[en] This article addresses the control problem of robots with unknown dynamics and manipulating flexible rubber objects of unknown elasticity. The manipulated rubber object is considered to be interacting with arbitrarily-switched constraints. Such a kind of robot system is shown to have switched impedance parameters during a task execution that results in an unknown hybrid nonlinear system with arbitrarily switched signal. A Model-Free Robust Adaptive Control (MFRAC) strategy is proposed for such a robot system that is proved to guarantee global stable performance with all closed loop signals are assured to be bounded. The suggested MFRAC strategy relies on the synergy of the Adaptive Fuzzy System (AFS), the Sliding Mode Control (SMC), and the notion of Common Lyapunov Functions (CLF). The AFS relaxes the need for knowing the precise robot dynamics, the SMC adds robustness against the drift of the dynamics parameters, and the CLF accommodates the arbitrary switching of the impedance parameters. The bounds of the impedance parameters are adapted online and incorporated in the MFRAC design such that a convergent performance is achieved. Experiment is conducted on a KUKA Lightweight Robot (LWR) doing flexible rubber peg-in-hole assembly process that falls in the category of systems considered in this article. From the experimental results, excellent tracking performance is reported when using the proposed MFRAC strategy for the considered robotic system despite the dynamics anonymity and the unknown impedance parameters arbitrary switching.