A method for capturing non-cooperative target spacecraft by space station

Abstract

The invention discloses a method for capturing a non-cooperative target spacecraft by a space station, which belongs to the field of space station safety technology. The capturing method covers three stages: an approach stage, a capture stage, and a towing back stage, and is realized by releasing a tracking spacecraft from the space station. In the approach stage, the tracking spacecraft completes the approach to the non-cooperative target spacecraft from the space station with a minimum control cost, thereby reducing the fuel consumption of the tracking spacecraft. In the capture stage, the tracking spacecraft completes the rapid capture of the non-cooperative target spacecraft with uncertain maneuvering behavior in the shortest time, thereby shortening the escape time of the target spacecraft. In the towing back stage, the tracking spacecraft tows the non-cooperative target spacecraft with uncertain struggling maneuvering behavior back in the safest way and completes the rendezvous and docking with the space station, thereby reducing the failure rate of the final rendezvous and docking, and solving the problem of a method for capturing a non-cooperative target spacecraft that affects safety near the operating orbit of the own space station.

Description

Technical Field

[0001] The invention belongs to the technical field of space station security, and in particular relates to a method for a space station to capture a non-cooperative target spacecraft. Background Art

[0002] As an important base for human exploration of space, the safe operation of the space station is directly related to the life safety of astronauts and the smooth progress of space experiment missions. Non-cooperative target spacecraft are spacecraft that do not communicate in information and do not cooperate in behavior, such as enemy spacecraft, failed satellites, space debris, etc. In particular, non-cooperative target spacecraft with the ability of close reconnaissance, harassment, and destruction are extremely unfriendly to the safety of the space station. Therefore, it is particularly important to capture non-cooperative target spacecraft that affect the safety of one's own space station in a timely manner.

[0003] At present, the capture technology for space target spacecraft has made some progress, but there are still many shortcomings. Existing research generally considers unilateral space autonomous rendezvous tasks, or studies the capture of targets in the action space of robotic arms or flying nets alone; this limits its scope of application, and it is still impossible to form a complete solution when facing the capture task of non-cooperative targets. The method of integrating rendezvous and capture of cooperative targets and non-cooperative targets with uncertain maneuvers or struggling behaviors at the same time remains to be studied. Moreover, the traditional method only considers a certain cost indicator or a certain stage. When facing non-cooperative target spacecraft with uncertain maneuvers and struggling behaviors after capture, the capture method has not yet been designed for the entire mission process, so its adaptability, cost and efficiency still need to be improved. Summary of the invention

[0004] The present invention aims to provide a method for a space station to capture a non-cooperative target spacecraft, thereby solving the problem of how to capture a non-cooperative target spacecraft near the orbit of the own space station.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is as follows:

[0006] A method for capturing a non-cooperative target spacecraft by a space station is provided, comprising:

[0007] Step 1: The tracking spacecraft approaches the target spacecraft: The ground base station continuously tracks the target spacecraft and obtains the orbit information of the target spacecraft. The tracking spacecraft departs from the space station and approaches the warning area of ​​the target spacecraft according to the orbit information of the target spacecraft.

[0008] Step 2: The tracking spacecraft captures the target spacecraft: After the tracking spacecraft enters the warning area of ​​the target spacecraft, the target spacecraft performs an escape maneuver, and the ground base station updates the orbit information of the target spacecraft at a fixed time interval. The tracking spacecraft continues to navigate until the distance between the tracking spacecraft and the target spacecraft reaches the capture distance, which is considered a successful capture;

[0009] Step 3: The tracking spacecraft drags back the target spacecraft: After successfully capturing the target spacecraft, the tracking spacecraft drags the target spacecraft toward the space station until the tracking spacecraft completely returns to the docking port of the space station, completing the capture mission of the target spacecraft in the space station.

[0010] Further, in step 1, the method of tracking a spacecraft approaching a target spacecraft includes:

[0011] Step 1.1, establish the target spacecraft orbit coordinate system: take the center of mass of the target spacecraft as the origin, establish the target spacecraft orbit coordinate system, the target spacecraft is located at O T X T Y T Z T The origin position in the coordinate system, the coordinate system moves with the target spacecraft, the position information and velocity information of the target spacecraft are both zero, at time k, the relative state vector of the tracking spacecraft relative to the target spacecraft is X k =[x k y k z k v xk v yk v zk ] T , x k y k z k The position of the tracking spacecraft relative to the target spacecraft is O T X T Y T Z T The components of the three coordinate axes of the coordinate system, v xk v yk v zk The speed of the tracking spacecraft relative to the target spacecraft is O T X T Y T Z T The components of the three coordinate axes of the coordinate system, the impulse maneuver of the tracking spacecraft is U k ; At time k+1, the relative state vector of the tracking spacecraft at time k+1 is X k+1 , the impulse maneuver of the tracking spacecraft is U k+1 ;

[0012] Step 1.2: Use the model predictive control algorithm as the guidance method for the tracking spacecraft approaching the target spacecraft; the expression of the model predictive control algorithm is:

[0013]

[0014] Among them, J(u k ,u k+1 , ..., u k+N ) represents the control variable u k+i , (i=0, 1, ..., N) is the optimization objective function of the independent variable, constraints represents the control variable u k+i , (i=0, 1, ..., N) are the constraints that need to be met, and N represents the prediction interval;

[0015] Step 1.3, select two optimization objective functions J1 and J2; the optimization objective function J1 considers the state vector error and control cost at the end of the prediction interval; the optimization objective function J2 considers the state vector error and control cost in the entire prediction interval;

[0016] Step 1.4, bring the optimization objective functions J1 and J2 into the model predictive control algorithm to obtain a variety of pulse model predictive control algorithms, so that the tracking spacecraft obtains different approach guidance strategies to approach the target spacecraft.

[0017] Furthermore, in step 1.3, the expression of the optimization objective function J1 is:

[0018]

[0019] Among them, X f represents the state vector that the tracking spacecraft will eventually reach; represents the state vector of the spacecraft tracked at time k+Np1; Np1 represents the prediction interval when J1 is used as the optimization objective function; matrices Q1 and R1 represent the weight information of the state vector error and pulse consumption during the optimization process, respectively, where Q1 is a 6×6 matrix and R1 is a 3×3 matrix, and both are symmetric semi-positive matrices, i.e., Q1±0, R1±0;

[0020] The expression of the optimization objective function J2 is:

[0021]

[0022] Among them, Np2 represents the prediction interval when J2 is used as the optimization objective function; X f represents the state vector that the spacecraft is expected to reach, X f =[x f y f z fv xf v yf v zf ] T , x f y f z f are the positions that the tracking spacecraft is expected to reach in the end. T X T Y T Z T The components of the three coordinate axes of the coordinate system, v xf v yf v zf are the final speeds that the tracking spacecraft is expected to reach in O T X T Y T Z T The components of the three coordinate axes of the coordinate system, X k+i represents the state vector of the spacecraft tracked at time k+i. Matrices Q2 and R2 represent the weight information of the state vector error and pulse consumption during the optimization process, respectively. Q2 is a 6×6 matrix and R2 is a 3×3 matrix, and both are symmetric semi-positive matrices, i.e., Q2±0, R2±0.

[0023] Furthermore, in step 1, considering that each pulse maneuver of the tracking spacecraft cannot be an arbitrary value, the calculation formula for the maximum value of a single pulse maneuver speed of the tracking spacecraft when approaching the target spacecraft is:

[0024]

[0025] Among them, U max with U min They represent the maximum single pulse maneuvering speed of the tracking spacecraft in the positive and negative directions of the axis respectively; Δt is the duration of a single pulse of the tracking spacecraft; I sp_c represents the specific thrust of the tracking spacecraft; g0 is the gravitational acceleration at sea level; M represents the rate of change of the mass consumed by the tracking spacecraft discharged through the nozzle; c represents the total mass of the tracking spacecraft; and it should be noted that as the tracking spacecraft continues to pulse maneuvers, the fuel will be reduced, which will inevitably lead to M c The reduction of the pulse maximum of the tracking spacecraft is a time-varying constraint.

[0026] Furthermore, in step 1.4, when J1 is used as the optimization objective function, the expression of the approaching single pulse model predictive control algorithm is:

[0027]

[0028] When J2 is used as the optimization objective function, the expression of the approach segment single pulse model predictive control algorithm is:

[0029]

[0030] Among them, X k+i represents the state vector information of the tracking spacecraft at time k+i. The interval from time k+i to time k+i+1 is a sampling time sample_T. Represents the state transition matrix of the tracking spacecraft from time k+i to time k+i+1; represents the input matrix for tracking the spacecraft from time k+i to time k+i+1;

[0031] When J1 is used as the optimization objective function, the expression of the approach segment multi-pulse model predictive control algorithm is:

[0032]

[0033] When J2 is used as the optimization objective function, the expression of the approach segment multi-pulse model predictive control algorithm is:

[0034]

[0035] Among them, X k+j_i , X k+j_i+1 , X k+j_n They represent the state vectors when the i-th, i+1-th, and n-th pulses are applied at the k+j sampling time, respectively; n represents the number of pulses of the tracking spacecraft at a sampling time sample_T; Represents the state transfer matrix within the interval between two pulses of tracking aerospace, represents the input matrix of the tracking spacecraft within the interval between two pulses. The interval between two pulses is an impulse_time, and (n-1)·impulse_time≤sample_T; Represents the state transition matrix from the last pulse in one sampling time to the beginning of the next sampling time, The input matrix represents the time from the last pulse in a sampling time to the start of the next sampling time. The time from the last pulse to the start of the next new sampling time is sample_T-(n-1)·impulse_time.

[0036] Furthermore, in step 2, the method for tracking the spacecraft to capture the target spacecraft includes:

[0037] Step 2.1, taking the tracking spacecraft as the coordinate origin, establish the tracking orbit coordinate system, and the target spacecraft moves relative to the tracking spacecraft;

[0038] Step 2.2: Calculate the relative state information of the target spacecraft based on the current orbit information of the tracking spacecraft. The calculation formula is:

[0039]

[0040] Among them, Y k+1 represents the relative motion state vector of the target spacecraft to the tracking spacecraft at time k+1; Y k At time k of the target spacecraft, the relative motion state vector of the tracking spacecraft is expressed as Y k =[x k y k z k v xk v yk v zk ] T ; represents the transfer matrix obtained by tracking the current orbit information of the spacecraft; V k represents the escape maneuver of the target spacecraft at time k;

[0041] Step 2.3: Calculate the maximum escape pulse velocity of the target spacecraft in the positive and negative axial directions. The calculation formula is:

[0042]

[0043] Among them, V max With V min Respectively represent the maximum escape pulse velocity of the target spacecraft in the positive and negative directions on the axis; I sp_t Indicates the specific thrust of the target spacecraft; M represents the rate of change of the mass consumed by the target spacecraft through the nozzle; t represents the total mass of the target spacecraft, and it should be noted that as the target spacecraft continues to escape pulse maneuvers, the fuel will be reduced, which will inevitably lead to M t This means that the maximum value of the escape pulse of the target spacecraft is a time-varying constraint;

[0044] Step 2.4: Tracking the spacecraft according to Y k+1 、V max and V min The target spacecraft is tracked by controlling the pulse number and pulse interval until the distance between the tracking spacecraft and the target spacecraft reaches 20m, completing the capture of the target spacecraft.

[0045] Further, in step 3, the method of tracking the spacecraft towing back the target spacecraft includes:

[0046] Step 3.1, take the center of mass of the space station as the origin, establish the target orbit coordinate system, track the motion of the spacecraft relative to the space station, and track the position information and velocity information of the spacecraft relative to the space station. The expression of the relative state vector is:

[0047] X k =[x k y k z k v xk v yk v zk ] T ;

[0048] Step 3.2, setting constraints, including pulse constraints set for the tracking spacecraft and the target spacecraft, prohibited areas set near the space station, and line-of-sight constraints for the tracking spacecraft;

[0049] Step 3.3: Based on the constraints, the model predictive control algorithm is used as the guidance method for the tracking spacecraft to tow the target spacecraft back to the space station.

[0050] Furthermore, in step 3.2, the impulse constraint is:

[0051]

[0052] Among them, U max with U min Respectively represent the maximum pulse velocity of the tracking spacecraft in the positive and negative directions on the axis, V max With V min Respectively represent the maximum struggling pulse speed of the target spacecraft in the positive and negative directions on the axis;

[0053] The prohibited areas are:

[0054] f=(r k -r koz ) T S(r k -r koz )≥1

[0055] Where f represents a nonlinear constrained ellipsoid space, r k Represents the current relative position information of the tracking spacecraft, r koz is the center position of the restricted area, S is the shape matrix of the ellipsoid;

[0056] The expression of S is:

[0057]

[0058] Among them, r x , r y, r z Respectively represent the semi-major axis lengths on the X, Y, and Z axes; the prohibited areas include KOZ1, KOZ2, and KOZ3, KOZ1 represents the restricted area of ​​the entire space station; KOZ2 represents the restricted area of ​​the main body of the space station; KOZ3 represents the restricted area of ​​the solar panels;

[0059] The line of sight constraint is composed of a four-sided cone. The cone originates from the docking port and forms two half angles around the docking axis. The expression of the line of sight constraint is:

[0060] n i ·(r k -r f )≤0(i=1,2,3,4)

[0061] Among them, n i Represents the unit normal vector of the i-th cone, pointing outward, r k Represents the position information of the tracking spacecraft relative to the center of mass of the space station, r f Represents the position information of the docking port relative to the center of mass of the space station.

[0062] Furthermore, in step 3.3, the process of towing the tracking spacecraft back to the target spacecraft is divided into three sub-stages:

[0063] Sub-stage 1: The tracking spacecraft is far away from the space station, so there is no need to consider the precise KOZ constraint of the space station. In the early stage of this stage, there is only the pulse constraint. When the distance between the tracking spacecraft and the space station is less than koz_distance, the KOZ3 constraint is added. Although the line of sight constraint is not added as a constraint condition in this stage, it is considered to be added to the optimization objective function as a penalty factor to guide the tracking spacecraft into the predetermined line of sight constraint, which can be regarded as a soft constraint.

[0064] Sub-stage 2: When the distance between the tracking spacecraft and the space station is less than los_distance and is within the line of sight constraint, it indicates that the tracking spacecraft and the space station have entered the final rendezvous and docking moment, and the line of sight constraint is used as a hard constraint, and the KOZ1 constraint becomes invalid. However, since the struggling behavior of the target spacecraft needs to be considered, if the target spacecraft suddenly maneuvers at this stage, the tracking spacecraft may still go beyond the LOS. Therefore, once the tracking spacecraft goes beyond the line of sight constraint range and is still a certain distance away from the prohibited area, jump to sub-stage 3 for emergency obstacle avoidance.

[0065] Sub-stage three is: In this stage, the tracking spacecraft needs to avoid collision with the space station because the target spacecraft struggles and maneuvers beyond the line of sight constraint. At the same time, in this stage, since the relative distance between the tracking spacecraft and the target spacecraft is relatively close, KOZ2 and KOZ3 constraints are added. Similar to the first stage, the line of sight constraint is added as a penalty factor to the optimization objective function to guide the tracking spacecraft to re-enter the line of sight constraint range, and then return to sub-stage two until the tracking spacecraft completely returns to the docking port of the space station, completing the capture mission of the target spacecraft in the space station.

[0066] Furthermore, in sub-phase 1, the guidance algorithm for tracking the spacecraft is:

[0067]

[0068] In sub-phase 2, the guidance algorithm for tracking the spacecraft is:

[0069]

[0070] In sub-phase three, the guidance algorithm for tracking the spacecraft is:

[0071]

[0072] In the above expression, r represents the distance between the tracking spacecraft and the space station, n j represents the unit normal vector of the jth face of the tetrahedron in the line of sight constraint (j=1,2,3,4), f j represents the jth prohibited area constraint during the rendezvous with the space station, and P represents the weight of the line of sight constraint.

[0073] The beneficial effects of the present invention are as follows: a method for capturing a non-cooperative target spacecraft by a space station in the present invention divides the capture process of the target spacecraft into three stages: an approach stage, a capture stage, and a towing back stage. For the target rendezvous guidance problem in the approach stage, the target spacecraft has no escape maneuvers, a terminal relative orbital state vector deviation, a control cost, and a pulse constraint in this stage are considered. By analyzing different optimization objective functions, prediction intervals, pulse numbers, and pulse intervals, a target rendezvous model predictive control guidance algorithm for the approach stage is designed, and the guidance instructions for the approach stage are obtained, so that the tracking spacecraft can complete the approach to the target spacecraft from the space station with the minimum control cost, thereby reducing the fuel consumption of the tracking spacecraft.

[0074] For the target rendezvous and guidance problem in the capture phase, taking into account the escape maneuver, terminal relative orbital state vector error, control cost and pulse constraint of the target spacecraft in this stage, a target rendezvous model predictive control guidance algorithm for the capture phase is designed through the analysis of different optimization objective functions, prediction intervals, number of pulses and pulse intervals. The guidance instructions for the capture phase are obtained, which enables the tracking spacecraft to capture the target spacecraft in the shortest capture time and shortens the escape time of the target spacecraft.

[0075] For the target rendezvous and guidance problem in the towback phase, taking into account the target spacecraft's struggle maneuvers, terminal relative orbit state vector error, control cost, pulse constraint, restricted area constraint and line of sight constraint, a towback phase target rendezvous model predictive control guidance algorithm is designed through the analysis of different correction strategies and prediction intervals. The guidance instructions for the towback phase are obtained, which enables the tracking spacecraft to complete the rendezvous and docking with the space station in the safest way and reduces the failure rate of the final rendezvous and docking. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 Schematic diagram of capturing the target spacecraft in the space station.

[0077] Figure 2 Schematic diagram of a tracking spacecraft approaching a target spacecraft.

[0078] Figure 3 Schematic diagram of a single pulse maneuver for a tracking spacecraft.

[0079] Figure 4 Schematic diagram of multiple pulse maneuvers for tracking spacecraft.

[0080] Figure 5 Schematic diagram of a tracking spacecraft capturing a target spacecraft.

[0081] Figure 6 Schematic diagram of the target spacecraft escape maneuver.

[0082] Figure 7 Schematic diagram of towing the target spacecraft back to the tracking spacecraft.

[0083] Figure 8 A schematic diagram of the prohibited area.

[0084] Fig. 9 Schematic diagram of linearization of prohibited area.

[0085] Fig.10 Schematic diagram of KOZ1, KOZ2, KOZ3 and KOZ1.

[0086] Fig.11 Schematic diagram of line of sight constraint.

[0087] Fig.12Schematic diagram of the three sub-stages of towing the target spacecraft back to the tracking spacecraft. DETAILED DESCRIPTION

[0088] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0089] The present invention provides a method for a space station to capture a non-cooperative target spacecraft, which comprises:

[0090] Step 1: The tracking spacecraft approaches the target spacecraft: Figure 1 As shown, the ground base station continuously tracks the target spacecraft, obtains the orbit information of the target spacecraft, and tracks the spacecraft departing from the space station and navigating to the warning area of ​​the target spacecraft according to the orbit information of the target spacecraft;

[0091] Step 2: Tracking spacecraft to capture target spacecraft: Figure 5 As shown, after the tracking spacecraft enters the warning area of ​​the target spacecraft, the target spacecraft performs an escape maneuver, and the ground base station updates the orbit information of the target spacecraft at a fixed time interval. The tracking spacecraft continues to navigate until the distance between the tracking spacecraft and the target spacecraft reaches the capture distance, which is considered a successful capture.

[0092] Step 3: The tracking spacecraft drags back the target spacecraft: Figure 7 As shown, after successfully capturing the target spacecraft, the tracking spacecraft drags the target spacecraft toward the space station until the tracking spacecraft completely returns to the docking port of the space station, completing the capture mission of the target spacecraft in the space station.

[0093] Specifically, in step 1, the method of tracking a spacecraft approaching a target spacecraft includes:

[0094] Step 1.1, establish the target spacecraft orbit coordinate system: Figure 2 As shown in the figure, the target spacecraft orbital coordinate system is established with the center of mass of the target spacecraft as the origin. The target spacecraft is located at O T X T Y T Z T The origin position in the coordinate system, the coordinate system moves with the target spacecraft, the position information and velocity information of the target spacecraft are both zero, at time k, the relative state vector of the tracking spacecraft relative to the target spacecraft is X k =[x k y kz k v xk v yk v zk ] T , x k y k z k The position of the tracking spacecraft relative to the target spacecraft is O T X T Y T Z T The components of the three coordinate axes of the coordinate system, v xk v yk v zk The speed of the tracking spacecraft relative to the target spacecraft is O T X T Y T Z T The components of the three coordinate axes of the coordinate system, the impulse maneuver of the tracking spacecraft is U k ; At time k+1, the relative state vector of the tracking spacecraft at time k+1 is X k+1 , the impulse maneuver of the tracking spacecraft is U k+1 ;

[0095] Step 1.2: Use the model predictive control algorithm as the guidance method for the tracking spacecraft to approach the target spacecraft. In the approach phase, since the tracking spacecraft knows the orbit information parameters of the target spacecraft, it can be regarded as a cooperative target rendezvous. Under this premise, the model predictive control method can be adopted, which is hereinafter referred to as the MPC algorithm (Model-Predictive-Control, MPC) as the guidance method for the tracking spacecraft to approach the target spacecraft. Model predictive control is a control method designed to solve the optimal control problem within a limited time range. The limited time range reduces the computational complexity, which makes it convenient for the onboard equipment on the spacecraft.

[0096] The expression of the model predictive control algorithm is:

[0097]

[0098] Among them, J(u k ,u k+1 ,…,u k+N ) represents the control variable u k+i , (i=0, 1, ..., N) is the optimization objective function of the independent variable, constraints represents the control variable u k+i, (i=0, 1, ..., N) are the constraints that need to be satisfied, and N represents the prediction interval; the core idea of ​​the control algorithm is to calculate the control sequence that minimizes the optimization objective function within a finite time range and satisfies the constraints, but only applies the first control input in the sequence to the system, and then repeats the above steps until the system reaches the expected state.

[0099] Step 1.3: For the MPC algorithm, selecting different optimization objective functions will have a direct impact on the control effect. In this embodiment, two optimization objective functions J1 and J2 are selected; the optimization objective function J1 considers the state vector error and control cost at the end of the prediction interval; the optimization objective function J2 considers the state vector error and control cost within the entire prediction interval;

[0100] Step 1.4, bring the optimization objective functions J1 and J2 into the model predictive control algorithm to obtain a variety of pulse model predictive control algorithms, so that the tracking spacecraft obtains different approach guidance strategies to approach the target spacecraft.

[0101] The expression of the optimization objective function J1 is:

[0102]

[0103] Among them, X f represents the state vector that the tracking spacecraft will eventually reach; represents the state vector of the spacecraft tracked at time k+Np1; Np1 represents the prediction interval when J1 is used as the optimization objective function; matrices Q1 and R1 represent the weight information of the state vector error and pulse consumption during the optimization process, respectively, where Q1 is a 6×6 matrix and R1 is a 3×3 matrix, and both are symmetric semi-positive matrices, i.e., Q1±0, R1±0;

[0104] The expression of the optimization objective function J2 is:

[0105]

[0106] Among them, Np2 represents the prediction interval when J2 is used as the optimization objective function; X f represents the state vector that the spacecraft is expected to reach, X f =[x f y f z f v xf v yf v zf ] T , x f y f z f are the positions that the tracking spacecraft is expected to reach in the end.T X T Y T Z T The components of the three coordinate axes of the coordinate system, v xf v yf v zf are the final speeds that the tracking spacecraft is expected to reach in O T X T Y T Z T The components of the three coordinate axes of the coordinate system, X k+i represents the state vector of the spacecraft tracked at time k+i. Matrices Q2 and R2 represent the weight information of the state vector error and pulse consumption during the optimization process, respectively. Q2 is a 6×6 matrix and R2 is a 3×3 matrix, and both are symmetric semi-positive matrices, i.e., Q2±0, R2±0.

[0107] Furthermore, in step 1, considering that each pulse maneuver of the tracking spacecraft cannot be an arbitrary value, such as Figure 3 and Figure 4 As shown in the figure, an impulse maneuver means that the spacecraft performs only one impulse maneuver in a sampling period of the MPC algorithm, and then performs another impulse maneuver in the next sampling period. A multiple impulse maneuver means that the spacecraft performs multiple impulse maneuvers with equal time intervals impulse_time in a sampling period sample_T of the MPC algorithm. The number of pulses and the time interval can be adjusted according to the actual situation, and multiple impulse maneuvers can be performed again in the next sampling period.

[0108] The calculation formula for the maximum single pulse maneuver speed of the tracking spacecraft when approaching the target spacecraft is:

[0109]

[0110] Among them, U max with U min They represent the maximum single pulse maneuvering speed of the tracking spacecraft in the positive and negative directions of the axis respectively; Δt is the duration of a single pulse of the tracking spacecraft; I sp_c represents the specific thrust of the tracking spacecraft; g0 is the gravitational acceleration at sea level; M represents the rate of change of the mass consumed by the tracking spacecraft discharged through the nozzle; c represents the total mass of the tracking spacecraft; and it should be noted that as the tracking spacecraft continues to pulse maneuvers, the fuel will be reduced, which will inevitably lead to M c The reduction of the pulse maximum of the tracking spacecraft is a time-varying constraint.

[0111] Furthermore, in step 1.4, when J1 is used as the optimization objective function, the expression of the approaching single pulse model predictive control algorithm is:

[0112]

[0113] When J2 is used as the optimization objective function, the expression of the approach segment single pulse model predictive control algorithm is:

[0114]

[0115] Among them, X k+i represents the state vector information of the tracking spacecraft at time k+i. The interval from time k+i to time k+i+1 is a sampling time sample_T. represents the state transition matrix of the tracking spacecraft from time k+i to time k+i+1, Represents the input matrix for tracking the spacecraft from time k+i to time k+i+1.

[0116] When J1 is used as the optimization objective function, the expression of the approach segment multi-pulse model predictive control algorithm is:

[0117]

[0118] When J2 is used as the optimization objective function, the expression of the approach segment multi-pulse model predictive control algorithm is:

[0119]

[0120] Among them, X k+j_i , X k+j_i+1 , X k+j_n They represent the state vectors when the i-th, i+1-th, and n-th pulses are applied at the k+j sampling time, respectively; n represents the number of pulses of the tracking spacecraft at a sampling time sample_T; Represents the state transfer matrix within the interval between two pulses of tracking aerospace, represents the input matrix of the tracking spacecraft within the interval between two pulses. The interval between two pulses is an impulse_time, and (n-1)·impulse_time≤sample_T; Represents the state transition matrix from the last pulse in one sampling time to the beginning of the next sampling time, The input matrix represents the time from the last pulse in a sampling time to the start of the next sampling time. The time from the last pulse to the start of the next new sampling time is sample_T-(n-1)·impulse_time.

[0121] Regardless of whether J1 or J2 is used as the MPC guidance algorithm for the optimization objective function, its ultimate goal is to calculate the minimum optimization objective function within the prediction interval Np1 or Np2 and satisfy the elliptical orbit dynamics equation (or ) and the pulse constraint U min ≤U k+i ≤U max (or U min ≤U k+j_i ≤U max ) under the condition of controlled variable U k (or U k_i ). The meaning of optimizing the minimum objective function includes X k+i (or X k+j_i ) as close to X as possible f and U k+i (or U k+j_i ) is as small as possible, which has two physical meanings: we hope that the tracking spacecraft can get as close to the target spacecraft as possible and save pulse consumption as much as possible.

[0122] like Figure 5 and Figure 6 In step 2, the tracking spacecraft has entered the warning area of ​​the target spacecraft. At this time, the target spacecraft will perform an escape maneuver. However, both parties can update each other's orbital information from the ground base station at intervals. This stage can be regarded as a rendezvous mission for non-cooperative targets. When the two are 20m apart, the capture is considered successful and enters the next stage. The capture stage is the second stage of the space target rendezvous mission. Its main purpose is that even if the target spacecraft makes an escape maneuver, the tracking spacecraft can still approach the target spacecraft to the capture range.

[0123] The methods for tracking spacecraft to capture target spacecraft include:

[0124] Step 2.1, taking the tracking spacecraft as the coordinate origin, establish the tracking orbit coordinate system, and the target spacecraft moves relative to the tracking spacecraft;

[0125] Step 2.2: Calculate the relative state information of the target spacecraft based on the current orbit information of the tracking spacecraft. The calculation formula is:

[0126]

[0127] Among them, Y k+1 represents the relative motion state vector of the target spacecraft to the tracking spacecraft at time k+1; Y k At time k of the target spacecraft, the relative motion state vector of the tracking spacecraft is expressed as Y k =[x k y k z kv xk v yk v zk ] T ; represents the transfer matrix obtained by tracking the current orbit information of the spacecraft; V k represents the escape maneuver of the target spacecraft at time k;

[0128] Step 2.3: Calculate the maximum escape pulse velocity of the target spacecraft in the positive and negative axial directions. The calculation formula is:

[0129]

[0130] Among them, V max With V min Respectively represent the maximum escape pulse velocity of the target spacecraft in the positive and negative directions on the axis; I sp_t Indicates the specific thrust of the target spacecraft; M represents the rate of change of the mass consumed by the target spacecraft through the nozzle; t represents the total mass of the target spacecraft, and it should be noted that as the target spacecraft continues to escape pulse maneuvers, the fuel will be reduced, which will inevitably lead to M t This means that the maximum value of the escape pulse of the target spacecraft is a time-varying constraint;

[0131] Step 2.4: Tracking the spacecraft according to Y k+1 、V max and V min The target spacecraft is tracked by controlling the pulse number and pulse interval until the distance between the tracking spacecraft and the target spacecraft reaches 20m, and the capture of the target spacecraft is completed. The capture process of the tracking spacecraft still considers J1 and J2 as the performance of the optimization objective function, and the constraint condition is still the pulse constraint.

[0132] like Figure 7 As shown in Figure 1, in step 3, it is planned to tow the target spacecraft back to the space station. In addition, since the captured satellite has not completely lost its maneuverability, the potential struggling behavior of the target spacecraft should also be considered until the tracking spacecraft completely returns to the docking port of the space station and the mission is completed. This stage is considered a rendezvous mission for the cooperative target. In this stage, even if the target spacecraft has a certain pulse maneuver during the towing back process, the tracking spacecraft maintains communication with the space station and knows the other party's orbital information. The tracking spacecraft will actively pulse maneuver to approach the space station. This stage can be considered a rendezvous for the cooperative target.

[0133] Specifically, the method of tracking the spacecraft and dragging it back to the target spacecraft includes:

[0134] Step 3.1, take the center of mass of the space station as the origin, establish the target orbit coordinate system, track the motion of the spacecraft relative to the space station, and track the position information and velocity information of the spacecraft relative to the space station. The expression of the relative state vector is:

[0135] X k =[x k y k z k v xk v yk v zk ] T ;

[0136] exist Figure 7 Middle,U k represents the impulse maneuver of the tracking spacecraft at time k. However, considering that the tracking spacecraft is captured within a sampling time sample_time, the target spacecraft may perform a struggle maneuver V at the time strggule_time; r f Indicates the docking port position information of the tracking spacecraft and the target spacecraft.

[0137] Step 3.2, setting constraints, including pulse constraints set for the tracking spacecraft and the target spacecraft, a prohibited zone (KOZ constraint) set near the space station, and line of sight constraints (LOS constraints) for the tracking spacecraft;

[0138] Specifically, in step 3.2, during the approach phase, considering that each pulse maneuver and struggle maneuver of the tracking spacecraft and the target spacecraft cannot be an arbitrary value, the maximum value of the pulse maneuver or struggle maneuver should be determined by the satellite engine carried by the tracking spacecraft or the target spacecraft and its own mass, and the pulse constraint is:

[0139]

[0140] Among them, U max with U min Respectively represent the maximum pulse velocity of the tracking spacecraft in the positive and negative directions on the axis, V max With V min Respectively represent the maximum struggling pulse speed of the target spacecraft in the positive and negative directions on the axis;

[0141] like Figure 8 to Figure 10 As shown, the prohibited areas are:

[0142] f=(r k -r koz ) T S(r k -r koz )≥1

[0143] Where f represents a nonlinear constrained ellipsoid space, r k Represents the current relative position information of the tracking spacecraft, r koz is the center position of the restricted area, S is the shape matrix of the ellipsoid;

[0144] The expression of S is:

[0145]

[0146] in, , , Respectively , , The length of the semi-major axis on the direction axis; for the space station, multiple ellipsoid envelope strategies are set to simulate its restricted area. The prohibited area includes , and , Indicates the restricted area of ​​the entire space station; Represents the restricted area of ​​the main body of the space station; Indicates a restricted area for solar panels;

[0147] For this nonlinear constraint, the linearization methods mainly include the rotation hyperplane linear method, the dual hyperplane linear method and the direct linear method. Here we consider using the direct linear method, using Taylor's first-order expansion, and the expansion point is the reference trajectory point calculated by the last MPC algorithm. and Intersection point of the line and the ellipsoid surface ,like Fig. 9 shown.

[0148] like Fig.11 As shown in the figure, the sight constraint is composed of a four-sided cone. The cone originates from the docking port and forms two half angles around the docking axis. The expression of the sight constraint is:

[0149] n i ·(r k -r f )≤0(i=1,2,3,4)

[0150] Among them, n i Represents the unit normal vector of the i-th cone, pointing outward, r k Represents the position information of the tracking spacecraft relative to the center of mass of the space station, r f Represents the position information of the docking port relative to the center of mass of the space station.

[0151] Step 3.3: Based on the constraints, the model predictive control algorithm is used as the guidance method for the tracking spacecraft to tow the target spacecraft back to the space station. Specifically, in step 3.3, in the towing back phase, compared with the approach phase and the capture phase, the constraints added KOZ constraints and LOS constraints. Considering that the two constraints are mainly near the space station, it is meaningless to consider these constraints when the distance from the space station is far. Therefore, the process of towing the tracking spacecraft back to the target spacecraft is divided into three sub-stages:

[0152] like Fig.12 As shown in the figure, the first sub-stage is: the tracking spacecraft is far away from the space station, and there is no need to consider the precise KOZ constraint of the space station. In the early stage of this stage, there is only the pulse constraint. When the distance between the tracking spacecraft and the space station is less than koz_distance, the KOZ3 constraint is added. Although the line of sight constraint is not added as a constraint condition in this stage, it is considered to be added to the optimization objective function as a penalty factor to guide the tracking spacecraft into the predetermined line of sight constraint, which can be regarded as a soft constraint.

[0153] Sub-stage 2: When the distance between the tracking spacecraft and the space station is less than los_distance and is within the line of sight constraint, it indicates that the tracking spacecraft and the space station have entered the final rendezvous and docking moment, and the line of sight constraint is used as a hard constraint, and the KOZ1 constraint becomes invalid. However, since the struggling behavior of the target spacecraft needs to be considered, if the target spacecraft suddenly maneuvers at this stage, the tracking spacecraft may still go beyond the LOS. Therefore, once the tracking spacecraft goes beyond the line of sight constraint range and is still a certain distance away from the prohibited area, jump to sub-stage 3 for emergency obstacle avoidance.

[0154] Sub-stage three is: In this stage, the tracking spacecraft needs to avoid collision with the space station because the target spacecraft struggles and maneuvers beyond the line of sight constraint. At the same time, in this stage, since the relative distance between the tracking spacecraft and the target spacecraft is relatively close, KOZ2 and KOZ3 constraints are added. Similar to the first stage, the line of sight constraint is added as a penalty factor to the optimization objective function to guide the tracking spacecraft to re-enter the line of sight constraint range, and then return to sub-stage two until the tracking spacecraft completely returns to the docking port of the space station, completing the capture mission of the target spacecraft in the space station.

[0155] Furthermore, in sub-stage 1, the single-shot MPC guidance algorithm for tracking the spacecraft is:

[0156]

[0157] In sub-phase 2, the single-shot MPC guidance algorithm for tracking the spacecraft is:

[0158]

[0159] In sub-stage three, the single-shot MPC guidance algorithm for tracking the spacecraft is:

[0160]

[0161] In the above expression, r represents the distance between the tracking spacecraft and the space station, n j represents the unit normal vector of the jth face of the tetrahedron in the line of sight constraint (j=1,2,3,4), f j represents the jth prohibited area constraint in the process of rendezvous with the space station, and P represents the weight of the line of sight constraint. The space station is established on the target orbital coordinate system, and the purpose of the towing back segment is explained; the optimization model of the space target towing back segment is studied, and the MPC algorithm is used as the controller. Considering the struggling behavior of the target spacecraft, two correction strategies for the tracking spacecraft are given; the simulation performance of different correction strategies in the towing back segment is studied. The simulation results show that the immediate correction strategy is more suitable for dealing with the potential struggling behavior of the target spacecraft during the process of tracking the spacecraft returning to the space station. Under this strategy, the rendezvous between the tracking spacecraft and the space station takes less time and has a higher success rate.

[0162] In summary, the present invention provides a method for a space station to capture a non-cooperative target spacecraft. In the approach phase, the tracking spacecraft starts from the space station with the minimum control cost to complete the approach to the non-cooperative target spacecraft, thereby reducing the fuel consumption of the tracking spacecraft. In the capture phase, the tracking spacecraft completes the rapid capture of the non-cooperative target spacecraft with uncertain maneuvering behavior in the shortest time, thereby shortening the escape time of the target spacecraft. In the towing back phase, the tracking spacecraft tows the non-cooperative target spacecraft with uncertain struggling maneuvering behavior back in the safest way and completes the rendezvous and docking with the space station, thereby reducing the failure rate of the final rendezvous and docking, and solving the problem of the method for capturing the non-cooperative target spacecraft that affects the safety near the operating orbit of the own space station.

Claims

1. A method for a space station to capture a non-cooperative target spacecraft, characterized in that: include: Step 1: The tracking spacecraft approaches the target spacecraft: The ground base station continuously tracks the target spacecraft and obtains the orbit information of the target spacecraft. The tracking spacecraft departs from the space station and approaches the warning area of ​​the target spacecraft according to the orbit information of the target spacecraft. In step 1, the method of tracking the spacecraft approaching the target spacecraft includes: Step 1.1, establish the target spacecraft orbital coordinate system: take the target spacecraft's center of mass as the origin, establish the target spacecraft orbital coordinate system, the target spacecraft is located at The origin position in the coordinate system, the coordinate system moves with the target spacecraft, the position information and velocity information of the target spacecraft are both zero, At time , the relative state vector of the tracking spacecraft relative to the target spacecraft is , The position of the tracking spacecraft relative to the target spacecraft is The components of the three coordinate axes of the coordinate system, are the speeds of the tracking spacecraft relative to the target spacecraft. The components of the three coordinate axes of the coordinate system, tracking the impulse maneuver of the spacecraft are ;exist Time, tracking spacecraft The relative state vector at time , the impulse maneuver of the tracking spacecraft is ; Step 1.2: Use the model predictive control algorithm as the guidance method for the tracking spacecraft approaching the target spacecraft; the expression of the model predictive control algorithm is: in, Represents the control variable is the optimization objective function of the independent variable, Represents the control variable The constraints that need to be met are represents the prediction interval; Step 1.3: Select two optimization objective functions J 1 and J 2. Optimize the objective function J 1 Consider the state vector error and control cost at the end of the prediction interval; optimize the objective function J 2 Consider the state vector error and control cost within the entire prediction interval; Step 1.4: Optimize the objective function J 1 and J 2 is introduced into the model predictive control algorithm to obtain a variety of pulse model predictive control algorithms, so that the tracking spacecraft can obtain different approach guidance strategies to approach the target spacecraft; Step 2: The tracking spacecraft captures the target spacecraft: After the tracking spacecraft enters the warning area of ​​the target spacecraft, the target spacecraft performs an escape maneuver, and the ground base station updates the orbit information of the target spacecraft at a fixed time interval. The tracking spacecraft continues to navigate until the distance between the tracking spacecraft and the target spacecraft reaches the capture distance, which is considered a successful capture; Step 3: The tracking spacecraft drags back the target spacecraft: After successfully capturing the target spacecraft, the tracking spacecraft drags the target spacecraft toward the space station until the tracking spacecraft completely returns to the docking port of the space station, completing the capture mission of the target spacecraft in the space station.

2. The method for capturing a non-cooperative target spacecraft by a space station according to claim 1, characterized in that: In step 1.3, optimize the objective function J The expression of 1 is: in, represents the state vector that the tracking spacecraft will eventually reach; express Keep track of the spacecraft's state vector at all times; Representative As the prediction interval when optimizing the objective function; matrix and Respectively represent the weight information of state vector error and pulse consumption during the optimization process, where for matrix, for matrices, and both are symmetric semi-positive matrices, that is , ; Optimizing the objective function J The expression of 2 is: in, Representative As a prediction interval when optimizing the objective function; represents the state vector that the tracking spacecraft will eventually reach, , The final expected position of the tracking spacecraft is The components of the three coordinate axes of the coordinate system, are the final speeds that the tracking spacecraft is expected to reach. The components of the three coordinate axes of the coordinate system, express Keep track of the spacecraft's state vector, matrix and Respectively represent the weight information of the state vector error and pulse consumption during the optimization process, where for matrix, for matrices, and both are symmetric semi-positive matrices, that is , .

3. The method for capturing a non-cooperative target spacecraft by a space station according to claim 2, characterized in that: In step 1, considering that each pulse maneuver of the tracking spacecraft cannot be an arbitrary value, the calculation formula for the maximum value of a single pulse maneuver speed of the tracking spacecraft when approaching the target spacecraft is: in, and They represent the maximum single pulse maneuvering speed of the tracking spacecraft in the positive and negative directions on the axis respectively; is the duration of a single pulse from a tracking spacecraft; It represents the specific thrust of the tracking spacecraft; is the acceleration due to gravity at sea level; represents the rate of change of mass consumed by the tracking spacecraft discharged through the nozzle; represents the total mass of the tracking spacecraft; and it should be noted that as the tracking spacecraft continues to pulse maneuvers, the fuel will be reduced, which will inevitably lead to The reduction of the pulse maximum of the tracking spacecraft is a time-varying constraint.

4. The method for capturing a non-cooperative target spacecraft by a space station according to claim 3, characterized in that: In step 1.4, When used as the optimization objective function, the expression of the approach segment single pulse model predictive control algorithm is: by When used as the optimization objective function, the expression of the approach segment single pulse model predictive control algorithm is: in, express The state vector information of the tracking spacecraft at all times, Time has come The interval between moments is a sampling time , Indicates tracking of spacecraft from Time has come The state transfer matrix at time; Indicates tracking of spacecraft from Time has come The input matrix at time instant; by When used as the optimization objective function, the expression of the approach segment multi-pulse model predictive control algorithm is: by When used as the optimization objective function, the expression of the approach segment multi-pulse model predictive control algorithm is: in, , , Respectively expressed in Sampling time applied , No. , No. The state vector at the time of the pulse; Represents the tracking spacecraft at a sampling time The number of pulses; Represents the state transfer matrix within the interval between two pulses of tracking aerospace, Represents the input matrix of the tracking spacecraft within the interval between two pulses, and the interval between the two pulses is one , and there are ; Represents the state transition matrix from the last pulse in one sampling time to the beginning of the next sampling time, Represents the input matrix from the last pulse in a sampling time to the start of the next sampling time. The time from the last pulse to the start of the next new sampling time is .

5. The method for capturing a non-cooperative target spacecraft by a space station according to claim 1, characterized in that: In step 2, the method for the tracking spacecraft to capture the target spacecraft includes: Step 2.1, taking the tracking spacecraft as the coordinate origin, establish the tracking orbit coordinate system, and the target spacecraft moves relative to the tracking spacecraft; Step 2.2: Calculate the relative state information of the target spacecraft based on the current orbit information of the tracking spacecraft. The calculation formula is: in, Represents the target spacecraft At time, the relative motion state vector of the tracking spacecraft; Target spacecraft At time , the relative motion state vector of the tracking spacecraft is expressed as ; represents the transfer matrix obtained by tracking the current orbit information of the spacecraft; ; Indicates the target spacecraft Escape maneuvers at all times; Step 2.3: Calculate the maximum escape pulse velocity of the target spacecraft in the positive and negative directions along the axis. The calculation formula is: in, and Respectively represent the maximum escape pulse velocity of the target spacecraft in the positive and negative axial directions; Indicates the specific thrust of the target spacecraft; It represents the rate of change of the mass consumed by the target spacecraft discharged through the nozzle; represents the total mass of the target spacecraft, and it should be noted that as the target spacecraft continues to escape pulse maneuvers, the fuel will be reduced, which will inevitably lead to This means that the maximum value of the escape pulse of the target spacecraft is a time-varying constraint; Step 2.4: Tracking the spacecraft based on , and The target spacecraft is tracked by controlling the pulse number and pulse interval until the distance between the tracking spacecraft and the target spacecraft reaches 20m, completing the capture of the target spacecraft.

6. The method for capturing a non-cooperative target spacecraft by a space station according to claim 5, characterized in that: In step 3, the method of the tracking spacecraft towing back the target spacecraft includes: Step 3.1, take the center of mass of the space station as the origin, establish the target orbit coordinate system, track the motion of the spacecraft relative to the space station, and track the position information and velocity information of the spacecraft relative to the space station. The expression of the relative state vector is: ； Step 3.2, setting constraints, including pulse constraints set for the tracking spacecraft and the target spacecraft, prohibited areas set near the space station, and line-of-sight constraints for the tracking spacecraft; Step 3.3: Based on the constraints, the model predictive control algorithm is used as the guidance method for the tracking spacecraft to tow the target spacecraft back to the space station.

7. The method for capturing a non-cooperative target spacecraft by a space station according to claim 5, characterized in that: In step 3.2, the impulse constraint is: in, and Respectively represent the maximum pulse speed of the tracking spacecraft in the positive and negative directions along the axis, and Respectively represent the maximum struggling pulse speed of the target spacecraft in the positive and negative directions on the axis; The prohibited areas are: in, represents a nonlinear constrained ellipsoidal space, Represents the current relative position information of the tracking spacecraft. The center of the restricted area. is the shape matrix of the ellipsoid; The expression is: in, , , Respectively , , The length of the semi-major axis on the direction axis; the forbidden area includes , and , Indicates the restricted area of ​​the entire space station; Represents the restricted area of ​​the main body of the space station; Indicates a restricted area for solar panels; The line of sight constraint is composed of a four-sided cone. The cone originates from the docking port and forms two half angles around the docking axis. The expression of the line of sight constraint is: in, Indicates The unit normal vector of the face cone points outward. Represents the position information of the tracking spacecraft relative to the center of mass of the space station, Represents the position information of the docking port relative to the center of mass of the space station.

8. The method for capturing a non-cooperative target spacecraft by a space station according to claim 7, characterized in that: In step 3.3, the process of towing the tracking spacecraft back to the target spacecraft is divided into three sub-stages: Sub-stage 1: The tracking spacecraft is far away from the space station, so there is no need to consider the precise KOZ constraints of the space station. In the early stage of this stage, there are only pulse constraints. When the distance between the tracking spacecraft and the space station is less than When adding Constraints: Although the line of sight constraint is not added as a constraint condition at this stage, it is considered to be added as a penalty factor to the optimization objective function to guide the tracking spacecraft into the predetermined line of sight constraint, which can be regarded as a soft constraint. Sub-stage 2: When the distance between the tracking spacecraft and the space station is less than And when it is already within the line of sight constraint, it indicates that the tracking spacecraft and the space station have entered the final rendezvous and docking moment, and the line of sight constraint condition is taken as a hard constraint. The constraint is invalid; however, since the struggling behavior of the target spacecraft needs to be considered, if the target spacecraft suddenly maneuvers in this stage, the tracking spacecraft may still exceed the LOS. Therefore, once the tracking spacecraft exceeds the visual constraint range and is still a certain distance away from the prohibited area, jump to sub-stage three for emergency obstacle avoidance; Sub-stage three: In this stage, the tracking spacecraft needs to avoid collision with the space station because the target spacecraft struggles and moves beyond the visual constraint range. At the same time, in this stage, the tracking spacecraft and the target spacecraft are relatively close, so the tracking spacecraft is added. and Constraint, as in the first stage, the line of sight constraint is added as a penalty factor to the optimization objective function to guide the tracking spacecraft to re-enter the line of sight constraint range, and then return to sub-stage two until the tracking spacecraft completely returns to the docking port of the space station, completing the capture mission of the target spacecraft in the space station.

9. The method for capturing a non-cooperative target spacecraft by a space station according to claim 8, characterized in that: In sub-phase 1, the guidance algorithm for tracking the spacecraft is: In sub-phase 2, the guidance algorithm for tracking the spacecraft is: In sub-phase three, the guidance algorithm for tracking the spacecraft is: In the above expression, Indicates the distance between the tracking spacecraft and the space station. Represents the first tetrahedron in the line of sight constraint Unit normal vector of the face , Indicates the first Prohibited area constraints, Indicates the weight of the line of sight constraint.

Images