Knot Tying with Single Piece Fixtures

1. Knot Tying with Single Piece Fixtures 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. 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

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