1. Motion Planning for Robotic Manipulation of Deformable Linear Objects (DLOs) Mitul Saha, Pekka Isto, and Jean-Claude Latombe Research supported by NSF, ABB and GM Artificial Intelligence Lab Stanford University

2. Objective and Motivation Develop a motion planner to aid robot arms perform complex tasks with Deformable Linear Objects (DLOs) like tieing self-knots and knots around objects. –Examples of DLO are ropes, strings, surgical sutures, cables etc. Bowline knot Figure-8 knot Sailing knot Surgeon’s knot Robotic knot tying Manual knot tying

3. Objective and Motivation Push the state of the art in robotic manipulation –Manipulating DLOs is perhaps one of the most challenging tasks in robotics Possible Impact/Applications –Could open many new domains for robotics application Enhance manipulation skills of Humanoids assisting humans in their common life activities Automated surgery

4. The Manipulation Problem Defining goal configurations –Topological goal vs geometric goal - This leads to the development of a topological path planner Geometrically different but topologically same: Bowline knot

5. The Manipulation Problem Defining goal configurations - Topological goal (aka “Crossing Configuration”) is defined with respect to a reference plane Crossing Configuration: (C1, C2, C3, C4): ((1,-6) -, (-2,5) -, (3,-8) -, (-4,7) - ) Planar projection of the DLO central axis Crossings DLO

6. The Manipulation Problem - Reduced alternating-Alternating with embedded slip loops We focus on two types of common knots: Crossing Configuration: ((1,-6) -, (-2,5) -, (3,-8) -, (-4,7) - ) over under over

7. The problem: –Start from unwound (State-0) DLO configuration and achieve a configuration and achieve a configuration with desired topology Given: –Physics of the DLO as a state function f –Manipulator arms Starting configuration A final configuration with desired topology DLO

8. Our Planning Approach - Manipulation using 2 cooperating robot arms - Use of static sliding supports (“tri-fingers”) to provide structural support

9. Defining “Forming Sequence” –Knots can be tied, state-by-state, in the order defined by their “forming sequence” Forming Sequence: C 2, C 1, C 4, C 3 A substate

10. Defining “hierarchy of components” The curves in red are “curve-pieces”: c 12, c 23, c 34, c 45, c 56, c 67, c 78. The component Co is bounded by {c 12, c 56 }. II II I-aII I-bIII I II III

11. “Hierarchy of components” is used to determine where to place static sliding supports (“tri-fingers”)

12. Our “topological” motion planner is based on Probabilistic RoadMaps (PRMs) -Knot is tied state by state using the “forming sequence” Forming Sequence: C 2, C 1, C 4, C 3

13. Our “topological” motion planner is based on Probabilistic RoadMaps (PRMs) Sample a new DLO configuration by randomly perturbing the grasped point of an existing configuration dQ = J + u + (I - J + J) dq u: motion of grasp J : Jacobian J + : right psuedo-inverse of J dq: small random robot motion dQ: robot motion producing u Need to find collision free robot motion that produces u, the small random move of the grasped point Grasping robot fails Robot A Robot B DLO Robot B Robot A

14. Our “topological” motion planner is based on Probabilistic RoadMaps (PRMs) -Use the “hierarchy of components” to determine when to place static sliding supports (“tri-fingers”)

15. Tying “bowline” knot