in concert with geometric realizations for a particular choice of hierarchical clustering method. These constructions yield computationally effective vector field planners for both hierarchically invariant as well as transitional navigation in the configuration space. We apply these methods to the centralized coordination and control of n perfectly sensed and actuated Euclidean spheres in a d-dimensional ambient space (for arbitrary n and d). Given a desired configuration supporting a desired hierarchy, we construct a hybrid controller which is quadratic in n and algebraic in d and prove that its execution brings all but a measure zero set of initial configurations to the desired goal with the guarantee of no collisions along the way.
This work was supported in part by AFOSR under the CHASE MURI FA9550–10–1−0567 and in part by ONR under the HUNT MURI N00014070829.
BibTeX entry
@TechReport{arslan_guralnik_kod_HierNavTechReport2015,
  Title                    = {Coordinated Robot Navigation via Hierarchical Clustering},
  Author                   = {Arslan, O. and Guralnik, D. P. and Koditschek, D. E.},
  Institution              = {University of Pennsylvania},
  Year                     = {2015},
  Note                     = {arXiv:1507.01637 [cs.RO]},
  Url                      = {http://arxiv.org/abs/1507.01637}
}

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