Résumé : In this study one considers the tracking control problem of a class of nonsmooth fully actuated Lagrangian systems subject to frictionless unilateral constraints. A passivity-based switching controller that guarantees some stability properties of the closed-loop system is designed. A particular attention is paid to transition (impacting) and detachment phases of motion. This paper extends previous works on the topic as it considers multiconstraint n-degree-of-freedom systems.