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Knot Tying with Single Piece Fixtures. Matthew Bell & Devin Balkcom Dartmouth College. Overview. Why are we tying knots? Why use fixtures? Knot fixture design Experimental and analytical observations Autonomous knot tying. Motivation. Why do we want to tie knots? Textile manufacturing

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knot tying with single piece fixtures

Knot Tying with Single Piece Fixtures

Matthew Bell & Devin Balkcom

Dartmouth College

overview
Overview
  • Why are we tying knots?
  • Why use fixtures?
  • Knot fixture design
  • Experimental and analytical observations
  • Autonomous knot tying
motivation
Motivation
  • Why do we want to tie knots?
    • Textile manufacturing
    • Fishing hook knots
    • Surgical robotics
  • Why is knot tying difficult?
    • Often uses many DOFs and complex sensing
    • Major issue is the flexibility of string
motivation4
Motivation
  • How can we manipulate flexible materials?
    • Scalability
    • Speed
    • Limited control
  • Can we achieve these goals with a fixture?
fixturing as manipulation
Fixturing as manipulation
  • Fixturing generally reduces complexity to 1 DOF (pushing motion)
  • Multiple contacts result in a complex grasp of an object
  • Can be used to constrain a non-rigid object by effectively grasping the entire object at once

L. Lu and S. Akella, "Folding Cartons with Fixtures: A Motion Planning Approach," IEEE Transactions on Robotics and Automation, August 2000.

knot fixture design
Knot fixture design
  • Exploit different behaviors of pushed vs. pulled string
  • Basis of knot box is a hollow tube in the shape of the knot
  • Interior regions are carved out to create space for tightened knot
observations
Observations
  • Boxes require up to 25 cm of string to tie a knot
  • Materials that compress or buckle significantly are difficult to push over this distance
  • Tube curvature must be less than some maximum (based on string properties)
  • Curvature should be monotonically increasing to avoid problems of shape memory
observations8
Observations
  • Volume swept by the string as it tightens into a knot must be topologically spherical for extraction
    • Not a sufficient condition
    • This suggests that having no concavities in the interior might be a sufficient condition
experimental results
Experimental Results
  • Manual knot tying
    • Different knot types
    • Overhand knot can be tied in as little as 15-20 seconds
    • Works with multiple materials
    • Knot location on string can be somewhat determined
autonomous knot tying
Autonomous Knot Tying
  • Autonomous system
    • 4DOF Cobra i600, with custom cutter/gripper
    • Knotbox mounted in clamp
    • Solder fed through wooden block to provide known grasp location
    • Entirely open-loop
open problems
Can we create knot boxes for new knot types?

How can we reduce the complexity of the autonomous system?

How can we broaden the range of materials?

Use of compressed air to push string

Open Problems
open problem 2 piece boxes
Open Problem - 2 piece boxes
  • How do we use compressed air?
    • Knot box must have solid tubes
    • Knot extraction requires the box to split into pieces
    • We can prove that 2 pieces are enough
open problem 2 piece boxes14
Open Problem - 2 piece boxes
  • Box will be two pieces if diagram is 2-colorable
  • Any knot can be formed from a loop using Reidemeister moves (RMs), followed by flipping crossings
  • A loop is 2-colorable
  • 2-colorability is preserved under RMs
  • Box outline can be added using RMs
open problem
Open Problem
  • Can we develop an algorithm to design a knot box from a knot description?
  • Two possible methods for approximating a knot:
    • Splines
    • Knot primitives
conclusions
Conclusions
  • Fixtures successfully used to tie knots in multiple materials
  • Knot fixtures are robust, and very scalable
  • Autonomous system uses fixtures to tie knots with a fairly simple set of motions