High-orbit remote autonomous rendezvous orbital transfer method and system based on sequential quadratic programming

Abstract

The invention discloses a high-orbit remote autonomous rendezvous orbital transfer method and system based on sequential quadratic programming, and the method comprises the steps: setting initial parameters; establishing an aircraft precise dynamic model; determining an orbital transfer strategy; constructing a nonlinear programming model according to the orbital transfer strategy; according to the nonlinear programming model and the initial parameters, adopting a sequential quadratic programming method to obtain orbital transfer parameter initial values; and according to the orbital transfer parameter initial value, adopting a Newton iteration method to obtain an orbital control parameter which accurately meets a terminal condition under a perturbation condition. According to the method, the calculation amount in the orbit control parameter solving process is greatly reduced while the model precision is guaranteed.

Description

Technical Field

[0001] The present invention belongs to the technical field of spacecraft orbit control, and in particular relates to a high-orbit long-range autonomous rendezvous and orbit change method and system based on sequential quadratic programming. Background Art

[0002] High orbits are where high-value satellites gather, and the development of high-orbit in-orbit services and other missions has put forward the need for autonomous rendezvous. Similar to manned rendezvous and docking in near-Earth space, the rendezvous process is divided into two stages: long-range autonomous rendezvous and short-range autonomous approach. Autonomous planning of long-range rendezvous refers to the use of certain mathematical means to plan a series of orbit changes (number of orbit changes, orbit change positions, pulse size and direction) so that the spacecraft arrives at the specified position at the predetermined time. Existing technologies are mostly aimed at low-orbit rendezvous and docking missions. Lambert rendezvous requires solving multiple circles of Lambert, which is computationally intensive. Methods based on near-circular deviation linear equations require solving a set of nonlinear equations, which is prone to non-convergence or slow convergence. Summary of the invention

[0003] The technical problem solved by the present invention is: to overcome the shortcomings of the prior art and provide a high-orbit long-distance autonomous rendezvous and orbit change method and system based on sequential quadratic programming, which greatly reduces the amount of calculation in the process of solving orbit control parameters while ensuring the accuracy of the model.

[0004] The object of the present invention is achieved through the following technical scheme: a high-orbit long-range autonomous rendezvous and orbit change method based on sequential quadratic programming, comprising: setting initial parameters; establishing an accurate dynamics model of an aircraft; determining an orbit change strategy; constructing a nonlinear programming model according to the accurate dynamics model of the aircraft and the orbit change strategy; according to the nonlinear programming model and the initial parameters, using a sequential quadratic programming method to obtain initial values ​​of orbit change parameters; according to the initial values ​​of the orbit change parameters, using a Newton iteration method to obtain orbit control parameters that accurately meet terminal conditions under perturbation conditions.

[0005] In the above-mentioned high-orbit long-distance autonomous rendezvous and orbit change method based on sequential quadratic programming, the initial parameters include: the orbit parameters of the tracking aircraft at the initial time t0, the orbit parameters of the target aircraft at the initial time t0, the time t consumed by the long-distance guidance segment f , the terminal time of the long-distance guidance segment t f , track the relative position and relative velocity of the aircraft in the target aircraft orbital coordinate system.

[0006] In the above-mentioned high-orbit long-distance autonomous rendezvous and trajectory change method based on sequential quadratic programming, the orbital parameter X of the tracking spacecraft at the initial time t0 is c (t0) = [a c0 ,e c0 ,i c0 ,Ω c0 ,ω c0 ,fc0 ] T ; Among them, a c0 is the semi-major axis of the spacecraft at the initial moment, e c0 is the eccentricity of the vehicle tracked at the initial moment, i c0 is the initial tracking orbit inclination of the spacecraft, Ω c0 is the right ascension of the ascending node of the spacecraft at the initial moment, ω c0 is the initial tracking moment of the vehicle's perigee argument, f c0 Track the true perigee angle of the aircraft at the initial moment;

[0007] The orbital parameters X of the target spacecraft at the initial time t0 t (t0) = [a t0 ,e t0 ,i t0 ,Ω t0 ,ω t0 ,f t0 ] T ; Among them, a t0 is the semi-major axis of the target aircraft at the initial moment, e t0 is the eccentricity of the target aircraft at the initial moment, i t0 is the orbit inclination of the target spacecraft at the initial moment, Ω t0 is the right ascension of the ascending node of the target aircraft at the initial moment, ω t0 is the target aircraft's perigee argument at the initial moment, f t0 is the true perigee angle of the target aircraft at the initial moment.

[0008] In the above-mentioned high-orbit long-distance autonomous rendezvous and trajectory change method based on sequential quadratic programming, the precise dynamic model of the aircraft is obtained by the following formula:

[0009]

[0010] in, is the derivative of the earth vector, v is the velocity, μ is the gravitational constant, r is the earth vector, r is the modulus of the earth vector, is the perturbation acceleration of J2, a sun is the gravitational acceleration of the sun, a moon is the gravitational acceleration of the moon, a F is the track change acceleration.

[0011] In the above-mentioned high-orbit long-range autonomous rendezvous and orbit change method based on sequential quadratic programming, the orbit change strategy is determined including: a total of four orbit changes; three orbit changes are performed within the orbital plane, namely the 1st, 3rd and 4th orbit changes; one orbit change is performed outside the orbital plane, namely the 2nd orbit change; wherein, the 1st orbit change is at the apogee, transferring from the initial orbit to the phase-adjusting transition orbit; the 2nd orbit change is at the intersection of the orbital planes of the tracking spacecraft and the target spacecraft; the 3rd orbit change is at the intermediate perigee, raising the apogee height to the terminal height of the long-distance guidance section; the 4th orbit change is at the apogee of the phase-adjusting transition orbit, transferring the phase-adjusting transition orbit to the circularized orbit of the terminal.

[0012] In the above-mentioned high-orbit long-distance autonomous rendezvous and orbit change method based on sequential quadratic programming, the nonlinear programming model includes optimization variables, constraints and optimization objectives; wherein, the optimization variables include the first pulse velocity increment, the second pulse position and velocity increment, the third pulse velocity increment, the fourth pulse position and velocity increment; the constraints include velocity increment constraints and orbit change terminal constraints, the velocity increment constraint is that the total velocity increment imposed is less than the maximum allowed velocity increment, and the orbit change terminal constraint is to meet the expected relative position and relative velocity; the optimization objective is to save the most fuel.

[0013] A high-orbit long-range autonomous rendezvous and orbit change system based on sequential quadratic programming comprises: a first module for setting initial parameters; a second module for establishing an accurate dynamics model of an aircraft; a third module for determining an orbit change strategy; a fourth module for constructing a nonlinear programming model according to the accurate dynamics model of the aircraft and the orbit change strategy; a fifth module for obtaining initial values ​​of orbit change parameters by using a sequential quadratic programming method according to the nonlinear programming model and the initial parameters; and a sixth module for obtaining orbit control parameters that accurately meet terminal conditions under perturbation conditions by using a Newton iteration method according to the initial values ​​of the orbit change parameters.

[0014] In the above-mentioned high-orbit long-distance autonomous rendezvous and orbit change system based on sequential quadratic programming, the initial parameters include: the orbit parameters of the tracking aircraft at the initial time t0, the orbit parameters of the target aircraft at the initial time t0, the time length t of the long-distance guidance segment f , the terminal time of the long-distance guidance segment t f , track the relative position and relative velocity of the aircraft in the target aircraft orbital coordinate system.

[0015] In the high-orbit long-distance autonomous rendezvous and trajectory change system based on sequential quadratic programming, the orbital parameter X of the tracking vehicle at the initial time t0 is c (t0) = [a c0 ,e c0 ,i c0 ,Ω c0 ,ω c0 ,f c0 ] T ; Among them, ac0 is the semi-major axis of the spacecraft at the initial moment, e c0 is the eccentricity of the vehicle tracked at the initial moment, i c0 is the initial tracking orbit inclination of the spacecraft, Ω c0 is the right ascension of the ascending node of the spacecraft at the initial moment, ω c0 is the initial tracking moment of the vehicle's perigee argument, f c0 Track the true perigee angle of the aircraft at the initial moment;

[0016] The orbital parameters X of the target spacecraft at the initial time t0 t (t0) = [a t0 ,e t0 ,i t0 ,Ω t0 ,ω t0 ,f t0 ] T ; Among them, a t0 is the semi-major axis of the target aircraft at the initial moment, e t0 is the eccentricity of the target aircraft at the initial moment, i t0 is the orbit inclination of the target spacecraft at the initial moment, Ω t0 is the right ascension of the ascending node of the target aircraft at the initial moment, ω t0 is the target aircraft's perigee argument at the initial moment, f t0 is the true perigee angle of the target aircraft at the initial moment.

[0017] In the above-mentioned high-orbit long-distance autonomous rendezvous and trajectory change system based on sequential quadratic programming, the precise dynamic model of the aircraft is obtained by the following formula:

[0018]

[0019] in, is the derivative of the earth vector, v is the velocity, μ is the gravitational constant, r is the earth vector, r is the modulus of the earth vector, is the perturbation acceleration of J2, a sun is the gravitational acceleration of the sun, a moon is the gravitational acceleration of the moon, a F is the track change acceleration.

[0020] Compared with the prior art, the present invention has the following beneficial effects:

[0021] (1) The present invention greatly reduces the amount of calculation in the process of solving orbit control parameters while ensuring the accuracy of the model as much as possible, and can solve the problem of autonomy of future high-orbit rendezvous and docking missions;

[0022] (2) The present invention solves the nonlinear model of multi-pulse rendezvous by using a sequential quadratic programming method and uses an analytical method to quickly extrapolate orbits, thereby improving computational efficiency and achieving rapid convergence, which can meet the requirements of a remote rendezvous terminal.

[0023] (3) After using sequential quadratic programming to obtain the initial values ​​of the orbit change parameters, the present invention uses the Newton iteration method to quickly obtain the orbit change parameters under orbit perturbation conditions, thereby improving the accuracy of the orbit change terminal. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Moreover, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:

[0025] Figure 1 It is a schematic diagram of in-plane track change of a long-distance rendezvous track provided by an embodiment of the present invention;

[0026] Figure 2 It is a schematic diagram of out-of-plane track change of a long-distance rendezvous orbit provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0027] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present disclosure and to be able to fully convey the scope of the present disclosure to those skilled in the art. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features described in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0028] This embodiment provides a high-orbit long-distance autonomous rendezvous and orbit change method based on sequential quadratic programming, the method comprising:

[0029] Set initial parameters;

[0030] Establish accurate dynamic model of aircraft;

[0031] Determine the track change strategy;

[0032] Construct a nonlinear programming model based on the precise dynamics model of the aircraft and the trajectory change strategy;

[0033] According to the nonlinear programming model and initial parameters, the sequential quadratic programming method is used to obtain the initial values ​​of the orbit change parameters; wherein the initial values ​​of the orbit change parameters include the first pulse velocity increment, the second pulse position and velocity increment, the third pulse velocity increment, and the fourth pulse position and velocity increment.

[0034] According to the initial values ​​of the orbit change parameters, the Newton iteration method is used to obtain the orbit control parameters that accurately meet the terminal conditions under the perturbation conditions. Among them, the initial values ​​of the orbit control parameters include the first pulse velocity increment, the second pulse position and velocity increment, the third pulse velocity increment, and the fourth pulse position and velocity increment.

[0035] The initial parameters include: the orbital parameters of the tracking aircraft at the initial time t0, the orbital parameters of the target aircraft at the initial time t0, the time t consumed by the long-distance guidance segment f , the terminal time of the long-distance guidance segment t f , track the relative position and relative velocity of the aircraft in the target aircraft orbital coordinate system.

[0036] Tracking spacecraft orbital parameters X at the initial time t0 c (t0) = [a c0 ,e c0 ,i c0 ,Ω c0 ,ω c0 ,f c0 ] T ; Among them, a c0 is the semi-major axis of the spacecraft at the initial moment, e c0 is the eccentricity of the vehicle tracked at the initial moment, i c0 is the initial tracking orbit inclination of the spacecraft, Ω c0 is the right ascension of the ascending node of the spacecraft at the initial moment, ω c0 is the initial tracking moment of the vehicle's perigee argument, f c0 Track the true perigee angle of the aircraft at the initial moment;

[0037] The orbital parameters X of the target spacecraft at the initial time t0 t (t0) = [a t0 ,e t0 ,i t0 ,Ω t0 ,ω t0 ,f t0 ] T ; Among them, a t0 is the semi-major axis of the target aircraft at the initial moment, e t0 is the eccentricity of the target aircraft at the initial moment, i t0 is the orbit inclination of the target spacecraft at the initial moment, Ω t0 is the right ascension of the ascending node of the target aircraft at the initial moment, ω t0is the target aircraft's perigee argument at the initial moment, f t0 is the true perigee angle of the target aircraft at the initial moment.

[0038] The precise dynamic model of the aircraft is obtained by the following formula:

[0039]

[0040] in, is the derivative of the earth vector, v is the velocity, μ is the gravitational constant, r is the earth vector, r is the modulus of the earth vector, is the perturbation acceleration of J2, a sun is the gravitational acceleration of the sun, a moon is the gravitational acceleration of the moon, a F is the track change acceleration.

[0041] The orbit change strategy is determined to include: a total of four orbit changes; three orbit changes are performed within the orbital plane, namely the 1st, 3rd and 4th orbit changes; one orbit change is performed outside the orbital plane, namely the 2nd orbit change; among them, the 1st orbit change is at the apogee, transferring from the initial orbit to the phase-adjusting transition orbit; the 2nd orbit change is at the intersection of the orbital planes of the tracking spacecraft and the target spacecraft; the 3rd orbit change is at the intermediate perigee, raising the apogee altitude to the terminal altitude of the long-distance guide segment; the 4th orbit change is at the apogee of the phase-adjusting transition orbit, transferring the phase-adjusting transition orbit to the circularized orbit of the terminal.

[0042] The nonlinear programming model includes optimization variables, constraints and optimization objectives; wherein, the optimization variables include the first pulse velocity increment, the second pulse position and velocity increment, the third pulse velocity increment, the fourth pulse position and velocity increment; the constraints include velocity increment constraint and trajectory change terminal constraint, the velocity increment constraint is that the total velocity increment imposed is less than the maximum allowed velocity increment, the trajectory change terminal constraint is to meet the expected relative position and relative velocity; the optimization objective is fuel optimization.

[0043] For a given initial orbital condition of the tracking aircraft, a trajectory change strategy can be found so that the tracking aircraft has the desired orbital condition at the terminal of the long-distance guidance segment, thereby satisfying a specific relative position and velocity relationship with the target aircraft.

[0044] This embodiment determines a trajectory change strategy for realizing autonomous rendezvous between a high-orbit tracking aircraft and a target aircraft, and proposes a method for solving the orbit control parameters corresponding to the trajectory change strategy. First, according to the mission requirements, the current orbit parameters of the tracking aircraft and the target aircraft, the expected trajectory change terminal position and the long-distance guidance segment duration are given. Secondly, according to the specified trajectory change strategy, a nonlinear programming model for trajectory change planning is established. The model is solved using the sequential quadratic method to obtain the trajectory change parameters. In order to reduce the amount of on-orbit calculations of the aircraft, an orbit prediction method based on the analytical method is used. Combining the orbit prediction and the initial value solution strategy, the initial value of the orbit control parameter can be solved. Finally, the initial value is used as the initial condition for the iteration of the exact solution, and the exact solution of the orbit control parameter is obtained in combination with the orbit extrapolation. Orbit control is implemented according to the orbit control parameters calculated in this embodiment, and the autonomous rendezvous between the tracking aircraft and the target aircraft can be realized.

[0045] The specific steps include:

[0046] 1. Set initial parameters

[0047] Assume that the orbital parameters of the tracking vehicle at the initial time t0 are X c (t0) = [a c0 ,e c0 ,i c0 ,Ω c0 ,ω c0 ,f c0 ] T ; Assume the orbital parameter X of the target spacecraft at the initial time t0 t (t0) = [a t0 ,e t0 ,i t0 ,Ω t0 ,ω t0 ,f t0 ] T ; The long-distance guidance segment takes t f ; Terminal time of long-distance guidance segment t f , track the relative position and relative velocity of the aircraft in the target aircraft orbital coordinate system [x d ,y d ,z d ,v xd ,v yd ,v zd ] T .

[0048] 2. Establish an accurate dynamic model of the aircraft

[0049] In the J2000 coordinate system, the exact dynamic model of the long-range orbit transfer problem is as follows.

[0050]

[0051] Where r and v are the position and velocity vector of the aircraft in the J2000 coordinate system, μ is the earth's gravitational constant, is the perturbation acceleration of the Earth's oblateness J2, a sun and a moon are the perturbation accelerations of the sun and moon’s gravity respectively; a F It is the trajectory change acceleration generated by the engine thrust.

[0052] 3. Determine the track change strategy and parameters

[0053] The orbit control strategy adopts the modified special point orbit change strategy. In order to achieve the rendezvous between the tracking aircraft and the target aircraft, it is necessary to apply the track impulse at the apogee or perigee of a specific circle, so that the tracking aircraft will have the desired relative position and velocity relationship with the target aircraft at the long-distance guidance terminal. The orbit control of the long-distance guidance segment is completed by changing the orbit separately within the orbital plane and outside the orbital plane. The details are as follows:

[0054] The first orbit change: Apply a track impulse Δv at the apogee of the N1th orbit t1 ; Wherein, N1 is the N1th orbit;

[0055] Second orbit change: Latitude and angle of the N2th circle Apply a normal impulse Δv at z2 , and simultaneously correct the orbital inclination and the right ascension deviation of the ascending node; where N2 is the N2th orbital operation;

[0056] The third orbit change: Applying a track impulse Δv at the N3th orbit perigee t3 Adjust the apogee height; N3 is the N3th orbit;

[0057] The fourth orbit change: near the apogee of the N4th orbit Apply a trajectorial impulse Δv t4 ; Among them, N4 is the N4th orbit;

[0058] In the above orbit control strategy, three orbit changes were made in the orbital plane, namely the 1st, 3rd and 4th orbit changes. Figure 1 As shown in the figure, the first orbit change is near the apogee, from the initial orbit to the phase transition orbit; the third orbit change is at the intermediate perigee, raising the apogee height to the terminal height of the long-distance guide segment; the fourth orbit change is near the apogee of the phase transition orbit, transferring the phase transition orbit to the circular orbit of the terminal. One orbit change is made outside the orbital plane, which is the second orbit change. Figure 2 As shown, in order to save propellant, the out-of-orbit maneuver is performed by performing a maneuver at the intersection of the two spacecraft orbital planes (node ​​1 or node 2) to achieve the correction of the orbital inclination and the right ascension of the ascending node.

[0059] The orbit control parameters that need to be solved can be obtained from the orbit control strategy

[0060] 4. Constructing nonlinear programming models

[0061] The key to solving the long-range rendezvous problem is to find the optimal flight trajectory, impulse magnitude, direction and time. For this type of problem, the optimal control problem is usually abstracted into a two-point boundary value problem using the Pondriagin minimum principle, which is computationally complex. This paper transforms this problem into a parameter optimization problem, establishes a nonlinear programming model, and avoids the complex mathematical operations of solving the two-point boundary value.

[0062] According to the description of the multi-pulse long-range rendezvous problem, the following nonlinear programming model is established, which can be described as finding the optimization variable X so that the objective function is minimized while satisfying the constraints.

[0063] J = minf(X)

[0064]

[0065] Among them, J is the objective function, f(X) is the objective function, X is the optimization variable, is the derivative of the state variable, Φ(x,t) is the state equation, x is the state of the aircraft, t is the time, ρ is the relative position, ρ t is the desired relative position, Δv total is the total velocity increment, Δv max is the maximum speed increment allowed.

[0066] (1) Dynamic constraints

[0067] The motion state of the aircraft is represented by x, which includes 3 positions and 3 velocities. Considering the applied maneuver pulse, the motion state of the aircraft satisfies the following dynamic constraints.

[0068]

[0069] (2) Optimization variables

[0070] According to the long-distance track change model, the first pulse speed increment Δv is required. t1 , 2nd pulse position and velocity increment Δv z2 , the third pulse velocity increment Δv t3 , 4th pulse position and velocity increment Δv t4 is the optimization variable X.

[0071]

[0072] Where: Δv iis the speed increment of the ith track change, u i is the latitude argument at the i-th orbit change.

[0073] (3) Speed ​​increment constraint

[0074] Assume that the maximum speed increment allowed for this task is Δv max , then the total velocity increment applied during the rendezvous process must satisfy

[0075] Δv total ≤Δv max (4)

[0076] in: n is the total number of track changes, Δv total is the total velocity increment, Δv i is the speed increment of the i-th track change, and i is the track change sequence number.

[0077] (4) Track change terminal constraints

[0078] The relative position and velocity of the aircraft relative to the target in its orbital coordinate system are defined as ρ and The remote track change terminal should meet the expected relative position and relative speed.

[0079]

[0080] Among them, x d is the tangential relative distance, y d is the normal relative distance, z d is the radial relative distance, v xd is the tangential relative velocity, v yd is the normal relative velocity, v zd is the radial relative velocity.

[0081] (5) Optimization goal

[0082] If the optimization goal is to save as much fuel as possible, the objective function is the sum of the speed increments of n orbit changes.

[0083]

[0084] Where f is the total velocity increment.

[0085] 5. Solving nonlinear programming models based on sequential quadratic programming method

[0086] The methods for solving nonlinear programming problems include penalty function method, approximate programming method, sequential quadratic programming method, etc. This paper uses sequential quadratic programming method for simulation solution. The SQP (sequential quadratic programming) algorithm was developed and matured in the mid-to-late 1980s. Numerical experiments show that SQP can maintain local super-first-order convergence while having overall convergence. Many large-scale optimization design systems abroad use SQP for optimization. The trajectory change maneuvering module of STK and GMAT uses SQP for trajectory optimization. The basic idea of ​​sequential quadratic programming is to use Taylor expansion to simplify the objective function of the nonlinear optimization problem into a quadratic function at the iteration point, and to simplify the constraint function into a linear function.

[0087] 6. Autonomous orbit prediction

[0088] When the tracking vehicle is planning the orbit change control parameters on orbit, the terminal state needs to be calculated, so autonomous orbit prediction (orbit extrapolation) is inevitably involved. Due to the limitation of on-orbit computing power, the orbit extrapolation method of numerical integration orbit perturbation equations usually used on the ground cannot be used. Considering this constraint, the analytical method is used to extrapolate the orbit.

[0089] Since most of the rendezvous and docking studies are currently completed in low-Earth orbit, the corresponding eccentricity is small, and singularities may occur when using analytical methods for orbital extrapolation. To avoid this phenomenon, the quasi-average root method is suitable for orbital extrapolation. The first type of singularity-free variable σ(t) is constructed according to the Kepler orbital roots as follows:

[0090] a,i,Ω,ξ=ecosω,

[0091] η=esinω,λ=M+ω (7)

[0092] Among them, a is the semi-major axis of the orbit, i is the orbit inclination, Ω is the right ascension of the ascending node, e is the eccentricity, ω is the argument of perigee, M is the mean anomaly, ξ is the X-direction component of the eccentricity, η is the Y-direction component of the eccentricity, and λ is the longitude. The above Kepler orbit elements can be obtained by the orbital parameters X in the cylindrical coordinate system. rel Conversion obtained.

[0093] For the non-spherical gravitational perturbation of the Earth (taking into account the J2 band harmonic coefficient), the quasi-average root method is used, and the perturbation solution without singular points is expressed as

[0094]

[0095] In a first-order sense, the form is:

[0096]

[0097] Where σ(t) is the instantaneous orbital element number, is the average orbital element number, is the first-order short-period term, is the second-order short-period term, σ1 is the first-order long-term term, σ2 is the second-order long-term term, is a first-order long-period term, the subscript “0” indicates the initial time t0, δ is [000001], is the horizontal motion speed, t is the current time, t0 is the initial time, is the difference of the first-order long-period term at the current moment, is the first-order long-period term at time t0, is the average orbital element number at time t0, σ0 is the instantaneous orbital element number at time t0, is the first-order short-period term at time t0, is the second-order short-period term at time t0.

[0098] The specific expressions of the first-order long-term term, the first-order short-period term, the first-order long-period term, and the second-order short-period term can be found in the relevant literature on orbital mechanics. Therefore, the autonomous orbit prediction steps are as follows: When the tracking spacecraft obtains the instantaneous orbital element σ0 at time t0 through autonomous orbit determination, the corresponding average orbital element at this time is obtained by the third formula of formula (9): According to the first formula of formula (9) and the perturbation expressions of each order, the average orbital elements at any time t are obtained: Finally, according to formula (8), the instantaneous orbital element σ(t) at time t is obtained.

[0099] 7. Accurate solution and iteration of orbit control parameters

[0100] Steps 4 and 5 give the initial value calculation method of the orbit control parameter x. The following describes how to iterate based on the initial value to obtain the orbit control parameter that accurately meets the terminal conditions under the perturbation condition.

[0101] Considering the limitation of on-orbit computing power, the simple and easy Newton iteration method is used for accurate solution. The nonlinear equation group h is constructed as follows:

[0102]

[0103] Among them, h(x) is the difference between the actual and expected states of the terminal, X rel (t f ) is the actual state of the terminal, is the desired aiming state, x is the trajectory change sequence, t f The terminal moment.

[0104] The goal is to find a set of trajectory change sequences x, substitute them into the perturbation model (6) and extrapolate to the terminal, so that the actual terminal state X rel (t f ) and the desired aiming state is consistent, that is, h(x) = 0. Written in scalar form:

[0105] h i (x1,x2,…,x n )=0 i=1,2,…,n (11)

[0106] The solution formula for the above equation is

[0107]

[0108] Among them, x k+1 is the k+1th track change sequence, x k is the kth track change sequence, H(x k ) is the Jacobi matrix, h(x k ) is the difference between the actual and expected states of the terminal, and k is the number of iterations.

[0109]

[0110] Each iteration corresponds to H(x k ) can be calculated by numerical difference method. When equation (10) meets certain convergence conditions, the iteration can be stopped to obtain the exact solution of orbit control parameter x.

[0111] The present embodiment also provides a high-orbit long-range autonomous rendezvous and trajectory change system based on sequential quadratic programming, the system comprising: a first module for setting initial parameters; a second module for establishing a precise dynamic model of the aircraft; a third module for determining the trajectory change strategy; a fourth module for constructing a nonlinear programming model according to the trajectory change strategy; a fifth module for obtaining initial values ​​of the trajectory change parameters by using a sequential quadratic programming method based on the nonlinear programming model and the initial parameters; and a sixth module for obtaining orbit control parameters that accurately meet terminal conditions under perturbation conditions by using a Newton iteration method based on the initial values ​​of the trajectory change parameters.

[0112] This embodiment can solve the problem of autonomy in future high-orbit rendezvous and docking missions. By adopting a precise orbital dynamics model, fixing the positions of the 1st and 2nd phase modulation pulses, taking the 1st and 3rd pulse velocity increments, the 2nd and 4th pulse positions and velocity increments as optimization variables, and taking the minimum total velocity increment as the optimization goal, a nonlinear programming model for multi-pulse rendezvous is established, and the sequential quadratic programming method is used to solve it. The orbit change strategy is solved through two steps, initial value calculation and exact solution iteration, to obtain the orbit change control parameters. While ensuring the accuracy of the model as much as possible, the amount of calculation in the process of solving the orbit control parameters is greatly reduced.

[0113] This embodiment greatly reduces the amount of calculation in the process of solving the orbit control parameters while ensuring the accuracy of the model as much as possible, and can solve the problem of autonomy of future high-orbit rendezvous and docking tasks; this embodiment solves the nonlinear model of multi-pulse rendezvous by a sequential quadratic programming method, and uses an analytical method to quickly extrapolate the orbit, thereby improving the calculation efficiency and achieving rapid convergence, which can meet the requirements of the remote rendezvous terminal; after obtaining the initial values ​​of the orbit change parameters by using sequential quadratic programming, this embodiment uses the Newton iteration method to quickly obtain the orbit change parameters under the orbit perturbation conditions, thereby improving the accuracy of the orbit change terminal.

[0114] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A high-orbit long-distance autonomous rendezvous and orbit change method based on sequential quadratic programming, characterized in that include: Set initial parameters; Establish accurate dynamic model of aircraft; Determine the track change strategy; Construct a nonlinear programming model based on the precise dynamics model of the aircraft and the trajectory change strategy; According to the nonlinear programming model and initial parameters, the sequential quadratic programming method is used to obtain the initial values ​​of the trajectory change parameters. According to the initial values ​​of the orbit change parameters, the Newton iteration method is used to obtain the orbit control parameters that accurately meet the terminal conditions under perturbation conditions.

2. The high-orbit remote autonomous rendezvous and orbit change method based on sequential quadratic programming according to claim 1 is characterized by: The initial parameters include: the orbital parameters of the tracking aircraft at the initial time t0, the orbital parameters of the target aircraft at the initial time t0, the time t consumed by the long-distance guidance segment f , the terminal time of the long-distance guidance segment t f , track the relative position and relative velocity of the aircraft in the target aircraft orbital coordinate system.

3. The high-orbit remote autonomous rendezvous and orbit change method based on sequential quadratic programming according to claim 2 is characterized by: Tracking spacecraft orbital parameters X at the initial time t0 c (t0) = [a c0 ,e c0 ,i c0 ,Ω c0 ,ω c0 ,f c0 ] T ; Among them, a c0 is the semi-major axis of the spacecraft at the initial moment, e c0 is the eccentricity of the vehicle tracked at the initial moment, i c0 is the initial tracking orbit inclination of the spacecraft, Ω c0 is the right ascension of the ascending node of the spacecraft at the initial moment, ω c0 is the initial tracking moment of the vehicle's perigee argument, f c0 Track the true perigee angle of the aircraft at the initial moment; The orbital parameters X of the target spacecraft at the initial time t0 t (t0) = [a t0 ,e t0 ,i t0 ,Ω t0 ,ω t0 ,f t0 ] T ; Among them, a t0 is the semi-major axis of the target aircraft at the initial moment, e t0 is the eccentricity of the target aircraft at the initial moment, i t0 is the orbit inclination of the target spacecraft at the initial moment, Ω t0 is the right ascension of the ascending node of the target aircraft at the initial moment, ω t0 is the target aircraft's perigee argument at the initial moment, f t0 is the true perigee angle of the target aircraft at the initial moment.

4. The high-orbit remote autonomous rendezvous and orbit change method based on sequential quadratic programming according to claim 1 is characterized by: The precise dynamic model of the aircraft is obtained by the following formula: in, is the derivative of the earth vector, v is the velocity, μ is the gravitational constant, r is the earth vector, r is the modulus of the earth vector, is the perturbation acceleration of J2, a sun is the gravitational acceleration of the sun, a moon is the gravitational acceleration of the moon, a F is the track change acceleration.

5. The high-orbit remote autonomous rendezvous and orbit change method based on sequential quadratic programming according to claim 1 is characterized by: The orbit change strategy is determined to include: a total of four orbit changes; three orbit changes are performed within the orbital plane, namely the 1st, 3rd and 4th orbit changes; one orbit change is performed outside the orbital plane, namely the 2nd orbit change; among them, the 1st orbit change is at the apogee, transferring from the initial orbit to the phase-adjusting transition orbit; the 2nd orbit change is at the intersection of the orbital planes of the tracking spacecraft and the target spacecraft; the 3rd orbit change is at the intermediate perigee, raising the apogee altitude to the terminal altitude of the long-distance guide segment; the 4th orbit change is at the apogee of the phase-adjusting transition orbit, transferring the phase-adjusting transition orbit to the circularized orbit of the terminal.

6. The high-orbit remote autonomous rendezvous and orbit change method based on sequential quadratic programming according to claim 1 is characterized by: The nonlinear programming model includes optimization variables, constraints and optimization objectives; among which, the optimization variables include the first pulse velocity increment, the second pulse position and velocity increment, the third pulse velocity increment, the fourth pulse position and velocity increment; the constraints include velocity increment constraint and track change terminal constraint, the velocity increment constraint is that the total velocity increment imposed is less than the maximum allowed velocity increment, and the track change terminal constraint is to meet the expected relative position and relative velocity; the optimization objective is to save the most fuel.

7. A high-orbit long-distance autonomous rendezvous and orbit change system based on sequential quadratic programming, characterized in that include: The first module is used to set initial parameters; The second module is used to establish an accurate dynamic model of the aircraft; The third module is used to determine the track change strategy; The fourth module is used to build a nonlinear programming model based on the precise dynamics model of the aircraft and the trajectory change strategy; The fifth module is used to obtain the initial values ​​of the trajectory change parameters using the sequential quadratic programming method according to the nonlinear programming model and the initial parameters; The sixth module is used to obtain the orbit control parameters that accurately meet the terminal conditions under perturbation conditions based on the initial values ​​of the orbit change parameters using the Newton iteration method.

8. The high-orbit long-distance autonomous rendezvous and trajectory change system based on sequential quadratic programming according to claim 7 is characterized by: The initial parameters include: the orbital parameters of the tracking aircraft at the initial time t0, the orbital parameters of the target aircraft at the initial time t0, the time t consumed by the long-distance guidance segment f , the terminal time of the long-distance guidance segment t f , track the relative position and relative velocity of the aircraft in the target aircraft orbital coordinate system.

9. The high-orbit long-distance autonomous rendezvous and trajectory change system based on sequential quadratic programming according to claim 8 is characterized by: Tracking spacecraft orbital parameters X at the initial time t0 c (t0) = [a c0 ,e c0 ,i c0 ,Ω c0 ,ω c0 ,f c0 ] T ; Among them, a c0 is the semi-major axis of the spacecraft at the initial moment, e c0 is the eccentricity of the vehicle tracked at the initial moment, i c0 is the initial tracking orbit inclination of the spacecraft, Ω c0 is the right ascension of the ascending node of the spacecraft at the initial moment, ω c0 is the initial tracking moment of the vehicle's perigee argument, f c0 Track the true perigee angle of the aircraft at the initial moment; The orbital parameters X of the target spacecraft at the initial time t0 t (t0) = [a t0 ,e t0 ,i t0 ,Ω t0 ,ω t0 ,f t0 ] T ; Among them, a t0 is the semi-major axis of the target aircraft at the initial moment, e t0 is the eccentricity of the target aircraft at the initial moment, i t0 is the orbit inclination of the target spacecraft at the initial moment, Ω t0 is the right ascension of the ascending node of the target aircraft at the initial moment, ω t0 is the target aircraft's perigee argument at the initial moment, f t0 is the true perigee angle of the target aircraft at the initial moment.

10. The high-orbit long-distance autonomous rendezvous and trajectory change system based on sequential quadratic programming according to claim 7 is characterized by: The precise dynamic model of the aircraft is obtained by the following formula: in, is the derivative of the earth vector, v is the velocity, μ is the gravitational constant, r is the earth vector, r is the modulus of the earth vector, is the perturbation acceleration of J2, a sun is the gravitational acceleration of the sun, a moon is the gravitational acceleration of the moon, a F is the track change acceleration.

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