Environment modeling for robot constrained tasks in the presence of friction and cutting forces

This paper deals with environmental modeling of constrained industrial robots. The considered constraints arise during the contact of a robot with an external object in its environment. Such a situation happens mainly if a robot is desired to apply forces and/or torques on an external surface for machining purposes, or if it is used to mate parts with limited clearances. A novel method that is based on task-space formulations and on the modes-of-motion approach is developed to represent constraints and constrained tasks. It is shown that this methodology can handle constrained motions generally without having any of the substantial limitations of other proposed methods. Special attention is paid in this paper to surface forces, a general reduction method is given where its results acknowledge the existence of these forces. Constrained systems under surface forces maybe not solvable: the sufficient and necessary condition for the existence of a solution is given and then illustrated by an example.