Sliding manipulation of rigid bodies on a controlled 6-DoF plate

Thomas H. Vose*, Paul Umbanhowar, Kevin M. Lynch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


We model the full dynamics of a rigid part in three-point frictional sliding contact with a flat rigid six-degree-of-freedom (6-DoF) plate. When the plate moves periodically, we show the part's dynamics are well approximated by a first-order system represented by an asymptotic velocity field that maps part configurations in SE(2) to unique velocities (linear and angular) in 2. The form of the asymptotic velocity field depends on the plate's motion, the location and friction coefficient of each contact point, and the inertial properties of the part. Asymptotic velocity vectors in the field approximate the part's cycle-averaged velocity at each configuration and are independent of time or the system's initial state. For the special case of a rigid part with infinitesimal thickness, we prove that asymptotic velocities are always unique and well defined. With the ability to program arbitrary periodic plate motions, part manipulation reduces to finding plate motions that generate asymptotic velocity fields to accomplish desired tasks. Several fields useful for manipulation tasks (e.g. sensorless part alignment) are verified in simulation and experiment.

Original languageEnglish (US)
Pages (from-to)819-838
Number of pages20
JournalInternational Journal of Robotics Research
Issue number7
StatePublished - Jun 2012


  • flexible automation
  • friction modeling
  • parts feeding
  • programmable vector fields
  • rigid body sliding
  • sensorless manipulation
  • vibratory manipulation

ASJC Scopus subject areas

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


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