Transcript Knot Tying with Single Piece Fixtures - Brown

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 a
Cinepak decompressor
are needed to see this picture.
QuickTime™ and a
Cinepak 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 a
Cinepak 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