Enabling and Exploiting Self-Similar Central Symmetry Formations

Abstract

This version is available at https://strathprints.strath.ac.uk/44352/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the AbstractIn 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.

Closed-Loop Control of the Orbit Evolution of “Smart Dust” Swarms

“…If both the source and sink terms are ignored in this equation, it is referred as the homogeneous evolution model. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] Solutions to the continuum evolution equation can be achieved by propagating the initial data for the swarm forward to describe the evolution of n as a function of both  and . The initial data function is defined as…”

“…[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] Moreover, the device deposition strategies proposed in Section III.II are considered to compensate for on-orbit failures, which act as a boundary controller in the classical PDE control problem. Compared with the active device controllers for individual devices in Section III.I, the boundary control is provided by the macroscopic deposition of new devices.…”

Distributed Processing of a Fractal Array Beamformer

“…Additionally, the Purina fractal's structural sparseness combines a significant aperture and therefore resolution while avoiding spatial aliasing as long as at least some sensors are sufficiently closely located [3][4][5][6], thus offering advantages that otherwise have to be achieved through thinning of arrays [7,8].…”