This paper aims to formulate a dynamic model of a pair of dual multi-DOF robotic fingers with rigid tips grasping a circular-shaped object and proposes a new control framework for dexterous manipulation. Firstly, based on the Lagrange method and Hamilton's principle, a dynamic model of the general object-fingers setup has been described as a system of algebraic differential equations composed of ordinary differential equations governing dynamics of the fingers and the object and a set of algebraic constraints governing rigid contacts between two finger-tips and object' surfaces. Secondly, a control algorithm for stable grasping of the object by the pair of fingers has been proposed. Thirdly, another control signal for desired orientation and position of the grasped object has been proposed and asymptotic convergence of the closed dynamics to the desired orientation and position has been analysed. The principle of linear superposition of control signals has been applied to ensure stale grasping while control desired motion. Numerical simulation results have reconfirmed the effectiveness of the proposed control law.

This paper proposes a manipulation of a circular object in a horizontal plane by a pair of finger robots. This method guarantees the dynamic stability of the system and does not require any object models and object sensing to manipulate the object. It is assumed that there is no friction between the object and the horizontal plane and it is possible to be adequately large friction between the fingertips and the object. We examine the condition of stable grasping of a circular object and propose controllers for stable grasping and for controlling its approximate relative orientation angle without object sensing. The experimental results show the validity of the controller.

This paper proposes a pair of single or multi-DOF robot fingers with soft and deformable tips that can pinch an object stably in a dynamic sense with the aid of real-time sensory feedback. To realize dynamic stable pinching, a practical method of using optical devices is proposed for measuring both the maximum displacement of finger-tip deformation and the relative angle between the object surface and each of finger links. It is shown that the overall closed-loop system of a pair of two single-DOF fingers with soft tips with real-time sensory feedback of the difference between the centers of two area-contacts at both sides of the object becomes asymptotically stable. This means that the pair achieves dynamic stable grasping (pinching). In the case of a pair of 1-DOF and 2-DOF fingers with soft tips, it is shown that the proposed method of closed-loop feedback of the difference between the centers of two area-contacts and the rotational angle of the object can establish not only dynamic stable grasping but also regulation of the posture of the object.

The paper is aimed at presenting a physical interpretation of practice-based learning (so-called "iterative learning control") for robotic tasks from the viewpoint of "bettering impedance matching". At first, the concepts of impedance and impedance matching that are inherent to linear electric circuits are generalized for a class of nonlinear dynamics including robotic tasks by means of passivity. It is then shown in the simplest case when the tool endpoint is free to move that a simple iterative scheme of learning enables robots to make a progressive advance in a sense of zero-impedance matching at every trial of operation. In the case of impedance control when a soft and deformable finger-tip presses a rigid object or environment, it is shown that, for a given desired periodic force, physical interaction between the soft fingertip and the rigid object, the robot learns steadily the desired task by monotonously increasing the grade of impedance matching pertaining to dynamics of the robot task with controller dynamics.

This paper proposes an iterative learning control scheme for impedance control of robotic tasks when the tool endpoint covered by soft and deformable material presses a rigid object or environment at a prescribed periodic force pattern. To this end, an iterative learning control scheme for a class of linear dynamical systems with a negative feedback structure is analyzed and convergence of the proposed learning update law after a sufficient number of repetitions is proved. It is shown that this convergence realizes impedance matching in a sense of electric circuit theory of the feedback system can be expressed as a lumped-parameter electric circuit. The iterative learning control scheme is then applied for a case of impedance control of robotic tasks when the characteristics of reproducing force of the deformable material is nonlinear in its displacement and unknown and the tool mass is uncertain. Simulation results are also presented, which show effectiveness of the proposed learning control scheme.