1,720,952 research outputs found
Hybrid optimization of low-thrust many-revolution trajectories with coasting arcs and longitude targeting for propellant minimization
No full textDespite the ongoing advancements in low-thrust propulsion technology and the rise of all-electric satellite platforms, low-thrust spacecraft trajectory optimization remains a complex field of research. Shape-based approximations are predominant in interplanetary applications, but they are generally unsuitable for many-revolution trajectories, common in terrestrial applications. Indirect optimization methods allow for global optimization of many-revolution trajectories, but their mathematical complexity generally requires significant simplifications of the dynamical model, and they must be re-derived for any modification to the system dynamics or constraints. Conversely, direct optimization methods exhibit larger convergence radii and are flexible for application in different problems yet suffer from impractical computational times due to large design vectors. This paper presents a methodology for the optimization of low-thrust many-revolution trajectories, employing a hybrid combination of indirect and direct optimization methods. Similar hybrid approaches have been shown to be highly reliable for minimum-time trajectories. This methodology preserves similar performance while additionally enabling minimum-propellant optimization, through a mechanism that allows for coasting (non-thrusting) arcs, as well as targeting of the final geodetic-longitude. To reduce the propagation load of the methodology, we combine an orbital averaging scheme with a differential evolution algorithm, leading to a global optimization process with a practical computational effort. The analytical nature of the methodology reduces the number of optimization variables and its computational counterpart provides unmatchable flexibility for a configurable force and perturbation model as well as operational constraints fulfilment. The approach is applied to an unperturbed and a J2-perturbed GTO-GEO transfer, revealing a 0.03% and a 0.4% error, for time- and propellant-minimization respectively, relative to the reference optimal trajectories. This proves that the method can match the performance of former hybrid approaches while additionally allowing for engine on/off switching. Moreover, the inclusion of the J2 perturbation shows that, in contrast to indirect methods, it can accommodate modifications to the system dynamics without the need to re-derive the optimal control laws. Furthermore, a superior convergence radius of the optimization problem is demonstrated for the hybrid method, with respect to a reference indirect method, through the simultaneous optimization for minimum-propellant expenditure and final geodetic-longitude targeting. This research constitutes a significant advancement for space mission design and satellite operations, because it simultaneously harnesses the advantages of indirect and direct methods with broader flexibility than the popular indirect approaches and enhanced functionality than the former hybrid methods published in literature.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Astrodynamics & Space Mission
Hybrid Optimization of Low-Thrust Many-Revolution Trajectories with Coasting Arcs and Longitude Targeting for Propellant Minimization
No full textElectric Propulsion (EP) has become one of the most efficient technologies for spacecraft propulsion. In contrast to conventional chemical propulsion, the low thrust force generated by EP thrusters can deliver a momentum transfer to the spacecraft that is up to twenty times greater, for an equivalent propellant expenditure. Despite decades of heritage, the topic of low-thrust spacecraft trajectory optimization remains an active field of research, with many approaches available yet much room for improvement. This MSc thesis presents the development of a novel methodology for low-thrust many-revolution trajectory optimization. It employs the state-of-the-art hybrid technique to harness the strengths of both indirect and direct optimization methods. Its indirect nature efficiently reduces the number of optimization variables and its direct counterpart provides an unmatchable flexibility in terms of a configurable force and perturbation model as well as operational constraints handling. This methodology was already shown in literature to be highly reliable for minimum-time trajectories. The research hereby presented maintains these results while enabling it to optimize minimum-propellant trajectories through a mechanism that allows for coasting (non-thrusting) arcs. This approach is additionally combined with an orbital averaging scheme to reduce the propagation load at the expense of accuracy for the rapidly changing variables. Nonetheless, it retains the continuous integration scheme to enable final geodetic longitude targeting in combination with propellant-minimization, which the former hybrid methodologies were incapable of solving for. The trajectory simulator is coupled with an enhanced objective function that reduces the user fine-tuning effort, and with a differential evolution algorithm that leads to a flexible global optimization process with a practical computational effort.This research is the outcome of the cooperation between the author, Delft University of Technology, and GMV Innovating Solutions, a technology business group with a strong leadership in space engineering. The specific interest of application of this research lies in many-revolution planetocentric trajectories, such as an orbital transfer to Geostationary Earth Orbit, where there are growing market opportunities for all-electric satellite platforms. The resulting software, integrated as part of GMV's Flight Dynamics solution, allows the user to include orbital perturbations and perform a multi-objective optimization with respect to time-of-flight, propellant expenditure, and final geodetic longitude. This research constitutes a quantum leap for the hybrid optimization method because it shows that its accuracy in propellant-minimization is comparable to the analytical global optima despite the simplified co-state dynamics. Furthermore, it is a significant advancement for space mission design and satellite operations because it demonstrates the superior convergence performance of the hybrid methodology relative to GMV's implementation of the indirect approach, particularly in complex problems that combine multiple optimization objectives with varied orbital perturbations and operational constraints fulfillment.Aerospace Engineerin
The Compaction of Moondust: A Combined Gravity and Light Polarisation Study of Lunar Regolith
No full textThe Moon is covered by a blanket of rock fragments and loosely bound dust particles called regolith. This layer is key in deciphering the evolution of the Moon and the terrestrial planets, including Earth. It is also a protagonist in the return of humanity to the Moon after its last visit over half a century ago. The main concern for lunar regolith studies is the determination of compactness. Compactness may be expressed as porosity and can be determined by the discrepancy between bulk density estimates from the gravity field and grain density estimates from material composition. New state-of-the-art gravity models of the Moon allow for small-scale gravity studies of regolith porosity, which have resulted in better understanding of the Moon's thermal evolution. However, regional variations in compactness are currently poorly known due to the ambiguous nature of gravity data. Ideally, an additional information source is desired to provide constraints on regolith compaction. It might be that the amount of reflected sunlight from the lunar surface provides additional constraints on regolith compactness. For example, incident light can enter a more porous material deeper, increasing the probability of absorption and decreasing the amount of reflected light. Therefore, this thesis will explore the scattering behaviour of reflected sunlight from the lunar surface as a potential additional information source.Aerospace Engineerin
Mars Surface Stress Modelling: Investigation on the crustal structure of Mars with Finite Element Method
No full textMars has been a target for space exploration for decades. Exploring the interior of the red planet could reveal information about its formation and evolution. In this thesis, the crustal structure of Mars is investigated by a power spectra analysis of both topographic and gravitational data. With models of flexural isostasy, the best-fitting lithospheric (crust + uppermost mantle) thickness is found to be between 136 km and 158 km globally. Possible values for the thickness of the lithosphere range from 120 km to 580 km. In addition, a 3D flat Finite Element Method (FEM) model is created for Mars. The FEM Mars model incorporates the above-mentioned crustal profiles and calculates the surface stresses in the regions of interest. The calculated stresses are compared to observed faults in Tharsis, Hellas, and Utopia to reveal information about the evolution of these regions.Aerospace Engineerin
Validating and improving the orbit determination of Cryosat-2
No full textThe Cryosat-2 mission is an European Space Agency mission with the main objective to measure and monitor the variation in sea-ice and main ice sheets on Earth, located at Greenland and Antarctic. The satellite's main instrument is a state of the art altimeter, which can measure the distance between the satellite and the ice surface with extreme accuracy. To extract the variation in height of the ice surfaces from these measurements, it is important to know where the satellite was at the time of the measurements. The method that is used to obtain this is called Precise Orbit Determination (POD). POD combines accurate measurements together with physical models related to the satellite, in such a way that it can determine accurate orbit solutions for the satellite. This report is a discussion about the validation and improvement of the orbit determination of the Cryosat-2 mission. The current orbit determination process that is available is validated on three different subjects. First, a new data format for Satellite Laser Ranging (SLR) measurements was investigated, which is called the Consolidated Ranging Data format. SLR measurements are accurate range measurements that are used to validate the orbit of Cryosat-2. A converter is written that could convert the new data format, in such a way that the current orbit determination software could use it. Several features of the new data format were examined, for potential improvements. The second investigation was about the generation of the Doris beacon coordinates and their effect on the POD. The Doris system is the main orbit determination system onboard the satellite. Due to different abrupt and slow motions of the Earth surface, the Doris beacons moves with respect to the defined reference frame. A new definition of the Doris beacon coordinates, called DPOD2008, is used in the Cryosat-2 orbit estimation. The solution of the coordinates sets were validated and other coordinate sets were used, to conclude that DPOD2008 was generating the best orbit solution for Cryosat-2. The final investigation was on the solar radiation pressure modeling of Cryosat-2. Currently, a 6-panel box model is used as defined by ESA. In the empirical residual accelerations a signal is visible which has correlation with the solar radiation pressure. It was decided to use micro models generated by the University College London at the research group of Prof. Marek Ziebart for the solar radiation pressure computations. Two micro models are constructed, although the implementation of the UCL models in the GEODYN software is delivering unsuspected results. Several bugs are fixed or bypassed in the implementation of the models, but still clear differences between the internal GEODYN model and the UCL model implementation are visible. Recommendations are given for further research in the micro model investigation for the solar radiation pressure computation.Astrodynamics & Space MissionsSpace EngineeringAerospace Engineerin
Portable Doppler Tracking Ground Station
No full textThis thesis analyses the possibility of creating a portable Doppler tracking ground station using commercial of the shelf components. This solution is called DopTrackBox and is based on TU Delft’s DopTrack. This system uses the Doppler shift of radio signals received from satellites to analyse their location and velocity. Different experiments were conducted to analyse the effects of various hardware components on the system. From the experiments can be concluded that the most impactful hardware change is switching from an omnidirectional antenna to a manually pointed directional one, as this introduces more variance to the system. When using the same omnidirectional antennas as DopTrack, DopTrackBox performs on par with the bigger system; achieving a higher SNR and lower range rate differences. More research is needed to look into the specific effects of the GPS clock and different SDR.Aerospace Engineering | Space FlightAerospace Engineering | Space Exploratio
Sensor Fusion in Autonomous Navigation for Asteroid Observation Missions
No full textSpacecraft navigation and control is difficult in deep space operations. Especially around asteroids, the irregular gravity field increases the difficulty of estimating the spacecraft trajectory. Autonomous navigation can increase the safety and accuracy for orbit proximity operations. Furthermore, it eliminates the need for continuous communication with the spacecraft. For the implementation of autonomous navigation in deep space, the onboard guidance navigation & control (GNC) should be able to accurately estimate the attitude and relative position of the spacecraft. By using sensor fusion, information from individual sensors can be combined to increase certainty and accuracy of the state estimation. A sensor fusion model is proposed, comprising an inertial measurement unit (IMU), star tracker and light detection and ranging (LiDAR) as navigation sensors. The aim of this research is to investigate the feasibility and performance applying sensor fusion for the spacecraft state estimation.A navigation filter is applied to a benchmark scenario that orbits an asteroid at 50 km. In this scenario, asteroid 433 Eros has been selected for its unique shape, which has been mapped during the Near Earth Asteroid Rendezvous (NEAR) mission. A simulation is performed to approximate the dynamics and kinematics of the mission environment. The simulation takes a polyhedron model of the asteroid, a third-body disturbance by the sun, and an additional acceleration due to solar radiation pressure into account. The simulation forms a base for the sensor measurement simulation. As the IMU consists of an accelerometer and a gyroscope, the measurements total to two sets of available data for position as well as attitude estimation.The navigation filter estimates the position, velocity, attitude and gravitational constant of the asteroid, by use of an extended Kalman filter (EKF). The EKF is augmented for the quaternion states to a multiplicative extended Kalman filter. The navigation filter is simulated for a benchmark scenario, as well as for different orbital heights and temporary loss of the star tracker as well as the LiDAR sensor.As a result, it is concluded that it is feasible with the given sensor set to approximate the position and attitude of a spacecraft in proximity of 433 Eros. For the position, a root-meansquare error (RMSE) of 0.5 m is found at an orbital height of 50 km. Using a time step of 0.1 s for the EKF is recommended after a trade-off between accuracy and computational time. It is concluded that the proposed model for state estimation is sufficiently accurate for position and attitude estimation for the given benchmark scenario. With this navigation filter, we come one step closer to the development of autonomous navigation for asteroid observing spacecraft.Mechanical Engineering | Systems and Contro
Seismic analysis of Mars using gravitational potential stresses - InSight
No full textThe 26th of November 2018, NASA's InSight mission successfully landed on Mars. InSight has a seismometer on board with as main science goal to determine the current level of seismic activity and the impact rate of meteorites on Mars. To process the incoming data of InSight as fast and efficient as possible, a-priori models of seismicity on Mars are needed. This thesis work consists out of making such models by using gravitational potential theory. Multiple interior density models of mars (crust and upper mantle) are created by use of isostatic assumptions, the Bouguer gravity or derived from literature. For each model, gravitational potential stresses are calculated which can be compared to the yield stress of the Martian lithosphere. Conclusions about the most likely sources of seismicity of Mars for varying interior density models are made.Aerospace Engineerin
Comparing global tomography-derived and gravity-based upper mantle density models
No full textCurrent seismic tomography models show a complex environment underneath the crust, corroborated by high-precision satellite gravity observations. Both data sets are used to independently explore the density structure of the upper mantle. However, combining these two data sets proves to be challenging. The gravity-data has an inherent insensitivity in the radial direction and seismic tomography has a heterogeneous data acquisition, resulting in smoothed tomography models with de-correlation between different models for the mid-to-small wavelength features. Therefore, this study aims to assess and quantify the effect of regularization on a seismic tomography model by exploiting the high lateral sensitivity of gravity data. Seismic tomography models, SL2013sv, SAVANI, SMEAN2 and S40RTS are compared to a gravity-based density model of the upper mantle. In order to obtain similar density solutions compared to the seismic-derived models, the gravity-based model needs to be smoothed with a Gaussian filter. Different smoothening characteristics are observed for the variety of seismic tomography models, relating to the regularization approach in the inversions. Various S40RTS models with similar seismic data but different regularization settings show that the smoothening effect is stronger with increasing regularization. The type of regularization has a dominant effect on the final tomography solution. To reduce the effect of regularization on the tomographymodels, an enhancement procedure is proposed. This enhancement should be performed within the spectral domain of the actual resolution of the seismic tomography model. The enhanced seismic tomography models show improved spatial correlationwith each other and with the gravity-based model. The variation of the density anomalies have similar peak-to-peak magnitudes and clear correlation to geological structures. The resolvement of the spectral misalignment between tomographic models and gravity-based solutions is the first step in the improvement of multidata inversion studies of the upper mantle and benefit from the advantages in both data sets.Astrodynamics & Space Mission
Gravity Field Constraints on the Upper Mantle of Northwestern Europe
No full textIn the last decade, the gravity field of the Earth has been observed with increased coverage due to dedicated satellite missions, which resulted in higher resolution and more accurate global gravity field models than were previously available. These models make it possible to study large scale processes such as solid Earth deformation after large loading events such as retreat of ice sheets or to study lateral density variation in the lithospheric part of the upper mantle. However, to use the gravity data successfully, unwanted signal needs to be removed in order to extract the information of interest. For example, with lithosphere studies the gravity signal coming from the crust and the deep mantle needs to be removed. This is commonly done by filtering out long-wavelength signals from the solution to remove deep mantle effects, and by removing the crustal signal by forward modelling seismic-derived crustal models. With improved models of crustal structure and more accurate gravity data, new information about the upper mantle and lithosphere can be obtained. Adopting the increased resolution and accuracy of the global gravity field models, I have developed new approaches that focus on spectral analysis of the gravity field, which result in new insights of the upper mantle.The forward gravity field modelling method that I improve upon in this dissertation is mostly used for topographic/isostatic mass reduction of gravity data. The methodology is able to transform density-models into gravitational potential fields using a spherical harmonic representation. I show that this methodology in the existing form is not suited to be used for density layers in lower crustal and upper mantle regions. The binomial series inherent to this methodology do not converge when applied to deep mass structures, and therefore it is not possible to truncate the series at a low degree to approximate the mass. This approximation is crucial for the computational efficiency of the methodology. I propose a correction that mitigates this erroneous behaviour, which enables this methodology to efficiently compute the potential field of deep situated masses. I benchmark the improved methodology with a tesseroid-based gravity-field modelling software, and I show that my software is accurate within ±4 mGal, when modelling the Moho density interface (with a range in signal of ±500 mGal. The improved methodology is used in the studies described in this thesis.With an efficient and accurate forward modelling methodology, I am able to use global gravity field data in studies of the solid Earth. In the central part of Fennoscandia the crust is currently uplifting, because of the delayed response of the viscous mantle to melting of the regional Late Pleistocene ice sheet. This process, called glacial isostatic adjustment (GIA), causes a negative anomaly in the present-day static gravity field as isostatic equilibrium has not been reached yet. Several studies have used this anomaly as a constraint on models of GIA, but the uncertainty in crustal and upper mantle structures had not been properly taken into account. In revisiting this problem, I show that the GIA gravity signal overlaps with mantle convection signals, such that a simple spherical harmonic truncation is not sufficient to separate these two phenomena. Furthermore, I find that, in contrast to the other studies, the effect of crustal anomalies on the gravity field cannot be effectively removed, because of the relative large uncertainties in the crustal density models. Therefore, I propose to correct the observed gravity field for GIA with numerical modelling results when constructing geophysical models that assume isostatic equilibrium. I show that correcting for GIA results in a significant vertical readjustment of the geometry of structural layers in the modelled crust of 5-10 percent. Correcting the gravity field for GIA prior to assuming isostatic equilibrium might be relevant in other areas with ongoing post-glacial rebound such as North America and the polar regions. Uncertainty in lithospheric density models is still the limiting factors in solid Earth studies and needs to be improved. Lithospheric density anomalies can, among other methods, be estimated from seismic tomography, gravity studies, or joint studies using both datasets. I compare different gravity-based density models of the lithosphere to a tomographic-derived solution and characterise the sources that introduce large uncertainties in the density models of the lithosphere. To study the uncertainty between global and regional crustal models, I select a region where the crust is explored in great measure with seismic profiles, namely the British Isles and surrounding areas, where I use three crustal models to quantify the crustal uncertainty: CRUST1.0, EUCrust-07, and a high-resolution regional P-wave velocity model of the region. The crustal models contribute to the uncertainty of the density of the lithosphere with ±110 kg/m3. Furthermore, I study various P-wave velocity-to-density conversions to quantify the uncertainty introduced by these conversion methods (±10 kg/m3. All different crustal density models are forward modelled into gravity anomalies using the improved methodology of Chapter 2 and these gravity anomalies are subsequently removed from the gravity observations. The unmodelled long-wavelength signal in the gravity field representing mass anomalies in the deep mantle are removed from the observation by spherical harmonic truncation, introducing an uncertainty of ±5 kg/m3. Also, the choice of density background model (±20 kg/m3) and lithosphere-asthenosphere boundary uncertainty (±30 kg/m3) have a small but significant effect on the estimated lithosphere densities. However, the inhomogeneous spatial distribution of profiles of controlled-source seismic exploration of the crustal thickness and density distribution proves to be the largest source of uncertainty (±110 kg/m3). The gravity-based lithospheric density solutions with a variation of ±100 kg/m3 are completely different in magnitude and spatial signature to the densities (±35 kg/m3) derived from a shear wave velocity model. This demonstrates that the tomographic model has a limited resolution, which can be related to regularisation that is used in the construction of global tomographic models. To account for this spectral imbalance, I spatially filter the gravity-based density models, resulting in similarities in spatial correlation and magnitude between that of the gravity-based and the tomographic-derived density. With the filtered gravity-based density I am able to estimate lateral varying conversion values between shear wave velocity and density for the lithosphere, which shows a correlation with major tectonic regions. This correlation shows that the independent gravity-based solutions, despite being filtered, can help in identifying different compositional domains in the lithosphere.Satellite observations also provide global data on the temporal variations of the gravity field. In the last study, I show that global gravity-change observations from the GRACE satellite mission can be used to study GIA in the Barents Sea Region. The Barents Sea is subject to ongoing postglacial uplift since the melting of the Weichselian ice sheet that covered this region. The deglaciation history is not well known because there is only data from locations close to the boundary of the former ice sheet, in Franz Joseph Land, Svalbard, and Novaya Zemlya. At these locations the magnitude of the GIA uplift is limited, reducing the signal-to-noise of the data. The GRACE mission measures the gravity-change due to GIA at the center of the Barents Sea, where the maximum uplift and ongoing gravity-change is situated. I show that the linear trend in the gravity-change derived from a decade of observations from the GRACE satellite mission can constrain the volume of the ice sheet after correcting for current ice-melt, hydrology and far-field gravitational effects. Regional ice loading models based on new geologically-inferred ice margin chronologies show a significantly better fit to the GRACE data than the global ice models ICE-5G and ICE-6G_C. The regional ice models in this study contain less ice mass during LGM in the Barents Sea than ICE-5G (5-6.3 m equivalent sea level vs. 8.5 m). Also, I show that the GRACE gravity-change is sensitive to the upper mantle viscosity underneath the Barents sea, for which I found a minimum value of 4x1020 Pas, regardless of the ice loading history. The GRACE gravity-change should be used as a constraint in any future GIA modelling of the Barents Sea, because it is the only measurement that captures the signal of maximum GIA.The high resolution and accurate global gravity field models do give new insights in the structure and density distribution of the upper mantle. The presented studies in this dissertation demonstrate that analysing the spectral signature of gravity data is very useful. Medium-to-short-scale features, like lateral density variation in the lithosphere and GIA gravity-change in the Barents Sea can be separate from other gravity-change sources by applying spectral filters. For longer wavelength signals, such as the GIA static gravity signal in Fennoscandia, this proves to be more difficult due to the overlap in the long-wavelength region by mantle convection signals and other deep mantle signals. On the whole, the global gravity field models and their spectral signature play an important part in building a global density model of the Earth, in which lithosphere, GIA, but also mantle convection and core-mantle boundary effects need to be combined to explain the gravity field.Astrodynamics & Space Mission
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