Actions of Drinfeld doubles of finite groups on Artin-Schelter regular algebras

For a finite group $G$ and $\mathbb{k}$ an algebraically closed field of characteristic zero we consider Artin-Schelter regular algebras $A$ on which the Drinfeld double $D(G)$ acts inner faithfully, and its associated algebras of invariants $A^{D(G)}$. Explicit computations for the cases when $G$ is the (generalized) quaternion group of order 8 and 16 are given.