1. Knot Tying Matthew Bell & Devin Balkcom Dartmouth College

2. Overview Why are we tying knots? Why use fixtures? Knot fixture design Experimental and analytical observations Autonomous knot tying

3. 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

4. Motivation How can we manipulate flexible materials? Scalability Speed Limited control Can we achieve these goals with a fixture?

5. 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.

6. 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

7. 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

8. 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

9. 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

10. 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

11. Autonomous Knot Tying

12. 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

13. 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

14. 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

15. 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

16. 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