Fractal patterns in fractionated spacecraft

Multi spacecraft architectures have been addressed in response to the demand for flexible architectures with high reliability and reduced costs compared to traditional monolithic spacecraft. A task that can be easily carried out by this kind of systems is the deployment of distributed antennas; these are composed of, typically, receiving elements carried on-board multiple spacecraft in precise formation. In this paper decentralised control means, based on artificial potential functions, together with a fractal-like connection network, are used to produce the autonomous and verifiable deployment and formation control of a swarm of spacecraft into a fractal-like pattern. The effect of using fractal-like routing of control data within the spacecraft generates complex formation shape patterns, while simultaneously reducing the amount of control information required to form such complex formation shapes. Furthermore, the techniques used ensure against swarm fragmentation, while exploiting communication channels anyway needed in a fractionated architecture. In particular, the superposition of potential functions operating at multiple levels (single agents, subgroups of agents, groups of agents) according to a self-similar adjacency matrix produces a fractal-like final deployment with the same stability property on each scale. Considering future high-precision formation flying and control capabilities, this paper considers, for the first time and as an example of a fractionated spacecraft, a decentralised multi-spacecraft fractal shaped antenna. A fractal antenna pattern provides multiple resonance peaks, directly related to the ratios of its characteristic physical lengths. Such a scenario would significantly improve the level of functionality of any multi-spacecraft synthetic aperture antenna system. Furthermore, multi-spacecraft architecture exploiting particular inter agent spacing can be considered to investigate multi-scale phenomena in areas such as cosmic radiation and space plasma physics. Both numerical simulations and analytic treatment are carried out demonstrating the feasibility of deploying and controlling a fractionated fractal antenna in space through autonomous decentralised means

Enhancing self-similar patterns by asymmetric artificial potential functions in partially connected swarms

The control of mobile robotic agents is required to be highly reliable. Artificial potential function (APF) methods have previously been assessed in the literature for providing stable and verifiable control, whilst maintaining a high degree of nonlinearity. Further, these methods can, in theory, be characterised by a full analytic treatment. Many examples are available in the literature of the employment of these methods for controlling large ensembles of agents that evolve into minimum energy configurations corresponding in many cases to regular lattices [1-2]. Although regular lattices can present naturally centric symmetry and self-similarity characteristics, more complex formations can also be achieved by several other means. In [3] the equilibrium configuration undergoes bifurcation by changing a parameter belonging to the part of artificial potential that couples the agents to the reference frame. In this work it is shown how the formation shape produced can be controlled in two further ways, resulting in more articulated patterns. Specifically the control applied is to alter the symmetry of interactions amongst agents, and/or by selectively rewiring interagent connections. In the first case, the network of connections remains the same, and may be fully connected

Swarm shape manipulation through connection control

The control of a large swarm of distributed agents is a well known challenge within the study of unmanned autonomous systems. However, it also presents many new opportunities. The advantages of operating a swarm through distributed means has been assessed in the literature for efficiency from both operational and economical aspects; practically as the number of agents increases, distributed control is favoured over centralised control, as it can reduce agent computational costs and increase robustness on the swarm. Distributed architectures, however, can present the drawback of requiring knowledge of the whole swarm state, therefore limiting the scalability of the swarm. In this paper a strategy is presented to address the challenges of distributed architectures, changing the way in which the swarm shape is controlled and providing a step towards verifiable swarm behaviour, achieving new configurations, while saving communication and computation resources. Instead of applying change at agent level (e.g. modify its guidance law), the sensing of the agents is addressed to a portion of agents, differentially driving their behaviour. This strategy is applied for swarms controlled by artificial potential functions which would ordinarily require global knowledge and all-to-all interactions. Limiting the agents' knowledge is proposed for the first time in this work as a methodology rather than obstacle to obtain desired swarm behaviour

A fractally fractionated spacecraft

The advantages of decentralised multi-spacecraft architectures for many space applications are well understood. Distributed antennas represent popularly envisaged applications of such an architecture; these are composed of, typically, receiving elements carried on-board multiple spacecraft in precise formation. In this paper decentralised control, based on artificial potential functions, together with a fractal-like connection network, is used to produce autonomous and verifiable deployment and formation control of a swarm of spacecraft into a fractal-like pattern. The effect of using fractal-like routing of control data within the spacecraft generates complex formation shape patterns, while simultaneously reducing the amount of control information required to form such complex formation shapes. Furthermore, the techniques used ensures against swarm fragmentation, which can otherwise be a consequence of the non-uniform connectivity of the communication graph. In particular, the superposition of potential functions operating at multiple levels (single agents, subgroups of agents, groups of agents) according to a self-similar adjacency matrix produces a fractal-like final deployment with the same stability property on each scale. Results from the investigations carried out indicate the approach is feasible, whilst outlining its robustness characteristics, and versatility in formation deployment and control. Considering future high-precision formation flying and control capabilities, this paper considers, for the first time and as an example of a fractally fractionated spacecraft, a decentralised multi-spacecraft fractal shaped antenna. Furthermore, multi-spacecraft architecture exploiting fractal-like formations can be considered to investigate multi-scale phenomena in areas such as cosmic radiation and space plasma physics. Both numerical simulations and analytic treatment are presented, demonstrating the feasibility of deploying and controlling a fractionated fractal antenna in space through autonomous decentralised means. This work frames the problem of architecture and tackles the one of control, whilst not neglecting actuation

Characteristics of swarms on the edge of fragmentation

Fragmentation of particle swarms into isolated subgroups occurs when interaction forces are weak or restricted. In the restricted case, the swarm experiences the onset of bottlenecks in the graph of interactions that can lead to the fragmentation of the system into subgroups. This work investigates the characteristics of such bottlenecks when the number of particles in the swarm increases. It is shown, for the first time, that certain characteristics of the bottleneck can be captured by considering only the number of particles in the swarm. Considering the case of a connected communication graph constructed in the hypothesis that each particle is influenced by a fixed number of neighbouring particles, a limit case is determined for which a lower limit to the Cheeger constant can be derived analytically without the need for extensive algebraic calculations. Results show that as the number of particles increases the Cheeger constant decreases. Although ensuring a minimum number of interactions per particle is sufficient, in theory, to ensure cohesion, the swarm may face fragmentation as more particles are added to the swarm

Low-cost, multi-agent systems for planetary surface exploration

The use of off-the-shelf consumer electronics combined with top-down design methodologies have made small and inexpensive satellites, such as CubeSats, emerge as viable, low-cost and attractive space-based platforms that enable a range of new and exciting mission scenarios. In addition, to overcome some of the resource limitation issues encountered with these platforms, distributed architectures have emerged to enable complex tasks through the use of multiple low complexity units. The low-cost characteristics of such systems coupled with the distributed architecture allows for an increase in the size of the system beyond what would have been feasible with a monolithic system, hence widening the operational capabilities without significantly increasing the control complexity of the system. These ideas are not new for Earth orbiting devices, but excluding some distributed remote sensing architectures they are yet to be applied for the purpose of planetary exploration. Experience gained through large rovers demonstrates the value of in-situ exploration, which is however limited by the associated high-cost and risk. The loss of a rover can and has happened because of a number of possible failures: besides the hazards directly linked to the launch and journey to the target-body, hard landing and malfunctioning of parts are all threats to the success of the mission. To overcome these issues this paper introduces the concept of using off-the-shelf consumer electronics to deploy a low-cost multi-rover system for future planetary surface exploration. It is shown that such a system would significantly reduce the programmatic-risk of the mission (for example catastrophic failure of a single rover), while exploiting the inherent advantages of cooperative behaviour. These advantages are analysed with a particular emphasis put upon the guidance, navigation and control of such architectures using the method of artificial potential field. Laboratory tests on multi-agent robotic systems support the analysis. Principal features of the system are identified and the underlying advantages over a monolithic single-agent system highlighted

Impact of a purina fractal array geometry on beamforming performance and complexity

This paper investigates the possible benefits of using a Purina fractal array for beamforming, since this particular fractal has recently been suggested as the flight formation for a fractionated space craft. We analyse the beam pattern created by this, and define power concentration as measure of focussing the main beam of a multi-dimensional array. Using this performance metric and the computation cost of the array, a comparison to full lattice arrays is made. We quantify the significant benefits of the Purina array offered over a full lattice array of same complexity particularly at lower frequencies, and the complexity advantages over full lattice arrays of same aperture, particularly if energy is to be concentrated within a small angular spread

Link Count Data-driven Static Traffic Assignment Models Through Network Modularity Partitioning

Accurate static traffic assignment models are important tools for the assessment of strategic transportation policies. In this article we present a novel approach to partition road networks through network modularity to produce data-driven static traffic assignment models from loop detector data on large road systems. The use of partitioning allows the estimation of the key model input of Origin-Destination demand matrices from flow counts alone. Previous network tomography-based demand estimation techniques have been limited by the network size. The amount of partitioning changes the Origin-Destination estimation optimisation problems to different levels of computational difficulty. Different approaches to utilising the partitioning were tested, one which degenerated the road network to the scale of the partitions and others which left the network intact. Applied to a subnetwork of England's Strategic Road Network and other test networks, our results for the degenerate case showed flow and travel time errors are reasonable with a small amount of degeneration. The results for the non-degenerate cases showed that similar errors in model prediction with lower computation requirements can be obtained when using large partitions compared with the non-partitioned case. This work could be used to improve the effectiveness of national road systems planning and infrastructure models.Comment: 29 pages, 11 figure

Resilient and complex infrastructure: conjugating opposite ends of the spectrum

<p>Solid lines in A-C represent simulated mean plasma concentration-time profiles, whereas dashed lines represent the 5^th and 95^th percentiles for the predicted values. The observed data points (●) are shown as mean ± SD or mean only. The solid lines in D and E illustrates unity, as well as a twofold deviation from unity; whereas the data points represent observed mean ± SD values with respective to the simulated mean ± SD values for <i>AUC</i> (D) and <i>C</i>_<i>max</i> (E).</p