1. Department of Computer Science, Iowa State University Robot Grasping of Deformable Objects Yan-Bin Jia (joint work with Ph.D. students Feng Guo and Huan Lin ) Department of Computer Science Iowa State University Ames, IA 50010, USA June 5, 2014

2. Department of Computer Science, Iowa State University Rigid Body Grasping – Form Closure The object has no degree of freedom (Reuleaux, 1875). frictionless contacts

3. Department of Computer Science, Iowa State University Rigid Body Grasping – Force Closure The contacts can apply an arbitrary wrench (force + torque) to the object (Nguyen 1988). contact friction cones Not form closure. Form closure does not imply force closure.

4. Department of Computer Science, Iowa State University Barrett Hand Grasping a Foam Object

5. Department of Computer Science, Iowa State University Deformable Body Grasping Is Difficult  Form closure impossible (infinite degrees of freedom)  Force closure inapplicable (changing geometry, growing contacts)  High computation cost of deformable modeling (using FEM) Very little research done in robotics (most limited to linear objects) Wakamatsu et al. (1996); Hirai et al. (2001); Gopalakrishnan & Goldberg (2005); Wakamatsu & Hirai (2004); Saha & Isto (2006); Ladd & Kavraki (2004)  Contact constraints needed for modeling do not exist at the start of a grasp operation.

6. Department of Computer Science, Iowa State University Displacement-Based Scheme A change of paradigm from rigid body grasping.  Specified forces cannot guarantee equilibrium after deformation.  Deformation computed under geometric constraints ensures force and torque equilibrium.  Easier to command a finger to move to a place than to exert a prescribed grasping force. Specify finger displacements rather than forces.

7. Department of Computer Science, Iowa State University Assumptions  Deformable, isotropic, planar or thin 2-1/2 D object  Two rigid grasping fingers coplanar with the object  Frictional point or area contacts  Gravity ignored  Small deformation (linear elasticity)

8. Department of Computer Science, Iowa State University Linear Plane Elasticity Displacement field:

9. Department of Computer Science, Iowa State University Strains Extensional strain – relative change in length before after Shear strain – rotation of perpendicular lines toward (or away) from each other.

10. Department of Computer Science, Iowa State University Finite Element Method (FEM) K: stiffness matrix (symmetric & positive semidefinite) Strain energy:

11. Department of Computer Science, Iowa State University Energy Minimization Total potential energy : load potential vector of all nodal forces

12. Department of Computer Science, Iowa State University Stiffness Matrix translations of all nodesrotation of all nodes Spectral decomposition: orthogonal matrix

13. Department of Computer Science, Iowa State University Deformation from Contact Displacements Forces at nodes not in contact: known

14. Department of Computer Science, Iowa State University Reduced Stiffness Matrix Forces at m contact nodes: Strain energy: finger placement. Deformation: reduced stiffness matrix

15. Department of Computer Science, Iowa State University Squeeze with Two Point Fingers Minimizing potential energy is equivalent to maximizing strain energy. Solution: squeeze depth

16. Department of Computer Science, Iowa State University Pure Squeeze  object translation or rotation during deformation. squeeze depth

17. Department of Computer Science, Iowa State University Example for Comparison (stable squeeze) (pure squeeze)

18. Department of Computer Science, Iowa State University Squeeze Grasp with Rounded Fingers Translate the fingers to squeeze the object.  Contact friction.  Contacts growing into segments.

19. Department of Computer Science, Iowa State University Positional Constraints & Contact Analysis Deformation update during a grasp needs positional constraints. Resort to varying finger contacts  Maintained by friction.  Contact regions grow or shrink.  Individual contact points slide or stick. Incrementally track contact configuration! Instantaneous deformation is assumed in classical elasticity theory. How can we predict the final contact configuration from the start?

20. Department of Computer Science, Iowa State University Contact Configuration  Which nodes are in contact.  Which of them are sticking and which are sliding. slidingsticking Deformation update based on FEM: Maintain two sets:

21. Department of Computer Science, Iowa State University Overview of Squeeze Algorithm

22. Department of Computer Science, Iowa State University Contact Events Check for all values of extra squeeze depth at which a event could happen, and select the minimum.  Event A – New Contact  Event B – Contact Break

23. Department of Computer Science, Iowa State University More Contact Events  Event C – Stick to Slip  Event D – Slip to Stick

24. Department of Computer Science, Iowa State University Termination of Squeeze  A grasping finger starts to slip. At either one of the following situations:  Strain at some node exceeds the material’s proportional limit.  The object can be picked up against its weight vertically. All contact nodes with the finger are slipping in the same direction.

25. Department of Computer Science, Iowa State University Experiment slip stick

26. Department of Computer Science, Iowa State University Stick to Slip

27. Department of Computer Science, Iowa State University Stick to Slip back to Stick Second (convex) shape

28. Department of Computer Science, Iowa State University Experiment with Ring-like Objects Degenerate shells.

29. Department of Computer Science, Iowa State University Summary  Displacement-based grasping strategy for deformable objects.  Stable and pure squeezes.  Event-driven algorithm combined with contact mode analysis.  Energy-based grasp optimality.  Computational efficiency from one-time matrix decomposition.

30. Department of Computer Science, Iowa State University Acknowledgement US National Science Foundation IIS-0915876