Analysis of Cartesian Sti ness in Robotics Application

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