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Operations Research, Systems Engineering and Industrial Engineering Commons

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Departmental Papers (ESE)

Controls and Control Theory

Navigation functions

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Full-Text Articles in Operations Research, Systems Engineering and Industrial Engineering

Exact Robot Navigation Using Power Diagrams, Omur Arslan, Daniel E. Koditschek May 2016

Exact Robot Navigation Using Power Diagrams, Omur Arslan, Daniel E. Koditschek

Departmental Papers (ESE)

We reconsider the problem of reactive navigation in sphere worlds, i.e., the construction of a vector field over a compact, convex Euclidean subset punctured by Euclidean disks, whose flow brings a Euclidean disk robot from all but a zero measure set of initial conditions to a designated point destination, with the guarantee of no collisions along the way. We use power diagrams, generalized Voronoi diagrams with additive weights, to identify the robot’s collision free convex neighborhood, and to generate the value of our proposed candidate solution vector field at any free configuration via evaluation of an associated convex ...


Coordinated Robot Navigation Via Hierarchical Clustering, Omur Arslan, Dan P. Guralnik, Daniel E. Koditschek Mar 2016

Coordinated Robot Navigation Via Hierarchical Clustering, Omur Arslan, Dan P. Guralnik, Daniel E. Koditschek

Departmental Papers (ESE)

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 ...