Motion tasks and force control for robot manipulators on embedded 2-D manifolds

In this paper we present a methodology to drive the end effector of a robotic manipulator across the surface of an object in the workspace, and at the same time the manipulator can apply a force to the object, through its end-effector. Three typical tasks are considered, namely stabilization of the end effector over the object's surface and applying a specific force on it, motion planning and eventually trajectory tracking of the end effector across the object's surface. The proposed controllers utilize navigation functions and are based on the belt zone vector fields concept. The derived dynamic controllers are realized using an integrator backstepping methodology. The derived feedback based controllers guarantee global convergence and collision avoidance. The closed form solution provides fast feedback rendering the methodology particularly suitable for implementation on real time systems. The properties of the proposed methodology are verified through non-trivial computer simulations.