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See detailSatellite Orbits in the Atmosphere: Uncertainty Quantification, Propagation and Optimal Control
Dell'Elce, Lamberto ULg

Doctoral thesis (2015)

From the massive international space station to nanosatellites, all space missions share a common principle: orbiting an object requires energy. The greater the satellite's mass, the higher the launch ... [more ▼]

From the massive international space station to nanosatellites, all space missions share a common principle: orbiting an object requires energy. The greater the satellite's mass, the higher the launch cost. In astrodynamics, this translates into the motto ``use whatever you can''. This concept encompasses a broad spectrum of missions, e.g., the Earth's oblateness is exploited for sun-synchronous orbits and the kinetic energy of a planet is used to accomplish fly-by maneuvers. Nowadays, the same paradigm is coming on stream in the context of distributed space systems, where complex missions are envisaged by splitting the workload of a single satellite into multiple agents. Orbital perturbations -- often regarded as disturbances -- can be turned into an opportunity to control the relative motion of the agents in order to reduce or even remove the need for on-board propellant. This thesis is an attempt to combine uncertainty quantification, analytical propagation, and optimal control of satellite trajectories in the atmosphere for effectively and robustly exploiting the aerodynamic force. Specifically, by means of a probabilistic estimation and prediction of the aerodynamic force and an efficient and consistent propagation of low-Earth orbits, a robust reference trajectory for the realization of relative maneuvers between two satellites in a realistic environment can be generated. [less ▲]

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See detailOptimal propellantless rendez-vous using differential drag
Dell'Elce, Lamberto ULg; Kerschen, Gaëtan ULg

in Acta Astronautica (2015), 109

Optimization of fuel consumption is a key driver in the design of spacecraft maneuvers. For this reason, growing interest in propellant-free maneuvers is observed in the literature. Because it allows us ... [more ▼]

Optimization of fuel consumption is a key driver in the design of spacecraft maneuvers. For this reason, growing interest in propellant-free maneuvers is observed in the literature. Because it allows us to turn the often-undesired drag perturbation into a control force for relative motion, differential drag is among the most promising propellantless techniques for low-Earth orbiting satellites. An optimal control approach to the problem of orbital rendez-vous using differential drag is proposed in this paper. Thanks to the scheduling of a reference maneuver by means of a direct transcription, the method is flexible in terms of cost function and can easily account for constraints of various nature. Considerations on the practical realization of differential-drag-based maneuvers are also provided. The developments are illustrated by means of high-fidelity simulations including coupled 6-degree-of-freedom simulations and an advanced aerodynamic model. [less ▲]

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See detailAnalytic solution for the relative motion of satellites in near-circular low-Earth orbits
Martinusi, Vladimir ULg; Dell'Elce, Lamberto ULg; Kerschen, Gaëtan ULg

in Proceedings of the AAS/AIAA Space FLight Mechanics Meeting (2015)

The paper presents the solution to the problem of the relative motion between two satellites orbiting Earth under the influence of the oblateness and atmospheric drag perturbations. Starting from the ... [more ▼]

The paper presents the solution to the problem of the relative motion between two satellites orbiting Earth under the influence of the oblateness and atmospheric drag perturbations. Starting from the analytic solution to the problem of the absolute motion, the closed-form equations of motion are obtained. No simplifying assumptions are made on the relative dynamics. [less ▲]

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See detailProbabilistic Assessment of Lifetime of Low-Earth-Orbit Spacecraft: Uncertainty Propagation and Sensitivity Analysis
Dell'Elce, Lamberto ULg; Kerschen, Gaëtan ULg

in Journal of Guidance Control & Dynamics (2014)

This paper is devoted to the probabilistic uncertainty quantification of orbital lifetime estimation of low-altitude satellites. Specifically, given a detailed characterization of the dominant sources of ... [more ▼]

This paper is devoted to the probabilistic uncertainty quantification of orbital lifetime estimation of low-altitude satellites. Specifically, given a detailed characterization of the dominant sources of uncertainty, we map this input into a probabilistic characterization of the orbital lifetime through orbital propagation. Standard Monte Carlo propagation is first considered. The concept of drag correction is then introduced to facilitate the use of polynomial chaos expansions and to make uncertainty propagation computationally effective. Finally, the obtained probabilistic model is exploited to carry out stochastic sensitivity analyses, which in turn allow gaining insight into the impact uncertainties have on orbital lifetime. The proposed developments are illustrated using one CubeSat of the QB50 constellation. [less ▲]

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See detailProbabilistic Assessment of the Lifetime of Low-Earth-Orbit Spacecraft: Uncertainty Characterization
Dell'Elce, Lamberto ULg; Arnst, Maarten ULg; Kerschen, Gaëtan ULg

in Journal of Guidance Control & Dynamics (2014)

Orbital lifetime estimation is a problem of great timeliness and importance in astrodynamics. In view of the stochastic nature of the thermosphere and of the complexity of drag modeling, any deterministic ... [more ▼]

Orbital lifetime estimation is a problem of great timeliness and importance in astrodynamics. In view of the stochastic nature of the thermosphere and of the complexity of drag modeling, any deterministic assessment of orbital lifetime is likely to be bound to failure. This is why the present paper performs uncertainty quantification of satellite orbital lifetime estimation. Specifically, this paper focuses on the probabilistic characterization of the dominant sources of uncertainty inherent to low-altitude satellites. Uncertainties in the initial state of the satellite and in the atmospheric drag force, as well as uncertainties introduced by modeling limitations associated with atmospheric density models, are considered. Mathematical statistics methods, in conjunction with mechanical modeling considerations, are used to infer the probabilistic characterization of these uncertainties from experimental data and atmospheric density models. This characterization step facilitates the application of uncertainty propagation and sensitivity analysis methods, which in turn allows gaining insight into the impact that these uncertainties have on the orbital lifetime. The proposed developments are illustrated using one CubeSat of the QB50 constellation. [less ▲]

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See detailUncertainty quantification of the orbital lifetime of a LEO spacecraft
Dell'Elce, Lamberto ULg; Kerschen, Gaëtan ULg

in Proceedings of the Astrodynamics Specialist Conference (2014)

Orbital lifetime estimation is a problem of great timeliness and importance in astrodynamics. In view of the stochastic nature of the thermosphere and of the complexity of drag modeling, any deterministic ... [more ▼]

Orbital lifetime estimation is a problem of great timeliness and importance in astrodynamics. In view of the stochastic nature of the thermosphere and of the complexity of drag modeling, any deterministic assessment of orbital lifetime is likely to be bound to failure. This is why the present paper performs uncertainty quantification of satellite orbital lifetime estimation. Uncertainties in the initial state of the satellite and in the atmospheric drag force, as well as uncertainties introduced by modeling limitations associated with atmospheric density models, are considered. Mathematical statistics methods in conjunction with mechanical modeling considerations are used to infer the probabilistic characterization of these uncertainties from experimental data and atmospheric density models. Monte Carlo propagation is then exploited to achieve a probabilistic description of the orbital lifetime. [less ▲]

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See detailRobust rendez-vous planning using the scenario approach and differential flatness
Dell'Elce, Lamberto ULg; Kerschen, Gaëtan ULg

in Advances in the Astronautical Sciences (2014)

There is a growing interest in uncertainty handling in the spacecraft dynamics community. In particular, robust optimization of spacecraft maneuvers is regarded as an important challenge. This paper ... [more ▼]

There is a growing interest in uncertainty handling in the spacecraft dynamics community. In particular, robust optimization of spacecraft maneuvers is regarded as an important challenge. This paper proposes an optimal control approach for orbital rendez-vous planning under stochastic dynamics and constraints. The method combines differential flatness theory with the scenario approach for optimization under uncertainties. By mapping state and control variables into a set of flat outputs, the enforcement of dynamics equations and boundary conditions is automatically satisfied. The rigorous foundations of the scenario approach lead to a finite-dimensional formulation of the problem which guarantees the feasibility of the solution within an arbitrary portion of the stochastic domain. The methodology is illustrated by means of two case studies involving a rendez-vous in elliptic orbit and a propellantless maneuver using differential drag, respectively. [less ▲]

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See detailAnalytic Model for The Motion About An Oblate Planet in The Presence Atmospheric Drag
Martinusi, Vladimir ULg; Dell'Elce, Lamberto ULg; Kerschen, Gaëtan ULg

in Advances in The Astronautical Sciences (2014)

The paper introduces a new model for the motion about an oblate planet under the influence of the atmospheric drag. Both qualitative and quantitative insights are revealed, as well as closed-form ... [more ▼]

The paper introduces a new model for the motion about an oblate planet under the influence of the atmospheric drag. Both qualitative and quantitative insights are revealed, as well as closed-form equations of motion. The main tool consists in averaging the effects of both perturbations (oblateness and drag), and deriving the variational equations for the vectorial orbital elements. The model is singularity-free and may serve as an initial guess for control problems, as well as an analytic propagator. [less ▲]

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See detailAnalytic Propagation for Satellites in Near-Circular Low-Earth Orbits
Martinusi, Vladimir ULg; Dell'Elce, Lamberto ULg; Kerschen, Gaëtan ULg

in Proceedings of the AIAA/AAS Astrodynamics Specialist Conference (2014)

The present work is focused on providing an analytic model for the motion of an low-Earth-orbiting satellite. The model incorporates the two dominant perturbations, namely the atmospheric drag and the ... [more ▼]

The present work is focused on providing an analytic model for the motion of an low-Earth-orbiting satellite. The model incorporates the two dominant perturbations, namely the atmospheric drag and the Earth oblateness. While the latter is modeled by the second zonal harmonic J 2 , both constant and exponential density distribution models of the atmosphere are considered. The satellite orbit is assumed to be almost circular. Closed-form equations of motion are obtained, even time-explicit in the case of a constant atmosphere. The analytic predictions are carefully validated against direct numerical simulations. The resulting model is suitable to be incorporated in onboard propagators for short-term orbit predictions. [less ▲]

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See detailRobust optimal rendezvous using differential drag
Dell'Elce, Lamberto ULg; Martinusi, Vladimir ULg; Kerschen, Gaëtan ULg

in Proceedings of the AIAA/AAS Astrodynamics Specialist Conference (2014)

The practical realization of the differential drag technique for orbital relative maneuvers must cope with the several and severe uncertainty sources affecting drag modeling. Neglecting these ... [more ▼]

The practical realization of the differential drag technique for orbital relative maneuvers must cope with the several and severe uncertainty sources affecting drag modeling. Neglecting these uncertainties might yield to oversimplified solutions whose representation of a real-life scenario is questionable. The first outcome of this study consists in the synthesis of a robust optimal controller which combines differential flatness theory and the scenario approach to generate a reference path which can be easily followed. The second outcome is the characterization of the relevant uncertainties of the differential drag problem, with a special focus on the aerodynamic force. The developments are validated in a highly detailed simulation environment including, among the perturbations, advanced drag modeling and coupled attitude and orbital dynamics. [less ▲]

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See detailValidation of differential drag propellantless maneuvers using 6 DoF simulations and stochastic dynamics
Dell'Elce, Lamberto ULg; Kerschen, Gaëtan ULg

in Proceedings of the 9th International ESA Conference on Guidance, Navigation & Control Systems (2014)

Differential drag is regarded as a promising technique in low-Earth orbits, since it allows to turn the often-undesired drag perturbation into a control force for relative maneuvers. Nonetheless, relevant ... [more ▼]

Differential drag is regarded as a promising technique in low-Earth orbits, since it allows to turn the often-undesired drag perturbation into a control force for relative maneuvers. Nonetheless, relevant uncertainties in drag modeling make its practical realization a challenge, especially if no other propulsive means is available to accommodate them. The main outcome of this study is the identification and characterization of the uncertainty sources affecting differential-drag-based maneuvers. This characterization is carried out by using statistical methods in conjunction with mechanical modeling considerations to infer a probabilistic model of the sources from observed data. The developments are illustrated in the framework of the QARMAN mission through high-fidelity simulations involving coupled attitude and orbital dynamics. [less ▲]

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See detailComparison between analytical and optimal control techniques in the differential drag based rendez-vous
Dell'Elce, Lamberto ULg; Kerschen, Gaëtan ULg

in Proceedings of the 5th International Conference on Spacecraft Formation Flying Missions & Technologies (2013, May 29)

The focus of this study is on differential drag for propellantless satellite rendez-vous. This technique is particularly attractive for low-Earth-orbit small satellites for which stringent weight ... [more ▼]

The focus of this study is on differential drag for propellantless satellite rendez-vous. This technique is particularly attractive for low-Earth-orbit small satellites for which stringent weight constraints apply. Most existing contributions are based on bang-bang strategies, which may be difficult to implement in practice. This is why the present paper proposes a novel strategy integrating pseudospectral optimal control for maneuver planning and model predictive control for dealing with uncertainties and unmodeled dynamics. One important advantage of this methodology is that it can naturally account for attitude dynamics and constraints, which, in turn, paves the way for the practical realization of differential drag-based rendez-vous. A realistic scenario involving two nanosatellites of the QB50 constellation is considered to illustrate and validate the proposed developments. In addition, a comparison of this numerical technique with an existing analytic solution is carried out, and their respective pros and cons are discussed. [less ▲]

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See detailUncertainty quantification of the aerodynamic force of a convex-shaped spacecraft in free-flow regime
Dell'Elce, Lamberto ULg; Kerschen, Gaëtan ULg

Conference (2013)

Non-spherical gravitational effects and aerodynamic force are the dominant perturbations for low-Earth-orbiting spacecraft. If the former can be modeled with arbitrary accuracy for most applications, it ... [more ▼]

Non-spherical gravitational effects and aerodynamic force are the dominant perturbations for low-Earth-orbiting spacecraft. If the former can be modeled with arbitrary accuracy for most applications, it is not possible for the latter. Uncertainties in the aerodynamic force invalidate any attempt to perform deterministic propagations of the position of the spacecraft, regardless the duration of the simulation. However, the effect of drag, which is largely the main component of the force, is a monotonic decrease of the semi-major axis of the orbit, so that these uncertainties are a major concern for long-term predictions. The purpose of this study is the characterization, propagation, and sensitivity analysis of the uncertainty source in the aerodynamic force of a convex-shaped spacecraft. To illustrate the usefulness of this analysis in real-life applications, the uncertainty quantification of the orbital lifetime of a QB50 nanosatellite is proposed as case study. [less ▲]

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See detailElements of stochastic processes 2012--2013: course material
Arnst, Maarten ULg; Dell'Elce, Lamberto ULg

Learning material (2013)

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See detailStochastic modeling in mechanics 2012--2013: course material
Arnst, Maarten ULg; Dell'Elce, Lamberto ULg

Learning material (2013)

Detailed reference viewed: 221 (87 ULg)
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See detailScientific and Technological Payloads Aboard the B3LSat CubeSat of the QB50 Network
Dell'Elce, Lamberto ULg; Kerschen, Gaëtan ULg; Delabie, Tjorven et al

in Proceedings of the 2nd IAA Conference on University Satellite Missions and Cubesat Workshop (2013)

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See detailPropellantless rendez-vous of QB50 nanosatellites
Dell'Elce, Lamberto ULg; Kerschen, Gaëtan ULg

in Proceedings of the 63rd IAC (2012)

Detailed reference viewed: 22 (4 ULg)