Extension of the proximity-quotient control law for low-thrust propulsion

In this paper, the proximity quotient control law, first developed by Petropoulos, is extended to account for both third body effects and solar radiation pressure. The perturbing effect of solar radiation pressure becomes relevant when dealing with solar sails, or large optics in space. Equations for the disturbing acceleration and disturbing potential function were derived for the perturbations, then analyzed to determine the minimum and maximum rate of changes of the Keplerian elements given the thrust vector and true anomaly of the spacecraft. These were then analytically incorporated into the Q-law feedback function. The complete mathematical derivations are presented. The extended Q-law is compared to the fully optimal control law, stemming from optimal control theory, for the same dynamical model. Two missions are used as test cases

Optimal design for a NEO tracking spacecraft formation

The following paper presents the design and methodology for developing an optimal set of spacecraft orbits for a NEO tracking mission. The spacecraft is designed to fly in close formation with the asteroid, avoiding the nonlinear gravity field produced by the asteroid. A periodic orbit is developed, and the initial conditions are optimized by use of a global optimizer for constrained nonlinear problems. The asteroid Apophis (NEO 2004 MN4) was used as the case study due the potential impact with Earth in 2036, and the need for more accurate ephemerides

Orbital debris removal with solar concentrators

In 1993 solar concentrators were first proposed to deflect asteroids away from a collision course with the Earth. The original concept was expanded by the authors, and proved to be effective and technologically feasible. One way to deflect the asteroid is to produce a slow decay of its orbit by inducing a thrust via concentrated solar light. Two mechanisms have been investigated: the sublimation of the surface of the asteroid to generate a jet of gas and the induced thrust by light pressure and enhanced Yarkovsky effect. If the concentrators are reduced in size, a similar concept can be adopted to remove orbital debris and inert satellites. In this paper, we present an orbital debris removal system based on concentrated solar light. We will show how enhanced solar pressure, generated by a formation of solar concentrators, can be used to accelerate the decay of small inert objects orbiting the Earth. A set of modified proximal motion equations is proposed to describe the relative dynamics of the solar concentrators with respect to the target piece of debris. The paper will provide an analysis of the cost of the optimal control of the concentrators during the deflection of the debris and a system engineering analysis. In particular, we will show that the concentrator acts as an active solar sail while not deflecting, and as a hybrid solar sail (i.e. the orbit is maintained with an auxiliary low-thrust engine) while deflecting the debris. The results will show that objects with even a small area-to-mass ratio (down to 0.01) can be brought from an 800 km to a 200 km altitude orbit in few hundred days of constant operation. The paper will discuss also the possibility to vaporize some small size targets with high power solar pumped laser

On the dynamics, navigation and control of a spacecraft formation of solar concentrators in the proximity of an asteroid

This purpose of this dissertation is to ascertain whether solar sublimation is a viable method for the deflection of a Near Earth Asteroid. From a research view point, the methods and analysis are applicable to proximal motion around a celestial body, in particular one with a non-Keplerian or irregular orbit as in the case here with the orbit being constantly altered by the deflection action and subject to perturbations, such as solar radiation pressure. Two concepts, and the corresponding dynamics and control, are presented based on previous trade-off and optimisation studies. The first uses a paraboloidic reflector to concentrate the solar radiation onto a solar-pumped laser, which is then directed onto a specific spot on the NEO by a small directional mirror. The spacecraft orbits are designed to fly in formation with the asteroid around the Sun, and are based on the orbital element differences. The formation orbits were optimised based on a number of single and multiple objective functions. A feedback control law is presented for the orbital maintenance required to counteract the solar radiation pressure (due primarily to the large surface area of the primary reflector), and the third-body effects due to the gravitational field of the asteroid. The second option takes advantage of the balance between the gravity attraction of the NEO and solar pressure acting on the collector. The mirror focuses the light directly onto the asteroid surface, controlling the beam by adjusting the focal point of the primary reflector. By altering the shape of the mirror surface, both the focal point and the vector of the solar radiation pressure can be manipulated. An interesting navigation strategy is proposed based on the attitude measurements, the inertial position of each spacecraft, the intersatellite position and velocity measurements, and a 2D image from a rotating onboard camera. The navigational data is used for both the orbital control of the spacecraft and for the beam pointing. The results of simulations of a hypothetical deflection mission of the asteroid Apophis are presented for the dynamics, control, attitude and navigation, accounting for solar radiation pressure, the gravity field of the asteroid, and the deviation of the NEO orbit. The results show that both concepts provide the required deflection with a feasible mass at launch, solving most of the issues related to the solar sublimation method. One of the critical aspects of this deflection concept is properly placing the concentrators in the proximity of the asteroid in order to avoid the plume impingement and the occultation from the asteroid itself. Issues regarding the contamination of the mirrors are addressed and compared with the simulated deflections predicted considering no contamination. Lastly, initial system mass budgets are presented

Prediction of the aerodynamic performance of re-usable single stage to orbit vehicles

Re-usable single stage to orbit launch vehicles promise to reduce the cost of access to space, but their success will be particularly reliant on accurate modelling of their aero-thermodynamic characteristics. Non-equilibrium effects due to the rarefaction of the gas in the atmosphere are important at the very high altitudes at which lifting R-SSTO configurations will experience their greatest thermal load during re-entry. Current limitations in modelling the behaviour of the gas and hence in capturing these effects have a strong impact on the accuracy with which the thermal and aerodynamic loading on the surface of the vehicle can be predicted during this design-critical flight regime. The problem is most apparent in the presence of strong shock interactions, and this is likely to exacerbate the problem of aerodynamic characterisation of re-usable single stage to orbit vehicles, especially given design pressures towards increased geometric complexity compared to historical spacecraft designs, and hence the complexity of the shock structures that the vehicle will produce in high-speed flight. The development of this class of vehicles will thus very likely be paced by the development of the specialised modelling tools that will be required to account fully for the properties of the gas at the high speeds and altitudes that are characteristic of their re-entry into the atmosphere of the earth

Deployed payload analysis for a single stage to orbit spaceplane

The growth of the small satellite market requires an affordable and flexible launcher to satisfy the demand for insertion to a varied range of specific orbits. This paper presents the application and results of a tool created for the preliminary analysis of a reusable lifting body vehicle to address the demand of small to medium sized payloads. Trajectory optimisation is performed on the ascent mission of the launcher from a nominal cruise altitude to the release of the payload into different orbits with different mission and vehicle objectives and constraints. Two vehicle configurations are studied and applied to test cases of insertion to 200 km circular orbits at different inclinations. Further analysis on the performances obtained at different altitudes is conducted to study the effect on maximum payload mass. The advantages and limitations of the single stage to orbit approach are discussed and ways to overcome the latter are further analysed with the introduction of a small upper stage or tug. This additional engine can perform small manoeuvres to correct the flight path for orbital insertion, which expands the type of orbits that can be reached, and is integrated in the optimisation routine. The overall performance of the different launch systems are optimised for each mission, and compared against each other looking at the total payload mass and required mass fraction to reach different orbits

Spaceplane trajectory optimisation with evolutionary-based initialisation

In this paper, an evolutionary-based initialisation method is proposed based on Adaptive Inflationary Differential Evolution algorithm, which is used in conjunction with a deterministic local optimisation algorithm to efficiently identify clusters of optimal solutions. The approach is applied to an ascent trajectory for a single stage to orbit spaceplane, employing a rocket-based combine cycle propulsion system. The problem is decomposed first into flight phases, based on user defined criteria such as a propulsion cycle change translating to different mathematical system models, and subsequently transcribed into a multi-shooting NLP problem. Examining the results based on 10 independent runs of the approach, it can be seen that in all cases the method converges to clusters of feasible solutions. In 40% of the cases, the AIDEA-based initialisation found a better solution compared to a heuristic approach using constant control for each phase with a single shooting transcription (representing an expert user). The problem was run using randomly generated control laws, only 2/20 cases converged, both times with a less optimal solution compared to the baseline heuristic approach and AIDEA

Designs of multi-spacecraft swarms for the deflection of apophis by solar sublimation

This paper presents two conceptual designs of multi-spacecraft swarms used for deflecting Apophis. Each spacecraft is equipped with a solar concentrator assembly, which focuses the solar light, and a beaming system that projects a beam of light onto the surface of the asteroid. When the beams from each spacecraft are superimposed, the temperature on the surface is enough to sublimate the rock, creating a debris plume with enough force to slowly alter the orbit of Apophis. An overview of the dynamics, control and navigation strategies are presented along with preliminary system budgets

Comparison of single and multi-spacecraft configurations for NEA deflection by solar sublimation

Since the first Near Earth Object (NEO) defence system, Project Icarus, was published in 1967, where the driving factor was a very short anticipating time (i.e. time available to act on the asteroid), the Near Earth Asteroid (NEA) hazard outlook has changed drastically. In the current state of NEO research, long-term missions are becoming more realistic and as such, the options for low thrust systems are being investigated as a viable option for deviating the asteroid path. Surface ablation approaches have been previously proposed using several techniques such as lasers and nuclear explosives. The method presented here hinges on directing solar energy using mirrors onto a small area on the surface of the asteroid. This concentrated heat then sublimates the surface matter creating narrow but expanding jets of gas and dust that produce a low continuous thrust. This low thrust would then alter the orbit of the NEA by producing a change in velocity, similar to the effect of the ‘tail’ on a comet. This paper adds a new important trade-off to the problem: a comparison between a single structure and a multi-mirror system. The systems analysed include both single and dual mirror configurations, for both a single spacecraft and multiple spacecraft in formation. The criteria include ease of launch, reliability, flexibility in achieving the mission objective, in-space mass and a basic cost analysis. The concept, and potential benefits, of formation flying have long been known. The barrier however, has been the high level of complexity involved in the control of the individual spacecraft within the formation. Advances in control algorithms and associated technologies have opened the door to using spacecraft formations for specialized missions, such as small-body missions which operate in highly perturbed environments. This paper compares the complexities of deploying and operating a large rigid structure around asteroids, with the control of a swarm of smaller structures. Configurations are presented for different NEAs, time-in-advance, and achieved deflections

Ascent trajectory optimisation for a single-stage-to-orbit vehicle with hybrid propulsion

This paper addresses the design of ascent trajectories for a hybrid-engine, high performance, unmanned, single-stage-to-orbit vehicle for payload deployment into low Earth orbit. A hybrid optimisation technique that couples a population-based, stochastic algorithm with a deterministic, gradient-based technique is used to maximize the nal vehicle mass in low Earth orbit after accounting for operational constraints on the dynamic pressure, Mach number and maximum axial and normal accelerations. The control search space is first explored by the population-based algorithm, which uses a single shooting method to evaluate the performance of candidate solutions. The resultant optimal control law and corresponding trajectory are then further refined by a direct collocation method based on finite elements in time. Two distinct operational phases, one using an air-breathing propulsion mode and the second using rocket propulsion, are considered. The presence of uncertainties in the atmospheric and vehicle aerodynamic models are considered in order to quantify their effect on the performance of the vehicle. Firstly, the deterministic optimal control law is re-integrated after introducing uncertainties into the models. The proximity of the final solutions to the target states are analysed statistically. A second analysis is then performed, aimed at determining the best performance of the vehicle when these uncertainties are included directly in the optimisation. The statistical analysis of the results obtained are summarized by an expectancy curve which represents the probable vehicle performance as a function of the uncertain system parameters. This analysis can be used during the preliminary phase of design to yield valuable insights into the robustness of the performance of the vehicle to uncertainties in the specification of its parameters