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    • 专利摘要:
    A method of orbiting a spacecraft using continuous or near-continuous thrust propulsion, the method comprising: acquiring, at least once in each half revolution of the spacecraft, measurements of its position and speed; Calculating a thrust control function as a function of said measurements; and driving said thrust in accordance with said control law; characterized in that said control law is obtained from a Lyapunov control function using orbital, preferably equinoxial, parameters of the spacecraft, averaged over at least one said half-revolution. An embedded system for piloting a spacecraft to implement such a method and spacecraft equipped with such a steering system.
    公开号:FR3043985A1
    申请号:FR1502429
    申请日:2015-11-20
    公开日:2017-05-26
    发明作者:Joel Amalric
    申请人:Thales SA；
    IPC主号:
    专利说明:

    d) où x est un vecteur d’état qui, dans le cas considéré ici, représente l’écart entre les paramètres orbitaux mesurés d’un vaisseau spatial et les paramètres de l’orbite cible, u un vecteur de commande qui définit la poussée (orientation et éventuellement intensité) et f(x,u) la fonction, issue des lois de la mécanique orbitale, qui exprime la variation temporelle du vecteur d’état en fonction de la valeur présente de ce vecteur et de la commande. Une fonction de contrôle de Lyapunov V(x) est une fonction dérivable de manière continue, strictement positive pour tout x sauf x=0, telle que V(x=0)=0 et que
    (2).
    Pour que le vecteur d’état évolue vers sa cible x=0 (c'est-à-dire pour que l’orbite du vaisseau spatial tende vers l’orbite cible), il faut minimiser V(x) ; il faut donc choisir une commande u qui rend sa dérivée temporelle v(x’u)aussi négative que possible. Il est donc naturel de prendre
    (3)
    Il s’agit donc de trouver une fonction de contrôle de Lyapunov qui fournisse, via l’équation (3), une loi de contrôle proche de l’optimalité. L’optimalité peut être définie, par exemple, par un temps de transfert minimal, une consommation de propulsant minimale ou par une combinaison de ces objectifs.
    Avant de proposer une forme pour la fonction de contrôle de Lyapunov, il convient de se pencher sur le choix du vecteur d’état x. Conformément à l’art antérieur, ce vecteur est défini à partir des cinq paramètres orbitaux « classiques », qui sont illustrés à l’aide de la figure 2 :
    le demi grand-axe « a » de l’orbite O (supposée circulaire ou elliptique) ; l’excentricité « e » (rapport de la distance centre C -foyer F au demi-grand-axe a ; vaut 0 dans le cas d’une orbite circulaire et est strictement comprise entre 0 et 1 pour une orbite elliptique) l’inclinaison « i » du plan orbital PO par rapport à un plan de référence PR, qui peut être par exemple l’écliptique ou l’équateur ; la longitude du nœud ascendant NA « Ω », mesurée par rapport à une direction de référence DR ; l’argument du périastre « ω », qui est l'angle formé par la ligne des nœuds NA-ND et la direction du périastre DPA dans le plan orbital.
    Ces paramètres orbitaux présentent l’inconvénient d’être mal définis, et donc de présenter des équations du mouvement singulières (division par zéro), pour des faibles excentricités (e»0) et pour des faibles inclinaisons (i*0). Pour cette raison, l’invention utilise des paramètres orbitaux, dits « équinoxiaux », dont les équations du mouvement ne sont jamais singulières et qui sont définis par :
    (4) où v est l’anomalie vraie, c'est-à-dire l’angle entre la direction du périastre DPA et la ligne reliant le centre C à la position du vaisseau spatial VS. On remarque que les paramètres ex, ey peuvent être considérés les composantes d’un vecteur « excentricité » de module « e » et ayant pour angle polaire la direction du périgée, tandis que les paramètres hx, hy sont les composantes d’un vecteur « inclinaison » de module tan(ï'/2) et ayant pour angle polaire la direction du nœud ascendant. L’utilisation des paramètres orbitaux équinoxiaux n’est pas une caractéristique essentielle de l’invention. Si l’orbite cible présente une
    excentricité et une inclinaison non négligeable il est également possible d’utiliser des paramètres orbitaux classiques.
    Les paramètres orbitaux - classiques ou équinoxiaux - sont définis uniquement pour une orbite képlérienne, ce qui n’est pas le cas d’un vaisseau spatial soumis à une poussée. Cependant, en connaissant à chaque instant la position et la vitesse du vaisseau spatial, il est possible de calculer les paramètres de son orbite osculatrice, c'est-à-dire de l’orbite que le vaisseau suivrait si la propulsion était instantanément coupée et en l’absence de toute autre perturbation. La position et la vitesse du vaisseau spatial sont généralement connues grâce à l’utilisation d’un système de navigation GNSS - par mesure directe ou interpolation entre deux mesures successives. L’invention n’utilise pas les paramètres orbitaux mesurés (ou, plus exactement, calculés à partir des mesures) en tant que tels, mais ces paramètres moyennés sur au moins une demi-période de révolution du vaisseau spatial. En effet, les paramètres orbitaux mesurés oscillent à la fréquence orbitale, ce qui nuit à la stabilité de la commande ; ces oscillations sont supprimées par l’opération de moyenne.
    Une fonction de contrôle de Lyapunov selon un mode de réalisation de l’invention peut s’écrire comme une somme pondérée d’erreurs quadratiques moyennes des paramètres orbitaux équinoxiaux. Plus précisément elle peut être donnée par :
    (5) où â,ëx,ëy,hx,hy sont les paramètres orbitaux équinoxiaux de l’orbite du vaisseau spatial moyennés sur au moins une demi-révolution, âT,ëXT,ëy,TT,hXT,hyTes paramètres orbitaux équinoxiaux de l’orbite cible, amax>^,max>^,max A,maxA.max|es dérives séculaires (c'est-à-dire les dérivées
    temporelles moyennes) des paramètres a, ex,ey,hx,hy obtenues par application de la loi de commande qui maximise ces dérives séculaires ou, de manière équivalente, l’incrément orbital de chaque paramètre orbital, et wy (j=a, ex, ey, hx, hy) des coefficients de pondération non négatifs, et de préférence strictement positifs. Dans le mode de réalisation le plus simple, qui donne néanmoins des résultats satisfaisants, ces coefficients de pondérations peuvent être tous égaux entre eux, et notamment être pris égaux à 1. En variante, afin de rapprocher la loi de contrôle de l’optimalité, il est possible de procéder à une optimisation numérique de ces performances. Cette optimisation peut être effectuée au sol, avant le début du transfert, en prenant par exemple comme fonction de coût à minimiser le temps de transfert. Il est aussi possible de répéter l’optimisation au cours du transfert, avec une cadence de répétition très faible (par exemple une fois tous les trois mois), ce qui nécessite de transmettre les nouveaux paramètres optimisés au processeur embarqués du vaisseau spatial.
    En pratique, pour trouver les valeurs ^max’^max’^maxA.maxA.mæ^ 0π intègre la loi de commande qui maximise la variation de chaque élément orbital équinoxial pour chaque position orbitale L ; puis on moyenne chaque dérivée temporelle sur la période considérée et sur toutes les valeurs de L en laissant les autres éléments orbitaux constants. Cette intégration peut se faire numériquement ou analytiquement. L’article précité « Optimisation of low-thrust orbit transfers using the Q-Law for the initial guess » préconise également une optimisation des coefficients de pondération de la Q-Law, mais en utilisant des algorithmes génétiques qui s’avèrent très lourds du point de vue computationnel. Dans le cas de l’invention, grâce à l’utilisation de paramètres orbitaux moyens, il est possible d’utiliser des techniques plus simples d’optimisation non-linéaire.
    Il est possible d’imposer des contraintes d’altitude (altitude du périastre rp supérieure ou égale à un premier seuil rp,mjn et/ou altitude de l’apoastre rp inférieure ou égale à un second seuil ra,max) en multipliant la fonction V(x) donnée par l’équation (5) par des fonctions barrière correspondantes Βε , Βε caractérisées par un paramètre numérique de lissage ε. Une fonction barrière est une fonction continue (et de préférence dérivable) dont la valeur tend rapidement vers l’infini à l’approche d’une valeur limite, tout en restant relativement plate loin de cette valeur. On peut écrire la fonction de contrôle de Lyapunov contrainte :
    (6) L’utilisation d’une fonction de contrôle de Lyapunov exprimée en fonction de paramètres orbitaux moyens présente plusieurs avantages : les paramètres moyens n’oscillent pas à la fréquence orbitale (contrairement aux paramètres orbitaux mesurés non moyennées) ; cela permet une intégration rapide de l’équation différentielle (1), nécessaire pour calculer le vecteur de commande u via l’équation (3) appliquée au système en dynamique moyennée, avec un pas temporel qui peut être de plusieurs révolutions ; l’évolution désirée de la poussée est plus lisse ; l’évolution temporelle du demi grand-axe est monotone (voir la figure 6a), ce qui permet de mettre en œuvre une méthode simple pour satisfaire une condition terminale de rendez-vous en longitude.
    Cette méthode consiste, à l’approche de l’orbite cible, à : prédire la longitude d’arrivée sur l’orbite cible, et estimer l’erreur de rendez-vous par rapport à la longitude souhaitée ; modifier, dans la fonction de contrôle de Lyapunov, le paramètre âT en calculant dynamiquement un petit écart à la cible pour ajuster la dérive moyenne en longitude géographique ; et avant la fin du transfert, restaurer la valeur initiale de ce paramètre. L’idée est de prévoir la longitude d’arrivée et, si elle ne correspond pas à la cible, à modifier le paramètre âT de manière à corriger l’erreur. De manière équivalente, cela revient à changer le poids numérique
    associé au demi-grand axe dans un rapport égal à {(â- â/)/(â - âT)}2. Cette correction est dynamique au sens où elle doit être recalculée plusieurs fois le long de la trajectoire de transfert, car la prédiction de la longitude d’arrivée est affectée d’une erreur qui a tendance à diminuer dans le temps.
    En général il n’est pas utile de mettre en œuvre la correction plus d’un mois ou deux avant la date d’arrivée prévisionnelle sur l’orbite cible, car les erreurs de prédiction seraient trop importantes. En outre, il faut arrêter la correction au moins une semaine ou deux avant la date d’arrivée prévisionnelle pour éviter que l’amplitude des corrections ne diverge (quand il reste peu de temps, il faut une modification importante de ïïT pour changer, même légèrement, la longitude d’arrivée). Dans la phase finale du transfert, on garde la dernière valeur modifiée du paramètre ατ, ou la dernière valeur modifiée de son poids.
    La figure 3 montre un ordinogramme d’un procédé selon l’invention.
    On commence par la mesure de la position et de la vitesse du vaisseau spatial, effectuée par GNSS (ou par télémétrie, mais on perd alors l’autonomie du vaisseau) au moins une fois par révolution. Cela permet de déterminer, à une pluralité d’instants, les paramètres orbitaux (équinoxiaux) du vaisseau spatial, qui sont ensuite moyennés. Les paramètres moyens ainsi obtenus sont utilisés pour calculer la fonction de contrôle de Lyapunov. Les coefficients de pondération de cette fonction peuvent être optimisés périodiquement par un ordinateur situé au sol, et transmis au processeur embarqué. En outre, un paramètre cible peut être modifié temporairement pour corriger une erreur estimée de rendez-vous en longitude, cette estimation étant à son tour calculée à partir des mesures RGNSS. Ensuite, la fonction de contrôle de Lyapunov est utilisée pour calculer la fonction de commande u, qui pilote le système de propulsion continue ou quasi-continue.
    En pratique, un récepteur GNSS acquiert des mesures de position et de vitesse à une cadence élevée (plusieurs fois par minute), mais l’on effectue généralement un filtrage de ces mesures pour ne retenir que quelques acquisitions (typiquement entre 1 et 4) par révolution.
    La figure 4 est un schéma fonctionnel très simplifié d’un vaisseau spatial VS équipé d’un système de pilotage selon l’invention. Le système de pilotage comprend : un récepteur GNSS (référence GNSS) qui fournit des mesures de position et de vitesse ; optionnellement un récepteur (référence RSS) qui reçoit d’une station au sol des mises à jour des paramètres de pondération de la fonction de contrôle de Lyapunov et/ou des mises à jour des paramètre de l’orbite cible et/ou d’autres commandes ; un processeur embarqué PE qui reçoit les signaux de position et de vitesse du récepteur GNSS (et éventuellement les données en provenance du récepteur RSS) et qui calcule un signal de commande u ; et un système de propulsion (généralement électrique) à poussée continue ou quasi-continue qui reçoit et applique ce signal de commande.
    Un procédé selon l’invention a été testé pour le cas de la mise à poste d’un satellite géostationnaire à partir d’une orbite d’injection elliptique et inclinée. Le tableau 1 ci-dessous donne les paramètres orbitaux (classiques) de l’orbite initiale et de l’orbite cible :
    Tableau 1
    Les paramètres « libres » sont traités en mettant à zéro le poids Wj correspondant, ou alors en fixant une cible orbitale égale au paramètre initial (cette deuxième méthode fonctionne moins bien que la première si l’on considère les perturbations naturelles dans la dynamique).
    Le satellite présente une masse initiale de 2000 kg, utilise un propulsant (Xénon) d’impulsion spécifique 2000 s et son système de propulsion électrique a une poussée de 0,35 N. On a considéré des solutions à temps minimal, dans lesquelles la poussée prend toujours sa valeur maximale et seule son orientation est pilotée.
    Le tableau 2 illustre les performances obtenues en utilisant un pilotage « optimal », au sens qu’il minimise la durée du transfert, calculé au moyen de la technique T_3D (voir l’article de T. Dargent cité plus haut) et par la méthode de l’invention (avec des coefficients de pondération unitaires). Les métriques de performance considérés sont la durée de transfert (en jours), la consommation de propulsant (en kg) et le Delta-V.
    Ces résultats sont très satisfaisants, car la méthode selon l’invention entraîne un surcoût très faible (1,05% pour la durée de transfert et la consommation de propulsant, 1,01% pour le Delta-V) par rapport à la solution optimale, tout en étant beaucoup moins coutèuse en termes de ressources de calcul, ce qui permet se mise en œuvre par un processeur embarqué. Et ces performances pourraient être encore améliorées en optimisant les coefficients de pondération de la fonction de contrôle de Lyapunov. L’application de la Q-Law (cf. l’article précité « Techniques for designing many-revolution, electric-propulsion trajectories », cas B) conduit à une consommation de Xénon sensiblement plus élevée : 221 kg. L’utilisation d’une optimisation par algorithme génétique permet de réduire cette consommation à 213 kg, mais au prix d’une augmentation considérable de la complexité computationnelle.
    Les figures 5a à 5d permettent de suivre l’historique du transfert orbital obtenu par la méthode T_3D. Plus précisément :
    La figure 5a montre l’évolution temporelle du demi-grand axe de l’orbite
    La figure 5b montre l’évolution temporelle de l’excentricité ;
    La figure 5c montre l’évolution temporelle de l’inclinaison ; et
    La figure 5d montre l’évolution temporelle du rayon orbital, qui oscille fortement à la demi-période orbitale.
    Les figures 6a à 6c permettent de suivre l'historique du transfert orbital obtenu par la méthode selon l’invention. Plus précisément :
    La figure 6a montre l’évolution temporelle du rayon à l’apogée ra (courbe pointillée la plus élevée), du rayon au périgée rp (courbe pointillée la moins élevée) et du demi-grand axe a (courbe trait continu) ; on peut remarquer que l’évolution du demi-grand axe est monotone, ce qui permet d’imposer le respect d’une condition de rendez-vous en longitude, comme cela a été expliqué plus haut. L’évolution du rayon à l’apogée, par contre, n’est pas monotone car il s’est avéré optimal de remonter l’apogée pour rendre plus efficace la correction de l’inclinaison. L’unité de longueur utilisée pour l’axe des ordonnées, désignées par DU, correspond à 10.000 km.
    La figure 6b montre l’évolution temporelle de l’excentricité ; et
    La figure 6c montre l’évolution temporelle de l’inclinaison.
    Les profils du demi-grand axe et de l’excentricité ressemblent beaucoup à ceux des solutions du contrôle optimal. En revanche, le profil en inclinaison est sensiblement différent, en particulier en fin de transfert. Cela signifie qu’il existe de nombreuses trajectoires, différentes entre elles mais qui sont « quasi optimales ». La méthode selon l’invention permet d’en trouver une.
    La figure 7a montre l’évolution de la fonction de contrôle de Lyapunov - en fait, de sa racine carrée, dont la dimension est celle d’un temps, et qui peut être considérée une approximation par excès de la durée restante du transfert. La ligne pointillée représente la vraie durée restante, déterminée a posteriori. La figure 7b représente les dérivées de la fonction de contrôle de Lyapunov rapport aux paramètres orbitaux équinoxiaux, qui permettent de déterminer la direction de la poussée.
    METHOD FOR THE ORBITAL TRANSFER OF A SPATIAL VESSEL USING CONTINUOUS OR QUASI-CONTINUOUS THRUST AND ON-LINE STEERING SYSTEM FOR IMPLEMENTING A
    This invention relates to the field of spaceflight. It relates to a method for carrying out the orbital transfer of a spacecraft using a continuous or quasi-continuous thrust, an onboard flight control system for the implementation of such a method and a spacecraft. equipped with such a system.
    Spacecraft - artificial satellites or probes - are usually injected by a launcher into a so-called injection orbit, which does not correspond to the orbit, not necessarily terrestrial, that it must reach to accomplish its mission ("upgrade"). station "), for example a geostationary orbit for a telecommunications satellite. In addition, the missions of space exploration probes generally comprise several phases, characterized by different orbits. It is therefore essential to be able to accurately perform orbital transfer maneuvers.
    In the case of "conventional", chemical propulsion spacecraft, orbital transfer is carried out using very intense and very short thrusts relative to an orbital period. Typically, a first thrust ejects the spacecraft from its initial orbit (eg, injection) and positions it in a so-called transfer orbit, which is chosen to cross the target orbit, or destination. When the spacecraft has arrived near the crossing point, a second thrust puts it on said target orbit.
    The electric propulsion systems are developing significantly because they can very strongly limit the mass of propulsion necessary to impart to the spacecraft a given impulse. This makes it possible to reduce the mass of the ship at launch and / or to prolong its life. Electric propulsion provides a lower thrust of several orders of magnitude in relation to chemical thrust, but can be sustained, continuously or intermittently, over comparable durations (for example, not less than one-tenth) in duration. orbital transfer; in this case we speak of continuous or "quasi-continuous" thrust. Orbital transfer is therefore quite different than in the case of chemical propulsion - by progressive deformation of the starting orbit. By way of example, FIG. 1 illustrates the progressive transfer of an initial elliptical orbit Ol into a circular OC target orbit.
    There is therefore the problem of controlling the intensity and orientation of the thrust throughout the transfer phase.
    Conventionally, the control is carried out in open loop: an optimal control law is calculated on the ground and transmitted to the computer of board which controls the system of propulsion. At regular intervals, for example once a week, a new control law is recalculated taking into account the actual position and speed of the spacecraft, which in general will not correspond exactly to those expected. Such an approach is cumbersome to implement because the trajectory optimization calculations are very complex (it is a question of solving a problem of nonlinear optimization under nonlinear constraints as well). Moreover, between two successive updates of the control law, the spacecraft can deviate significantly from its ideal trajectory, which increases the duration of the transfer phase and the consumption of propulsion. Thierry Dargent's article "Averaging technique in T-3D: an integrated tool for continuous optimal control in orbit transfers", AAS 14-312 (2014) describes a technique for calculating an optimal control law for continuous thrust. or quasi-continuous that can be used in an open-loop approach.
    It is also known to use heuristic-type techniques, called stabilization techniques, which are implicitly based on the minimization of a Lyapunov control function. A technique of this type, called "Q-Law", used mainly as a predimensioning method, is described in the following articles: AE Petropoulos, S. Lee "Optimization of low-thrust orbit transfers using the Q-Law for the initial guess AAS / AIAA Astrodynamics Specialists Conference, 2005; S. Lee et al. "Design and Optimization of Low-Thrust Orbit Transfer" in: Aerospace Conference, 2005 IEEE. IEEE, 2005. p. 855-869; AE Petropoulos et al. "Techniques for designing many-revolution, electric-propulsion trajectories", AAS 14-373, 2014.
    This technique does not give full satisfaction. On the one hand, it presents problems of instability, especially in the case of orbits with low eccentricity and low inclination, which are of very significant practical interest (it is enough to think of geostationary orbits, which have an eccentricity and an inclination null), on the other hand it leads to results rather far from an optimal control law, unless sophisticated techniques are used (optimization of weighting coefficients using genetic algorithms). Moreover, it does not make it possible to manage the constraints of rendezvous in longitude, which are very important in the case of the posting of the geostationary satellites.
    To overcome the disadvantages of open loop control, it would be desirable to adopt a closed-loop approach (feedback loop), in which an on-board processor calculates in real time the command to be applied to the propulsion system taking into account the position and speed of the spacecraft, determined for example by a satellite navigation system (GNSS) of the "Global Navigation Satellite System". The computing power of the embedded processors being limited, it seems however difficult to implement an optimal control law in closed loop. The invention aims to overcome the aforementioned drawbacks of the prior art, and more particularly to provide a closed-loop control technique of the continuous or quasi-continuous thrust to achieve an orbital transfer that is both stable, simple to put implemented and close to optimality. Advantageously, such a technique can make it possible to manage the constraints of appointments in longitude.
    According to the invention, this goal is achieved by using a heuristic control law which, as in the case of Q-Law, is obtained from a Lyapunov control function but which: expresses this function by means of equinoxial orbital parameters, instead of the "conventional" orbital parameters used in the prior art; and uses orbital (equinoxial) parameters averaged over at least half a revolution period.
    Thus, an object of the invention is a method of orbital transfer of a spacecraft using continuous or quasi-continuous thrust propulsion, the method comprising: the acquisition, at least once in each revolution of the spacecraft, measurements of position and speed; Calculating a thrust control function as a function of said measurements; and driving said thrust in accordance with said control law; characterized in that said control law is obtained from a Lyapunov control function proportional to a weighted sum of terms, each term being representative of a quadratic error between a measured orbital parameter of an averaged spacecraft orbit on at least one half-revolution and the corresponding orbital parameter of an arrival target orbit, normalized with respect to the maximum value of the drift, averaged over at least half a revolution, of said orbital parameter of said spacecraft.
    According to particular embodiments of such a method: Said or each said orbital parameter may be an equinoxial orbital parameter. The acquisition of said position and speed measurements can be performed on board said spacecraft by means of a GNSS receiver.
    Said calculation of a control function can be performed by a processor embedded on board said spacecraft.
    The said Lyapunov control function may comprise at least one multiplicative term consisting of a barrier function imposing a maximum or minimum altitude constraint of said spacecraft.
    The weights of said weighted sum may be constant and non-negative. In particular, they can all be equal.
    As a variant, the method may comprise a step of numerical optimization of the weights of said weighted sum, this step being performed by a computer on the ground before the start of the transfer and at least once during the transfer.
    The method may also include, after an initial phase of the transfer: • calculating an estimate of a longitude rendezvous error on the target target orbit; Modifying, in said Lyapunov control function, an orbital parameter of said target target orbit representing its half-major axis or a weighting coefficient of this parameter; and during a terminal phase of the transfer, maintaining a constant value of said orbital parameter and its weighting coefficient.
    Said propulsion may be of the electric type.
    Steering said thrust may include determining at least its orientation.
    Another object of the invention is an onboard spacecraft control system comprising: a continuous or quasi-continuous thrust propulsion system; a GNSS receiver configured to acquire, at least once in each revolution of the spacecraft, measurements of its position and speed; a processor programmed to calculate a thrust control function as a function of said measurements and to drive said thrust propulsion system continuously or quasi-continuously in accordance with said control law; characterized in that said processor is programmed to calculate said control law from a Lyapunov control function proportional to a weighted sum of terms, each term being representative of a quadratic error between a measured orbital parameter of an orbit a spacecraft averaged over at least half a revolution and the corresponding orbital parameter of a target target orbit normalized to the maximum value of the rate of change of said orbital parameter, averaged over at least one half revolution of said spacecraft .
    Advantageously, said or each said orbital parameter is an equinoxial orbital parameter.
    Yet another object of the invention is a spacecraft equipped with such an onboard piloting system. Other characteristics, details and advantages of the invention will emerge on reading the description given with reference to the accompanying drawings given by way of example and which represent, respectively:
    Figure 1, the orbital transfer of a satellite obtained using a continuous or quasi-continuous thrust;
    Figure 2, the definition of orbital parameters;
    FIG. 3 is a flow chart of a method according to one embodiment of the invention;
    Figure 4, a simplified block diagram of a spacecraft equipped with a control system according to an embodiment of the invention;
    Figures 5a to 5d graphs illustrating the implementation of a control method according to the prior art; and
    FIGS. 6a to 6c and 7a, 7b, graphs illustrating the implementation of a control method according to one embodiment of the invention.
    As mentioned above, the invention uses a control law obtained from a Lyapunov control function ("Control-Lyapunov function" in English). It is therefore important to define such a function and its use to obtain a control law.
    We consider a system governed by the differential equation
    d) where x is a state vector which, in the case considered here, represents the difference between the measured orbital parameters of a spacecraft and the parameters of the target orbit, u a control vector which defines the thrust (orientation and possibly intensity) and f (x, u) the function, resulting from the laws of orbital mechanics, which expresses the temporal variation of the state vector as a function of the present value of this vector and the control. A Lyapunov control function V (x) is a continuously differentiable, strictly positive function for all x except x = 0, such that V (x = 0) = 0 and that
    (2).
    For the state vector to move towards its target x = 0 (ie, for the spacecraft's orbit to tend toward the target orbit), V (x) must be minimized; we must therefore choose a command u which makes its time derivative v (x'u) as negative as possible. It is therefore natural to take
    (3)
    It is therefore necessary to find a Lyapunov control function that provides, via equation (3), a control law close to optimality. The optimality can be defined, for example, by a minimum transfer time, a minimum power consumption or a combination of these objectives.
    Before proposing a form for the Lyapunov control function, the choice of the state vector x should be considered. According to the prior art, this vector is defined from the five "conventional" orbital parameters, which are illustrated using FIG.
    the semi-major axis "a" of the orbit O (assumed to be circular or elliptical); the eccentricity "e" (ratio of the center distance C -Foyer F to the half-major-axis a, is 0 in the case of a circular orbit and is strictly between 0 and 1 for an elliptical orbit) inclination "I" of the orbital plane PO with respect to a reference plane PR, which can be for example the ecliptic or the equator; the longitude of the ascending node NA "Ω", measured with respect to a reference direction DR; the "ω" periastrophe argument, which is the angle formed by the line of NA-ND nodes and the direction of the DPA periph- eral in the orbital plane.
    These orbital parameters have the disadvantage of being poorly defined, and therefore of presenting singular motion equations (division by zero), for small eccentricities (e "0) and for small inclinations (i * 0). For this reason, the invention uses orbital parameters, called "equinoxial" parameters, whose equations of motion are never singular and which are defined by:
    (4) where v is the true anomaly, that is, the angle between the direction of the DPA perimeter and the line connecting the center C to the position of the spacecraft VS. We note that the parameters ex, ey can be considered the components of an "eccentricity" vector of module "e" and having for polar angle the direction of the perigee, while the parameters hx, hy are the components of a vector " tan (ï '/ 2) tilt and having polar angle the direction of the ascending node. The use of equinoxial orbital parameters is not an essential feature of the invention. If the target orbit has a
    eccentricity and a sizeable inclination it is also possible to use conventional orbital parameters.
    The orbital parameters - classical or equinoxial - are defined only for a Keplerian orbit, which is not the case for a spacecraft subjected to a thrust. However, knowing the position and speed of the spacecraft at any moment, it is possible to calculate the parameters of its osculating orbit, that is to say of the orbit that the ship would follow if the propulsion was instantly cut off. in the absence of any other disturbance. The position and speed of the spacecraft are generally known through the use of a GNSS navigation system - by direct measurement or interpolation between two successive measurements. The invention does not use measured orbital parameters (or, more accurately, calculated from the measurements) as such, but these parameters averaged over at least half a revolution period of the spacecraft. Indeed, the measured orbital parameters oscillate at the orbital frequency, which affects the stability of the control; these oscillations are suppressed by the average operation.
    A Lyapunov control function according to one embodiment of the invention can be written as a weighted sum of mean squared errors of the equinoctial orbital parameters. More precisely, it can be given by:
    (5) where,, ëx, ëy, hx, hy are the equinoctial orbit parameters of the spacecraft orbit averaged over at least half a revolution, TT, ëXT, ëy, TT, hXT, hyT equinoxial orbital parameters of the target orbit, amax> ^, max> ^, max A, maxA.max | secular drifts (that is, derivatives
    temporal averages) of the parameters a, ex, ey, hx, hy obtained by applying the control law that maximizes these secular drifts or, equivalently, the orbital increment of each orbital parameter, and wy (j = a, ex , ey, hx, hy) non-negative, and preferably strictly positive, weighting coefficients. In the simplest embodiment, which nevertheless gives satisfactory results, these weighting coefficients may all be equal to each other, and in particular be equal to 1. As a variant, in order to bring the control law closer to optimality, it is possible to perform a numerical optimization of these performances. This optimization can be done on the ground, before the start of the transfer, taking for example as a cost function to minimize the transfer time. It is also possible to repeat the optimization during the transfer, with a very low repetition rate (for example once every three months), which requires transmitting the new optimized parameters to the embedded processor of the spacecraft.
    In practice, to find the values ^ max '^ max' ^ maxA.maxA.mæ ^ 0π integrates the control law which maximizes the variation of each equinoctial orbital element for each orbital position L; then we average each time derivative over the period considered and on all the values of L leaving the other orbital elements constant. This integration can be done numerically or analytically. The aforementioned article "Optimization of low-thrust orbit transfers using the Q-Law for the initial guess" also recommends an optimization of the weighting coefficients of the Q-Law, but by using genetic algorithms which are very heavy from the point computational view. In the case of the invention, through the use of average orbital parameters, it is possible to use simpler techniques of non-linear optimization.
    It is possible to impose altitude constraints (altitude of the perimeter rp greater than or equal to a first threshold rp, mjn and / or altitude of apoastre rp less than or equal to a second threshold ra, max) by multiplying the function V (x) given by equation (5) by corresponding barrier functions Βε, Βε characterized by a numerical smoothing parameter ε. A barrier function is a continuous (and preferably differentiable) function whose value tends rapidly towards infinity when approaching a limit value, while remaining relatively flat far from this value. One can write the Lyapunov constraint control function:
    (6) The use of a Lyapunov control function expressed as a function of average orbital parameters has several advantages: the average parameters do not oscillate at the orbital frequency (in contrast to the measured orbital parameters that are not averaged); this allows a fast integration of the differential equation (1), necessary to calculate the control vector u via the equation (3) applied to the system in dynamic averaged, with a time step which can be of several revolutions; the desired evolution of the thrust is smoother; the temporal evolution of the semi-major axis is monotonous (see Figure 6a), which makes it possible to implement a simple method to satisfy a terminal terminal condition in longitude.
    This method involves, when approaching the target orbit, to: predict the longitude of arrival in the target orbit, and estimate the error of rendezvous with respect to the desired longitude; modifying, in the Lyapunov control function, the parameter âT by dynamically calculating a small deviation from the target to adjust the mean drift in geographical longitude; and before the end of the transfer, restore the initial value of this parameter. The idea is to predict the longitude of arrival and, if it does not correspond to the target, to modify the parameter âT so as to correct the error. Equivalently, this amounts to changing the digital weight
    associated with the half-major axis in a ratio equal to {(â- â /) / (â - âT)} 2. This correction is dynamic in the sense that it must be recalculated several times along the transfer path, because the prediction of the arrival longitude is affected by an error which tends to decrease over time.
    In general it is not useful to implement the correction more than a month or two before the target arrival date in the target orbit, as the prediction errors would be too important. In addition, the correction must be stopped at least a week or two before the expected arrival date to prevent the range of corrections from diverge (when there is little time, there must be a major change in the currency to change even slightly, the arrival longitude). In the final phase of the transfer, we keep the last modified value of the parameter ατ, or the last modified value of its weight.
    Figure 3 shows a flow chart of a method according to the invention.
    We begin by measuring the position and speed of the spacecraft, performed by GNSS (or telemetry, but then lose the autonomy of the vessel) at least once per revolution. This makes it possible to determine, at a plurality of instants, the orbital (equinoxial) parameters of the spacecraft, which are then averaged. The average parameters thus obtained are used to calculate the Lyapunov control function. The weighting coefficients of this function can be periodically optimized by a computer located on the ground, and transmitted to the onboard processor. In addition, a target parameter may be temporarily changed to correct an estimated longitude rendezvous error, which estimate is in turn calculated from the RGNSS measurements. Next, the Lyapunov control function is used to calculate the control function u, which drives the continuous or near-continuous propulsion system.
    In practice, a GNSS receiver acquires position and speed measurements at a high rate (several times per minute), but these measurements are generally filtered to retain only a few acquisitions (typically between 1 and 4) by revolution.
    FIG. 4 is a very simplified block diagram of a spacecraft VS equipped with a control system according to the invention. The control system comprises: a GNSS receiver (GNSS reference) which provides position and speed measurements; optionally a receiver (RSS reference) which receives from a ground station updates of the weighting parameters of the Lyapunov control function and / or updates of the parameters of the target orbit and / or other orders ; an embedded processor PE which receives the position and speed signals of the GNSS receiver (and possibly the data from the RSS receiver) and which calculates a control signal u; and a propulsion system (generally electric) with continuous or quasi-continuous thrust which receives and applies this control signal.
    A method according to the invention has been tested for the case of the setting of a geostationary satellite post from an elliptical and inclined injection orbit. Table 1 below gives the (conventional) orbital parameters of the initial orbit and the target orbit:
    Table 1
    The "free" parameters are processed by setting to zero the corresponding weight Wj, or else by setting an orbital target equal to the initial parameter (this second method works less well than the first if we consider the natural disturbances in the dynamics).
    The satellite has an initial mass of 2000 kg, uses a propulsive (Xenon) specific pulse 2000 s and its electric propulsion system has a thrust of 0.35 N. We considered solutions in minimal time, in which the thrust always takes its maximum value and only its orientation is controlled.
    Table 2 illustrates the performances obtained using an "optimal" control, in the sense that it minimizes the duration of the transfer, calculated using the T_3D technique (see the article by T. Dargent cited above) and by the method of the invention (with unit weighting coefficients). The performance metrics considered are the transfer time (in days), the propulsant consumption (in kg) and the Delta-V.
    These results are very satisfactory, because the method according to the invention entails a very low additional cost (1.05% for the transfer time and propulsant consumption, 1.01% for the Delta-V) compared to the optimal solution. , while being much less expensive in terms of computing resources, which allows implementation by an embedded processor. And these performances could be further improved by optimizing the weighting coefficients of the Lyapunov control function. The application of the Q-Law (see the aforementioned article "Techniques for designing many-revolution, electric-propulsion trajectories", case B) leads to a significantly higher consumption of Xenon: 221 kg. The use of a genetic algorithm optimization reduces this consumption to 213 kg, but at the cost of a considerable increase in computational complexity.
    FIGS. 5a to 5d make it possible to follow the history of the orbital transfer obtained by the T_3D method. More precisely :
    Figure 5a shows the temporal evolution of the semi-major axis of the orbit
    Figure 5b shows the temporal evolution of eccentricity;
    Figure 5c shows the temporal evolution of the inclination; and
    Figure 5d shows the temporal evolution of the orbital radius, which oscillates strongly at the half orbital period.
    FIGS. 6a to 6c make it possible to follow the history of the orbital transfer obtained by the method according to the invention. More precisely :
    Figure 6a shows the temporal evolution of radius at apogee ra (highest dotted curve), radius at perigee rp (lowest dotted curve) and half-major axis a (continuous line curve); we can notice that the evolution of the semi-major axis is monotonous, which makes it possible to impose the respect of a rendezvous condition in longitude, as explained above. The evolution of the radius at the apogee, on the other hand, is not monotonous because it has proved optimal to go back to the climax to make the correction of the inclination more effective. The length unit used for the ordinate axis, denoted by DU, is 10,000 km.
    Figure 6b shows the temporal evolution of eccentricity; and
    Figure 6c shows the temporal evolution of the inclination.
    The profiles of the semi-major axis and the eccentricity are very similar to those of the optimal control solutions. On the other hand, the inclination profile is substantially different, especially at the end of the transfer. This means that there are many trajectories, different from each other but which are "almost optimal". The method according to the invention makes it possible to find one.
    Figure 7a shows the evolution of the Lyapunov control function - in fact, its square root, whose size is that of a time, and which can be considered an approximation by excess of the remaining duration of the transfer. The dotted line represents the true remaining duration, determined a posteriori. Figure 7b shows the derivatives of the Lyapunov control function relative to the equinoctial orbital parameters, which make it possible to determine the direction of the thrust.
    权利要求:
    Claims (14)
    [1" id="c-fr-0001]
    A method of orbital transfer of a spacecraft (VS) using continuous or near-continuous thrust propulsion, the method comprising: acquiring, at least once in each revolution of the spacecraft, measurements of its position and its speed; Calculating a control function (u) of the thrust as a function of said measurements; and driving said thrust in accordance with said control law; characterized in that said control law is obtained from a Lyapunov control function proportional to a weighted sum of terms, each term being representative of a quadratic error between a measured orbital parameter of an averaged spacecraft orbit on at least one half-revolution and the corresponding orbital parameter of an arrival target orbit, normalized with respect to the maximum value of the drift, averaged over at least half a revolution, of said orbital parameter of said spacecraft.
    [2" id="c-fr-0002]
    2. The method of claim 1 wherein said or each said orbital parameter is an equinoctial orbital parameter.
    [3" id="c-fr-0003]
    3. Method according to one of the preceding claims wherein the acquisition of said position and speed measurements is performed on board said spacecraft by means of a GNSS receiver (RGNSS).
    [4" id="c-fr-0004]
    4. Method according to one of the preceding claims wherein said calculation of a control function is performed by an embedded processor (PE) on board said spacecraft.
    [5" id="c-fr-0005]
    5. Method according to one of the preceding claims wherein said Lyapunov control function comprises at least one multiplicative term consisting of a barrier function imposing a maximum or minimum altitude constraint of said spacecraft.
    [6" id="c-fr-0006]
    6. Method according to one of the preceding claims wherein the weight of said weighted sum are constant and non-negative.
    [7" id="c-fr-0007]
    The method of claim 6 wherein the weights of said weighted sum are all equal.
    [8" id="c-fr-0008]
    8. Method according to one of claims 1 to 5 comprising a step of digitally optimizing the weight of said weighted sum, this step being performed by a computer on the ground before the start of the transfer and at least once during the transfer.
    [9" id="c-fr-0009]
    9. Method according to one of the preceding claims also comprising, after an initial phase of the transfer: • calculating an estimate of a longitude rendezvous error on the target target orbit; Modifying, in said Lyapunov control function, an orbital parameter of said target target orbit representing its half-major axis or a weighting coefficient of this parameter; and during a terminal phase of the transfer, maintaining a constant value of said orbital parameter and its weighting coefficient.
    [10" id="c-fr-0010]
    10. Method according to one of the preceding claims wherein said propulsion is of the electric type.
    [11" id="c-fr-0011]
    11. Method according to one of the preceding claims wherein the steering of said thrust comprises the determination of at least its orientation.
    [12" id="c-fr-0012]
    An onboard spacecraft pilot system comprising: a continuous or quasi-continuous thrust propulsion system (SPPC); a GNSS receiver (RGNSS) configured to acquire, at least once in each revolution of the spacecraft, measurements of its position and speed; a processor (PE) programmed to calculate a thrust control function as a function of said measurements and to drive said thrust propulsion system continuously or quasi-continuously in accordance with said control law; characterized in that said processor is programmed to calculate said control law from a Lyapunov control function proportional to a weighted sum of terms, each term being representative of a quadratic error between a measured orbital parameter of an orbit a spacecraft averaged over at least half a revolution and the corresponding orbital parameter of a target target orbit normalized to the maximum value of the rate of change of said orbital parameter, averaged over at least one half revolution of said spacecraft .
    [13" id="c-fr-0013]
    The system of claim 12 wherein said or each said orbital parameter is an equinoctial orbital parameter.
    [14" id="c-fr-0014]
    14. Spacecraft (VS) equipped with an on-board piloting system according to one of claims 12 or 13.
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    EP3170752A1|2017-05-24|
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    引用文献:
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    US6845950B1|2003-11-26|2005-01-25|Lockheed Martin Corporation|System for high efficiency spacecraft orbit transfer|
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    EP3243756B1|2015-01-09|2020-12-30|Mitsubishi Electric Corporation|Orbit control device and satellite|CN109001550A|2018-07-04|2018-12-14|天津大学|A kind of extracting method for Dual-Phrase Distribution of Gas olid electrostatic transfer charge signal|
    CN109398763B|2018-10-31|2020-08-18|湖北航天技术研究院总体设计所|Spacecraft accurate orbit entry control method based on limited thrust and limited working time|
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    CN109552670B|2018-12-03|2021-11-02|中科星图测控技术有限公司|Application of low-thrust control in geostationary satellite orbit dip angle maintenance|
    CN113184220B|2021-04-21|2021-11-19|中国人民解放军63923部队|Orbit control method and device for geosynchronous orbit communication satellite|
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    优先权:
    申请号 | 申请日 | 专利标题
    FR1502429|2015-11-20|
    FR1502429A|FR3043985B1|2015-11-20|2015-11-20|METHOD FOR ORBITAL TRANSFER OF A SPATIAL VESSEL USING CONTINUOUS OR QUASI-CONTINUOUS THRUST AND ON-LINE STEERING SYSTEM FOR IMPLEMENTING SUCH A METHOD|FR1502429A| FR3043985B1|2015-11-20|2015-11-20|METHOD FOR ORBITAL TRANSFER OF A SPATIAL VESSEL USING CONTINUOUS OR QUASI-CONTINUOUS THRUST AND ON-LINE STEERING SYSTEM FOR IMPLEMENTING SUCH A METHOD|
    EP16197977.8A| EP3170752B1|2015-11-20|2016-11-09|Orbital transfer method of a spacecraft using a continuous or quasi-continuous thrust and on-board piloting system for implementing such a method|
    US15/347,579| US10532829B2|2015-11-20|2016-11-09|Orbit transfer method for a spacecraft using a continuous or quasi-continuous thrust and embedded driving system for implementing such a method|
    CA2948860A| CA2948860A1|2015-11-20|2016-11-18|Orbit transfer method for a spacecraft using a continuous or quasi-continuous thrust and embedded driving system for implementing such a method|
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