Computational Modeling, Visualization, and Control of 2-D and 3-D Grasping under Rolling Contacts

This chapter presents a computational methodology for modeling 2-dimensional grasping of a 2-D object by a pair of multi-joint robot fingers under rolling contact constraints. Rolling contact constraints are expressed in a geometric interpretation of motion expressed with the aid of arclength parameters of the fingertips and object contours with an arbitrary geometry. Motions of grasping and object manipulation are expressed by orbits that are a solution to the Euler-Lagrange equation of motion of the fingers/object system together with a set of first-order differential equations that update arclength parameters. This methodology is then extended to mathematical modeling of 3-dimensional grasping of an object with an arbitrary shape. Based upon the mathematical model of 2-D grasping, a computational scheme for construction of numerical simulators of motion under rolling contacts with an arbitrary geometry is presented, together with preliminary simulation results. The chapter is composed of the following three parts. Part 1 Modeling and Control of 2-D Grasping under Rolling Contacts between Arbitrary Smooth Contours Authors: S. Arimoto and M. Yoshida Part 2 Simulation of 2-D Grasping under Physical Interaction of Rolling between Arbitrary Smooth Contour Curves Authors: M. Yoshida and S. Arimoto Part 3 Modeling of 3-D Grasping under Rolling Contacts between Arbitrary Smooth Surfaces Authors: S. Arimoto, M. Sekimoto, and M. Yoshid