Verifiable control of a swarm of unmanned aerial vehicles

This article considers the distributed control of a swarm of unmanned aerial vehicles (UAVs) investigating autonomous pattern formation and reconfigurability. A behaviour-based approach to formation control is considered with a velocity field control algorithm developed through bifurcating potential fields. This new approach extends previous research into pattern formation using potential field theory by considering the use of bifurcation theory as a means of reconfiguring a swarm pattern through a free parameter change. The advantage of this kind of system is that it is extremely robust to individual failures, is scalpable, and also flexible. The potential field consists of a steering and repulsive term with the bifurcation of the steering potential resulting in a change of the swarm pattern. The repulsive potential ensures collision avoidance and an equally spaced final formation. The stability of the system is demonstrated to ensure that desired behaviours always occur, assuming that at large separation distances the repulsive potential can be neglected through a scale separation that exists between the steering and repulsive potential. The control laws developed are applied to a formation of ten UAVs using a velocity field tracking approach, where it is shown numerically that desired patterns can be formed safely ensuring collision avoidance

Passive orbit control for space-based geo-engineering

In this Note we consider using solar sail propulsion to stabilize a spacecraft about an artificial libration point. It has been demonstrated that the constant acceleration from a solar sail can be used to generate artificial libration points in the Earth-Sun three-body problem. This is achieved by directing the thrust due to the sail such that it adds to the centripetal and gravitational forces. These libration points have the potential for future space physics and Earth observation missions. Of particular interest is the possibility of placing solar reflectors at the L1 artificial libration point to offset natural and human driven climate change. One engineering challenge that presents itself is that these artificial libration points are highly unstable and require active control for station-keeping. Previous work has shown that it is possible to stabilize a solar sail about artificial libration points using variations in both pitch and yaw angles. However, in a practical sense, solar sails are large structures and active control of the sail's attitude is a challenging engineering problem. Passive stabilization of such reflectors is to be investigated here to reduce the complexity of space-based geo-engineering schemes

On-orbit assembly using superquadric potential fields

The autonomous on-orbit assembly of a large space structure is presented using a method based on superquadric artificial potential fields. The final configuration of the elements which form the structure is represented as the minimum of some attractive potential field. Each element of the structure is then considered as presenting an obstacle to the others using a superquadric potential field attached to the body axes of the element. A controller is developed which ensures that the global potential field decreases monotonically during the assembly process. An error quaternion representation is used to define both the attractive and superquadric obstacle potentials allowing the final configuration of the elements to be defined through both relative position and orientation. Through the use of superquadric potentials, a wide range of geometric objects can be represented using a common formalism, while collision avoidance can make use of both translational and rotation maneuvers to reduce total maneuver cost for the assembly process

Control of solar sail periodic orbits in the elliptic three-body problem

A solar sail essentially consists of a large mirror that uses the momentum change due to photons reflecting off the sail for its impulse. Solar sails are therefore unique spacecraft, as they do not require fuel for propulsion [1]. In this Note we consider using the solar sail to continuously maintain a periodic orbit above the ecliptic plane using variations in the sail's orientation. Positioning a spacecraft continuously above the ecliptic would allow continuous observation and communication with the poles

Displaced geostationary orbits using hybrid low-thrust propulsion

In this paper, displaced geostationary orbits using hybrid low-thrust propulsion, a complementary combination of Solar Electric Propulsion (SEP) and solar sailing, are investigated to increase the capacity of the geostationary ring that is starting to become congested. The SEP propellant consumption is minimized in order to maximize the mission lifetime by deriving semi-analytical formulae for the optimal steering laws for the SEP and solar sail accelerations. By considering the spacecraft mass budget, the performance is also expressed in terms of payload mass capacity. The analyses are performed both for the use of pure SEP and hybrid low-thrust propulsion to allow for a comparison. It is found that hybrid low-thrust control outperforms the pure SEP case both in terms of payload mass capacity and mission lifetime for all displacements considered. Hybrid low-thrust propulsion enables payloads of 255 to 487 kg to be maintained in a 35 km displaced orbit for 10 to 15 years. Adding the influence of the J2 and J22 terms of the Earth’s gravity field has a small effect on this lifetime, which becomes almost negligible for small values of the sail lightness number. Finally, two SEP transfers that allow for an improvement in the performance of hybrid low-thrust control are optimized for the propellant consumption by solving the accompanying optimal control problem using a direct pseudospectral method. The first type of transfer enables a transit between orbits displaced above and below the equatorial plane, while the second type of transfer enables customized service for which a spacecraft is transferred to a Keplerian parking orbit when geostationary coverage is not needed. While the latter requires a modest propellant budget, the first type of transfer comes at the cost of an almost negligible SEP propellant consumption

Parallel spinors and holonomy groups

In this paper we complete the classification of spin manifolds admitting parallel spinors, in terms of the Riemannian holonomy groups. More precisely, we show that on a given n-dimensional Riemannian manifold, spin structures with parallel spinors are in one to one correspondence with lifts to Spin_n of the Riemannian holonomy group, with fixed points on the spin representation space. In particular, we obtain the first examples of compact manifolds with two different spin structures carrying parallel spinors.Comment: 10 pages, LaTeX2

Crossing of the w=-1 barrier in viscous modified gravity

We consider a modified form of gravity in which the action contains a power alpha of the scalar curvature. It is shown how the presence of a bulk viscosity in a spatially flat universe may drive the cosmic fluid into the phantom region (w<-1) and thus into a Big Rip singularity, even if it lies in the quintessence region (w>-1) in the non-viscous case. The condition for this to occur is that the bulk viscosity contains the power (2 alpha-1) of the scalar expansion. Two specific examples are discussed in detail. The present paper is a generalization of the recent investigation dealing with barrier crossing in Einstein's gravity: I. Brevik and O. Gorbunova, Gen. Relativ. Grav. 37 (2005) 2039.Comment: 12 pages, latex, no figure

Diabetic foot disease in the United Kingdom: about time to put feet first

Diabetes is now the biggest cause of amputation, stroke, blindness and end stage renal failure. It causes many deaths from cardiovascular disease. Foot ulcers and amputations reduce the quality of life, increase mortality and involve lengthy stay in hospital. Many people who have an ulcer eventually require surgery. The economic cost to the nation is spiralling out of control with estimates of 10% of the entire NHS budget spent on diabetes. This paper aims to explore the burden of diabetic complications and how policy, guidelines and audit highlight the discrepancies in the quality of diabetes care with particular reference to diabetes foot services. The findings suggest that the NICE guidelines for diabetes foot care are not being adhered to and that the variation in preventative amputations across England is unacceptable. Diabetes UK, the national charity for diabetes is leading a campaign to improve diabetic foot care in light of the available published health information

Design of optimal Earth pole-sitter transfers using low thrust propulsion

Recent studies have shown the feasibility of an Earth pole-sitter mission using low-thrust propulsion. This mission concept involves a spacecraft following the Earth's polar axis to have a continuous, hemispherical view of one of the Earth's poles. Such a view will enhance future Earth observation and telecommunications for high latitude and polar regions. To assess the accessibility of the pole-sitter orbit, this paper investigates optimum Earth pole-sitter transfers employing low-thrust propulsion. A launch from low Earth orbit (LEO) by a Soyuz Fregat upper stage is assumed after which a solar-electric-propulsion thruster transfers the spacecraft to the pole-sitter orbit. The objective is to minimise the mass in LEO for a given spacecraft mass to be inserted into the pole-sitter orbit. The results are compared with a ballistic transfer that exploits the manifolds winding off the pole-sitter orbit. It is shown that, with respect to the ballistic case, low-thrust propulsion can achieve significant mass savings in excess of 200 kg for a pole-sitter spacecraft of 1000 kg upon insertion. To finally obtain a full low-thrust transfer from LEO up to the pole-sitter orbit, the Fregat launch is replaced by a low-thrust, minimum time spiral through an orbital averaging technique, which provides further mass savings, but at the cost of an increased time of flight

Studies of novel photoanodic materials for solar water splitting

Anthropogenic climate change presents an unrivalled threat to environmental stability and the prosperity of future generations. Utilising abundant, renewable resources in energy generation and storage will be essential to halt climate change and its effects. Solar water splitting is an excellent tool in the renewable energy arsenal for countering climate change, as it utilises both sunlight and water, two of the most abundant resources available on earth. Furthermore, the direct formation of a chemical fuel, hydrogen, is thought to be more practical for storing in large quantities than electricity. Work in this thesis covers the investigation of a variety of materials, fabricated by aerosol assisted chemical vapour deposition (AACVD), for their ability to carry out photoelectrochemical water splitting. In one project, thin films of Bi2Ti2O7 (BTO), specifically of the pyrochlore crystal structure, are fabricated by AACVD and analysed for their photoelectrochemical properties. The resulting thin films are found to be phase pure with a band gap of 2.88 eV, which is 0.32 eV smaller than TiO2. Efforts to dope the BTO thin films are further investigated through the addition of iron. Significant modification to the band gap is observed, leading to a confirmed pyrochlore thin film exhibiting a band gap of 2.5 eV, a reduction of 0.38 eV from undoped BTO. The resulting thin film had a photocurrent 5 times higher than that of undoped BTO. Finally, efforts to fabricate Fe2Ti2O7 are outlined. It is discovered that a stable phase of Fe2TiO5 is preferentially formed over the pyrochlore phase, even with dramatic modification to the deposition parameters and precursor stoichiometry. The high stability of this phase, coupled with the limiting features of the glass substrates, highlights the challenges with forming certain pyrochlore thin films. In a second project, the effect of depositing titanium nanoclusters onto the surface of bismuth vanadate is investigated. Nanoclusters are of huge interest because their properties lie between those of atoms and bulk materials. Additionally, nanoscale clusters can be fabricated with incredible precision, allowing one to select discrete diameter particles for deposition on surfaces. Ti nanoclusters over a range of sizes are deposited onto BiVO4 photoanodes. It is discovered that the deposition of ultralow loadings of Ti2000 clusters results in an 80 % enhancement in the photocurrent of the BiVO4 substrates. Further experimentation highlights that the photocurrent enhancement is linked to the size of the nanocluster and the density of the clusters on the surface. A mechanism is outlined, whereby the Ti nanoclusters partially reduce the surface of the BiVO4, leading to enhanced electron transport within the thin films due to the presence of oxygen vacancies. In a final project, polycrystalline InN, GaN and systematically controlled InxGa1-xN composite thin films are fabricated on FTO glass by a facile, low-cost and scalable aerosol assisted chemical vapor deposition technique. Variation of the indium content in the composite films leads to a dramatic shift in the optical absorbance properties, which correlates with the band edges shifting between those of GaN to InN. Moreover, the photoelectrochemical properties are shown to vary with indium content, with the 50 % indium composite having an external quantum efficiency of around 8 %. Whilst the overall photocurrent is found to be low, the photocurrent stability is shown to be excellent, with little degradation seen over 1 hour. Subsequent attempts to modify the morphology by conducting vertical-AACVD are also outlined. Thin films fabricated using vertical-AACVD are found to grow via a different mechanism, leading to undesired split phase growth, where two different compositions form on the same substrate