Robot grasping of deformable objects is an under-researched area. The difficulty comes from both mechanics and computation. First, deformation caused by the grasp operations changes object's global geometry. Second, under deformation, an object's contacts with the fingers grow from points into areas. Inside such a contact area, points that stick to the finger may later slide while points that slide may later stick. The torques exerted by the grasping fingers vary, in contrast with rigid body grasping whose torques are invariant under forces.

In this thesis the object's deformation and configuration of contact with fingers and the plane are tracked with finite element method(FEM) in an event-driven manner based on the contact displacements induced by the finger movements.

The first part of the thesis analyzes two-finger squeeze grasping of deformable objects with a focus on two special classes: stable squeezes, which minimize the potential energy of the object among squeezes of the same depth, and pure squeezes, which eliminate all euclidean motions from the resulting deformations. Based on them an algorithm to characterize the best resistance by a grasp to an adversary finger is proposed which minimizes the work done by the grasping fingers. An optimization scheme is offered to handle the general case of frictional segment contact. Simulations and multiple experiments with a Barrett Hand on a rubber foam object are presented.

The second part of this thesis describes a strategy for a two-finger robot hand to grasp and lift a 3D deformable object resting on the plane. Inspired by the human hand grasping, the strategy employs two rounded fingers to squeeze the object until a secure grasp is achieved under contact friction. And then lift it by translating upward to pick up the object. During the squeeze, a lift test is repeatedly conducted until it is successful based on the metrics and then trigger the upward translation. The gravitational force acting on the object is accounted for. Simulation is presented and shows some good promise for the sensorless grasping approach for deformable objects.