Pinching 2D object with arbitrary shape by two robot fingers under rolling constraints

Modeling of pinching an object with arbitrary shape by a pair of robot fingers with hemispherical ends in a horizontal plane is proposed in a mathematical and computational manner. Since the curvature of an object contour with an arbitrary curve is variable according to the change of the contact point between the object surface and the rigid finger tip, the arclength paremeter "s" explicitly appears in the overall fingers-object dynamics. It is shown that the overall fingers-object system should be accompanied with the first-order differential equation of the parameter "s" that includes the curvatures of both the object contour and finger-tip curve. A control input, which is of the same category as the control input called "blind grasping" appeared in our former papers, is utilized for the realization of stable grasp. The control input does neither need to use the kinematic information of the object nor use any external sensing. Finally, numerical simulations are carried out in order to confirm the effectiveness of our proposed model and control input.