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 Fishing hook knots Surgical robotics

Why is knot tying difficult? Often uses many DOFs and complex

sensing Major issue is the flexibility of string

Motivation

How can we manipulate flexible materials? Scalability Speed Limited control

Can we achieve these goals with a fixture?

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 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

QuickTime™ and aCinepak decompressor

are needed to see this picture.

QuickTime™ and aCinepak decompressor

are needed to see this picture.

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

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 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

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

Autonomous Knot Tying

QuickTime™ and aCinepak decompressor

are needed to see this picture.

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 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 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 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 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