A Quality Measure for Compliant Grasps and Fixtures Based on the Principal Stiffness Parameters

This paper presents a systematic approach to quantifying the effectiveness of compliant grasps and fixtures of an object. The approach is physically motivated and applies to the grasping of 2D and 3D objects by any number of fingers. We characterize the frame-invariant features of a grasp or fixture stiffness matrix. Then we define frame-invariant characteristic stiffness parameters, and provide physical and geometric interpretation for these parameters. Using a physically meaningful scheme to make the stiffness parameters comparable, we define a frame-invariant quality measure called the stiffness quality measure. The quality measure is then applied to the optimal grasping of polygonal objects by three and four fingers. We develop practical methods for computing the globally optimal three and four-finger arrangement, and provide examples which show that the resulting optimal grasps are intuitively