Motion tasks for robot manipulators on embedded 2-D manifolds under input constraints

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. We develop controllers for stabilizing the end effector to a point, and for tracking a trajectory on this surface, while respecting the input constraints. We show that the resulting closed loop system is uniformly asymptotically stable and we verify our analytical development with computer simulations.