Departmental Papers (ESE)

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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.

For more information: Kod*lab

Sponsor Acknowledgements

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.

Document Type

Journal Article

Subject Area

GRASP, Kodlab

Date of this Version

3-21-2016

Publication Source

IEEE Transactions on Robotics

Volume

32

Issue

2

Start Page

352

Last Page

371

DOI

10.1109/TRO.2016.2524018

Keywords

Multirobot systems, navigation functions, formation control, swarm robots, configuration space, coordinated motion planning, hierarchical clustering, cohesion, segregation

Bib Tex

@Article{arslan_guralnik_kod_TRO2016, Title = {Coordinated Robot Navigation via Hierarchical Clustering}, Author = {Omur Arslan and Dan P. Guralnik and Daniel E. Koditschek}, Journal = {IEEE Transactions of Robotics}, Year = {2016},
Month = {April},
Volume = {32},
Number = {2},
Pages = {352 - 371},
Doi = {10.1109/TRO.2016.2524018}
}

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Date Posted: 26 October 2016

This document has been peer reviewed.