  In this paper we prove graded versions of the Darboux Theorem and Weinstein's
tubular neighbourhood Theorem in order to study the deformation theory of
Lagrangian $Q$-submanifolds of degree $n$ symplectic $Q$-manifolds. Using
Weinstein's tubular neighbourhood Theorem, we attach to every Lagrangian
$Q$-submanifold an $L_\infty$-algebra, which controls its deformation theory.
The main examples are coisotropic submanifolds of Poisson manifolds and
(higher) Dirac structures with support in (higher) Courant algebroids.
