Development of a physically-based method for delineation of hydrologically homogeneous regions and flood quantile estimation in ungauged basins via the index flood method

Regional flood frequency techniques are commonly used to estimate flood quantiles when flood data is unavailable or the record length at an individual gauging station is insufficient for reliable analyses. These methods compensate for limited or unavailable data by pooling data from nearby gauged sites. This requires the delineation of hydrologically homogeneous regions in which the flood regime is sufficiently similar to allow the spatial transfer of information. It is generally accepted that hydrologic similarity results from similar physiographic characteristics, and thus these characteristics can be used to delineate regions and classify ungauged sites. However, as currently practiced, the delineation is highly subjective and dependent on the similarity measures and classification techniques employed. A standardized procedure for delineation of hydrologically homogeneous regions is presented herein. Key aspects are a new statistical metric to identify physically discordant sites, and the identification of an appropriate set of physically based measures of extreme hydrological similarity. A combination of multivariate statistical techniques applied to multiple flood statistics and basin characteristics for gauging stations in the Southeastern U.S. revealed that basin slope, elevation, and soil drainage largely determine the extreme hydrological behavior of a watershed. Use of these characteristics as similarity measures in the standardized approach for region delineation yields regions which are more homogeneous and more efficient for quantile estimation at ungauged sites than those delineated using alternative physically-based procedures typically employed in practice. The proposed methods and key physical characteristics are also shown to be efficient for region delineation and quantile development in alternative areas composed of watersheds with statistically different physical composition. In addition, the use of aggregated values of key watershed characteristics was found to be sufficient for the regionalization of flood data; the added time and computational effort required to derive spatially distributed watershed variables does not increase the accuracy of quantile estimators for ungauged sites. This dissertation also presents a methodology by which flood quantile estimates in Haiti can be derived using relationships developed for data rich regions of the U.S. As currently practiced, regional flood frequency techniques can only be applied within the predefined area used for model development. However, results presented herein demonstrate that the regional flood distribution can successfully be extrapolated to areas of similar physical composition located beyond the extent of that used for model development provided differences in precipitation are accounted for and the site in question can be appropriately classified within a delineated region.

Algorithms for spacecraft formation flying navigation based on wireless positioning system measurements

Spacecraft formation flying navigation continues to receive a great deal of interest. The research presented in this dissertation focuses on developing methods for estimating spacecraft absolute and relative positions, assuming measurements of only relative positions using wireless sensors. The implementation of the extended Kalman filter to the spacecraft formation navigation problem results in high estimation errors and instabilities in state estimation at times. This is due tp the high nonlinearities in the system dynamic model. Several approaches are attempted in this dissertation aiming at increasing the estimation stability and improving the estimation accuracy. A differential geometric filter is implemented for spacecraft positions estimation. The differential geometric filter avoids the linearization step (which is always carried out in the extended Kalman filter) through a mathematical transformation that converts the nonlinear system into a linear system. A linear estimator is designed in the linear domain, and then transformed back to the physical domain. This approach demonstrated better estimation stability for spacecraft formation positions estimation, as detailed in this dissertation. The constrained Kalman filter is also implemented for spacecraft formation flying absolute positions estimation. The orbital motion of a spacecraft is characterized by two range extrema (perigee and apogee). At the extremum, the rate of change of a spacecraft’s range vanishes. This motion constraint can be used to improve the position estimation accuracy. The application of the constrained Kalman filter at only two points in the orbit causes filter instability. Two variables are introduced into the constrained Kalman filter to maintain the stability and improve the estimation accuracy. An extended Kalman filter is implemented as a benchmark for comparison with the constrained Kalman filter. Simulation results show that the constrained Kalman filter provides better estimation accuracy as compared with the extended Kalman filter. A Weighted Measurement Fusion Kalman Filter (WMFKF) is proposed in this dissertation. In wireless localizing sensors, a measurement error is proportional to the distance of the signal travels and sensor noise. In this proposed Weighted Measurement Fusion Kalman Filter, the signal traveling time delay is not modeled; however, each measurement is weighted based on the measured signal travel distance. The obtained estimation performance is compared to the standard Kalman filter in two scenarios. The first scenario assumes using a wireless local positioning system in a GPS denied environment. The second scenario assumes the availability of both the wireless local positioning system and GPS measurements. The simulation results show that the WMFKF has similar accuracy performance as the standard Kalman Filter (KF) in the GPS denied environment. However, the WMFKF maintains the position estimation error within its expected error boundary when the WLPS detection range limit is above 30km. In addition, the WMFKF has a better accuracy and stability performance when GPS is available. Also, the computational cost analysis shows that the WMFKF has less computational cost than the standard KF, and the WMFKF has higher ellipsoid error probable percentage than the standard Measurement Fusion method. A method to determine the relative attitudes between three spacecraft is developed. The method requires four direction measurements between the three spacecraft. The simulation results and covariance analysis show that the method’s error falls within a three sigma boundary without exhibiting any singularity issues. A study of the accuracy of the proposed method with respect to the shape of the spacecraft formation is also presented.

VISUAL-INERTIAL INTEGRATION FOR HUMAN MOTION TRACKING AND NAVIGATION IN FREE-LIVING ENVIRONMENTS

The aging population has become a burning issue for all modern societies around the world recently. There are two important issues existing now to be solved. One is how to continuously monitor the movements of those people having suffered a stroke in natural living environment for providing more valuable feedback to guide clinical interventions. The other one is how to guide those old people effectively when they are at home or inside other buildings and to make their life easier and convenient. Therefore, human motion tracking and navigation have been active research fields with the increasing number of elderly people. However, motion capture has been extremely challenging to go beyond laboratory environments and obtain accurate measurements of human physical activity especially in free-living environments, and navigation in free-living environments also poses some problems such as the denied GPS signal and the moving objects commonly presented in free-living environments. This thesis seeks to develop new technologies to enable accurate motion tracking and positioning in free-living environments. This thesis comprises three specific goals using our developed IMU board and the camera from the imaging source company: (1) to develop a robust and real-time orientation algorithm using only the measurements from IMU; (2) to develop a robust distance estimation in static free-living environments to estimate people’s position and navigate people in static free-living environments and simultaneously the scale ambiguity problem, usually appearing in the monocular camera tracking, is solved by integrating the data from the visual and inertial sensors; (3) in case of moving objects viewed by the camera existing in free-living environments, to firstly design a robust scene segmentation algorithm and then respectively estimate the motion of the vIMU system and moving objects. To achieve real-time orientation tracking, an Adaptive-Gain Orientation Filter (AGOF) is proposed in this thesis based on the basic theory of deterministic approach and frequency-based approach using only measurements from the newly developed MARG (Magnet, Angular Rate, and Gravity) sensors. To further obtain robust positioning, an adaptive frame-rate vision-aided IMU system is proposed to develop and implement fast vIMU ego-motion estimation algorithms, where the orientation is estimated in real time from MARG sensors in the first step and then used to estimate the position based on the data from visual and inertial sensors. In case of the moving objects viewed by the camera existing in free-living environments, a robust scene segmentation algorithm is firstly proposed to obtain position estimation and simultaneously the 3D motion of moving objects. Finally, corresponding simulations and experiments have been carried out.

DYNAMIC MODEL BASED STATE ESTIMATION IN A HEAVY DUTY DIESEL AFTERTREATMENT SYSTEM FOR ONBOARD DIAGNOSTICS AND CONTROLS

Estimating un-measurable states is an important component for onboard diagnostics (OBD) and control strategy development in diesel exhaust aftertreatment systems. This research focuses on the development of an Extended Kalman Filter (EKF) based state estimator for two of the main components in a diesel engine aftertreatment system: the Diesel Oxidation Catalyst (DOC) and the Selective Catalytic Reduction (SCR) catalyst. One of the key areas of interest is the performance of these estimators when the catalyzed particulate filter (CPF) is being actively regenerated. In this study, model reduction techniques were developed and used to develop reduced order models from the 1D models used to simulate the DOC and SCR. As a result of order reduction, the number of states in the estimator is reduced from 12 to 1 per element for the DOC and 12 to 2 per element for the SCR. The reduced order models were simulated on the experimental data and compared to the high fidelity model and the experimental data. The results show that the effect of eliminating the heat transfer and mass transfer coefficients are not significant on the performance of the reduced order models. This is shown by an insignificant change in the kinetic parameters between the reduced order and 1D model for simulating the experimental data. An EKF based estimator to estimate the internal states of the DOC and SCR was developed. The DOC and SCR estimators were simulated on the experimental data to show that the estimator provides improved estimation of states compared to a reduced order model. The results showed that using the temperature measurement at the DOC outlet improved the estimates of the CO , NO , NO2 and HC concentrations from the DOC. The SCR estimator was used to evaluate the effect of NH3 and NOX sensors on state estimation quality. Three sensor combinations of NOX sensor only, NH3 sensor only and both NOX and NH3 sensors were evaluated. The NOX only configuration had the worst performance, the NH3 sensor only configuration was in the middle and both the NOX and NH3 sensor combination provided the best performance.

Energy harvesting from body motion using rotational micro-generation

Autonomous system applications are typically limited by the power supply operational lifetime when battery replacement is difficult or costly. A trade-off between battery size and battery life is usually calculated to determine the device capability and lifespan. As a result, energy harvesting research has gained importance as society searches for alternative energy sources for power generation. For instance, energy harvesting has been a proven alternative for powering solar-based calculators and self-winding wristwatches. Thus, the use of energy harvesting technology can make it possible to assist or replace batteries for portable, wearable, or surgically-implantable autonomous systems. Applications such as cardiac pacemakers or electrical stimulation applications can benefit from this approach since the number of surgeries for battery replacement can be reduced or eliminated. Research on energy scavenging from body motion has been investigated to evaluate the feasibility of powering wearable or implantable systems. Energy from walking has been previously extracted using generators placed on shoes, backpacks, and knee braces while producing power levels ranging from milliwatts to watts. The research presented in this paper examines the available power from walking and running at several body locations. The ankle, knee, hip, chest, wrist, elbow, upper arm, side of the head, and back of the head were the chosen target localizations. Joints were preferred since they experience the most drastic acceleration changes. For this, a motor-driven treadmill test was performed on 11 healthy individuals at several walking (1-4 mph) and running (2-5 mph) speeds. The treadmill test provided the acceleration magnitudes from the listed body locations. Power can be estimated from the treadmill evaluation since it is proportional to the acceleration and frequency of occurrence. Available power output from walking was determined to be greater than 1mW/cm³ for most body locations while being over 10mW/cm³ at the foot and ankle locations. Available power from running was found to be almost 10 times higher than that from walking. Most energy harvester topologies use linear generator approaches that are well suited to fixed-frequency vibrations with sub-millimeter amplitude oscillations. In contrast, body motion is characterized with a wide frequency spectrum and larger amplitudes. A generator prototype based on self-winding wristwatches is deemed to be appropriate for harvesting body motion since it is not limited to operate at fixed-frequencies or restricted displacements. Electromagnetic generation is typically favored because of its slightly higher power output per unit volume. Then, a nonharmonic oscillating rotational energy scavenger prototype is proposed to harness body motion. The electromagnetic generator follows the approach from small wind turbine designs that overcome the lack of a gearbox by using a larger number of coil and magnets arrangements. The device presented here is composed of a rotor with multiple-pole permanent magnets having an eccentric weight and a stator composed of stacked planar coils. The rotor oscillations induce a voltage on the planar coil due to the eccentric mass unbalance produced by body motion. A meso-scale prototype device was then built and evaluated for energy generation. The meso-scale casing and rotor were constructed on PMMA with the help of a CNC mill machine. Commercially available discrete magnets were encased in a 25mm rotor. Commercial copper-coated polyimide film was employed to manufacture the planar coils using MEMS fabrication processes. Jewel bearings were used to finalize the arrangement. The prototypes were also tested at the listed body locations. A meso-scale generator with a 2-layer coil was capable to extract up to 234 µW of power at the ankle while walking at 3mph with a 2cm³ prototype for a power density of 117 µW/cm³. This dissertation presents the analysis of available power from walking and running at different speeds and the development of an unobtrusive miniature energy harvesting generator for body motion. Power generation indicates the possibility of powering devices by extracting energy from body motion.

Future value based single assignment program representations and optimizations

An optimizing compiler internal representation fundamentally affects the clarity, efficiency and feasibility of optimization algorithms employed by the compiler. Static Single Assignment (SSA) as a state-of-the-art program representation has great advantages though still can be improved. This dissertation explores the domain of single assignment beyond SSA, and presents two novel program representations: Future Gated Single Assignment (FGSA) and Recursive Future Predicated Form (RFPF). Both FGSA and RFPF embed control flow and data flow information, enabling efficient traversal program information and thus leading to better and simpler optimizations. We introduce future value concept, the designing base of both FGSA and RFPF, which permits a consumer instruction to be encountered before the producer of its source operand(s) in a control flow setting. We show that FGSA is efficiently computable by using a series T1/T2/TR transformation, yielding an expected linear time algorithm for combining together the construction of the pruned single assignment form and live analysis for both reducible and irreducible graphs. As a result, the approach results in an average reduction of 7.7%, with a maximum of 67% in the number of gating functions compared to the pruned SSA form on the SPEC2000 benchmark suite. We present a solid and near optimal framework to perform inverse transformation from single assignment programs. We demonstrate the importance of unrestricted code motion and present RFPF. We develop algorithms which enable instruction movement in acyclic, as well as cyclic regions, and show the ease to perform optimizations such as Partial Redundancy Elimination on RFPF.

Comparisons between OMI SO2 data and ground-based SO2 measurements at Turrialba volcano

Turrialba is one of the largest and most active stratovolcanoes in the Central Cordillera of Costa Rica and an excellent target for validation of satellite data using ground based measurements due to its high elevation, relative ease of access, and persistent elevated SO2 degassing. The Ozone Monitoring Instrument (OMI) aboard the Aura satellite makes daily global observations of atmospheric trace gases and it is used in this investigation to obtain volcanic SO2 retrievals in the Turrialba volcanic plume. We present and evaluate the relative accuracy of two OMI SO2 data analysis procedures, the automatic Band Residual Index (BRI) technique and the manual Normalized Cloud-mass (NCM) method. We find a linear correlation and good quantitative agreement between SO2 burdens derived from the BRI and NCM techniques, with an improved correlation when wet season data are excluded. We also present the first comparisons between volcanic SO2 emission rates obtained from ground-based mini-DOAS measurements at Turrialba and three new OMI SO2 data analysis techniques: the MODIS smoke estimation, OMI SO2 lifetime, and OMI SO2 transect techniques. A robust validation of OMI SO2 retrievals was made, with both qualitative and quantitative agreements under specific atmospheric conditions, proving the utility of satellite measurements for estimating accurate SO2 emission rates and monitoring passively degassing volcanoes.

Parameter estimation for transformer modeling

Large Power transformers, an aging and vulnerable part of our energy infrastructure, are at choke points in the grid and are key to reliability and security. Damage or destruction due to vandalism, misoperation, or other unexpected events is of great concern, given replacement costs upward of $2M and lead time of 12 months. Transient overvoltages can cause great damage and there is much interest in improving computer simulation models to correctly predict and avoid the consequences. EMTP (the Electromagnetic Transients Program) has been developed for computer simulation of power system transients. Component models for most equipment have been developed and benchmarked. Power transformers would appear to be simple. However, due to their nonlinear and frequency-dependent behaviors, they can be one of the most complex system components to model. It is imperative that the applied models be appropriate for the range of frequencies and excitation levels that the system experiences. Thus, transformer modeling is not a mature field and newer improved models must be made available. In this work, improved topologically-correct duality-based models are developed for three-phase autotransformers having five-legged, three-legged, and shell-form cores. The main problem in the implementation of detailed models is the lack of complete and reliable data, as no international standard suggests how to measure and calculate parameters. Therefore, parameter estimation methods are developed here to determine the parameters of a given model in cases where available information is incomplete. The transformer nameplate data is required and relative physical dimensions of the core are estimated. The models include a separate representation of each segment of the core, including hysteresis of the core, λ-i saturation characteristic, capacitive effects, and frequency dependency of winding resistance and core loss. Steady-state excitation, and de-energization and re-energization transients are simulated and compared with an earlier-developed BCTRAN-based model. Black start energization cases are also simulated as a means of model evaluation and compared with actual event records. The simulated results using the model developed here are reasonable and more correct than those of the BCTRAN-based model. Simulation accuracy is dependent on the accuracy of the equipment model and its parameters. This work is significant in that it advances existing parameter estimation methods in cases where the available data and measurements are incomplete. The accuracy of EMTP simulation for power systems including three-phase autotransformers is thus enhanced. Theoretical results obtained from this work provide a sound foundation for development of transformer parameter estimation methods using engineering optimization. In addition, it should be possible to refine which information and measurement data are necessary for complete duality-based transformer models. To further refine and develop the models and transformer parameter estimation methods developed here, iterative full-scale laboratory tests using high-voltage and high-power three-phase transformer would be helpful.

Estimation of vertical groundwater fluxes into a streambed through continuous temperature profile monitoring and the relationship of groundwater fluxes to coaster brook trout spawning habitat

We hypothesized that the spatial distribution of groundwater inflows through river bottom sediments is a critical factor associated with the selection of coaster brook trout (a life history variant of Salvelinus fontinalis,) spawning sites. An 80-m reach of the Salmon Trout River, in the Huron Mountains of the upper peninsula of Michigan, was selected to test the hypothesis based on long-term documentation of coaster brook trout spawning at this site. Throughout this site, the river is relatively similar along its length with regard to stream channel and substrate features. A monitoring well system consisting of an array of 27 wells was installed to measure subsurface temperatures underneath the riverbed over a 13-month period. The monitoring well locations were separated into areas where spawning has and has not been observed. Over 200,000 total temperature measurements were collected from 5 depths within each of the 27 monitoring wells. Temperatures within the substrate at the spawning area were generally cooler and less variable than river temperatures. Substrate temperatures in the non-spawning area were generally warmer, more variable, and closely tracked temporal variations in river temperatures. Temperature data were inverted to obtain subsurface groundwater velocities using a numerical approximation of the heat transfer equation. Approximately 45,000 estimates of groundwater velocities were obtained. Estimated velocities in the spawning and non-spawning areas confirmed that groundwater velocities in the spawning area were primarily in the upward direction, and were generally greater in magnitude than velocities in the non-spawning area. In the non-spawning area there was a greater occurrence of velocities in the downward direction, and velocity estimates were generally lesser in magnitude than in the spawning area. Both the temperature and velocity results confirm the hypothesis that spawning sites correspond to areas of significant groundwater influx to the river bed.

High precision range estimation techniques for multi-path wireless environments

Range estimation is the core of many positioning systems such as radar, and Wireless Local Positioning Systems (WLPS). The estimation of range is achieved by estimating Time-of-Arrival (TOA). TOA represents the signal propagation delay between a transmitter and a receiver. Thus, error in TOA estimation causes degradation in range estimation performance. In wireless environments, noise, multipath, and limited bandwidth reduce TOA estimation performance. TOA estimation algorithms that are designed for wireless environments aim to improve the TOA estimation performance by mitigating the effect of closely spaced paths in practical (positive) signal-to-noise ratio (SNR) regions. Limited bandwidth avoids the discrimination of closely spaced paths. This reduces TOA estimation performance. TOA estimation methods are evaluated as a function of SNR, bandwidth, and the number of reflections in multipath wireless environments, as well as their complexity. In this research, a TOA estimation technique based on Blind signal Separation (BSS) is proposed. This frequency domain method estimates TOA in wireless multipath environments for a given signal bandwidth. The structure of the proposed technique is presented and its complexity and performance are theoretically evaluated. It is depicted that the proposed method is not sensitive to SNR, number of reflections, and bandwidth. In general, as bandwidth increases, TOA estimation performance improves. However, spectrum is the most valuable resource in wireless systems and usually a large portion of spectrum to support high performance TOA estimation is not available. In addition, the radio frequency (RF) components of wideband systems suffer from high cost and complexity. Thus, a novel, multiband positioning structure is proposed. The proposed technique uses the available (non-contiguous) bands to support high performance TOA estimation. This system incorporates the capabilities of cognitive radio (CR) systems to sense the available spectrum (also called white spaces) and to incorporate white spaces for high-performance localization. First, contiguous bands that are divided into several non-equal, narrow sub-bands that possess the same SNR are concatenated to attain an accuracy corresponding to the equivalent full band. Two radio architectures are proposed and investigated: the signal is transmitted over available spectrum either simultaneously (parallel concatenation) or sequentially (serial concatenation). Low complexity radio designs that handle the concatenation process sequentially and in parallel are introduced. Different TOA estimation algorithms that are applicable to multiband scenarios are studied and their performance is theoretically evaluated and compared to simulations. Next, the results are extended to non-contiguous, non-equal sub-bands with the same SNR. These are more realistic assumptions in practical systems. The performance and complexity of the proposed technique is investigated as well. This study’s results show that selecting bandwidth, center frequency, and SNR levels for each sub-band can adapt positioning accuracy.

HIGH PERFORMANCE, LOW COST SUBSPACE DECOMPOSITION AND POLYNOMIAL ROOTING FOR REAL TIME DIRECTION OF ARRIVAL ESTIMATION: ANALYSIS AND IMPLEMENTATION

This thesis develops high performance real-time signal processing modules for direction of arrival (DOA) estimation for localization systems. It proposes highly parallel algorithms for performing subspace decomposition and polynomial rooting, which are otherwise traditionally implemented using sequential algorithms. The proposed algorithms address the emerging need for real-time localization for a wide range of applications. As the antenna array size increases, the complexity of signal processing algorithms increases, making it increasingly difficult to satisfy the real-time constraints. This thesis addresses real-time implementation by proposing parallel algorithms, that maintain considerable improvement over traditional algorithms, especially for systems with larger number of antenna array elements. Singular value decomposition (SVD) and polynomial rooting are two computationally complex steps and act as the bottleneck to achieving real-time performance. The proposed algorithms are suitable for implementation on field programmable gated arrays (FPGAs), single instruction multiple data (SIMD) hardware or application specific integrated chips (ASICs), which offer large number of processing elements that can be exploited for parallel processing. The designs proposed in this thesis are modular, easily expandable and easy to implement. Firstly, this thesis proposes a fast converging SVD algorithm. The proposed method reduces the number of iterations it takes to converge to correct singular values, thus achieving closer to real-time performance. A general algorithm and a modular system design are provided making it easy for designers to replicate and extend the design to larger matrix sizes. Moreover, the method is highly parallel, which can be exploited in various hardware platforms mentioned earlier. A fixed point implementation of proposed SVD algorithm is presented. The FPGA design is pipelined to the maximum extent to increase the maximum achievable frequency of operation. The system was developed with the objective of achieving high throughput. Various modern cores available in FPGAs were used to maximize the performance and details of these modules are presented in detail. Finally, a parallel polynomial rooting technique based on Newton’s method applicable exclusively to root-MUSIC polynomials is proposed. Unique characteristics of root-MUSIC polynomial’s complex dynamics were exploited to derive this polynomial rooting method. The technique exhibits parallelism and converges to the desired root within fixed number of iterations, making this suitable for polynomial rooting of large degree polynomials. We believe this is the first time that complex dynamics of root-MUSIC polynomial were analyzed to propose an algorithm. In all, the thesis addresses two major bottlenecks in a direction of arrival estimation system, by providing simple, high throughput, parallel algorithms.

RAPID SPACE TRAJECTORY GENERATION USING A FOURIER SERIES SHAPE-BASED APPROACH

With the insatiable curiosity of human beings to explore the universe and our solar system, it is essential to benefit from larger propulsion capabilities to execute efficient transfers and carry more scientific equipment. In the field of space trajectory optimization the fundamental advances in using low-thrust propulsion and exploiting the multi-body dynamics has played pivotal role in designing efficient space mission trajectories. The former provides larger cumulative momentum change in comparison with the conventional chemical propulsion whereas the latter results in almost ballistic trajectories with negligible amount of propellant. However, the problem of space trajectory design translates into an optimal control problem which is, in general, time-consuming and very difficult to solve. Therefore, the goal of the thesis is to address the above problem by developing a methodology to simplify and facilitate the process of finding initial low-thrust trajectories in both two-body and multi-body environments. This initial solution will not only provide mission designers with a better understanding of the problem and solution but also serves as a good initial guess for high-fidelity optimal control solvers and increases their convergence rate. Almost all of the high-fidelity solvers enjoy the existence of an initial guess that already satisfies the equations of motion and some of the most important constraints. Despite the nonlinear nature of the problem, it is sought to find a robust technique for a wide range of typical low-thrust transfers with reduced computational intensity. Another important aspect of our developed methodology is the representation of low-thrust trajectories by Fourier series with which the number of design variables reduces significantly. Emphasis is given on simplifying the equations of motion to the possible extent and avoid approximating the controls. These facts contribute to speeding up the solution finding procedure. Several example applications of two and three-dimensional two-body low-thrust transfers are considered. In addition, in the multi-body dynamic, and in particular the restricted-three-body dynamic, several Earth-to-Moon low-thrust transfers are investigated.