Manipulation of 2D object with arbitrary shape by robot finger under rolling constraint

Contact of two contours of a pinched object and a robot finger tip, with arbitrary shape, is expressed in terms of differential geometry. The overall finger-object dynamics with rolling and contact constraints is derived as Euler-Lagrange´ equation of motion and the first differential equation with curvatures of the contours is derived for updating the length parameters. Despite the complicated mathematical structure, a control input signal is proposed, which can be constructed without using object geometrical information or external sensing, and it is shown that it is effective to stabilize rotation of the object. Consequently, numerical simulations are carried out in order to demonstrate the practicality of the proposed model and control signal.