Mechanics and quasi-static manipulation of planar elastic kinematic chains

Timothy Bretl, Zoe McCarthy

Research output: Contribution to journalArticle


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 discrete-time 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 straight-line 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.

Original languageEnglish (US)
Article number6327684
Pages (from-to)1-14
Number of pages14
JournalIEEE Transactions on Robotics
Issue number1
StatePublished - Jan 1 2013


  • Deformable objects
  • manipulation planning
  • motion and path planning
  • optimal control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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