Quasi-static manipulation of a Kirchhoff elastic rod based on a geometric analysis of equilibrium configurations

Timothy Bretl, Zoe McCarthy

Research output: Contribution to journalArticle

Abstract

Consider a thin, flexible wire of fixed length that is held at each end by a robotic gripper. Any curve traced by this wire when in static equilibrium is a local solution to a geometric optimal control problem, with boundary conditions that vary with the position and orientation of each gripper. We prove that the set of all local solutions to this problem over all possible boundary conditions is a smooth manifold of finite dimension that can be parameterized by a single chart. We show that this chart makes it easy to implement a sampling-based algorithm for quasi-static manipulation planning. We characterize the performance of such an algorithm with experiments in simulation.

Original languageEnglish (US)
Pages (from-to)48-68
Number of pages21
JournalInternational Journal of Robotics Research
Volume33
Issue number1
DOIs
StatePublished - Jan 1 2014

Keywords

  • Manipulation planning
  • design and control
  • manipulation
  • mechanics
  • path planning for manipulators

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • Mechanical Engineering
  • Artificial Intelligence
  • Electrical and Electronic Engineering
  • Applied Mathematics

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