Stabilization and output tracking for underactuated mechanical systems with inequality state constraints

The paper presents a method to determine the feasibility of stabilization to an equilibrium manifold or exact output tracking for underactuated mechanical systems that are subject to inequality state constraints. Even for minimum phase systems, internal dynamics may evolve in an unacceptable way and has to be confined within certain limits. Such restrictions arise in deformable object manipulation tasks. It is shown that the problem of output tracking under inequality state constraints is equivalent to output tracking with bounded input. The paper provides sufficient conditions for exact output tracking and stabilization to an equilibrium manifold which guarantee that the internal dynamics is bounded with adjustable bounds