This paper presents the development of a robust sizing method to efficiently estimate and compare key performance parameters in the conceptual design stage for the two main classes of fully electric vertical take-off and landing (eVTOL) aircraft, the powered lift and wingless aircraft types. The paper investigates hybrids of classical root-finding methods: the bisection, fixed-point and Newton-Rapson methods for use in eVTOL aircraft sizing. The improved convergence efficiency of the hybrid methods is at least 70% faster than the standard methods. This improved efficiency is significant for complex sizing problems. The developed sizing method is used to investigate the comparative performance of the wingless and powered lift eVTOL aircraft types for varying mission lengths. For a generic air taxi mission with a payload of 400 kg, the powered lift type demonstrates its mass efficiency when sized for missions above 10 km in range. However, the simpler architecture of the wingless eVTOL aircraft type makes it preferable for missions below 10 km in range when considering energy efficiency. The results of the sizing study were compared against a selection of eVTOL aircraft data. The results showed a good agreement between the estimated aircraft mass using the proposed sizing method and published eVTOL aircraft data.

This paper proposed a new attitude determination method for low-orbit spacecraft. The attitude prediction accuracy is greatly improved by adding the unmodeled environmental torque to the dynamic equation. Specifically, the environmental torque extraction algorithm based on extended Kalman filter and series extended state observer is introduced, and the unmodeled part of dynamic is identified through the inverse dynamic model. Then, the collected data are analyzed and trained by a backpropagation neural network, resulting in an attitude-torque mapping network with compensation ability. The simulation results show that the proposed feedback attitude prediction algorithm can outperform standard methods and provide a high accurate picture of prediction and reliability with discontinuous measurement.

In various applications, the extended Kalman filter (EKF) has been vital in estimating a vehicle’s translational and angular motion in 3-dimensional (3D) space. It is also essential for the fusion of data from multiple sensors. However, for the EKF to perform effectively, the optimal process noise covariance matrix (Q) and measurement noise covariance matrix (R) must be chosen correctly. The use of EKF has been challenging due to the need for an easy mechanism to select Q and R values. As a result, this research focused on developing an algorithm that can be easily applied to determine Q and R, allowing us to harness the full potential of EKF. Accordingly, an EKF innovation consistency statistics-driven Bayesian optimization algorithm was employed to achieve this goal. Q and R values were tuned until the expected result met the performance requirement for minimum error through improved measurement innovation consistency. The comprehensive results demonstrate that when the optimum Q and R, as tuned by the suggested technique, were used, the performance of the EKF significantly improved.

In this paper, we introduce mREAL-GAN, a generative adversarial network (GAN) for the parallel generation of multiple residential electrical appliance load (mREAL) profiles. mREAL-GAN is intended for use in community-scale low-voltage network analysis, and represents a departure from previous methods for this purpose, which break the generation of appliance load profiles into several steps and largely model each appliance independently. Instead, mREAL-GAN models appliance load profiles in an end-to-end manner, and generates multiple appliance load profiles in parallel in a way that captures inter-dependencies. We show that mREAL-GAN generates load profiles for individual appliance-types with greater fidelity than a popular example of previous methods, and demonstrate its ability to capture inter-dependencies between appliances.

Close proximity operations around small bodies are extremely challenging due to their uncertain dynamical environment. Autonomous guidance and navigation around small bodies require fast and accurate modeling of the gravitational field for potential on-board computation. In this paper, we investigate a model-based, data-driven approach to compute and predict the gravitational acceleration around irregular small bodies. More specifically, we employ Extreme Learning Machine (ELM) theories to design, train and validate Single-Layer Feedforward Networks (SLFN) capable of learning the relationship between the spacecraft position and the gravitational acceleration. ELM-base neural networks are trained without iterative tuning therefore dramatically reducing the training time. Analysis of performance in constant density models for asteroid 25143 Itokawa and comet 67/P Churyumov-Gerasimenko show that ELM-based SLFN are able learn the desired functional relationship both globally and in selected localized areas near the surface. The latter results in a robust neural algorithm for on-board, real-time calculation of the gravity field needed for guidance and control in close-proximity operations near the asteroid surface.

This paper presents a comparison of bottom up models that generate appliance load profiles. The comparison is based on their ability to accurately distribute load over time-of-day. This is a key feature of model performance if the model is used to assess the impact of low carbon technologies and practices on the network. No work has yet assessed models on this basis. In this work, the temporal characteristics of load are captured using histograms, and similarity between the histogram representations of measured and generated data is assessed using the Wasserstein distance. This is then applied to compare the results of three models, which were developed here by adopting approaches used in previous research. One is based on occupant presence, one on occupant activity, and one on empirical data. Typical statistical tests showed that the comparison method is robust and can be used for this purpose.

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This paper addresses the problem of finding periodic solutions in the circular restricted three-body problem (CRTBP) with the Earth and Moon as the two primaries and the third massless body a solar sail. These orbits were accomplished by using an optimal choice of the sail pitch angle, which maximize the out-of-plane distance. Based upon the first-order approximation, an analytical formulation of the periodic orbits at linear order is presented. The approximate analytical solutions found are utilized in a numerical search to determine Lissajous trajectories in the full nonlinear model. In order to illustrate the near term and possible future orbits that can be achieved, we have generated the results for several values of the characteristic acceleration.

A study of novel families of highly non-Keplerian orbits (NKO) for spacecraft utilizing either solar sail or solar electric propulsion (SEP) at linear order are investigated in the circular restricted three-body problem (CRTBP). In addition to a detailed investigation of the dynamics and control of highly NKO, effort will be devoted to develop a strategy that uses maneuvers executed impulsively at discrete time intervals. Thus, impulse control is investigated as a means of generating displaced orbits. In order to compare the continuous thrust and impulse control orbits, linearized equations of motion will be considered for small displacements. The requirements for impulse control and continuous thrust for different values of out-of-plane distance are presented.

Recent work in the literature has advocated using the Earth-Moon-planetoid Lagrangian points as observables, in order to test general relativity and effective field theories of gravity in the solar system. However, since the three-body problem of classical celestial mechanics is just an approximation of a much more complicated setting, where all celestial bodies in the solar system are subject to their mutual gravitational interactions, while solar radiation pressure and other sources of nongravitational perturbations also affect the dynamics, it is conceptually desirable to improve the current understanding of solar system dynamics in general relativity, as a first step towards a more accurate theoretical study of orbital motion in the weak-gravity regime. For this purpose, starting from the Einstein equations in the de Donder-Lanczos gauge, this paper arrives first at the Levi-Civita Lagrangian for the geodesic motion of celestial bodies, showing in detail under which conditions the effects of internal structure and finite extension get cancelled in general relativity to first post-Newtonian order. The resulting nonlinear ordinary differential equations for the motion of planets and satellites are solved for the Earth's orbit about the Sun, written down in detail for the Sun-Earth-Moon system, and investigated for the case of planar motion of a body immersed in the gravitational field produced by the other bodies (e.g. planets with their satellites). At this stage, we prove an exact property, according to which the fourth-order time derivative of the original system leads to a linear system of ordinary differential equations. This opens an interesting perspective on forthcoming research on planetary motions in general relativity within the solar system, although the resulting equations remain a challenge for numerical and qualitative studies.

The one-loop long distance quantum corrections to the Newtonian potential imply tiny but observable effects in the restricted three-body problem of celestial mechanics, i.e., both at the Lagrangian points of stable equilibrium and at those of unstable equilibrium the Newtonian values of planetoid's coordinates are changed by a few millimetres in the Earth-Moon system. First, we find that the equations governing the position of both noncollinear and collinear quantum libration points are algebraic fifth degree and ninth degree equations, respectively. Second, we discuss the prospects to measure, with the help of laser ranging, the above departure from the equilateral triangle picture, which is a challenging task. On the other hand, a modern version of the planetoid is the solar sail, and much progress has been made, in recent years, on the displaced periodic orbits of solar sails at all libration points. By taking into account the quantum corrections to the Newtonian potential, displaced periodic orbits of the solar sail at libration points are again found to exist.

We examine quantum corrections of time delay arising in the gravitational field of a spinning oblate source. Low-energy quantum effects occurring in Kerr geometry are derived within a framework where general relativity is fully seen as an effective field theory. By employing such a pattern, gravitational radiative modifications of Kerr metric are derived from the energy-momentum tensor of the source, which at lowest order in the fields is modelled as a point mass. Therefore, in order to describe a quantum corrected version of time delay in the case in which the source body has a finite extension, we introduce a hybrid scheme where quantum fluctuations affect only the monopole term occurring in the multipole expansion of the Newtonian potential. The predicted quantum deviation from the corresponding classical value turns out to be too small to be detected in the next future, showing that new models should be examined in order to test low-energy quantum gravity within the solar system.

Close proximity operations around small bodies are extremely challenging due to their uncertain dynamical environment. Autonomous guidance and navigation around small bodies require fast and accurate modeling of the gravitational field for potential on-board computation. In this paper, we investigate a model-based, data-driven approach to compute and predict the gravitational acceleration around irregular small bodies. More specifically, we employ Extreme Learning Machine (ELM) theories to design, train and validate Single-Layer Forward Networks (SLFN) capable of learning the relationship between the spacecraft position and the gravitational acceleration. ELMs-base neural networks are trained without iterative tuning therefore dramatically reducing the training time. Analysis of performance in constant density models for 433 Eros and 25143 Itokawa show that ELM-based SLFN are able learn the desired functional relationship both globally and in localized areas near the surface. The latter results in a robust neural algorithm for on-board, real-time calculation of the gravity field needed for close-proximity operations near the asteroid surface.

Solar sail technology offers new capabilities for space missions due to the opportunities for non-Keplerian orbits. In this paper, novel families of highly non-Keplerian orbits for spacecraft utilising solar sail at linear order are investigated in the Earth-Moon circular restricted three-body problem. Firstly, it is assumed implicitly that the solar sail is a perfect reflector. Based upon the first-order approximation, an analytical formulation of the periodic orbits at linear order is presented. The approximate analytical solutions offer useful insights into the nature of the motion in the vicinity of the libration points, and are used to give periodic solutions numerically in the full nonlinear system. These orbits were accomplished by using an optimal choice of the sail pitch angle, which maximize the out-of-plane distance. Thereafter, the resulting effects of the non-ideal flat sail model have been computed and compared with an ideal solar sail. A square sail configuration, which is likely to be chosen for various near-term sail missions is used to illustrate the concept. The main effect of the non-perfect sail is to reduce the out-of-plane displacement distance which may be achieved for a given characteristic acceleration. It is also observed that there is a significant deviation in force magnitude between the realistic solar sail and the ideal solar sail model.

An Optimal Sliding Guidance (OSG) is implemented in the Circular Restricted Three-Body Problem and Restricted Four-Body Problem for spacecraft near libration points of the Earth-Moon system. Based on a combination of generalized Zero-Effort-Miss/Zero-Effort-Velocity and time-dependent sliding control theory, OSG is capable of generating closed-loop guided trajectories that are demonstrated to be globally finite-time stable against uncertain perturbing accelerations with known upper bound. The application of the OSG for Halo orbit station-keeping and orbital transfer are studied in a perturbed four body dynamical model in order to evaluate response and effectiveness of the proposed guidance approach.

Devising closed-loop guidance algorithms for autonomous relative motion is an important problem within the field of orbital dynamics. In this paper, we study the guided relative motion of two spacecraft for which one of them is executing an autonomous rendezvous via the ZEM/ZEV feedback guidance and its robustified Optimal Sliding Guidance (OSG) counterpart. Starting from the classical Clohessy-Wiltshire (CW) model, we systematically analyze the ability of the ZEM/ZEV feedback guidance to generate closed loop trajectories that drive the deputy spacecraft to the chief satellite and evaluate its performance in terms of target accuracy and propellant consumption. It is shown that the guidance gains and the time of flight predicted by the theoretical solution generates a class of feedback trajectories that are accurate but suboptimal with respect to the open-loop fuel-optimal solution. Indeed, a parametric study shows that a different set of gains may generate relative guided trajectories that yields fuel consumption closer to the ideal optimal. The guidance algorithms are also demonstrated to be accurate in guiding the relative motion of the deputy toward a chief spacecraft in highly elliptical orbit where the Linearized Equations of Relative Motions (LERM) are employed to compute the Zero-Effort-Miss (ZEM) and Zero-Effort-Velocity (ZEV) necessary to compute the acceleration command as prescribed by the theory.

We first analyze the restricted four-body problem consisting of the Earth, the Moon, and the Sun as the primaries and a spacecraft as the planetoid. This scheme allows us to take into account the solar perturbation in the description of the motion of a spacecraft in the vicinity of the stable Earth-Moon libration points L-4 and L-5 both in the classical regime and in the context of effective field theories of gravity. A vehicle initially placed at L-4 or L-5 will not remain near the respective points. In particular, in the classical case the vehicle moves on a trajectory about the libration points for at least 700 days before escaping. We show that this is true also if the modified long-distance Newtonian potential of effective gravity is employed. We also evaluate the impulse required to cancel out the perturbing force due to the Sun in order to force the spacecraft to stay precisely at L-4 or L-5. It turns out that this value is slightly modified with respect to the corresponding Newtonian one. In the second part of the paper, we first evaluate the location of all Lagrangian points in the Earth-Moon system within the framework of general relativity. For the points L-4 and L-5, the corrections of coordinates are of order a few millimeters and describe a tiny departure from the equilateral triangle. After that, we set up a scheme where the theory which is quantum corrected has as its classical counterpart the Einstein theory, instead of the Newtonian one. In other words, we deal with a theory involving quantum corrections to Einstein gravity, rather than to Newtonian gravity. By virtue of the effective-gravity correction to the long-distance form of the potential among two masses, all terms involving the ratio between the gravitational radius of the primary and its separation from the planetoid get modified. Within this framework, for the Lagrangian points of stable equilibrium, we find quantum corrections of order 2 mm, whereas for Lagrangian points of unstable equilibrium we find quantum corrections below a millimeter. In the latter case, for the point L-1, general relativity corrects Newtonian theory by 7.61 m, comparable, as an order of magnitude, with the lunar geodesic precession of about 3 m per orbit. The latter is a cumulative effect accurately measured at the centimeter level through the lunar laser ranging positioning technique. Thus, it is possible to study a new laser ranging test of general relativity to measure the 7.61 m correction to the L-1 Lagrangian point, an observable never used before in the Sun-Earth-Moon system. Performing such an experiment requires controlling the propulsion to precisely reach L-1, using an instrumental accuracy comparable to the measurement of the lunar geodesic precession, and understanding systematic effects resulting from thermal radiation and multibody gravitational perturbations. This will then be the basis to consider a second-generation experiment to study deviations of effective field theories of gravity from general relativity in the Sun-Earth-Moon system.

Recent work in the literature has shown that the one-loop long distance quantum corrections to the Newtonian potential imply tiny but observable effects in the restricted three-body problem of celestial mechanics, i.e., at the Lagrangian libration points of stable equilibrium the planetoid is not exactly at equal distance from the two bodies of large mass, but the Newtonian values of its coordinates are changed by a few millimeters in the Earth-Moon system. First, we assess such a theoretical calculation by exploiting the full theory of the quintic equation, i.e., its reduction to Bring-Jerrard form and the resulting expression of roots in terms of generalized hypergeometric functions. By performing the numerical analysis of the exact formulas for the roots, we confirm and slightly improve the theoretical evaluation of quantum corrected coordinates of Lagrangian libration points of stable equilibrium. Second, we prove in detail that also for collinear Lagrangian points the quantum corrections are of the same order of magnitude in the Earth-Moon system. Third, we discuss the prospects to measure, with the help of laser ranging, the above departure from the equilateral triangle picture, which is a challenging task. On the other hand, a modern version of the planetoid is the solar sail, and much progress has been made, in recent years, on the displaced periodic orbits of solar sails at all libration points, both stable and unstable. The present paper investigates therefore, eventually, a restricted three-body problem involving Earth, Moon and a solar sail. By taking into account the one-loop quantum corrections to the Newtonian potential, displaced periodic orbits of the solar sail at libration points are again found to exist.