Analysis of cartesian stiffness in robotics application

Cartesian stiffness is usually described by a 6 x 6 matrix which is vital in the study of rigid body grasping by multiple robot fingers. In this thesis, a closed form expression is derived for evaluating the grasped object stiffness based on the contact geometry and stiffness properties of individual robot fingers. The kinematics of manipulation by elastic fingers is also developed which describes the infinitesimal motion of the grasped object in response to small motions of individual finger tips. Another more difficult problem is to identify the stiffness and configuration of individual fingers from the given stiffness of the grasped object. A number of algorithms have been published for this problem, mostly aiming at partitioning the desired stiffness matrix in a pure algebraic manner. In this thesis, a new algorithm will be developed which considers the geometric property of the fingers and makes the method practical to robotics application. Some geometric properties of isotropic stiffness matrix (those that can be constructed by simple line springs) are observed. For instance, a novel reference frame invariant property of isotropic stiffness matrix is discovered. A "Background Mathematics" chapter will firstly explain the related mathematical tools and terminology used in subsequent chapters, leading to the definition of contact kinematics and spatial stiffness. The concepts of these two items will be further illustrated with practical experimental examples in a following chapter