Controlling the Motion of Robot Manipulators on Constrained Surfaces

We present a methodology to steer the end effector of a robotic manipulator, which is constrained in terms of joint rates, on the surface within the workspace, to perform surface tasks. We develop smooth controllers for stabilizing the end effector to a point, and for tracking a trajectory on this surface, while respecting the input constraints, and the same time applying a specific force on it. We show that the resulting closed loop system is uniformly asymptotically stable and we verify our analytical development with computer simulations.