Fundamental properties of stiffness control in grasping and dextrous manipulation in robotics

In this dissertation, we study the stiffness control and dextrous sliding manipulation of robotic grasping and manipulation. Sliding manipulation using soft fingers is presented. A new theory in stiffness control and conservative congruence transformation is proposed, along with extension of such theory to general 6x6 Cartesian space.; The dextrous sliding manipulation with friction at contact is first explored by using soft fingers under force and position controls. The motion trajectory of sliding manipulation under force control as well as the force/moment trajectory on the limit surface under (trajectory planning) as applied in sliding manipulation has been found and defined.; The conservative properties of a stiffness matrix is determined by two criteria: symmetry and exactness. Namely, a stiffness matrix is conservative if the force resulting from the stiffness matrix is conservative, and the work done by such force along a closed path is zero. Based on both conservative criteria, the numerical simulation results show that the conventional formulation derived by Salisbury in 1980 will result in nonconservative properties between the joint and Cartesian stiffness matrices. This leads to contradictions of fundamental physic properties of conservative system. A new theory is needed to rectify this conventional formulation.; The conservative congruence transformation (CCT) is derived and proposed to rectify the well-known Salisbury's theory which is only valid at unloaded equilibrium configuration. The inconsistency of the conventional formulation will significantly affect the accuracy of stiffness control theory; therefore, it must be formulated correctly via the CCT. The CCT accounts for the change in geometry via the differential Jacobian (Hessian matrix) of a robot manipulator when the external force is applied. Thus, the CCT, which gives rise to consistent and correct interpretation of any system involving stiffness or compliance modeling, has lead to an important discovery of research in robotics and theory of stiffness control. In particular, the CCT defines the fundamental theory of stiffness control, and builds up the knowledge related to stiffness matrix and control in science and engineering, which still lacks consistent framework of theory or is incorrect in some cases.; Finally, the properties of the 6x6 Cartesian stiffness matrices of a rigid body are investigated by using the geometrical methods and the stiffness congruence transformation. It shows that the 6x6 Cartesian stiffness matrix is asymmetric when the system is subjected to external loads. The skew-symmetric part of the stiffness matrix is equal to the negative one-half of the cross-product matrix formed by the externally applied load, referenced to the inertial frame. In addition, the Cartesian stiffness matrix of a manipulator is modeled via the CCT and geometrical methods. The computation algorithm is presented and applied to the example of a 6R manipulator.