Automatic optimal control method for regression orbit under small thrust condition

Abstract

A regression orbit autonomous optimal control method under a small thrust condition belongs to the field of satellite orbit control, and comprises the following steps: constructing Poincare mapping based on a differential algebraic method and representing the Poincare mapping as a high-order Taylor expansion polynomial; a high-order Taylor expansion polynomial is used for achieving recursive calculation of the satellite orbit state quantity after a regression period; establishing a second-order cone optimal control problem that the orbit enters a regression orbit state from an initial state under the action of orbit control maneuvering; designing a multi-batch orbit control strategy suitable for realizing a low-thrust propulsion mode; and a global optimal control quantity is obtained through a second-order convex optimization method. The multi-batch orbit control strategy designed by the invention is small in calculated amount and globally optimal, can be compatible with two thrust control modes of pulse thrust and continuous small thrust at the same time, can be applied to autonomous implementation on a satellite, and reduces the burden of ground management and control. According to the invention, under the condition that the initial condition of the regression orbit is accurate, the controlled satellite enters the regression orbit state with relatively high precision.

Description

Technical Field

[0001] The invention belongs to the technical field of satellite orbit control, and in particular relates to an autonomous optimal control method for a regression orbit under low thrust conditions. Background Art

[0002] The regression orbit has been widely used in various types of earth remote sensing missions. It has the advantages of ground trajectory regression and repeatability, and can complete the revisit of the target at equal intervals, thereby realizing periodic observation. The satellite is perturbed by non-conservative forces such as atmospheric drag in orbit, which will cause the actual flight orbit of the satellite to deviate from the strictly designed regression orbit, causing the sub-satellite point trajectory to deviate from the nominally designed trajectory, which brings inconvenience to the periodic observation of the target. In order to maintain the precise regression characteristics of the satellite orbit, orbit maintenance control is required to compensate for the perturbation effect, so that the satellite always flies with orbital characteristics that meet the regression conditions.

[0003] The control method of the regression orbit is mainly based on the design of maintaining the nominal value of the regression orbit, and its goal is to make the ground or space trajectory change near the designed regression mode. In the existing control methods, non-conservative perturbation factors such as atmospheric drag and solar pressure are ignored in the orbit design stage, but are taken into account in the orbit control stage. Considering that among the non-conservative forces, especially atmospheric drag, the actual ground sub-satellite point trajectory of the orbit deviates from the nominal regression characteristics, orbit maintenance control is required to compensate for this perturbation factor. Some orbit maintenance problem research based on the nominal value design of the regression orbit aims to keep the ground trajectory changing near the nominal trajectory corresponding to the designed regression characteristics. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides an autonomous optimal control method for a regression orbit under low thrust conditions. In view of the need to maintain the regression orbit, the present invention designs a multi-batch orbit control strategy that maintains the characteristics of the regression orbit and is suitable for implementation in a low thrust propulsion mode. The control strategy has the characteristics of low computational complexity and global optimization. The present invention is compatible with both pulse thrust and continuous low thrust thrust control modes, and can be applied to autonomous implementation on board, thereby reducing the burden of ground control. The present invention avoids the shortcomings of the traditional control method's lack of precision, and ensures that when the initial conditions of the regression orbit are accurate, the controlled satellite enters the regression orbit state with high precision.

[0005] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0006] The present invention provides an autonomous optimal control method for a regressive orbit under low thrust conditions, comprising the following steps:

[0007] Step S1: construct a Poincaré map based on differential algebra method and express it as a high-order Taylor expansion polynomial, through which any point on the equatorial plane is projected onto the equatorial plane after a regression cycle;

[0008] Step S2: using a high-order Taylor expansion polynomial to implement a step-by-step rapid recursive calculation of the satellite orbit state quantity after a regression cycle;

[0009] Step S3: Establishing a second-order cone optimal control problem for the orbit to enter the regressive orbit state from the initial state under the orbit control maneuver;

[0010] Step S4: designing a multi-batch orbit control strategy that maintains the recurrent orbit characteristics and is suitable for small thrust propulsion mode;

[0011] Step S5: Obtain the global optimal control quantity through a second-order convex optimization method.

[0012] Furthermore, in step S1, a deviation threshold between the actual track and the nominal track is first set. When it is detected that the deviation between the actual track and the nominal track exceeds the preset threshold, the maximum allowable time interval T of the track maintenance is set. C Discretized into N equally divided time grids, each of which includes N+1 time points t 0 ,……,t N-1 ,t N , the time step is Δt, N = min(floor(T C / Δt),N max ), min represents the minimum value function, floor represents the floor rounding function, N max Indicates the maximum allowed time interval T C The number of orbital controls allowed to be completed within t N -t N-1 ≥Δt.

[0013] Further, in step S1, at each time point t i , each of which applies an orbital control maneuver, and the velocity increment of each orbital control maneuver is Δv i , i = 0,…,N; the nominal orbit is given by i=0,…,N, Represents the position state quantity, represents the speed state quantity, and r T Indicates the target orbit position state after completing the orbit control batch, v T It represents the target orbit speed state after completing the orbit control batch; for each group of state X i, i = 0, ..., N-1, calculate the k-order Taylor approximation polynomial of its state transfer mapping:

[0014]

[0015] Among them, the superscripts “-” and “+” respectively represent the state quantities before and after each orbit control; Indicates that at t i+1 The track position state quantity before track control, Indicates that at t i+1 The track speed state before track control, r i + Indicates that at t i The track position state after track control, Indicates that at t i The orbit speed state after orbit control, represents the track position state transfer mapping, represents the orbit velocity state transfer map, δ represents the deviation of the orbit position or velocity state relative to the nominal orbit, Indicates that at t i+1 The orbit position state deviation obtained after state transfer mapping, Indicates that at t i+1 The orbital velocity state deviation obtained after state transfer mapping, δr i + , indicating that at t i The track position state deviation after track control, Indicates that at t i The orbit speed state deviation after orbit control; Formula (1) represents the orbit control sequence Δv 0 ,Δv 1 ,Δv 2 ,…,Δv N-1 ,Δv N The deviation sequence of orbital state quantities under the action relative to the uncontrolled nominal orbit.

[0016] Furthermore, in step S2, for each time point t i , i=0,…,N-1, according to the applied orbit control maneuver, the relationship between position and velocity deviation is established:

[0017]

[0018] The superscripts “-” and “+” represent the state before and after each orbit control respectively; r i - Indicates that at t i The track position state quantity before track control, Indicates that at t iTrack speed state quantity before track control, δr i + Indicates that at t i Track position state deviation after track control, δr i- Indicates that at t i The track position state deviation before track control, Indicates that at t i The orbit speed state deviation before orbit control; Formula (2) represents the orbit control sequence Δv 0 ,Δv 1 ,Δv 2 ,…,Δv N-1 ,Δv N The deviation sequence of orbital state quantities under the action relative to the uncontrolled nominal orbit.

[0019] Furthermore, in step S2, for the starting time point t i = 0, indicating that the first orbital control maneuver is applied at t 0 , so the initialization condition is: Indicates that at the starting point time t 0 Track position state deviation after track control, Indicates that at the starting point time t 0 The orbit velocity state deviation after orbit control; for i = 1, ..., N-1, the mapping shown by the high-order Taylor expansion polynomial realizes the i , i = 0, 1, ..., N orbit control maneuvers under the forward recursion of the position and velocity state deviation, thereby obtaining the position state deviation sequence and speed state deviation sequence For t N At this moment, there are the following constraints: and Indicates that at the end time t N Track speed state quantity before track control, Indicates that at the end time t N The orbit position state after orbit control indicates that the orbit after control enters the target orbit and starts a new return condition.

[0020] Further, in step S3, based on the orbit control sequence Δv 0 ,Δv 1 ,Δv 2 ,…,Δv N-1 ,Δv N For the control process of the regression orbit, the multi-batch orbit control problem is modeled as a nonlinear optimization problem, and its objective function and nonlinear constraints are:

[0021]

[0022] Where, ΔV i represents the magnitude of the velocity increment for each orbital control maneuver; v m The velocity increment ΔV for each orbital control maneuver i The maximum speed increment limit, i = 0, ..., N; ΔV in the nonlinear constraint condition i ≤v m Indicates that the speed increment of each orbital maneuver is no greater than the maximum limit v m , It means that the speed state is the target speed state after the last orbital maneuver control. Indicates that the position state is the target position state after the last orbital maneuver control.

[0023] Furthermore, in step S4, slack variables and lossless optimization methods are introduced to transform the nonlinear optimization problem into a convex optimization problem.

[0024] Further, in step S4, the speed increment size ΔV of each orbit control maneuver is i As its slack variables, each orbit control maneuver consists of four variables [Δv i ,ΔV i ] T Indicates that the velocity increment Δv of each orbit control is i It is composed of three directional components: radial, transverse and normal, namely Δv i =[Δv i,x ,Δv i,y ,Δv i,z ] T , and the optimization variables of the multi-batch trajectory control problem are converted to [Δv 0 ,...,Δv N ,ΔV 0 ...,ΔV N ] T , the objective function is transformed into the following linear form:

[0025]

[0026] The nonlinear constraints are transformed into a second-order cone format:

[0027]

[0028] in, Indicates the velocity increment Δv i The radial component of Indicates the velocity increment Δv i The lateral component of Indicates the velocity increment Δv i The normal component of .

[0029] And the slack variable constraints are:

[0030] 0≤ΔV i ≤v m (6).

[0031] Furthermore, in step S5, the linear part of the mapping shown by the high-order Taylor expansion polynomial is extracted for linearization, and the obtained linear matrix is:

[0032]

[0033] Among them, the matrix A i (i=0,...,N-1) represents the linear part of the mapping, A δr,i Represents the orbital position state mapping, A δv,i Represents the orbital velocity state quantity mapping.

[0034] Furthermore, for t N The final target state at the moment can be expressed by decomposing the linear matrix, and the result is as follows:

[0035]

[0036] in, Indicates that at the end time t N Track position state deviation before track control, Indicates that at the end time t N Track speed state deviation before track control, A N-1 ·A N-2 ·...·A δv,0 ,A N-2 ·A N-3 ·...·A δv,1 ,...,A δv,N-1 They represent the multiplication combination of each mapping, realizing the transfer from velocity increment to orbital position and velocity state quantity.

[0037] Define M = [A N-1 ·A N-2 ·...·A δv,0 ,A N-2 ·A N-3 ·...·A δv,1 ,...,A δv,N-1 ]; because at t N At time , the last orbit control maneuver is applied to reach the target orbit state, so the linear expression of the constraint is:

[0038]

[0039] Where I represents the identity matrix.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] 1. Aiming at the demand for maintaining regression orbit, the present invention designs a multi-batch orbit control strategy that maintains the characteristics of regression orbit and is suitable for small thrust propulsion mode. Based on the solution of the second-order cone problem, the orbit tracking control that meets the regression conditions is realized. The orbit control strategy has the characteristics of small computational complexity and global optimization. Specifically, the present invention converts the multi-batch velocity increment function into a second-order cone problem through a lossless convex optimization method, linearizes the nonlinear constraints, and completes the solution to the optimal control quantity. Since the size of each velocity increment can be constrained and the time step can be discretized more finely, the present invention can be compatible with both pulse thrust and continuous small thrust control modes. It should be noted that due to the uniqueness of the optimal solution of the convex optimization problem and the simplicity of calculation, the orbit control algorithm and strategy designed and implemented accordingly can be applied to autonomous implementation on the satellite, thereby reducing the burden of ground control.

[0042] 2. The present invention includes the effects of earth perturbations and various non-conservative force perturbations in the orbit control strategy design method. Among them, the earth perturbations include the complete gravitational perturbations of the earth such as band harmonic terms and field harmonic terms, and the non-conservative force perturbations include atmospheric drag, solar radiation pressure, and the gravity of the sun and the moon, etc., which avoids the shortcomings of traditional control methods that only consider atmospheric drag and have insufficient accuracy, and ensures that when the initial conditions of the regression orbit are accurate, the controlled satellite enters the regression orbit state with high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Schematic diagram of multiple batches of orbital control maneuvers.

[0044] Figure 2 It is the optimal continuous thrust control time history.

[0045] Figure 3 It is the space trajectory of the orbit entering the target state under the action of continuous thrust control. DETAILED DESCRIPTION

[0046] The present invention will be further described below in conjunction with the accompanying drawings.

[0047] Given an initial value that satisfies the regression condition (calculated and solved according to the specific mission requirements by satisfying the regression condition), the satellite regression orbit starting from the initial value point will cause the orbit to gradually deviate from the ideal nominal trajectory in space due to the influence of perturbation factors and errors in orbit design. Therefore, in order to ensure that the actual orbit runs along the nominal regression orbit, it is necessary to apply orbit control operations to ensure that the deviation is eliminated. The present invention proposes a strategy of implementing a batch of orbit control sequences within the previous orbital period before reaching the equatorial intersection position determined by the target orbit to achieve regression orbit correction. Thus, by solving the optimal multi-batch regression orbit control quantity, the actual orbit that deviates from the nominal regression condition is continuously compensated and corrected in a real perturbation environment, thereby achieving maintenance control of the regression orbit.

[0048] The present invention provides an autonomous optimal control method for the regression orbit under low thrust conditions, which models the regression orbit control problem as a nonlinear programming problem and transforms it into a convex optimization problem. The specific implementation process is as follows:

[0049] Step S1: construct a Poincaré map based on differential algebra method and express it as a high-order Taylor expansion polynomial. Through this map, any point on the equatorial plane can be projected onto the equatorial plane after a regression cycle.

[0050] First, when the deviation between the actual orbit and the nominal orbit detected on the ground or on the satellite exceeds the preset threshold, the maximum allowable time interval T of the orbit needs to be maintained. C Discretized into N equally divided time grids, each of which includes N+1 time points t 0 ,……,t N-1 ,t N , the time step is Δt, such as Figure 1 As shown. Where N = min(floor(T C / Δt),N max ), min represents the minimum value function, floor represents the floor rounding function, N max Indicates the maximum allowed time interval T C The number of orbital controls allowed to be completed within t N -t N-1 ≥Δt.

[0051] At each time point t i , each can apply an orbital control maneuver, and the speed increment of each orbital control maneuver is Δv i , i = 0,…,N. The nominal orbit is given by i=0,…,N, where r i * Represents the position state quantity, represents the speed state quantity, and r T Indicates the target orbit position state after completing the orbit control batch, v T It represents the target orbit speed state after completing the orbit control batch. For each group of state X i , i = 0, ..., N-1, it is necessary to calculate the k-order Taylor approximation polynomial of the state transfer mapping:

[0052]

[0053] Among them, the superscripts “-” and “+” respectively represent the state quantities before and after each orbit control; Indicates that at t i+1 The track position state quantity before track control, Indicates that at t i+1 The track speed state before track control, r i + Indicates that at t i The track position state after track control, Indicates that at t i The orbit speed state after orbit control, represents the track position state transfer mapping, represents the orbit velocity state transfer map, δ represents the deviation of the orbit position or velocity state relative to the nominal orbit, Indicates that at t i+1 The orbit position state deviation obtained after state transfer mapping, Indicates that at t i+1 The orbital velocity state deviation obtained after state transfer mapping, δr i + , indicating that at t i The track position state deviation after track control, Indicates that at t i The track speed state deviation after track control.

[0054] Step S2: Use high-order Taylor expansion polynomials to implement the gradual and rapid recursive calculation of the satellite orbit state quantity after a regression cycle.

[0055] The above state transfer mapping is based on N differential algebraic integrals with natural uncontrolled orbits as reference values ​​under a high-precision model. Since the required velocity correction value is small, a lower order can be selected for the above state transfer mapping to ensure the approximate accuracy of the Taylor approximation polynomial for differential algebraic integrals.

[0056] The correction process of the deviation from the nominal orbit by orbit control maneuver is as follows: Figure 1 As shown, the specific implementation process is as follows:

[0057] For each time point t i , i = 0, ..., N-1, according to the applied orbit control maneuver, the following position and velocity deviation relationship expression is established:

[0058]

[0059] The superscripts “-” and “+” represent the state before and after each orbit control respectively; r i- Indicates that at t i The track position state quantity before track control, Indicates that at t i Track speed state quantity before track control, δr i + Indicates that at t i Track position state deviation after track control, δr i- Indicates that at t i The track position state deviation before track control, Indicates that at t i The track speed state deviation before track control.

[0060] Both equations (1) and (2) represent the orbit control sequence Δv 0 ,Δv 1 ,Δv 2 ,…,Δv N-1 ,Δv N The offset sequence of orbit state quantities under the action relative to the uncontrolled nominal orbit. For the starting time point t i = 0, indicating that the first orbital control maneuver is applied at t 0 , so the initialization condition is: Indicates that at the starting point time t 0 Track position state deviation after track control, Indicates that at the starting point time t 0 The track speed state deviation after track control. For i = 1, ..., N-1, the mapping shown in formula (1) realizes the i The forward recursion of the position and velocity state deviations under the orbital control maneuvers (i=0,1,…,N) can thus obtain the position state deviation sequence and speed state deviation sequence For t N At this moment, there are the following constraints: and Indicates that at the end time t N Track speed state quantity before track control, Indicates that at the end time t NThe orbit position state after orbit control indicates that the orbit after control enters the target orbit and starts a new return condition.

[0061] Step S3: Establish a second-order cone optimal control problem for the orbit to enter the regression orbit state from the initial state under the orbit control maneuver.

[0062] Based on the above orbital control sequence Δv 0 ,Δv 1 ,Δv 2 ,…,Δv N-1 ,Δv N For the control process of the regression orbit, the multi-batch orbit control problem can be modeled as a nonlinear optimization problem, and its objective function and nonlinear constraints are as follows:

[0063]

[0064] Where, ΔV i represents the magnitude of the velocity increment for each orbital control maneuver; v m The velocity increment ΔV for each orbital control maneuver i The maximum speed increment limit, i = 0, ..., N; ΔV in the nonlinear constraint condition i ≤v m Indicates that the speed increment of each orbital maneuver is no greater than the maximum limit v m , It means that the speed state is the target speed state after the last orbital maneuver control. Indicates that the position state is the target position state after the last orbital maneuver control.

[0065] Step S4: Design a multi-batch orbit control strategy that maintains the characteristics of the regression orbit and is suitable for small thrust propulsion.

[0066] In order to adapt to the operation of autonomous control strategy on the satellite, it is necessary to reduce the amount of calculation and ensure the rapid convergence of the results. The slack variables and lossless optimization method are introduced to transform the nonlinear optimization problem into a convex optimization problem. The velocity increment size ΔV of each orbital control maneuver is i As its slack variables, each orbit control maneuver consists of four variables [Δv i ,ΔV i ] T Indicates that the velocity increment Δv of each orbit control is i It is composed of three directional components: radial, transverse and normal, namely Δv i =[Δv i,x ,Δv i,y ,Δv i,z ] T , and the optimization variables of the multi-batch trajectory control problem are converted to [Δv0 ,...,Δv N ,ΔV 0 ...,ΔV N ] T , the objective function is transformed into the following linear form:

[0067]

[0068] The nonlinear constraints are transformed into a second-order cone format:

[0069]

[0070] in, Indicates the velocity increment Δv i The radial component of Indicates the velocity increment Δv i The lateral component of Indicates the velocity increment Δv i The normal component of .

[0071] And the slack variable constraints are:

[0072] 0≤ΔV i ≤v m (6)

[0073] Step S5: Obtain the global optimal control quantity through a second-order convex optimization method.

[0074] The convexification process of the above problem is a lossless transformation process. The optimal solution to the second-order cone problem is also the optimal solution to the original multi-batch orbit control problem. In order to optimize the solution of the second-order cone problem, the dynamic equation needs to be linearized. This can be done by extracting the linear part of the mapping described by equation (1). The obtained linear matrix is:

[0075]

[0076] Among them, the matrix A i (i=0,...,N-1) represents the linear part of the mapping. Specifically, A δr,i Represents the orbital position state mapping, A δv,i Represents the orbital velocity state quantity mapping.

[0077] For t N The final target state at the moment can be expressed by decomposing the linear matrix, and the result is as follows:

[0078]

[0079] in, Indicates that at the end time t N Track position state deviation before track control, Indicates that at the end time t N Track speed state deviation before track control, A N-1 ·A N-2 ·…·A δv,0 ,A N-2 ·A N-3 ·…·A δv,1 ,…,A δv,N-1 They represent the multiplication combination of each mapping, realizing the transfer from velocity increment to orbital position and velocity state quantity.

[0080] Define M = [A N-1 ·A N-2 ·...·A δv,0 ,A N-2 ·A N-3 ·...·A δv,1 ,...,A δv,N-1 ]. Because at t N At time , the target orbit state is reached by applying the last orbit control maneuver, so the following linear expression of the constraint can be obtained:

[0081]

[0082] Where I represents the identity matrix.

[0083] A regression orbit with a regression period of 11 days and 167 regression circles is used as a simulation implementation example to illustrate an autonomous optimal control method for a regression orbit under low thrust conditions of the present invention.

[0084] Set the maximum speed increment limit v m =6mm / s, time interval is 1min (equivalent to a single small thrust control speed increment of up to 10 -4 m / s 2 ). The optimized orbit control results are as follows Figure 2 As shown. Figure 3 In the figure, the small arrow on the regression track indicates each small thrust orbit control maneuver, the arrow at the starting position, i.e., the dot symbol, indicates the position of the first orbit control maneuver applied, and the box symbol indicates the target position reached. During this period of time, the total speed increment required is 0.0898 m / s, and the speed increment solved above is the optimal control amount.

[0085] The autonomous optimal control method for the regression orbit under low thrust conditions provided by the present invention has certain universality and can be applied to orbit control problems involved in various regression orbit missions.

[0086] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for autonomous optimal control of a regressive orbit under low thrust conditions, characterized in that: The following steps are involved: Step S1: construct a Poincaré map based on differential algebra method and express it as a high-order Taylor expansion polynomial, through which any point on the equatorial plane is projected onto the equatorial plane after a regression cycle; Step S2: using a high-order Taylor expansion polynomial to implement a step-by-step rapid recursive calculation of the satellite orbit state quantity after a regression cycle; Step S3: Establishing a second-order cone optimal control problem for the orbit to enter the regression orbit state from the initial state under the orbit control maneuver; Step S4: designing a multi-batch orbit control strategy that maintains the recurrent orbit characteristics and is suitable for small thrust propulsion mode; Step S5: Obtain the global optimal control quantity through a second-order convex optimization method.

2. The autonomous optimal control method for the return orbit under low thrust conditions according to claim 1 is characterized in that: In step S1, a deviation threshold between the actual track and the nominal track is set. When the deviation between the actual track and the nominal track exceeds the preset threshold, the maximum allowable time interval T of the track maintenance is set. C Discretized into N equally divided time grids, each of which includes N+1 time points t0, ..., t N-1 ,t N , the time step is Δt, N = min(floor(T C / Δt),N max ), min represents the minimum value function, floor represents the floor rounding function, N max Indicates the maximum allowed time interval T C The number of orbital controls allowed to be completed within t N -t N-1 ≥Δt.

3. The autonomous optimal control method for the return orbit under low thrust conditions according to claim 1 is characterized in that: In step S1, at each time point t i , each of which applies an orbital control maneuver, and the velocity increment of each orbital control maneuver is Δv i , i = 0,…,N; the nominal orbit is given by i=0,…,N, Represents the position state quantity, represents the speed state quantity, and r T Indicates the target orbit position state after completing the orbit control batch, v T It represents the target orbit speed state after completing the orbit control batch; for each group of state X i =[r i ,v i ] T , i = 0, ..., N-1, calculate the k-order Taylor approximation polynomial of its state transfer mapping: Among them, the superscripts "-" and "+" respectively represent the state quantities before and after each orbit control; Indicates that at t i+1 The track position state quantity before track control, Indicates that at t i+1 The track speed state before track control, Indicates that at t i The track position state after track control, Indicates that at t i The orbit speed state after orbit control, represents the track position state transfer mapping, represents the orbit velocity state transfer map, δ represents the deviation of the orbit position or velocity state relative to the nominal orbit, Indicates that at t i+1 The orbit position state deviation obtained after state transfer mapping, Indicates that at t i+1 The orbital velocity state deviation obtained after state transfer mapping is Indicates that at t i The track position state deviation after track control, Indicates that at t i The orbit velocity state deviation after orbit control; Formula (1) represents the orbit control sequence Δv0, Δv1, Δv2, …, Δv N-1 ,Δv N The deviation sequence of orbital state quantities under the action relative to the uncontrolled nominal orbit.

4. The autonomous optimal control method for the return orbit under low thrust conditions according to claim 1 is characterized in that: In step S2, for each time point t i , i=0,…,N-1, according to the applied orbit control maneuver, the relationship between position and velocity deviation is established: Among them, the superscripts "-" and "+" respectively represent the state quantities before and after each orbit control; Indicates that at t i The track position state quantity before track control, Indicates that at t i The track speed state before track control, Indicates that at t i The track position state deviation after track control, Indicates that at t i The track position state deviation before track control, Indicates that at t i The orbit velocity state deviation before orbit control; Formula (2) represents the orbit control sequence Δv0, Δv1, Δv2, …, Δv N-1 ,Δv N The deviation sequence of orbital state quantities under the action relative to the uncontrolled nominal orbit.

5. The autonomous optimal control method for the return orbit under low thrust conditions according to claim 1 is characterized in that: In step S2, for the starting time point t i =0, indicating that the first orbit control maneuver is applied at t0, so the initialization condition is: It indicates the deviation of the track position state after track control at the starting point time t0. represents the orbit velocity state deviation after orbit control at the starting point time t0; for i = 1, ..., N-1, the mapping shown by the high-order Taylor expansion polynomial realizes the i , i = 0, 1, ..., N orbit control maneuvers under the forward recursion of the position and velocity state deviation, thereby obtaining the position state deviation sequence and speed state deviation sequence For t N At this moment, there are the following constraints: and Indicates that at the end time t N Track speed state quantity before track control, Indicates that at the end time t N The orbit position state after orbit control indicates that the orbit after control enters the target orbit and starts a new return condition.

6. The autonomous optimal control method for the return orbit under low thrust conditions according to claim 1 is characterized in that: In step S3, based on the trajectory control sequence Δv0, Δv1, Δv2, ..., Δv N-1 ,Δv N For the control process of the regression orbit, the multi-batch orbit control problem is modeled as a nonlinear optimization problem, and its objective function and nonlinear constraints are: Where, ΔV i represents the magnitude of the velocity increment for each orbital control maneuver; v m The velocity increment ΔV for each orbital control maneuver i The maximum speed increment limit, i = 0, ..., N; ΔV in the nonlinear constraint condition i ≤v m Indicates that the speed increment of each orbital maneuver is no greater than the maximum limit v m , It means that the speed state is the target speed state after the last orbital maneuver control. Indicates that the position state is the target position state after the last orbital maneuver control.

7. The autonomous optimal control method for the return orbit under low thrust conditions according to claim 6 is characterized in that: In step S4, slack variables and lossless optimization methods are introduced to transform the nonlinear optimization problem into a convex optimization problem.

8. The autonomous optimal control method for the return orbit under low thrust conditions according to claim 7 is characterized in that: In step S4, the speed increment ΔV of each orbit control maneuver is i As its slack variables, each orbit control maneuver consists of four variables [Δv i ,ΔV i ] T Indicates that the velocity increment Δv of each orbit control is i It is composed of three directional components: radial, transverse and normal, namely Δv i =[Δv i,x ,Δv i,y ,Δv i,z ] T , and the optimization variables of the multi-batch trajectory control problem are converted to [Δv0,...,Δv N ,ΔV0...,ΔV N ] T , the objective function is transformed into the following linear form: The nonlinear constraints are transformed into a second-order cone format: in, Indicates the velocity increment Δv i The radial component of Indicates the velocity increment Δv i The lateral component of Indicates the velocity increment Δv i The normal component of . And the slack variable constraints are: 0≤ΔV i ≤v m (6)。 9. The autonomous optimal control method for the return orbit under low thrust conditions according to claim 8 is characterized in that: In step S5, the linear part of the mapping shown by the high-order Taylor expansion polynomial is extracted for linearization, and the obtained linear matrix is: Among them, the matrix A i (i=0,...,N-1) represents the linear part of the mapping, A δr,i Represents the orbital position state mapping, A δv,i Represents the orbital velocity state quantity mapping.

10. The autonomous optimal control method for the return orbit under low thrust conditions according to claim 9, characterized in that: For t N The final target state at the moment can be expressed by decomposing the linear matrix, and the result is as follows: in, Indicates that at the end time t N Track position state deviation before track control, Indicates that at the end time t N Track speed state deviation before track control, A N-1 ·A N-2 ·...·A δv,0 ,A N-2 ·A N-3 ·...·A δv,1 ,...,A δv,N-1 They represent the multiplication combination of each mapping, realizing the transfer from velocity increment to orbital position and velocity state quantity. Define M = [A N-1 ·A N-2 ·...·A δv,0 ,A N-2 ·A N-3 ·...·A δv,1 ,...,A δv,N-1 ]; because at t N At time , the last orbit control maneuver is applied to reach the target orbit state, so the linear expression of the constraint is: Where I represents the identity matrix.

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