Grasp admittance center: a concept and its implementation in soft fingered robotic hands

This thesis presents the conceptualization, development and demonstration of a new approach to achieving decoupled dynamic behavior in multifingered robotic hands. The approach is based on a new concept termed in this thesis as the Grasp Admittance Center. This concept is a generalized version of the Compliance Center concept, well known within the robotics literature for over a decade. The proposed admittance center concept provides a framework for simultaneously achieving three useful features in robotic grasps1: (i) decoupled2 force-motion relationship—a relationship between a motion imposed on the object and the reaction force that the object exerts to resist the motion; (ii) decoupled time-response —the motion response of the system to a force disturbance; and (iii) stability—the ability of the grasp to be in equilibrium despite disturbances. These three features play important roles in the functioning of robotic hands, particularly when engaged in constrained manipulation tasks. Achieving these features in robotic grasps requires that the grasp impedance parameters3 satisfy certain analytical conditions. These conditions are collectively referred to in this thesis as the admittance center concept. The admittance center based approach to achieving the above features involves a systematic planning and regulation of the impedances of the grasping fingers such that the required analytical conditions are satisfied. In this approach, the force-motion relationship of the object could be suitably designed while also satisfying the time-response requirements in a desired frame of reference. In addition, the grasp achieves stability as a by-product. Here, the reference frame origin—termed the admittance center—has an important role. Placing the center suitably during constrained manipulation tasks can substantially reduce undesirable forces. In this thesis, the mathematical conditions that form the admittance concept (that lead to decoupled dynamic behavior) have been identified. They are: (i) the impedance parameters—namely the inertia, damping and stiffness matrices—must be diagonal and positive definite; (ii) the natural frequency and the damping ratio matrices of the grasp must have identical diagonal entries. The thesis has also formulated a method to select the admittance parameters for a few typical tasks, and has developed a way to compute the impedances required at the fingertips in order to generate an admittance center at a desired location on the grasped object. The sensitivity of this method to two possible types of errors has also been analyzed. An experimental device has been built to demonstrate the features of the admittance center concept. Finally, an experimental comparison of a few chosen materials, suitable for constructing soft-tipped robotic fingers, has been presented. The generality of the concept is that it applies to all closed-kinematic-chain robotic systems such as the Stewart platforms, cooperating multi-arm systems as well as to multi-legged mobile robots. 1A grasp is a system where an object is held by the fingers of a robotic hand. 2The behavior of a grasp is said to be decoupled if its response on a given degree of freedom is spurred by a disturbance experienced on that degree of freedom only. 3The spring, damper and mass coefficients are collectively called the impedance parameters.