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Aaron Johnson

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Cellular Decomposition and Classification of a Hybrid System

Presented as a poster at the Northeast Robotics Colloquium, October, 2014.

Aaron M. Johnson and D. E. Koditschek
Electrical and Systems Engineering, University of Pennsylvania
Abstract PDF | Conference Website

Abstract
       Robots are often modeled as hybrid systems providing a consistent, formal account of the varied dynamics associated with the loss and gain of kinematic freedom as a machine impacts and breaks away from its environment. This hybrid structure induces an abstract simplicial complex indexed by the active contact constraints, where each vertex in the complex is a single constraint. This complex provides a concise description of the possible edges of the hybrid system through impacts - they must lie in the closure of the star of the current cell (i.e. (I, J) ∈ Γ ⇔ J ∈ Cl St I). This structure is in some sense dual to the “ground reaction complex” wherein constraints reduce dimension and the equivalent adjacency property is instead the star of the closure (i.e. (I, J) ∈ Γ ⇔ J ∈ StCl I). Under either formulation, sequences of contact conditions (“letters”) define smooth families of executions (“words”). Points of discontinuity lie within the boundaries between words, but in certain cases the evaluation can still be continuous over an open set including these boundaries, even though the associated words change abruptly. We present examples of these “convergent” and “divergent” word boundaries.
This work was supported by the ARL/GDRS RCTA project, Coop. Agreement #W911NF-1020016.

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