Research on swarm robotics has become increasingly important in the last three decades. One of the major research directions in swarm robotics is the control of the formation of swarm robots to perform various tasks in 2D or 3D environments. In this paper, we propose a new planar (2D) formation control framework based on a dynamic version of elliptic Fourier descriptors (EFDs) and develop formation controllers that enable robots to form the desired shapes. The main advantage of this method over more traditional approaches in the literature is its flexibility in the representation of the desired shape. The formation can be virtually any arbitrary planar closed curve. Representation by EFDs becomes much more powerful as the number of harmonics in the representation increases. Performance of the proposed formation controller is tested in three simulations where desired swarm formations modelled by EFDs with two, three and six harmonics are considered. Results are quite promising.