Enabling and exploiting self-similar central symmetry formations

In this work a formation flying based architecture is presented within the context of a distributed antenna array. An artificial potential function method is used to control the formation whereby deviation from an all-to-all interaction
scheme and swarm shaping are enabled through a self-similar connection network. Introduction of an asymmetric term in the potential function formulation results in the emergence of structures with a central symmetry. The connection network then groups these identical structures through a hierarchical scheme. This produces a fractal shape which is considered for the first time as a distributed antenna array exploiting the recursive arrangement of its elements to augment performance. A 5-element Purina fractal is used as the base formation which is then replicated a number of times increasing the antenna-array aperture and resulting in a highly directional beam from a relatively low number of elements. Justifications are provided in support of the claimed benefits for distributed antenna arrays exploiting fractal geometries. The formation deployment is simulated in Earth orbit together with analytical proofs completing the arguments aimed to demonstrate feasibility of the concept and the advantages provided by grouping antenna elements into coherent structures.