Self Balanced Bare Electrodynamic Tethers. Space Debris Mitigation and other Applications

The research on electrodynamic tethers (EDT) has been a fruitful field since the 70’s. This technology has been developed thanks to both theoretical studies and demonstration missions. During this period, several technical issues were identified and overcome. Among those problems, two of them would entail an important reduction in the operational capabilities of these devices. First, the efficient collection of electrons in rarefied plasma and, second, the dynamic instability of EDTs in inclined orbits. The bare tether concept represents the surmounting of the current scarcity in low density plasma. This method of interaction with the ionosphere promises to considerably increase the intensity along the tether. In turn, the dynamic instability could be avoided by balancing the EDT, as it has been proposed with the Self Balanced Electrodynamic Tether (SBET) concept. The purpose of this thesis is to prove the suitability of both concepts working together in several space applications: from mitigation of the space debris to capture in a Jovian orbit. The computation of the electron collection by a bare tether is faced in first place. The semi-analytical method derived in this work allows to calculate accurately and efficiently the intensity which flows along a tether working on the OML (orbit-motion-limited) regime. Then, an energy study is derived, where the EDT is analyzed as an energy converter. This approach provides a link among the different aspects of the problem, from both electrical and dynamical points of view. All the previous considerations will lead to the introduction of control laws based on the SBET concept, enhancing its capabilities. These analysis will be tested in a couple of particular scenarios of interest. Mitigation of space debris has become an issue of first concern for all the institutions involved in space operations. In this context, EDTs have been pointed out as a suitable and economical technology to de-orbit spacecrafts at the end of their operational life. Throughout this dissertation the numerical simulation of different de-orbiting missions by means of EDTs will allow to highlight its main characteristics and recognize the different parameters which are involved. The simulations will assess the suitability of electrodynamic tethers to perform these kind of mission. On the other hand, one of the foremost objectives within Solar System exploration is Jupiter, its moons and their surroundings. Due to the presence of magnetic field and plasma environment, this scenario turns out to be particularly appropriate for the utilization of EDTs. These devices would be capable to generate power and thrust without propellant consumption. Orbital maneuvers and power generation will be therefore ensured. In this work, the possibility of using self balanced bare electrodynamic tethers to perform a capture in Jovian orbit is analyzed. In addition, within this research, the analysis of the dynamics of a tether in the neighborhoods of a Lagrangian point results to be interesting since it models the motion of a space system near a Jupiter’s moon. That would allow to study the establishment of a permanent observatory for scientific observation in Jovian orbit. The analysis of the restricted three body problem is developed without taking into account the electrodynamic perturbation, leaving the inclusion of this feature for further research. Finally, within the frame of this dissertation, an additional analysis is presented. The study is related to the possible role of EDT in geodetic missions. The work gathered here describes an initial analysis of the capabilities of a tethered system to recover gravitational signals by means of measuring its tension

Singularities in DROMO formulation. Analysis of deep flybys

The singularities in Dromo are characterized in this paper, both from an analytical and a numerical perspective. When the angular momentum vanishes, Dromo may encounter a singularity in the evolution equations. The cancellation of the angular momentum occurs in very speci?c situations and may be caused by the action of strong perturbations. The gravitational attraction of a perturbing planet may lead to rapid changes in the angular momentum of the particle. In practice, this situation may be encountered during deep planetocentric ?ybys. The performance of Dromo is evaluated in di?erent scenarios. First, Dromo is validated for integrating the orbit of Near Earth Asteroids. Resulting errors are of the order of the diameter of the asteroid. Second, a set of theoretical ?ybys are designed for analyzing the performance of the formulation in the vicinity of the singularity. New sets of Dromo variables are proposed in order to minimize the dependency of Dromo on the angular momentum. A slower time scale is introduced, leading to a more stable description of the ?yby phase. Improvements in the overall performance of the algorithm are observed when integrating orbits close to the singularity

Jovian Capture of a Spacecraft with a Self-Balanced Electrodynamic Bare Tether

This paper proposes and analyzes the use of a nonrotating tethered system for a direct capture in Jovian orbit using the electrodynamic force generated along the cable. A detailed dynamical model is developed showing a strong gravitational and electrodynamic coupling between the center of mass and the attitude motions. This paper shows the feasibility of a direct capture in Jovian orbit of a rigid tethered system preventing the tether from rotating. Additional mechanical–thermal requirements are explored, and preliminary operational limits are defined to complete the maneuver. In particular, to ensure that the system remains nonrotating, a nominal attitude profile for a self-balanced electrodynamic tether is proposed, as well as a simple feedback control

Initial orbit determination methods for track-to-track association

The detection and identification of Resident Space Objects (RSOs) from survey tracks requires robust and efficient orbit determination methods for the association of observations of the same RSO. Both Initial Orbit Determination (IOD) and Orbit Determination (OD) methods perform the orbital estimation in which the association of tracks relies. The choice of proper IOD and OD methods is essential for the whole data association, since they are in charge of providing the estimation required to evaluate the figure of merit of the association. In this paper, we review the state of the art and propose a novel method that does not require initialisation, accounts for measurement noise and provides a full estimation (i.e., state vector and covariance) from an arbitrary number of optical observations. To do so, a boundary value problem is formulated to find a pair of ranges leading to a minimum residuals of the observations. The proposed methods are compared against classical alternatives simulated in scenarios representative of the current space debris environment.This project has received funding from the "Comunidad de Madrid" under "Ayudas destinadas a la realización de doctorados industriales" program (project IND2017/TIC7700). Besides, the authors would like to acknowledge the contributions from Alfredo Miguel Antón Sácnchez, Pablo García Sánchez and Adrián Díez Martín from GMV for their support, review and advice

Track-to-track association methodology for operational surveillance scenarios with radar observations

This paper proposes a novel track-to-track association methodology able to detect and catalogue resident space objects (RSOs) from associations of uncorrelated tracks (UCTs) obtained by radar survey sensors. It is a multi-target multi-sensor algorithm approach able to associate data from surveillance sensors to detect and catalogue objects. The association methodology contains a series of steps, each of which reduces the complexity of the combinational problem. The main focus are real operational environments, in which brute-force approaches are computationally unaffordable. The hypotheses are scored in the measurement space by evaluating a figure of merit based on the residuals of the observations. This allows us to filter out most of the false hypotheses that would be present in brute-force approaches, as well as to distinguish between true and false hypotheses. The suitability of the proposed track-to-track association has been assessed with a simulated scenario representative of a real operational environment, corresponding to 2 weeks of radar survey data obtained by a single survey radar. The distribution and evolution of the hypotheses along the association process is analysed and typical association performance metrics are included. Most of the RSOs are detected and catalogued and only one false positive is obtained. Besides, the rate of false positives is kept low, most of them corresponding to particular cases or objects with high eccentricity or limited observability.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This project has received funding from the “Comunidad de Madrid” under “Ayudas destinadas a la realizacion doctorados industriales” program (project IND2017/TIC7700

A survey on low-thrust trajectory optimization approaches

In this paper, we provide a survey on available numerical approaches for solving low-thrust trajectory optimization problems. First, a general mathematical framework based on hybrid optimal control will be presented. This formulation and their elements, namely objective function, continuous and discrete state and controls, and discrete and continuous dynamics, will serve as a basis for discussion throughout the whole manuscript. Thereafter, solution approaches for classical continuous optimal control problems will be briefly introduced and their application to low-thrust trajectory optimization will be discussed. A special emphasis will be placed on the extension of the classical techniques to solve hybrid optimal control problems. Finally, an extensive review of traditional and state-of-the art methodologies and tools will be presented. They will be categorized regarding their solution approach, the objective function, the state variables, the dynamical model, and their application to planetocentric or interplanetary transfers

Efficient computation of current collection in bare electrodynamic tethers in and beyond OML regime

One key issue in the simulation of bare electrodynamic tethers (EDTs) is the accurate and fast computation of the collected current, an ambient dependent operation necessary to determine the Lorentz force for each time step. This paper introduces a novel semianalytical solution that allows researchers to compute the current distribution along the tether efficient and effectively under orbital-motion-limited (OML) and beyond OML conditions, i.e., if tether radius is greater than a certain ambient dependent threshold. The method reduces the original boundary value problem to a couple of nonlinear equations. If certain dimensionless variables are used, the beyond OML effect just makes the tether characteristic length L* larger and it is decoupled from the current determination problem. Avalidation of the results and a comparison of the performance in terms of the time consumed is provided, with respect to a previous ad hoc solution and a conventional shooting method

Robust Aircraft Trajectory Planning under Wind Uncertainty using Optimal Control

Uncertainty in aircraft trajectory planning and prediction generates major challenges for the future Air Traffic Management system. Therefore, understanding and managing uncertainty will be necessary to realize improvements in air traffic capacity, safety, efficiency and environmental impact. Meteorology (and, in particular, winds) represents one of the most relevant sources of uncertainty. In the present work, a framework based on optimal control is introduced to address the problem of robust and efficient trajectory planning under wind forecast uncertainty, which is modeled with probabilistic forecasts generated by Ensemble Prediction Systems. The proposed methodology is applied to a flight p l anning s c enario u n der a f r ee-routing operational paradigm and employed to compute trajectories for different sets of user preferences, exploring the trade-off between average flight cost and p r edictability. Results show how the impact of wind forecast uncertainty in trajectory predictability at a pre-tactical planning horizon can be not only quantified, b ut a l so r educed t hrough t he application of the proposed approach.This work has been partially supported by project TBO-MET project, which has receivedfunding from the SESAR JU under grant agreement No 699294 under the European Union’s Horizon 2020 research and innovation program. This work is also partially supported by the Spanish Government through Project entitled Analysis and optimisation of aircraft trajectories under the effects of meteorological uncertainty (TRA2014-58413-C2-2-R); this project has been funded under R&D&I actions of Programa Estatal de Investigación, Desarrollo e Innovación Orientada a los Retos de la Sociedad (call 2014)

Modeling and stability analysis of tethered kites at high altitudes

A systematic analysis of the role played by several physical mechanisms in the longitudinal stability of a tethered kite is presented. A simple model, which artificially constrains the pitch motion of the kite and approximates the tether by a massless and rigid bar, is improved progressively to include the kite pitch motion as well as the tether inertia, flexibility, wind load, and elasticity. The models are presented as compact sets of ordinary differential equations without algebraic constraints, which are explicitly eliminated by making an extensive use of Lagrangian mechanics. The contributions of each physical mechanism on kite stability are investigated separately, and a tradeoff between the complexity and computational costs of the models against their accuracy and reliability is carried out. The wind load on the tether is identified as a key effect stabilizing the steady state of the kites. The optimal bridle design and tether length selections to compute the kite ceiling are discussed.This work was supported by Fundación BBVA under the Convocatoria 2015 de Ayudas BBVA a Investigadores y Creadores Culturales grant no. IN[15]_TIC_ING_0313. G. Sánchez-Arriaga was supported by the Ministerio de Economía y Competitividad of Spain (grant no. RYC-2014-15357)Publicad

A new automated strategy for optimizing inclined interplanetary low-thrust trajectories

This study proposes a new automated strategy for designing and optimizing three-dimensional interplanetary low-thrust (LT) trajectories. The method formulates the design as a hybrid optimal control problem and solves it using a two-step approach. In Step 1, a three-dimensional model based on generalized logarithmic spirals is used with heuristics in combination with a gradient-based solver to perform an automated multi-objective global search of trajectories and optimize for parameters defining the spirals, the launch date, as well as the number, sequence and configuration of the planetary flybys. In Step 2, candidate solutions from Step 1 are refined by further optimization with a direct method. Results show that, compared to similar algorithms based on two-dimensional models, the strategy implemented in Step 1 leads to better estimates of the optimal trajectories, especially when the orbits of the involved bodies are inclined with respect to the ecliptic plane. The proposed approximate method (Step 1) yields better agreement with high-fidelity solutions (Step 2) in terms of launch, flyby and arrival dates, in-plane and out-of-plane average LT accelerations and propellant consumption, leading to improved convergence when the Step 1 trajectories are employed to initiate the search in Step 2