Coordinated Robot Navigation via Hierarchical Clustering

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 differe...

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Bibliographic Details
Published in:IEEE transactions on robotics 2016-04, Vol.32 (2), p.352-371
Main Authors: Arslan, Omur, Guralnik, Dan P., Koditschek, Daniel E.
Format: Article
Language:English
Subjects:
Aerospace electronics
Algebra
Algorithms
Cluster analysis
Cohesion
Collision avoidance
Combinatorial analysis
Computation
configuration space
Construction
coordinated motion planning
Euclidean space
formation control
hierarchical clustering
Invariants
multirobot systems
Navigation
navigation functions
Planning
Robot kinematics
Robot sensing systems
Robots
segregation
swarm robots
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Summary: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 the 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 that 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.
ISSN:1552-3098
1941-0468
DOI:10.1109/TRO.2016.2524018