Autonomous optimal control method for low-thrust return orbit

Abstract

The application discloses a small-thrust autonomous optimal control method for a return orbit, and belongs to the field of satellite orbit control.The method comprises the following steps: constructing a Poincaré mapping based on a differential algebraic method and representing the Poincaré mapping as a high-order Taylor expansion polynomial; using the high-order Taylor expansion polynomial to realize recursive calculation of satellite orbit state quantity after one return period; establishing a second-order convex optimal control problem for the orbit to enter a return orbit state from an initial state under the action of an orbit control maneuver; designing a multi-batch orbit control strategy suitable for a small-thrust propulsion mode; and obtaining global optimal control quantity through a second-order convex optimization method.The multi-batch orbit control strategy designed by the application has small calculation amount and global optimality, can be compatible with both pulse thrust and continuous small thrust control modes, can be applied to autonomous implementation on a satellite, and can reduce the ground control burden.The application ensures that a controlled satellite enters a return orbit state with high accuracy under the condition that the initial condition of the return orbit is accurate.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of satellite orbit control, and particularly relates to a method for autonomous optimal control of a recurrent orbit under small thrust conditions. BACKGROUND

[0002] The recurrent orbit has been widely applied in various earth remote sensing tasks, has the advantages of ground track recurrence and repeatability, and can complete equal-interval revisit to a target, thereby realizing periodic observation. The satellite in orbit is affected by non-conservative perturbation such as atmospheric drag, which causes the actual flight orbit of the satellite to deviate from the strictly designed recurrent orbit, and causes the sub-satellite point track to deviate from the nominally designed track, thereby bringing inconvenience to the periodic observation of the target. In order to maintain the accurate recurrence characteristics of the satellite orbit, orbit maintenance control needs to be performed to compensate for the perturbation effect, so that the satellite always flies with the orbit characteristics that meet the recurrence condition.

[0003] The control method of the recurrent orbit is mainly based on the design of keeping the nominal value of the recurrent orbit, and the goal is to make the ground or space track change near the designed recurrent mode. In the existing control method, the non-conservative perturbation factors such as atmospheric drag and solar pressure are ignored in the orbit design stage, and are considered in the orbit control stage. Considering that the non-conservative force, especially the atmospheric drag, will cause the actual ground sub-satellite point track to deviate from the nominal recurrence characteristics, orbit maintenance control is needed to compensate for the perturbation factor. Some researches on orbit maintenance problems based on the design of the nominal value of the recurrent orbit are carried out, and the goal is to keep the ground track near the nominal track corresponding to the designed recurrence characteristics. SUMMARY

[0004] In view of the deficiencies of the prior art, the application provides a method for autonomous optimal control of a recurrent orbit under small thrust conditions. The application designs a multi-batch orbit control strategy for keeping the recurrence orbit characteristics and suitable for implementation of small thrust propulsion, which has the characteristics of small calculation amount and global optimality. The application can simultaneously compatible with both pulse thrust and continuous small thrust control modes, and can be applied to autonomous implementation on the satellite, thereby reducing the ground control burden. The application avoids the precision deficiency of the traditional control method, and ensures that the controlled satellite enters the recurrent orbit state with high precision under the condition that the initial conditions of the recurrent orbit are accurate.

[0005] The technical solution adopted by the application to solve the technical problems is as follows:

[0006] The application provides a method for autonomous optimal control of a recurrent orbit under small thrust conditions, which comprises the following steps:

[0007] Step S1: constructing a Poincaré mapping based on the differential algebraic method and representing 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 period;

[0008] Step S2: implementing step-by-step fast recursive calculation of the satellite orbit state after a regression period by using the high-order Taylor expansion polynomial;

[0009] Step S3: establishing a second-order cone optimal control problem for the orbit to enter a regression orbit state from an initial state under the action of an orbit control maneuver;

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

[0011] Step S5: obtaining the globally optimal control quantity by a second-order convex optimization method.

[0012] Further, in step S1, first set the deviation threshold between the actual orbit and the nominal orbit, when it is detected that the deviation between the actual orbit and the nominal orbit exceeds the preset threshold, maintain the maximum allowed time interval T C is divided into N equal length grids, the N equal length grids include N+1 time points t0,……,t N-1 , N , the time step is Δt, N=min(floor(T C / Δt),N max ), min represents the minimum function, floor represents the floor function, N max represents the maximum allowed number of orbit control times within the maximum allowed time interval T C , t N -t N-1 ≥Δt.

[0013] Further, in step S1, at each time point t i , an orbit control maneuver is applied once, the velocity increment of each orbit control maneuver is Δv i , i=0,…,N; the nominal orbit is composed of i=0,…,N, represents the position state quantity, represents the velocity state quantity, and r T represents the target orbit position state quantity after completing the orbit control batch, v T represents the target orbit velocity state quantity after completing the orbit control batch; for each set of state quantities X i , i=0,…,N-1, calculate the k-order Taylor approximation polynomial of the state transition mapping thereof:

[0014]

[0015] where the superscripts "-" and "+" denote the state quantities before and after each orbit control, respectively; denotes the orbit position state quantity at t i+1 before orbit control, denotes the orbit velocity state quantity at t i+1 before orbit control, r i + denotes the orbit position state quantity at t i after orbit control, denotes the orbit velocity state quantity at t i after orbit control, denotes the orbit position state transfer map, denotes the orbit velocity state transfer map, δ denotes the deviation of the orbit position or velocity state quantity from the nominal orbit, denotes the orbit position state deviation quantity obtained after the state transfer map at t i+1 , denotes the orbit velocity state deviation quantity obtained after the state transfer map at t i+1 , δr i + denotes the orbit position state deviation quantity after orbit control at t i , denotes the orbit velocity state deviation quantity after orbit control at t i ; formula (1) denotes the deviation sequence of the orbit state quantity from the uncontrolled nominal orbit under the action of the orbit control sequence Δv0, Δv1, Δv2, …, Δv N-1 , Δv N .

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

[0017]

[0018] where the superscripts "-" and "+" denote the state quantities before and after each orbit control, respectively; r i - denotes the orbit position state quantity at t i before orbit control, denotes the orbit velocity state quantity at t i before orbit control, δr i + denotes the orbit position state quantity at t iThe deviation of the track position after track control, δr i- Indicates at t i The deviation of the track position before track control. Indicates at t i The deviation of the track velocity state before track control; Equation (2) represents the deviation of the track velocity state before track control; N-1 ,Δv N The offset sequence of orbital state variables relative to the uncontrolled nominal orbit under the action.

[0019] Furthermore, in step S2, for the initial time point t i =0 indicates that the first orbital control maneuver is applied at time t0, therefore the initialization condition is: This represents the deviation of the track position after track control at the initial time t0. This represents the deviation of the orbital velocity state after orbital control at the initial time t0; for i = 1, ..., N-1, the mapping shown by the higher-order Taylor expansion polynomial realizes the deviation at different time points t. i The forward recursion of position and velocity state deviations under orbital control maneuvers for i = 0, 1, ..., N yields the sequence of position state deviations. and velocity state quantity deviation sequence For t N At any given time, the following constraints apply: and Indicates the time at the end t N Track velocity state variables before track control Indicates the time at the end t N The orbital position state after orbital control indicates that the controlled orbit has entered the target orbit and started a new regression condition.

[0020] Furthermore, in step S3, based on the orbital control sequence Δv0, Δv1, Δv2, ..., Δv N-1 ,Δv N The control process for the return trajectory is modeled as a nonlinear optimization problem, with the objective function and nonlinear constraints as follows:

[0021]

[0022] Where, ΔV i This indicates the magnitude of the speed increment for each orbital control maneuver; v m The magnitude of the velocity increment ΔV for each orbital control maneuver is represented by this value. i Maximum velocity increment limit, i = 0, ..., N; ΔV in nonlinear constraintsi ≤v m denotes that the velocity increment size of each orbit maneuver is not greater than the maximum limit v m , denotes that the velocity state after the last orbit maneuver control is the target velocity state, denotes that the position state after the last orbit maneuver control is the target position state.

[0023] Further, in step S4, the relaxation variable and the lossless optimization method are introduced to convert the nonlinear optimization problem into a convex optimization problem.

[0024] Further, in step S4, the velocity increment size ΔV i of each orbit control maneuver is taken as the relaxation variable, and then each orbit control maneuver is composed of 4 variables [Δv i , ΔV i ] T denotes, wherein the velocity increment Δv i of each orbit control is composed of radial, lateral and normal direction components, that is, Δv i = [Δv i,x , Δv i,y , Δv i,z ] T , and the optimization variables of the multi-batch orbit control problem are converted to [Δv0,..., Δv N , ΔV0,..., ΔV N ] T , and the objective function is converted to the following linear form:

[0025]

[0026] And the nonlinear constraint is converted to the second-order cone format:

[0027]

[0028] wherein, denotes the radial component of the velocity increment Δv i , denotes the lateral component of the velocity increment Δv i , denotes the normal component of the velocity increment Δv i .

[0029] And the relaxation variable constraint is:

[0030] 0≤ΔV i ≤v m (6).

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

[0032]

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

[0034] Further, for the final target state quantity at time t N , the expression thereof can be obtained by decomposing the linear matrix, and the result is as follows:

[0035]

[0036] wherein, represents the orbit position state deviation quantity before the orbit control at the ending time t N represents the orbit velocity state deviation quantity before the orbit control at the ending time t N N-1 ·A N-2 ·...·A δv,0 ,A N-2 ·A N-3 ·...·A δv,1 ,...,A δv,N-1 respectively represent the multiplication combination of each mapping, and realize the transmission from the velocity increment to the orbit 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 ]; since at time t N , the last orbit control maneuver is applied, i.e. the target orbit state is reached, therefore the linear expression of the constraint is obtained as:

[0038]

[0039] wherein I represents the unit matrix.

[0040] Compared with the prior art, the present application has the beneficial effects that:

[0041] ​​1. The present application is directed to the need for regression orbit maintenance, and a multi-batch orbit control strategy is designed to maintain the characteristics of the regression orbit and is suitable for small-thrust propulsion mode implementation. Based on the solution of the second-order cone problem, the orbit tracking control that meets the regression condition is realized, and the orbit control strategy has the characteristics of small calculation amount and global optimization. Specifically, the present application converts the multi-batch velocity increment function into a second-order cone problem by a lossless convex optimization method, linearizes the nonlinear constraint condition, and completes the solution of the optimal control amount. Since the size of each velocity increment can be constrained, and the time step can be discretized more finely, the present application can simultaneously compatible with both pulse thrust and continuous small thrust control modes. It needs to be particularly pointed out that due to the uniqueness of the optimal solution of the convex optimization problem and the simplicity of the calculation, the orbit control algorithm and strategy designed and implemented accordingly can be applied to on-board autonomous implementation, thereby reducing the ground control burden.

[0042] 2. The present application includes the earth perturbation and the perturbation of each non-conservative force in the design method of the orbit control strategy, wherein the earth perturbation includes the earth complete gravity perturbation such as the zonal term and the tesseral term, the non-conservative force perturbation includes the atmospheric resistance, the solar radiation pressure and the lunar three-body gravity, etc., avoiding the shortcomings of the traditional control method which only considers the atmospheric resistance and has insufficient precision, ensuring that the controlled satellite enters the regression orbit state with high precision under the condition of accurate initial conditions of the regression orbit. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 It is a multi-batch orbit control maneuver schematic diagram.

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

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

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

[0047] Given the initial value that meets the regression condition (calculated and solved according to the specific task requirements that meet 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, orbit control operation needs to be applied to ensure that the deviation is eliminated. The present application proposes a strategy of implementing a batch of orbit control sequences within one orbit period before reaching the determined equinox intersection position of the target orbit to realize the regression orbit correction. Thus, by solving the optimal multi-batch regression orbit control amount, the actual orbit deviating from the nominal regression condition is continuously compensated and corrected in the real perturbation environment, thereby realizing the maintenance control of the regression orbit.

[0048] This invention provides an autonomous optimal control method for a return trajectory under low thrust conditions. The return trajectory control problem is modeled as a nonlinear programming problem and transformed into a convex optimization problem. The specific implementation process is as follows:

[0049] Step S1: Construct the Poincaré map based on the differential algebra method and express it as a higher-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 a preset threshold, the maximum allowable time interval T for maintaining the orbit needs to be extended. C Discretize into N equally divided time grids, each containing N+1 time points t0, ..., 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 function, N max Indicates the maximum allowed time interval T C The number of orbital control operations allowed to be completed within the time limit, therefore t N -t N-1 ≥Δt.

[0051] At each time point t i Each can apply one orbital control maneuver, with a velocity increment of Δv for each maneuver. i , i = 0,…,N. The nominal orbit is formed by The sequence consists of i = 0, ..., N, where r i * Indicates the position status quantity. Represents the velocity state variable, and r T v represents the target orbital position state after the completion of the orbital control batch. T This represents the target orbital velocity state variable after completing a batch of orbital control operations. For each set of state variables X... i For i = 0, ..., N-1, the k-th order Taylor approximation polynomial of the state transfer mapping needs to be calculated:

[0052]

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

[0054] Step S2: Use a high-order Taylor expansion polynomial to perform a stepwise and rapid recursive calculation of the satellite orbital state variables after one regression cycle.

[0055] The aforementioned state transfer mapping is based on N differential algebraic integrals with a naturally uncontrolled trajectory as the reference value under a high-precision model. Since the required velocity correction is relatively small, a lower order can be chosen for the above state transfer mapping to ensure the approximate accuracy of the Taylor approximation polynomial over the differential algebraic integral.

[0056] The process of correcting errors in deviation from the nominal track by track control maneuvers is as follows: Figure 1 As shown, the specific implementation process is as follows:

[0057] For each time point t i For i = 0, ..., N-1, based on the applied trajectory control maneuvers, the following expression is established to express the relationship between position and velocity deviation:

[0058]

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

[0060] Equations (1) and (2) both represent the orbital control sequence Δv0, Δv1, Δv2, ..., Δv N-1 ,Δv N The sequence of offsets of the orbital state variables relative to the uncontrolled nominal orbit under the influence of the control. For the initial time point t i =0 indicates that the first orbital control maneuver is applied at time t0, therefore the initialization condition is: This represents the deviation of the track position after track control at the initial time t0. This represents the deviation of the orbital velocity state after orbital control at the initial time t0. For i = 1, ..., N-1, the mapping shown in equation (1) realizes the deviation at different time points t0. i The forward recursion of position and velocity state deviations under orbital control maneuvers (i = 0, 1, ..., N) yields the sequence of position state deviations. and velocity state quantity deviation sequence For t N At any given time, the following constraints apply: and Indicates the time at the end t N Track velocity state variables before track control Indicates the time at the end t N The orbital position state after orbital control indicates that the controlled orbit has entered the target orbit and started a new regression condition.

[0061] Step S3: Establish a second-order cone optimal control problem for the trajectory to enter the return trajectory state from the initial state under the action of trajectory control maneuvers.

[0062] Based on the above orbital control sequence Δv0, Δv1, Δv2, ..., Δv N-1 ,Δv N The process of controlling the return trajectory can be modeled as a nonlinear optimization problem, with the objective function and nonlinear constraints as follows:

[0063]

[0064] Where, ΔV idenotes the magnitude of the velocity increment of each orbit control maneuver; v m denotes the magnitude of the velocity increment of each orbit control maneuver i maximum velocity increment limit, i = 0,..., N; ΔV in the nonlinear constraint condition i ≤ v m denotes that the magnitude of the velocity increment of each orbit control maneuver is not greater than the maximum limit v m , denotes that the velocity state after the last orbit control maneuver is the target velocity state, denotes that the position state after the last orbit control maneuver is the target position state.

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

[0066] In order to adapt to the operation of implementing the control strategy autonomously on the satellite, the calculation amount needs to be reduced and the result needs to be ensured to converge quickly. A relaxation variable and a lossless optimization method are introduced to convert the nonlinear optimization problem into a convex optimization problem. The magnitude of the velocity increment of each orbit control maneuver ΔV i is taken as the relaxation variable thereof, and each orbit control maneuver is represented by 4 variables [Δv i , ΔV i ] T , wherein the velocity increment Δv i of each orbit control is composed of radial, transverse, and normal direction components, i.e., Δv i = [Δv i,x , Δv i,y , Δv i,z ] T , and the optimization variables of the multi-batch orbit control problem are converted to [Δv0,..., Δv N , ΔV0..., ΔV N ] T , and the objective function is converted into the following linear form:

[0067]

[0068] and the nonlinear constraint is converted into a second-order cone format:

[0069]

[0070] wherein, denotes the radial component of the velocity increment Δv i , denotes the transverse component of the velocity increment Δv i , denotes the normal component of the velocity increment Δv i .

[0071] and the slack variable constraints are:

[0072] 0≤ΔV i ≤v m (6)

[0073] Step S5: Obtain the global optimal control variable by the second-order convex optimization method.

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

[0075]

[0076] Where, the matrix A i (i=0,...,N-1) represents the linear part of the mapping. Specifically, A δr,i represents the orbit position state mapping, A δv,i represents the orbit velocity state mapping.

[0077] For the final target state quantity at time t N , its expression can be obtained by decomposing the linear matrix, and the result is as follows:

[0078]

[0079] Where, represents the orbit position state deviation quantity before orbit control at the end time t N , represents the orbit velocity state deviation quantity before orbit control at the end time t N , N-1 , N-2 , δv,0 , N-2 , N-3 , δv,1 , δv,N-1 respectively represent the multiplication combination of each mapping, realizing the transmission from the velocity increment to the orbit position and velocity state quantity.

[0080] Define M=[A N-1 , N-2 , δv,0 , N-2 , N-3 , δv,1 , δv,N-1 ]. Since at t NAt the time when the last orbit control maneuver is applied, i.e., the target orbit state is reached, the following linear expression of the constraints can be obtained:

[0081]

[0082] where I denotes the identity matrix.

[0083] The regression orbit with a regression period of 11 days and a regression number of 167 is taken as a simulation implementation example to explain the autonomous optimal control method for the regression orbit under the condition of small thrust.

[0084] The maximum velocity increment limit v m = 6 mm / s is set, and the time interval is 1 min (equivalent to the maximum velocity increment of 10 -4 m / s for single small thrust control). 2 The optimal orbit control result is shown in Figure 2 In Figure 3 , the small arrows on the regression orbit represent each small thrust orbit control maneuver, the arrow at the starting position, i.e., the dot symbol, represents the position of the first orbit control maneuver, and the box-shaped symbol represents the target position. During this period, the total required velocity increment is 0.0898 m / s, and the above-solved velocity increment is the optimal control quantity.

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

[0086] The above only describes the preferred embodiments of the present application, and it should be noted that, for ordinary skilled persons in the art, several improvements and refinements can be made without departing from the principles of the present application, and these improvements and refinements should also be regarded as the protection scope of the present application.

Claims

1. A method for autonomous optimal control of a low-thrust return trajectory, characterized in that, The method comprises the following steps: Step S1: constructing a Poincaré mapping based on a differential algebraic method and representing it as a high-order Taylor expansion polynomial, and projecting any point on an equatorial plane to the equatorial plane after a regression period through the mapping; Step S2: realizing step-by-step fast recursive calculation of satellite orbit state quantities after a regression period by using the high-order Taylor expansion polynomial; Step S3: establishing a second-order cone optimal control problem of entering a regression orbit state from an initial state under the action of an orbit control maneuver; Step S4: designing a multi-batch orbit control strategy suitable for small-thrust propulsion mode implementation and keeping the regression orbit characteristics; Step S5: obtaining global optimal control quantities by a second-order convex optimization method.

2. The autonomous optimal control method for low-thrust return orbit according to claim 1, characterized in that, In step S1, a deviation threshold between the actual track and the nominal track is first set, and when it is detected that the deviation between the actual track and the nominal track exceeds the preset threshold, the maximum allowed time interval T C is maintained for the track N-1 N The time interval is discretized into N equal grids, and the N equal grids include N+1 time points t0, …, t C N+1 max , where N is the number of equal grids, and T max is the maximum allowed time interval for the track C , and Δt is the time step, N N = min(floor(T N-1 / Δt), N C ), min represents the minimum function, floor represents the floor function, N N-1 represents the maximum number of track controls allowed to be completed within the maximum allowed time interval T N , and t C -t max ≥Δt.

3. The autonomous optimal control method for low-thrust return orbit according to claim 2, characterized in that, In step S1, at each time point t i , a trajectory control maneuver is applied once, with a speed increment of Δv i for each trajectory control maneuver, i = 0,..., N; the nominal trajectory consists of i = 0,..., N, denotes the position state quantity, denotes the speed state quantity, and r T denotes the target trajectory position state quantity after completion of the trajectory control batch, v T denotes the target trajectory speed state quantity after completion of the trajectory control batch; for each set of state quantities X i = [r i , v i ] T , i = 0,..., N - 1, a kth order Taylor polynomial of the state transition mapping thereof is calculated: where the superscripts "-" and "+" represent the state quantities before and after each orbit control, respectively; represents the orbit position state quantity before orbit control at t i+1 , represents the orbit velocity state quantity before orbit control at t i+1 , represents the orbit position state quantity after orbit control at t i , represents the orbit velocity state quantity after orbit control at t i , represents the orbit position state transfer map, represents the orbit velocity state transfer map, and δ represents the deviation of the orbit position or velocity state quantity from the nominal orbit, represents the orbit position state quantity deviation obtained after state transfer map at t i+1 , represents the orbit velocity state quantity deviation obtained after state transfer map at t i+1 , represents the orbit position state quantity deviation after orbit control at t i , represents the orbit velocity state quantity deviation after orbit control at t i ; and formula (1) represents the deviation sequence of the orbit state quantity from the uncontrolled nominal orbit under the action of the orbit control sequence Δv0, Δv1, Δv2, …, Δv N-1 , Δv N .

4. The autonomous optimal control method for low-thrust orbit regression according to claim 3, characterized in that, In step S2, for each time point t i i = 0,..., N - 1, a position and velocity deviation relationship expression is established according to the applied orbit control maneuver: where the superscripts "-" and "+" denote the state quantities before and after each orbit control, respectively; denotes the orbit position state quantity before orbit control at t i , denotes the orbit velocity state quantity before orbit control at t i , denotes the orbit position state deviation quantity after orbit control at t i , denotes the orbit position state deviation quantity before orbit control at t i , denotes the orbit velocity state deviation quantity before orbit control at t i ; and equation (2) denotes the orbit state quantity deviation sequence relative to the nominal orbit without control under the action of the orbit control sequence N-1 , N .

5. The autonomous optimal control method for low-thrust orbit regression according to claim 4, characterized in that, In step S2, for the initial time point t i = 0, indicating that the first time point of applying the orbit control maneuver is t0, thus the initial condition is: represents the orbit position state deviation amount after the orbit control at the initial time point t0, represents the orbit velocity state deviation amount after the orbit control at the initial time point t0; for i = 1, …, N-1, the mapping realized by the high-order Taylor expansion polynomial realizes the forward recursion of the position and velocity state amounts under the action of the orbit control maneuver at different time points t i , i = 0, 1, …, N, thus obtaining the position state amount deviation sequence and the velocity state amount deviation sequence For the time point t N , there are the following constraints: and represents the orbit velocity state amount before the orbit control at the end time point t N represents the orbit position state amount after the orbit control at the end time point t N , indicating that the orbit after the control enters the target orbit and starts a new return condition.​ 6. The autonomous optimal control method for low-thrust orbit regression according to claim 5, characterized in that, In step S3, the control sequence Δv0, Δv1, Δv2,..., Δv N-1 ,Δv N The control process of the regression orbit is modeled as a nonlinear optimization problem, whose objective function and nonlinear constraint conditions are as follows: where ΔV i denotes the magnitude of the velocity increment for each orbit control maneuver; v m denotes the maximum velocity increment limit for the magnitude of the velocity increment ΔV i for each orbit control maneuver, i = 0,..., N; ΔV i ≤ v m denotes that the magnitude of the velocity increment for each orbit control maneuver is not greater than the maximum velocity increment limit v m , denotes that the velocity state after the last orbit control maneuver is the target velocity state, denotes that the position state after the last orbit control maneuver is the target position state.

7. The autonomous optimal control method for low-thrust orbit regression according to claim 6, characterized in that, In step S4, a slack variable and a lossless optimization method are introduced to convert the nonlinear optimization problem into a convex optimization problem.

8. The autonomous optimal control method for low-thrust return orbit according to claim 7, characterized in that, In step S4, the speed increment ΔV for each orbital control maneuver is... i As its slack variable, each orbital control maneuver consists of 4 variables [Δv] i ,ΔV i ] T This indicates that the velocity increment Δv for each orbital control maneuver is... i It consists of three directional components: radial, transverse, and normal, i.e., Δv i =[Δv i,x ,Δv i,y ,Δv i,z ] T The optimization variables for the multi-batch track control problem are transformed into [Δv0,...,Δv] N ,ΔV0...,ΔV N ] T The objective function is transformed into the following linear form: And the nonlinear constraint is converted into a second-order cone format: wherein denotes the radial component of the velocity increment Δv i denotes the lateral component of the velocity increment Δv i denotes the normal component of the velocity increment Δv i ​​​ And the slack variable constraint is: 0 < ΔV i ≤ v m (6).

9. The autonomous optimal control method for low-thrust orbit regression according to claim 8, characterized in that, In step S5, linearization is performed by extracting the linear part of the mapping shown by the high-order Taylor expansion polynomial, and the obtained linear matrix is: where the matrix A i (i = 0,..., N - 1) represents the linear part of the mapping, A δr,i represents the orbit position state quantity mapping, A δv,i represents the orbit velocity state quantity mapping.

10. The autonomous optimal control method for low-thrust return orbit according to claim 9, wherein, For t N the final target state quantity at time t, whose expression can be obtained by decomposing the linear matrix, as follows: wherein, denotes the orbit position state deviation quantity before orbit control at the end time t N denotes the orbit velocity state deviation quantity before orbit control at the end time t denotes the orbit position state deviation quantity before orbit control at the end time t N denotes the orbit velocity state deviation quantity before orbit control at the end time t N-1 denotes the orbit position state deviation quantity before orbit control at the end time t N-2 denotes the orbit velocity state deviation quantity before orbit control at the end time t δv,0 denotes the orbit position state deviation quantity before orbit control at the end time t N-2 denotes the orbit velocity state deviation quantity before orbit control at the end time t N-3 denotes the orbit position state deviation quantity before orbit control at the end time t δv,1 denotes the orbit velocity state deviation quantity before orbit control at the end time t δv,N-1 denote the multiplied combinations of each mapping, respectively, to realize the transfer from the velocity increment to the orbit position and velocity state quantities; M = [A N-1 ·A N-2 ·…·A δv,0 ,A N-2 ·A N-3 ·…·A δv,1 ,…,A δv,N-1 ] ; since at the instant t N the last orbital control maneuver is applied, i.e. the target orbit state is reached, the linear expression of the constraints is obtained as: Wherein, I represents a unit matrix.

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