TY - GEN

T1 - Equilibrium configurations of a kirchhoff elastic rod under quasi-static manipulation

AU - Bretl, Timothy

AU - McCarthy, Zoe

N1 - Funding Information:
This material is based upon work supported by the National Science Foundation under CPS-0931871 and CMMI-0956362. The authors would like to thank Don Shimamoto for helpful comments, leading to the current proof of Lemma 4. Thanks also to the organizers, anonymous reviewers, and audience at WAFR 2012, whose suggestions improved this paper.
Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2013.

PY - 2013

Y1 - 2013

N2 - Consider a thin, flexible wire of fixed length that is held at each end by a robotic gripper. The curve traced by this wire can be described as a local solution to a geometric optimal control problem, with boundary conditions that vary with the position and orientation of each gripper. The set of all local solutions to this problem is the configuration space of the wire under quasi-static manipulation. We will show that this configuration space is a smooth manifold of finite dimension that can be parameterized by a single chart. Working in this chart—rather than in the space of boundary conditions—makes the problem of manipulation planning very easy to solve. Examples in simulation illustrate our approach.

AB - Consider a thin, flexible wire of fixed length that is held at each end by a robotic gripper. The curve traced by this wire can be described as a local solution to a geometric optimal control problem, with boundary conditions that vary with the position and orientation of each gripper. The set of all local solutions to this problem is the configuration space of the wire under quasi-static manipulation. We will show that this configuration space is a smooth manifold of finite dimension that can be parameterized by a single chart. Working in this chart—rather than in the space of boundary conditions—makes the problem of manipulation planning very easy to solve. Examples in simulation illustrate our approach.

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U2 - 10.1007/978-3-642-36279-8_5

DO - 10.1007/978-3-642-36279-8_5

M3 - Conference contribution

AN - SCOPUS:85009471732

SN - 9783642362781

T3 - Springer Tracts in Advanced Robotics

SP - 71

EP - 87

BT - Springer Tracts in Advanced Robotics

A2 - Frazzoli, Emilio

A2 - Roy, Nicholas

A2 - Lozano-Perez, Tomas

A2 - Rus, Daniela

PB - Springer

T2 - 10th International Workshop on the Algorithmic Foundations of Robotics, WAFR 2012

Y2 - 13 June 2012 through 15 June 2012

ER -