From Unconstrained Motion Control to Constrained Case for Holonomic Mechanical Systems

This paper discusses a constructive stabilization approach for holonomic mechanical systems. Our approach uses the fact that the nonreduced order dynamics of the constrained system is composed of the original dynamics and the (nonlinear) term of constraint. We show that the stabilization problem of the constrained system given by its obtained nonlinear reduced order dynamics is equivalent to the stabilization problem of the original dynamics under some regularity assumptions. More importantly, using this stabilization technique, very simple stabilizing global output feedback tracking control laws for nonlinear constrained systems with linear original dynamics (e.g., Cartesian structure robots) can be designed. Further, we explain how this output stability result can be discussed for more general mechanical systems. Numerical simulations are provided to demonstrate the effectiveness of the proposed approach