Stabilizing manipulator motion along a given surface

We consider mechanical systems like a manipulating robot, an excavator, and other similar devices. Known solutions for the general problem of manipulator motion stability have been obtained under rather strong assumptions. A special but important case of the stability problem under natural assumptions is solved in this work. We have constructed a control law that stabilizes the motions of a system lying inside a given surface. One example of such surface might be the surface along which a welding seam goes in the problem of automated welding with a manipulator.