Modeling and Computer simulation of 3D object Grasping and Manipulation by dual fingers under nonholonomic constraints

Construction of a numerical simulator for 3-D object pinching and manipulation by a pair of robot fingers is described on the basis of mathematical modeling of physical interactions between the object and fingers under rolling constraints. The simulator consists of a set of Lagrange\´s equations of motion of the fingers and object under holonomic constrains and differential equations of nonholonomic constraints expressing rotational motion of the rigid object. By using this simulator, numerical simulation results of 3-D object pinching and manipulation under the gravity effect based on the control law rendering "blind grasping" without use of any object kinematics or any external sensing is carried out in a case that the fingers have excess joints. Numerical results show the validity of mathematical modeling and the control method