1. Feeding Polyhedral Parts

2. Feeding Polyhedral Parts
Related Work
Paul (1973), Birk (1974), Salisbury (1982)
Fearing (1986), Nguyen (1986)
Tournassound, Lozano-Perez, and Mazer (1987)
Ponce and Faverjon (1992), Rus (1992)
Erdmann, Mason, and Vanecek (1993)

3. Pivoting
Animation

4. Pivoting Gripper

5. Problem: Choose Grasp Axis

6. Problem Definition Stable poses of the polyhedron
“Hard-finger” contacts:
resists forces and torques,
except about grasp axis.
Input:
Shape of polyhedral part with n faces,
Center of mass,
Coefficient of friction,
Initial and Desired poses.
Criteria:
Grasp Axis is parallel to workable,
Grasp won’t slip,
Part will rotate due to gravity when lifted,
When replaced, part will assume desired pose.
Output:
Pivoting Axis for each pair of stable poses
m x m Transition Matrix

9. Rao, Kriegman, Goldberg (1996)
Complete Algorithm
Computes m x m Transition Matrix in time
O (m2n log n).

10. Result:
1. We can find candidate grasps in time O (n3):
Slicing part at critical heights,
“Effective” ,
Nguyen regions,
Algebraic formulation of stability: f (z) = 0
2. A pivoting grasp always exists if:
Part is convex with interior com, and
no slip.

12. Future Work “Capture Regions” Active Pivot Grasps (APGs)
Avoiding Collisions with Nearby Parts
Toppling
Learning Transition Probabilities