Modeling and Control of Pinching 2d Object with Arbitrary Shape by a Pair of Robot Fingers under Rolling Constraints

Abstract. Modeling and control of grasping an object with arbitrary shape by a pair of robot fingers with hemispherical ends in a horizontal plane are proposed in a mathematical and computational standpoint. The curvature of an object contour is variable due to the change of the contact point between the finger tip and object surface. Therefore, not only the time parameter “t” but also the arclength parameter “s” are needed to describe motion of the overall fingersobject system. It is shown that Euler-Lagrange’s equation of motion of the overall fingers-object system should be accompanied with the first-order differential equation of arclength parameter “s”, which traces out the object contour and at the same time the finger-tip circle. A control input, which is of the same category as the control input called “blind grasping”, is proposed to stabilize rotational motion of the object. The control input does neither use the kinematics information of the object nor any external sensing. Finally numerical simulations evaluate the effectiveness of the proposed model and control input.