Time-delayed autosynchronous swarm control

In this paper a general Morse potential model of self-propelling particles is considered in the presence of a time-delayed term and a spring potential. It is shown that the emergent swarm behavior is dependent on the delay term and weights of the time-delayed function which can be set to induce a stationary swarm, a rotating swarm with uniform translation and a rotating swarm with a stationary center-of-mass. An analysis of the mean field equations shows that without a spring potential the motion of the center-of-mass is determined explicitly by a multi-valued function. For a non-zero spring potential the swarm converges to a vortex formation about a stationary center-of-mass, except at discrete bifurcation points where the center-of-mass will periodically trace an ellipse. The analytical results defining the behavior of the center-of-mass are shown to correspond with the numerical swarm simulations

Pattern transition in spacecraft formation flying using bifurcating potential field

Many new and exciting space mission concepts have developed around spacecraft formation flying, allowing for autonomous distributed systems that can be robust, scalable and flexible. This paper considers the development of a new methodology for the control of multiple spacecraft. Based on the artificial potential function method, research in this area is extended by considering the new approach of using bifurcation theory as a means of controlling the transition between different formations. For real, safety or mission critical applications it is important to ensure that desired behaviours will occur. Through dynamical systems theory, this paper also aims to provide a step in replacing traditional algorithm validation with mathematical proof, supported through simulation. This is achieved by determining the non-linear stability properties of the system, thus proving the existence or not of desired behaviours. Practical considerations such as the issue of actuator saturation and communication limitations are addressed, with the development of a new bounded control law based on bifurcating potential fields providing the key contribution of this paper. To illustrate spacecraft formation flying using the new methodology formation patterns are considered in low-Earth-orbit utilising the Clohessy-Wiltshire relative linearised equations of motion. It is shown that a formation of spacecraft can be driven safely onto equally spaced projected circular orbits, autonomously reconfiguring between them, whilst satisfying constraints made regarding each spacecraft

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

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

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

Modeling the Daily Variations of the Coronal X-ray Spectral Irradiance with Two Temperatures and Two Emission Measures

The Miniature X-ray Solar Spectrometer (MinXSS-1) CubeSat observed solar X-rays between 0.5 and 10 keV. A two-temperature, two-emission measure model is fit to each daily averaged spectrum. These daily average temperatures and emission measures are plotted against the corresponding daily solar 10.7 cm radio flux (F10.7) value and a linear correlation is found between each that we call the Schwab Woods Mason (SWM) model. The linear trends show that one can estimate the solar spectrum between 0.5 keV and 10 keV based on the F10.7 measurement alone. The cooler temperature component of this model represents the quiescent sun contribution to the spectra and is essentially independent of solar activity, meaning the daily average quiescent sun is accurately described by a single temperature (1.70 MK) regardless of solar intensity and only the emission measure corresponding to this temperature needs to be adjusted for higher or lower solar intensity. The warmer temperature component is shown to represent active region contributions to the spectra and varies between 5 MK to 6 MK. GOES XRS-B data between 1-8 Angstroms is used to validate this model and it is found that the ratio between the SWM model irradiance and the GOES XRS-B irradiance is close to unity on average. MinXSS-1 spectra during quiescent solar conditions have very low counts beyond around 3 keV. The SWM model can generate MinXSS-1 or DAXSS spectra at very high spectral resolution and with extended energy ranges to fill in gaps between measurements and extend predictions back to 1947

Lens mounting techniques for precise radial location of fragile lenses in the NGS2 and Veloce instruments

We present novel methods for mounting lenses in a pair of instruments that presented challenging optical and mechanical requirements. The first instrument is the replacement Natural Guide Star Sensor (NGS2) for CANOPUS at Gemini South, which incorporates an objective consisting of a stack of six lenses mounted in a common bore. A compliant radial spacer was used to eliminate lens decentre resulting from the additional radial clearance required to accommodate differential thermal strains between the low thermal expansion lenses and a common bore. In the same instrument, tangent contact toroidal spacers were deployed in place of traditional conical spacers to further reduce contact stresses in fragile calcium fluoride lens elements. The toroidal faces were specified with a 10µm profile tolerance to avoid possible edge contact between the spacers and lenses. We investigated milling and turning machining processes for the production of the spacers by comparing their results via Coordinate Measuring Machine (CMM) measurements. In the second instrument, Veloce, built for the Anglo-Australian Telescope, a lens decentre requirement of 40µm led us to develop a simple means of in-situ centring adjustment of the cell mounted lens. Physical testing of the finished instruments verified the performance of each of these methods. NGS2 produced images at the factory acceptance test in which 94% of encircled energy was captured by a single 16um detector pixel, surpassing the specification of 80%. Bench testing of Veloce during assembly showed that the adjustment mechanism allowed centring of the lens over a range of +/- 0.1mm with a precision of 5µm