Visible to the public Mechanics and Quasi-Static Manipulation of Planar Elastic Kinematic ChainsConflict Detection Enabled

TitleMechanics and Quasi-Static Manipulation of Planar Elastic Kinematic Chains
Publication TypeJournal Article
Year of Publication2012
AuthorsTimothy Bretl, University of Illinois at Urbana-Champaign, Zoe McCarthy, University of Illinois at Urbana-Champaign
JournalIEEE Transactions on Robotics
Start Page1
Date Published10/2012
Keywordsdeformable objects, manipulation, NSA SoS Lablets Materials, optimal control, planning motion and path planning, science of security, Theoretical Foundations of Threat Assessment by Inverse Optimal Control, UIUC

In this paper, we study quasi-static manipulation of a planar kinematic chain with a fixed base in which each joint is a linearly elastic torsional spring. The shape of this chain when in static equilibrium can be represented as the solution to a discretetime optimal control problem, with boundary conditions that vary with the position and orientation of the last link. We prove that the set of all solutions to this problem is a smooth three-manifold that can be parameterized by a single chart. Empirical results in simulation show that straight-line paths in this chart are uniformly more likely to be feasible (as a function of distance) than straightline paths in the space of boundary conditions. These results, which are consistent with an analysis of visibility properties, suggest that the chart we derive is a better choice of space in which to apply a sampling-based algorithm for manipulation planning. We describe such an algorithm and show that it is easy to implement.

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Mechanics and Quasi-Static Manipulation of Planar Elastic Kinematic Chains