We numerically and theoretically investigate the behavior of a granular gas driven by asymmetric plates. The injection of energy in the dissipative system differs from one side to the opposite one. We prove that the dynamical clustering which is expected for such a system is affected by the asymmetry. As a consequence, the cluster position can be fully controlled. This property could lead to various applications in the handling of granular materials in low-gravity environment. Moreover, the dynamical cluster is characterized by natural oscillations which are also captured by a model. These oscillations are mainly related to the cluster size, thus providing an original way to probe the clustering behavior