  A singular (or Hermann) foliation on a smooth manifold $M$ can be seen as a
subsheaf of the sheaf $\mathfrak{X}$ of vector fields on $M$. We show that if
this singular foliation admits a resolution (in the sense of sheaves)
consisting of sections of a graded vector bundle of finite type, then one can
lift the Lie bracket of vector fields to a Lie $\infty$-algebroid structure on
this resolution, that we call a universal Lie $\infty$-algebroid associated to
the foliation. The name is justified because it is isomorphic (up to homotopy)
to any other Lie $\infty$-algebroid structure built on any other resolution of
the given singular foliation.
