Force/motion control of constrained manipulators without velocity measurements

In this note we deal with the problem of force/tracking control of constrained manipulators without velocity measurements interacting with an innnitely stii environment. We use a reduced order model for which the coordinates space is restricted to a subset where the constraints Jacobian is guaranteed to be non singular. In contrast to other similar approaches, we do not assume that the generalized trajectories belong to the subset all the time thus, our contribution is to prove that if the trajectories start within the subset , they remain in it. Furthermore, we prove uniform asymptotic stability considering only position and force measurements.