Robotic grasping of deformable objects is inherently different from that of rigid objects, and is an under-researched area. Difficulties arise not only from expensive deformable modeling, but also from the changing object geometry under grasping force.

This dissertation studies strategies of grasping deformable objects using two robotic fingers. Discovering the inapplicability of the traditional force-centered grasping strategies for rigid objects, I have designed an approach for grasping deformable objects that specifies finger displacements. This not only ensures equilibrium under the elasticity theory, but also enhances stability and simplifies finger control in the implementation.

Deformable modeling is carried out using the Finite Element Method (FEM), for which our analysis establishes uniqueness of the shape of a grasped object given the finger displacements. Meanwhile, preprocessing based on the Singular Value Decomposition greatly reduces the complexity of computation. Grasping strategies have been investigated for both 2D and 3D objects. With a hollow 2D object, the grasping fingers make point contacts. The condition of a successful grasp is that the friction cones at the two contacts must contain the line segment through them before and after the deformation. With a solid planar object, the fingers make area contacts. Grasp computation is carried out by an event-driven algorithm, which has been validated by our robot experiments. For 3D objects, a simple squeeze-and-test strategy has been designed to lift them off the supporting table against gravity with a method that predicts the squeeze amounts.

In reality, objects shapes are affected to various degrees by gravity, but such a effect has been ignored in the FEM-based modeling. For accuracy, the gravity-free shape of an object is sometimes needed. I have introduced an iterative algorithm that will converge to such shape as a "fixed point".

In the last part of my thesis, I study planning of the finger squeeze paths, not to limited by straight movements. The objective is to not only enlarge the range of finger placements for successful grasps, but also improve stability and energy efficiency. I have designed a path planning algorithm based on the Rapidly-exploring Random Trees (RRT) that is able to achieve certain optimalities.