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Publication Point cloud simulator for space in-orbit close range autonomous operations(Copernicus Publications, 2022-05-30) Gonzalez De Santos, L. M.; Gonzalez Jorge, H.; Sanjurjo Rivo, Manuel; Michinel, H.In recent years, many different in-orbit close-range autonomous operations have been developed for multiple purposes, such as rendezvous and docking operations or ADR operations. In both cases, the systems have to calculate the relative position between the spacecraft and the target in order to control the orbital manoeuvres and the physic interaction between both systems. One of the sensors used for the pose calculation for these operations are LiDAR sensors, developing pose calculation algorithms that process the point cloud acquired by these sensors. One of the main problems for the development and testing of these algorithms is the lack of real data acquired in orbit and the difficulty of acquiring this data. This makes it fundamental to develop a simulator to generate realistic point clouds that can be used to develop and test pose calculation algorithms. This work presents a simulator developed for this purpose, that is the generation of realistic point clouds for algorithm development for pose calculation using LiDAR sensors for space in-orbit close range autonomous operations. The simulator uses the LiDAR sensor specifications, in order to introduces measurement errors and the scanning pattern, and 3D model of the satellite or object that is scanned.Publication BETsMA v2.0: a friendly software for the analysis of electrodynamic tether missions in Jupiter(Europlanet Society, 2020-09-21) Borderes Motta, Gabriel; Sánchez Arriaga, Gonzalo; European Commission; Ministerio de Ciencia e Innovación (España)Space Electrodynamic Tethers (EDTs) are km-long conductors that exchange momentum and energy with a planet magnetosphere through the Lorentz force exerted by the planet's magnetic field on the tether current. Since the conducting medium (plasma) and the magnetic field of the planetary environment are essential for their operation, tether are appropriate for applications in Low Earth Orbits (LEO) and the neighborhood of giant planets like Jupiter [1, 2, 3, 4], Saturn [5], and Neptune [6]. However, the design and analysis of missions in outer planets typically requires deep knowledge on tethers modeling. The main goal of this work is spreading the use of tethers and presenting a friendly software for the mission analysis and simulation of tethers in Jupiter.Publication Simulations without data updates using analytical attitude propagator GSAM for spin stabilized satellites(IOP Publishing Ltd, 2019) Zanardi, M. Cecilia; Mota, Víctor; Borderes Motta, GabrielThe objective of this work is to validate the GSAM propagator using new data provided by the National Institute for Space Research (INPE) from SCD1 and SCD2 data collection satellites, with emphasis on long interval simulations without daily data updates. Originally, only 40 days of data were available to test the program, constraining any attempts to measure its precision more accurately. Recently, over two decades of data regarding both satellites' orbital and attitude parameters were provided, allowing further studies and validation of the program. The rotational motion equations are composed by the gravity gradient torque, aerodynamic torque, solar radiation pressure torque, residual and eddy current magnetic torques, the latter using a dipole geomagnetic model. The results are considered fitting when the mean deviation between the calculated variables and the real satellite data stay within 0.5× for the right ascension and declination angles and 0.5 rpm for the spin velocity. Intervals that meet the required precision were found for all years, from three to up to 15 days of simulation without data update. The consistent detection of such intervals further corroborate the use of the propagator to estimate the orientation of the satellites studied in their missions.Publication Comparison of technologies for deorbiting spacecraft from low-earth-orbit at end of mission(Elsevier, 2017-09-01) Sánchez Arriaga, Gonzalo; Sanmartín, Juan Ramón; Lorenzini, Enrico; Ministerio de Economía y Competitividad (España)An analytical comparison of four technologies for deorbiting spacecraft from Low-Earth-Orbit at end of mission is presented. Basic formulas based on simple physical models of key figures of merit for each device are found. Active devices - rockets and electrical thrusters - and passive technologies - drag augmentation devices and electrodynamic tethers - are considered. A basic figure of merit is the deorbit device-to-spacecraft mass ratio, which is, in general, a function of environmental variables, technology development parameters and deorbit time. For typical state-of-the-art values, equal deorbit time, middle inclination and initial altitude of 850 km, the analysis indicates that tethers are about one and two orders of magnitude lighter than active technologies and drag augmentation devices, respectively; a tether needs a few percent mass-ratio for a deorbit time of a couple of weeks. For high inclination, the performance drop of the tether system is moderate: mass ratio and deorbit time increase by factors of 2 and 4, respectively. Besides collision risk with other spacecraft and system mass considerations, such as main driving factors for deorbit space technologies, the analysis addresses other important constraints, like deorbit time, system scalability, manoeuver capability, reliability, simplicity, attitude control requirement, and re-entry and multi-mission capability (deorbit and re-boost) issues. The requirements and constraints are used to make a critical assessment of the four technologies as functions of spacecraft mass and initial orbit (altitude and inclination). Emphasis is placed on electrodynamic tethers, including the latest advances attained in the FP7/Space project BETs. The superiority of tape tethers as compared to round and multi-line tethers in terms of deorbit mission performance is highlighted, as well as the importance of an optimal geometry selection, i.e. tape length, width, and thickness, as function of spacecraft mass and initial orbit. Tether system configuration, deployment and dynamical issues, including a simple passive way to mitigate the well-known dynamical instability of electrodynamic tethers, are also discussed.Publication The E.T.PACK Project: towards a fully passive and consumable-less deorbit kit based on low work-function tether technology(Elsevier, Ltd., 2020-12) Sánchez Arriaga, Gonzalo; Naghdi, Samira; Wätzig, K.; Schilm, J.; Lorenzini, Enrico C.; Tajmar, Martin; Urgoiti Bolumburu, Eduardo; Tarabini Castellani, Lorenzo; Plaza, J. F.; Post, A.; Comunidad de Madrid; European Commission; Ministerio de Economía y Competitividad (España)The Electrodynamic Tether Technology for Passive Consumable-less Deorbit Kit (E.T.PACK) is a project aimed at the development of a deorbit kit based on low-work-function Tether (LWT) technology, i.e., a fully passive and electrically floating system made of a long conductive tape coated with a low-work-function material. The LWT interacts passively with the environment (ambient plasma, magnetic field, and solar radiation) to exchange momentum with the planet's magnetosphere, thus enabling the spacecraft to de-orbit and/or re-boost without the need for consumables. The main goal is to develop a deorbit kit and related software with Technology Readiness Level 4 and promote a follow-up project to carry out an in-orbit experiment. The planned kit in the experiment has three modes of operation: fully passive LWT and conventional electrodynamic tether equipped with an active electron emitter in passive and active modes. Several activities of the project pivot around the C12A7 : e- electride, which will be used in four hardware elements: (i) LWT (ii) hollow cathode, (iii) photo-enhanced thermionic emission device to convert solar photon energy into electrical energy, and (iv) a hollow cathode thruster. These elements, some of which do not belong to the deorbit kit, are synergetic with the main stream of the project and common to some tether applications like in-orbit propulsion and energy generation. This work explains the activities of E.T.PACK and the approach for solving its technological challenges. After reviewing past progresses on electrodynamic tethers and thermionic materials, we present a preliminary concept of the kit for the in-orbit experiment, some simulation results, and the key hardware elements.Publication A constraint-free flight simulator package for airborne wind energy systems(IOP, 2018-06-19) Sánchez Arriaga, Gonzalo; Pastor Rodríguez, Alejandro; Borobia Moreno, Ricardo; Schmehl, Roland; European Commission; Ministerio de Economía y Competitividad (España)The LAgrangian Kite SimulAtor (LAKSA) is a freely available software for the dynamic analysis of tethered flying vehicles, such as kites and fixed-wing drones, applied to airborne wind energy generation. This software comprises four simulators. The one, two and four-line simulators, which consider flexible but inelastic tethers, are based on minimal coordinate Lagragian formulations and can be used for the analysis of fly and ground generation systems, kite-based traction systems, and kitesurfing applications, respectively. The configuration of the mechanical system in the fourth simulator can be defined by the user, who can select the number of flying vehicles and the properties of the elastic and flexible tethers linking them. In all the software tools, the kites or tethered fixed-wing drones are represented as rigid bodies and the dynamic equations of the tether-bridle-vehicle systems, together with the user-defined and time-dependent control variables, are solved self-consistently. Academic and research analysis can take advantage of the modularity of the simulators and their inputs and outputs interfaces, which follow a common and user-friendly architecture.Publication Collisional effects in non-stationary plasma expansions along convergent-divergent magnetic nozzles(2018-05) Zhou, Jiewei; Sánchez Arriaga, Gonzalo; Ahedo Galilea, Eduardo Antonio; Martinez-Sánchez, M.; Ramos, Jesús JoséThe electron-electron collisional effect on the nonstationary expansion of a plasma in a convergentdivergent magnetic nozzle is studied. Under paraxial and fully magnetized plasmas approximations, an Eulerian code has been adapted to solve Poisson's equation coupled with the kinetic transport equations for plasma species, i.e. a Vlasov equation for singly-charged ions and a Boltzmann equation with a Bhatnagar-Gross-Kook operator for electrons. The study is focused on weakly collisional plasma plumes, which have a collisional time scale larger than the transit time in the nozzle of typical electrons. A kinetic analysis shows that phasespace regions of isolated, doubly-trapped electrons that are nearly empty in the collisionless case are progressively populated due to the electron-electron collisions. Such a higher density of trapped electrons modifies the profile of the electrostatic potential, which keeps almost unaltered the density of free electrons and decreases the density of the reflected ones. As compared with the collisionless case, the collisions decrease the length of the downstream sheath and the parallel electron temperature while increasing the normal one. Therefore the steady plasma state is more isotropic. The simulations show that collisions erase the time history of the system and, unlike the collisionless case, the steady state is unique.Publication Robust Optimal Trajectory Planning under Uncertain Winds and Convective Risk(2017-11) González Arribas, Daniel; Soler Arnedo, Manuel Fernando; Sanjurjo Rivo, Manuel; García-Heras Carretero, Javier; Sacher, Daniel; Gelhardt, Ulrike; Lang, Juergen; Hauf, Thomas; Simarro, JuanThe existence of significant uncertainties in the models and systems required for trajectory prediction represent a major challenge for Trajectory-Based Operations concept. Weather can be considered as one of the most relevant sources of uncertainty. Understanding and managing the impact of these uncertainties is necessary in order to increase the predictability of the ATM system. We present preliminary results on robust trajectory planning in which weather is assumed to be the unique source of uncertainty. State-of-the-art forecasts from Ensemble Prediction Systems are used as input data for the wind field and to calculate convective risk. The term convective area is defined here as an area within which individual convective storms may develop, i.e., a necessary (though not sufficient) condition. An ad-hoc robustoptimal control methodology is presented. A set of Pareto-optimal trajectories is obtained for different preferences between predictability, convective risk and average efficiency.Publication Effects of Reducing Wind-Induced Trajectory Uncertainty on Sector Demand(2017-11) Valenzuela, Alfonso; Franco, Antonio; Rivas, Damián; García-Heras Carretero, Javier; Soler Arnedo, Manuel FernandoIn this paper, a first step to analyse the effects of reducing the uncertainty of aircraft trajectories on sector demand is presented. The source of uncertainty is wind, forecasted by Ensemble Prediction Systems, which are composed of different possible atmosphere realizations. A trajectory predictor determinesthe routes to be followed by the different flights to reduce the uncertainty of the arrival times. The sector demand is described in terms of entry count, that is, the number of flights entering the sector during a selected time period, which is uncertain because so are the the entry times to the sector. Results are presented for a realistic application, where the dispersion of the entry count isshown to be reduced when the dispersion of the arrival times is also reduced.Publication Optimal Aircraft Trajectory Planning in the Presence of Stochastic Convective Weather Cells(American Institute Of Aeronautics And Astronautics (AIAA), 2017-06) González Arribas, Daniel; Hentzen, Daniel; Sanjurjo Rivo, Manuel; Soler Arnedo, Manuel Fernando; Kamgarpour, MaryamThe Air Traffic Management system is heavily influenced by meteorological uncertainty, and convective weather cells represent one of the most relevant uncertain meteorological phenomena. They are weather hazards that must be avoided through tactical trajectory modifications. As a consequence of the existence in uncertainty in meteorological forecasts and nowcasts, it is important to consider the convective weather cells to be avoided as a stochastic, time-dependent process. In this paper we present a comparative analysis of two methodologies for handling stochastic storms in trajectory planning: one based on stochastic reachability and a second one, based on robust optimal control. In the former, the thunderstorm avoidance problem is modelled as a stochastic reach-avoid problem, considering the motion of the aircraft as a discrete-time stochastic system and the weather hazards as random set-valued obstacles. Dynamic programming is used to compute a Markov feedback policy that maximizes the probability of reaching the target before entering the unsafe set, i.e., the hazardous weather zones. For the latter, the stochastic dynamics of the storms are modeled in continuous time. We implement an optimal control formulation that allows different possible realizations of the stochastic process to be considered. The resulting problem is then transcribed to a nonlinear programming (NLP) problem through the use of direct numerical methods. A benchmark case study is presented, in which the effectiveness of the two proposed approaches are analyzed.Publication Wind-Based Robust Trajectory Optimization using Meteorological Ensemble Probabilistic Forecasts(Eurocontrol, 2016-11-08) González Arribas, Daniel; Soler Arnedo, Manuel Fernando; Sanjurjo Rivo, ManuelA major challenge for Trajectory-Based Operations is the existence of significant uncertainties in the models and systems required for trajectory prediction. In particular, weather uncertainty has been acknowledged as one of the most (if not the most) relevant ones. In the present paper we present preliminary results on robust trajectory planning at the pre-tactical level. The main goal is to plan trajectories that are efficient, yet predictable. State-of-the-art forecasts from Ensemble Prediction Systems are used as input data for the wind field, which we assume to be the unique source of uncertainty. We develop an ad-hoc optimal control methodology to solve trajectory planning problems considering uncertainty in wind fields. A set of Paretooptimal trajectories is obtained for different preferences between predictability and average efficiency; in particular, we present and discuss results for the minimum average fuel trajectory and the most predictable trajectory, including the trade-off between fuel consumption and time dispersion. We show how uncertainty can be quantified and reduced by proposing alternative trajectories.Publication Numerical simulation of heat transfer in a pipe with non-homogeneous thermal boundary condition(Elsevier, 2015-10) Antoranz Perales, Antonio; Gonzalo Grande, Alejandro; Flores Arias, Óscar; García-Villalba Navaridas, ManuelDirect numerical simulations of heat transfer in a fully-developed turbulent pipe flow with circumferentially-varying thermal boundary conditions are reported. Three cases have been considered for friction Reynolds number in the range 180–360 and Prandtl number in the range 0.7–4. The temperature statistics under these heating conditions are characterized. Eddy diffusivities and turbulent Prandtl numbers for radial and circumferential directions are evaluated and compared to the values predicted by simple models. It is found that the usual assumptions made in these models provide reasonable predictions far from the wall and that corrections to the models are needed near the wall.Publication En-Route Optimal Flight Planning Constrained to Pass Through Waypoints using MINLP(2011-06-14) Soler, Manuel; Olivares, Alberto; Bonami, Pierre; Staffetti, ErnestoAbstract: In this paper we study the en-route strategic flight planning of a commercial aircraft constrained to pass through a set of waypoints whose sequence is not predefined. This problem has been solved as an hybrid optimal control problem in which, given the dynamic model of the aircraft, the initial and final states, the path constraints constituting the envelope of flight, and a set of waypoints in the European air space, one has to find the control inputs, the switching times, the optimal sequence of waypoints and the corresponding trajectory of the aircraft that minimize the direct operating cost during the flight. The complete layout of waypoints in the European airspace is reduced and waypoints are gathered into a small number of clusters. The aircraft is constrained to pass through one waypoint inside every cluster of waypoints. The presence of multi point constraints makes the optimal control problem particularly difficult to solve. The hybrid optimal control problem is converted into a mixed integer non linear programming problem first making the unknown switching times part of the state, then introducing binary variable to enforce the constraint of passing through one waypoint inside every cluster, and finally applying a direct collocation method. The resulting mixed integer non linear programming problem has been solved using a branch and bound algorithm. The cases studied and the numerical results show the effectiveness, efficiency and applicability of this method for enroute strategic flight plans definition.Publication A Numerical Framework and Benchmark Case study for Muti-modal Fuel Efficient Aircraft Conflict Avoidance(2014-05-26) Soler, Manuel; Kamgarpour, Maryam; Lygeros, JohnAbstract: We formulate fuel optimal conflict free aircraft trajectory planning as a hybrid optimal control problem. The discrete modes of the hybrid system capture the air traffic procedures for conflict resolution, e. g., speed and turn advisories. In order to solve problems of realistic dimension arising from air traffic sector planning, we formulate a numerically tractable approach to solve the hybrid optimal control problem. The approach is based on introducing binary functions for each mode, relaxing the binary functions and including a penalty term on relaxation. The transformed and discretized problem is a nonlinear program. We use the approach on a benchmark case study for resolving conflict while minimizing fuel consumption of 8 Airbus 320 aircraft in a symmetrical set up.Publication Hybrid Optimal Control for Aircraft Trajectory Design with a Variable Sequence of Modes(Ifac Papers Online, 2011) Kamgarpour, Maryam; Soler, Manuel; Tomlin, Claire J.; Olivares, Alberto; Lygeros, JohnThe problem of aircraft trajectory planning is formulated as a hybrid optimal control problem. The aircraft is modeled as a switched system, that is, a class of hybrid dynamical systems. The sequence of modes, the switching times, and the inputs for each mode are the control variables. An iterative bi-level optimization algorithm is employed to solve the optimal control problem. At the lower level, given a pre-de ned sequence of ight modes, the optimal switching times and the input for each mode are determined. This is achieved by extending the continuous state to include the switching times and then solving a conventional optimal control problem for the extended state. At the higher level, the algorithm modi es the mode sequence in order to decrease the value of the cost function. We illustrate the utility of the problem formulation and the solution approach with two case studies in which short horizon aircraft trajectories are optimized in order to reduce fuel burn while avoiding hazardous weather.Publication Hybrid Optimal Control Approach to Commercial Aircraft 3D Multiphase Trayectory Optimization(American Institute Of Aeronautics And Astronautics, Inc., 2010) Soler, Manuel; Olivares, Alberto; Staffetti, ErnestoGiven the sequence of phases and flights modes conforming the flight profile os a comercial aircraft, the initial and final states, a set of path constraints and real wind forecast data, we solve the multiphase problem of finding optimal control inputs, switching times between flight modes and the corresponding trajectory of the aircraft that minimizes fuel consumption. The aircraft in flight is modelled as a hybriddynamical system, i.e., a system that has contibuos and discrete dynamics, where the distinct discrete dynamics corresponds to different fight phases and swwitches betwrrn them occur either in response to control law or when the state of the system reaches prescribed regions of the state space. The three dimensional motion of the aircraft over a spherical earth is described by a point variable-mass dynamic model. The hybrid optimal control problem is converted into a conventional optimal control problem by a parameterization of the switching instants and solved using a collocation method. This approach provides an overall optimal solution for a complete fight including the optimal switching instants between phases. An application to a realistic 13-phase A-340-300 fight is solved and discussed.