Feeding Polyhedral Parts

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)

Pivoting Animation

Pivoting Gripper

Problem: Choose Grasp Axis

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

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

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.

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