A sequential convex optimization method for distributed migration maneuvers of multiple spacecraft

Abstract

The present invention discloses a sequential convex optimization method for distributed migration maneuvers of multiple spacecraft, which belongs to the field of aerospace technology. The implementation method of the present invention is as follows: establishing a dynamic model of cluster migration maneuvers; establishing an optimization model for large-scale cluster migration maneuvers based on the control mode, obstacle avoidance, and fuel saving mission characteristics of cluster migration maneuvers. The maneuver optimization problem is convexified by relaxing nonlinear equality constraints, and the cluster migration maneuver optimization problem is decomposed by decoupling the obstacle avoidance constraints. The time-varying continuous distributed decoupled optimal problem is converted into a discrete subproblem of convex optimization through numerical integration. The convexified discrete subproblem is used as the inner link of each iteration step, and the optimal cluster large-scale migration maneuver transfer trajectory and corresponding control are obtained by solving it in a finite number of steps using a sequential iterative approximation strategy. The present invention can realize the online optimization of the continuous thrust migration maneuver trajectory of cluster spacecraft under the premise of considering multiple taboo path constraints and time constraints.

Description

Technical Field

[0001] The present invention relates to a sequential convex optimization method for distributed migration maneuvers of multiple spacecraft, and in particular to a transfer trajectory optimization method suitable for distributed maneuvers of large-scale near-Earth star clusters, belonging to the field of aerospace technology. Background Art

[0002] As spacecraft capabilities continue to increase, satellite mass is increasing, leading to a corresponding increase in satellite launch costs and exponentially higher launch risks. Faced with increasingly complex and diverse space missions, swarm spacecraft, due to their flexibility, distribution, and high fault tolerance, are becoming a development trend for future spacecraft systems. For swarm spacecraft, different mission modes and requirements require different configurations. For swarm spacecraft performing multiple space missions, configuration maneuver planning techniques that adapt to these diverse mission requirements are key to accommodating complex future space activities. For example, swarm initialization requires deploying swarm satellites from their initial positions to a fixed mission configuration. If a satellite fails within a swarm configuration or switches to a new mission mode, the entire swarm must be reconfigured. Maneuver planning that adapts to these emergencies is essential for maintaining the swarm's normal operation. For swarm missions, satellites must arrive at fixed orbital positions synchronously and meet corresponding terminal velocity constraints. Therefore, rapid planning of swarm migration maneuvers within a specific time and space range is crucial for ensuring the implementation of multi-spacecraft on-orbit missions. Compared to single-spacecraft orbital maneuvers, multi-spacecraft distributed migration maneuvers require not only time synchronization but also inter-satellite distance constraints for collision avoidance. This means that during cluster maneuvers, most satellites must perform a certain degree of orbital maneuvering. To ensure synchronization, the relative distances between satellites must be kept safe, i.e., to avoid collision risks, while also ensuring smooth inter-satellite communication. Consequently, orbital maneuver planning problems exhibit challenges such as sensitive initial value guesses and poor convergence, making trajectory optimization for multi-satellite distributed maneuvers a typical challenge in current aerospace technology.

[0003] In the developed multi-spacecraft distributed migration maneuver planning technology [1] (see: Wang J, Zhang J, Cao X, et al. Optimal Satellite Formation Reconfiguration Strategy Based on Relative Orbital Elements [J]. Acta Astronautica, 2012, 76: 99-114.), an analytical cluster migration reconstruction planning strategy is proposed. Although this method solves the fuel consumption reconstruction problem in both free and fixed terminal states through constraint expansion, it is not suitable for efficient optimization of large-scale continuous thrust migration maneuvers.

[0004] Prior art [2] (see: Peng Haijun, Gao Qiang, Wu Zhigang. Optimal trajectory planning method and its application in balanced energy consumption reconstruction of spacecraft formation at libration point [J]. Chinese Journal of Computational Mechanics, 2014, 31(1): 18-24.) proposed a new method for solving migration maneuver planning problems with the interpolation of three types of variables, namely state, co-state and control, as the core. By converting the nonlinear optimal control problem expressed in continuous time into the solution of a nonlinear equation system through the variational principle, the Jacobi matrix of the nonlinear equation system in the display format is derived, thereby improving the computational efficiency of the nonlinear equation system. However, this method does not take into account the constraints of intersatellite collision avoidance and communication, and is not suitable for large-scale cluster tasks. Summary of the Invention

[0005] The technical problem to be solved by the sequential convex optimization method for distributed migration maneuvers of multiple spacecraft disclosed in the present invention is: to provide a highly versatile trajectory rapid optimization method that can quickly solve the orbital migration maneuvers of large-scale cluster spacecraft, and to achieve online and efficient optimization of the continuous thrust migration maneuver trajectory of cluster spacecraft under the premise of considering multiple taboo path constraints and time constraints, thereby improving the efficiency of distributed migration maneuvers of cluster spacecraft.

[0006] The purpose of the present invention is achieved through the following technical solutions.

[0007] The present invention discloses a sequential convex optimization method for distributed multi-spacecraft migration maneuvers. Given the number of orbital elements of the swarm's flight center, the number of swarm spacecraft, the initial and final migration times, and the maximum and minimum thrust, specific impulse, and initial mass of each spacecraft in the swarm, a dynamic model for the swarm migration maneuver is established. Based on the control, obstacle avoidance, and fuel conservation characteristics of the swarm migration maneuver, endpoint constraints and optimization performance indicators for the large-scale swarm migration maneuver are given, and an optimization model for the large-scale swarm migration maneuver is established. The nonlinear large-scale swarm migration maneuver optimization problem is convexified through nonlinear equality constraint relaxation. By decoupling the obstacle avoidance constraints within the swarm migration maneuver optimization problem, the swarm migration maneuver optimization problem is decomposed, resulting in a specific form of a distributed decoupled convex optimization problem for the swarm migration maneuver trajectory. Numerical integration is used to transform the convexified, time-varying, and continuous distributed decoupled optimization problem into discrete subproblems for convex optimization. Using the convexified discrete subproblems as the inner steps of each iteration, a sequential iterative approximation strategy is used to rapidly solve the optimal swarm large-scale migration maneuver trajectory and the corresponding control strategy in a finite number of steps. According to the optimized control strategy, all spacecraft in the cluster execute corresponding control and perform migration maneuvers to reach their respective predetermined positions in a fuel-optimized manner. Through migration maneuvers, the cluster's configuration reconstruction, obstacle avoidance, and close-in capture of large space targets are achieved. The present invention has a fast optimization speed and high optimization efficiency, and can be used for online trajectory optimization, which helps to improve the flexibility and real-time performance of cluster spacecraft in applications such as obstacle avoidance and close-in capture of large space targets, and improve the success rate of obstacle avoidance and close-in capture. At the same time, the present invention uses fuel optimization as an optimization indicator, which helps to reduce the fuel consumption of cluster spacecraft during migration maneuvers and increase the life of cluster spacecraft.

[0008] The present invention discloses a sequential convex optimization method for distributed migration maneuvers of multiple spacecraft, comprising the following steps:

[0009] Step 1: Given the orbital root number of the cluster spacecraft, the number of cluster spacecraft N, the initial transfer time t0, and the end transfer time t f , the maximum thrust T of each spacecraft in the cluster max , minimum thrust T min Specific impulse I sp and the initial mass m0, a dynamic model of cluster migration maneuvers is established.

[0010] Given the center of a spacecraft cluster, since the center of the spacecraft cluster is a virtual uncontrolled orbit, the corresponding orbital elements can be considered known. Therefore, a relative motion coordinate system is established with the cluster center as the center. In this relative motion coordinate system, for any individual spacecraft in the cluster, its dynamic equations are established in the relative coordinate system of the cluster center. The corresponding relative motion dynamics are:

[0011]

[0012] Where [x, y, z] represents the position of a single spacecraft in the cluster, T = [T x ,T y ,T z ] is the thrust vector of the spacecraft, θ is the true anomaly, is the kinetic coefficient, I sp and g represent the spacecraft thrust specific impulse and the Earth's horizontal acceleration respectively; μ is the Earth's gravitational constant, is the instantaneous angular velocity of the target aircraft; is the instantaneous angular acceleration of the target aircraft; is the average angular velocity of the target aircraft; is the position vector of the target spacecraft; a is the semi-major axis of the cluster center orbit; e is the eccentricity of the cluster center orbit.

[0013] make u=[T x ,T y ,T z ,T] T , then the relative motion equation corresponding to formula (1) can be written in the following matrix form:

[0014]

[0015] in,

[0016]

[0017]

[0018] Step 2: Based on the control mode, obstacle avoidance, and fuel saving mission characteristics of cluster migration maneuvers, the endpoint constraints and optimization performance indicators of large-scale cluster migration maneuvers are constructed, and an optimization model for large-scale cluster migration maneuvers is established.

[0019] First, according to the control method of the cluster spacecraft, the thrust component constraint must be met, namely:

[0020] ||T||=T (5)

[0021] T min ≤T≤T max (6)

[0022] In this cluster spacecraft migration maneuver trajectory optimization problem, we hope to obtain the fuel-optimal migration maneuver process and minimize the spacecraft fuel consumption as much as possible. Therefore, the performance index of the optimization problem is set as:

[0023] J=-m(tf ) (7)

[0024] Since the departure time of the cluster spacecraft is known, the state of the spacecraft at the initial time and the state of the migration maneuver target position are both determined, so the corresponding initial and final state parameters are:

[0025]

[0026]

[0027] Where t0 and t f are the start and end times respectively. At the same time, the initial mass of the cluster spacecraft satisfies m(t0)=m0, and the final mass of the cluster spacecraft satisfies m(t f ) No constraints.

[0028] The collision constraints for cluster spacecraft migration maneuver planning are:

[0029]

[0030] where r min The minimum safe distance for collision avoidance is denoted by the subscripts i and j, respectively. The constraints corresponding to equations (5), (6), and (10) need to be considered throughout the entire migration maneuver process. Equations (5)-(10) are the constraints and performance indicators for the migration maneuver optimization problem. Based on the constraints and performance indicators in equations (5)-(10), the following optimization model for the large-scale cluster migration maneuver problem is established:

[0031]

[0032] Step 3: By relaxing the nonlinear equality constraints, the nonlinear large-scale cluster migration maneuvering optimization problem is convexified. By decoupling the obstacle avoidance constraints in the cluster migration maneuvering optimization problem, the cluster migration maneuvering optimization problem is decomposed, and then the specific form of the distributed decoupled cluster migration maneuvering trajectory sequence convex optimization problem is obtained. While ensuring accuracy, the variable dimension of the cluster migration maneuvering trajectory sequence convex optimization problem is reduced, thereby improving the solution efficiency.

[0033] The control quantity in the dynamic equation (2) belongs to the affine form, and only the thrust coefficient matrix B belongs to the nonlinear expression. In the sequence iteration process, the control coefficient matrix is directly calculated by the state obtained by the previous iteration, so there is no need for convexification. Let X k is a solution of the kth iteration in the continuous approximation process, then in the k+1th iteration process, the dynamic equation is expressed as:

[0034]

[0035] By transforming the dynamic equation (2) into equation (12), the dynamic linearization is achieved, thus ensuring the convexity of the dynamic equation. In addition, the nonlinear constraint function of the thrust vector in equation (1) is non-convex, so it needs to be transformed into a convex constraint. Relaxing the equal sign in the equation to an inequality sign, the problem is equivalent. Then, after being transformed into an inequality sign, the constraint has the form of a cone constraint, that is, it is transformed into a convex constraint, which is:

[0036] ||T||≤T (13)

[0037] By transforming Equation (12) and Equation (13), the convex relaxation of the inequality of nonlinear equality constraints can be achieved.

[0038] Since the collision constraints between spacecraft are non-convex constraints and the collision constraints are coupled with each other, they need to be convexified and decoupled. i (t) sequence, the optimal r obtained by each iteration i (t) serves as the initial value for the next iteration The linear, decoupled collision constraint expression is obtained:

[0039]

[0040] And the credible interval constraints:

[0041]

[0042] Among them, ε r is the confidence interval boundary value. Adding the corresponding constraint of Equation (15) can ensure the effectiveness of linear decoupling and the convergence of the problem. According to Equations (12)-(15), for the i-th spacecraft in the cluster, the decoupled cluster migration maneuver trajectory sequence convex optimization problem model is as follows:

[0043]

[0044] The problem variables in Equation (16) are only related to the state quantity X of the i-th spacecraft. i and the control quantity u i Compared with Equation (11), the corresponding problem variable dimension is smaller and the solution speed is faster. Equation (16) also belongs to a time-varying continuous optimization problem and needs to be further converted into a discrete optimization problem using numerical integration.

[0045] Step 4: Convert the convexified time-varying continuous distributed decoupling optimal problem into a discrete sub-problem of convex optimization through numerical integration. Using the convexified discrete sub-problem as the inner link of each iteration, the optimal cluster large-scale migration maneuver transfer trajectory and the corresponding control u are quickly solved in a limited number of steps through a sequential iterative approximation strategy. * .

[0046] Given the time interval of cluster migration maneuver process [t0,t f ], the number of numerical integration points is M+1, and the state vector and control variable of the sth numerical integration point are respectively denoted as X s 、u s . Then the linearized dynamics numerical integration is:

[0047]

[0048] Where Δt=(t f -t0) / M is the time interval of numerical integration, I is the identity matrix of the same type as A, and the subscript s represents the expression of the corresponding variable / matrix calculated at the s-th numerical integration point.

[0049] Since the transformation involves the approximation of nonlinear terms, the convex subproblem is not equivalent to the original problem. It is necessary to perform a sequential convex optimization approximation on it in order to iteratively solve the optimal cluster migration maneuver trajectory. The process of sequential convex optimization is as follows:

[0050] First, let k = 0. Since the mass is the only nonlinear state variable in dynamics, we only need to give a guess value m for the initial mass profile. 0 Here m is given 0 It allows to directly draw a straight line from the initial value to the guessed final value, so the initial value is very convenient to give, thus ensuring the universality and versatility of the method.

[0051] Then, for the (k+1)th iteration, solve the N decoupled sub-problems corresponding to Equation (16) in parallel, and select the solution Xk of the kth iteration as the guessed initial value of the state vector. The solution is {X k+1 ,u k+1}.

[0052] Check whether the convergence conditions are met:

[0053]

[0054] Where ε is the accuracy requirement. When the above inequality is satisfied, it is equivalent to iterative convergence, that is, the distributed migration planning maneuver solution of cluster spacecraft is realized.

[0055] By using formulas (16) and (17), and combining the termination condition of formula (18), the optimal solution X can be quickly obtained in a limited number of steps using sequential convex optimization. * =X k+1 That is the optimized cluster spacecraft migration maneuver flight trajectory, u * =u k+1 That is the corresponding optimal thrust parameter.

[0056] Step 5: Get the control u according to the optimization in step 4* , all spacecraft in the cluster execute corresponding control and perform migration maneuver transfer to achieve f Always arrive at your designated location in a fuel-optimal manner.

[0057] The system also includes step six: performing migration maneuvers based on step five to achieve swarm configuration reconfiguration, obstacle avoidance, and close-in capture of large space targets. This improves the flexibility and real-time performance of swarm spacecraft in these applications, increasing the success rate of obstacle avoidance and close-in capture. Furthermore, the migration maneuver process uses fuel optimization as an optimization metric, reducing fuel consumption during the maneuver and extending the lifespan of the swarm spacecraft.

[0058] Beneficial effects:

[0059] 1. This invention discloses a sequential convex optimization method for distributed multi-spacecraft migration maneuvers. Given the number of orbital elements of the swarm's flight center, the number of swarm spacecraft, the initial and final migration times, and the maximum and minimum thrust, specific impulse, and initial mass of each spacecraft in the swarm, a dynamic model for the swarm migration maneuver is established. Based on the control, obstacle avoidance, and fuel conservation characteristics of the swarm migration maneuver, endpoint constraints and optimization performance indicators for the large-scale swarm migration maneuver are given, and an optimization model for the large-scale swarm migration maneuver is established. The nonlinear large-scale swarm migration maneuver optimization problem is convexified by relaxing nonlinear equality constraints. By decoupling the obstacle avoidance constraints within the swarm migration maneuver optimization problem, the swarm migration maneuver optimization problem is decomposed, resulting in a specific form of a distributed decoupled convex optimization problem for the swarm migration maneuver trajectory. Numerical integration is used to transform the convexified, time-varying, and continuous distributed decoupled optimization problem into discrete subproblems for convex optimization. Using the convexified discrete subproblems as the inner steps of each iteration, a sequential iterative approximation strategy is used to rapidly solve the optimal swarm large-scale migration maneuver trajectory and its corresponding control within a finite number of steps. Based on the optimized control, all spacecraft in the cluster execute corresponding control and perform migration maneuvers to reach their respective predetermined positions in a fuel-optimized manner. Through migration maneuvers, the cluster can reconfigure its configuration, avoid obstacles, and close in on large space targets.

[0060] 2. The present invention discloses a sequential convex optimization method for distributed migration maneuvers of multiple spacecraft, which realizes distributed optimization of the migration maneuvers of multiple spacecraft by decoupling the coupled obstacle avoidance constraints. It can improve the optimization efficiency, significantly reduce the calculation time of the optimization, and effectively enhance the flexibility and real-time performance of the migration maneuvers of multiple spacecraft.

[0061] 3. The present invention discloses a sequential convex optimization method for distributed migration maneuvers of multiple spacecraft. It does not require strict restrictions on the number of star clusters and the starting and ending positions of the migration maneuver. Therefore, it is universal for spacecraft cluster missions and has no strict restrictions and constraints on cluster migration maneuver missions. Therefore, it has strong robustness and high repeatability.

[0062] 4. The disclosed sequential convex optimization method for distributed multi-spacecraft migration maneuvers, while achieving the aforementioned beneficial effects, can be used for online spacecraft trajectory optimization, enhancing the flexibility and real-time performance of swarm spacecraft in applications such as obstacle avoidance and close-range capture of large space targets, and improving the success rate of obstacle avoidance and close-range capture. Furthermore, by using fuel optimization as an optimization metric during the migration maneuver, the method can reduce fuel consumption during the swarm and increase its lifespan. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 Schematic diagram of the relative motion coordinate system in this embodiment;

[0064] Figure 2 It is a flow chart of a sequential convex optimization method for distributed migration maneuvers of multiple spacecraft according to the present invention;

[0065] Figure 3 is the transfer trajectory of the optimal cluster migration maneuver obtained in this embodiment. DETAILED DESCRIPTION

[0066] In order to better illustrate the purpose and advantages of the present invention, the following cluster configuration transformation task is used as the background to provide a simulation analysis of migration maneuver trajectory optimization to explain the present invention in detail.

[0067] Example 1:

[0068] like Figure 2 As shown, this embodiment discloses a sequential convex optimization method for distributed migration maneuvers of multiple spacecraft, and the specific implementation steps are as follows:

[0069] Step 1: Given the orbital root number of the cluster spacecraft, the number of cluster spacecraft N, the initial transfer time t0, and the end transfer time t f , the maximum thrust T of each spacecraft in the cluster max , minimum thrust T min Specific impulse I sp As well as the initial mass m0, a dynamic model of cluster migration maneuvers is established.

[0070] The orbital elements of the cluster spacecraft flight center are as follows: the center semi-major axis is 7400 km, the eccentricity is 0, the orbital inclination, right ascension of the ascending node, argument of perigee, and true perigee are all 0 degrees; the number of cluster spacecraft N = 8, the transfer initial time t0 = 0, the transfer end time t f =7200s, maximum thrust of each spacecraft in the cluster T max =500mN, minimum thrust T min =0mN, specific impulse I sp =3000s and initial mass m0=1000kg.

[0071] Step 2: Based on the control mode, obstacle avoidance, and fuel saving mission characteristics of the cluster migration maneuver, the endpoint constraints and optimization performance indicators of the large-scale cluster migration maneuver problem are given, and the optimization model of the large-scale cluster migration maneuver problem is established. The initial and final states of the migration maneuver transfer trajectory of the eight spacecraft are shown in Tables 1 and 2 respectively. The minimum safety distance is set to r min =100m.

[0072] Table 1 Initial status of cluster spacecraft

[0073] x / m y / m z / m <![CDATA[v x / (m / s)]]> <![CDATA[v y / (m / s)]]> <![CDATA[v z / (m / s)]]> Spacecraft 1 -850 20 0 0.1 0.1 0.1 Spacecraft 2 -850 420 0 0.1 0.1 0.1 Spacecraft 3 -850 220 200 0.1 0.1 0.1 Spacecraft 4 -1050 200 -200 0.1 0.1 0.1 Spacecraft 5 -1050 20 0 0.1 0.1 0.1 Spacecraft 6 -1050 420 0 0.1 0.1 0.1 Spacecraft 7 -1050 220 200 0.1 0.1 0.1 Spacecraft 8 -850 200 -200 0.1 0.1 0.1

[0074] Table 2 Target status of cluster spacecraft

[0075] x / m y / m z / m <![CDATA[v x / (m / s)]]> <![CDATA[v y / (m / s)]]> <![CDATA[v z / (m / s)]]> Spacecraft 1 50 -50 50 0 0 0 Spacecraft 2 50 -50 50 0 0 0 Spacecraft 3 50 50 50 0 0 0 Spacecraft 4 50 50 -50 0 0 0 Spacecraft 5 -50 -50 50 0 0 0 Spacecraft 6 -50 -50 50 0 0 0 Spacecraft 7 -50 50 50 0 0 0 Spacecraft 8 -50 50 -50 0 0 0

[0076] Step 3: By relaxing the nonlinear equality constraints, the nonlinear large-scale cluster migration maneuver optimization problem is convexified. By decoupling the obstacle avoidance constraints in the cluster migration maneuver optimization problem, the cluster migration maneuver optimization problem is decomposed, and the specific form of the distributed decoupled cluster migration maneuver trajectory sequence convex optimization problem is obtained. The convergence accuracy is set to ε = [1m, 1m, 1m, 10 -3 m / s,10 -3 m / s,10 -3 m / s,10 -3 kg] T Confidence interval ε of collision avoidance constraint r =1km.

[0077] Step 4: Convert the optimal problem of the time-varying continuous distributed decoupling after convexification into a discrete sub-problem of convex optimization through numerical integration. Using the discrete sub-problem after convexification as the inner link of each iteration, the optimal cluster large-scale migration maneuver transfer trajectory and the corresponding control u are quickly solved in a limited number of steps using the sequential iterative approximation strategy. * .

[0078] Step 5: Get the control u according to the optimization in step 4 *All spacecraft in the cluster execute corresponding control and perform migration maneuvers to achieve f The optimal transfer trajectory of the corresponding cluster migration maneuver process is as follows: Figure 3 shown.

[0079] Step 6: Through migration maneuvers, the swarm achieves configuration reconfiguration, obstacle avoidance, and close-in capture of large space targets. This improves the flexibility and real-time performance of the swarm spacecraft in these applications, increasing the success rate of obstacle avoidance and close-in capture. Furthermore, the migration maneuver uses fuel optimization as an optimization metric, which can reduce fuel consumption during the maneuver and extend the lifespan of the swarm spacecraft.

[0080] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention, which is used to explain the present invention and is not used to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A sequential convex optimization method for distributed multi-spacecraft migration maneuvers, characterized by: The following steps are included: Step 1: Given the orbital root number of the cluster spacecraft, the number of cluster spacecraft N, the initial transfer time t0, and the end transfer time t f , the maximum thrust T of each spacecraft in the cluster max , minimum thrust T min Specific impulse I sp and initial mass m0, to establish a dynamic model of cluster migration maneuvers; Step 2: Based on the control mode, obstacle avoidance, and fuel conservation characteristics of swarm migration maneuvers, we construct endpoint constraints and optimization performance indicators for the large-scale swarm migration maneuvering problem, and establish an optimization model for the large-scale swarm migration maneuvering problem. Step 3: The nonlinear large-scale cluster migration maneuver optimization problem is convexified by relaxing nonlinear equality constraints. The cluster migration maneuver optimization problem is decomposed by decoupling the obstacle avoidance constraints in the cluster migration maneuver optimization problem. This leads to the specific form of the distributed decoupled cluster migration maneuver trajectory sequence convex optimization problem. This reduces the variable dimension of the convex optimization problem while ensuring accuracy, improving solution efficiency. Step 4: Convert the optimal problem of the time-varying continuous distributed decoupling after convexification into a discrete sub-problem of convex optimization through numerical integration; use the discrete sub-problem after convexification as the inner link of each iteration, and quickly solve the optimal cluster large-scale migration maneuver transfer trajectory and the corresponding control u in a limited number of steps through the sequential iterative approximation strategy. * ; Step 5: Get the control u according to the optimization in step 4 * , all spacecraft in the cluster execute corresponding control and perform migration maneuver transfer to achieve f Always arrive at your designated location in a fuel-optimal manner.

2. The sequential convex optimization method for distributed multi-spacecraft migration maneuvers according to claim 1, characterized in that: It also includes step six, performing migration maneuvers according to step five to achieve cluster configuration reconstruction, obstacle avoidance, and close-in capture of large space targets, thereby improving the flexibility and real-time performance of cluster spacecraft in obstacle avoidance and close-in capture of large space targets, and improving the success rate of obstacle avoidance and close-in capture; at the same time, the migration maneuvering process uses fuel optimization as an optimization indicator, which can reduce the fuel consumption of cluster spacecraft during the migration maneuvering process and improve the life of cluster spacecraft.

3. A sequential convex optimization method for distributed multi-spacecraft migration maneuvers according to claim 1 or 2, characterized in that: The implementation method of step one is: Given the center of a spacecraft cluster, since the center of the spacecraft cluster is a virtual uncontrolled orbit, the corresponding orbital elements can be considered known. Therefore, a relative motion coordinate system is established with the cluster center as the center. In this relative motion coordinate system, for any single spacecraft in the cluster, its dynamic equation is established in the relative coordinate system of the cluster center, and the corresponding relative motion dynamics is: Where [x, y, z] represents the position of a single spacecraft in the cluster, T = [T x ,T y ,T z ] is the thrust vector of the spacecraft, θ is the true anomaly, is the kinetic coefficient, I sp and g represent the spacecraft thrust specific impulse and the Earth's horizontal acceleration respectively; μ is the Earth's gravitational constant, is the instantaneous angular velocity of the target aircraft; is the instantaneous angular acceleration of the target aircraft; is the average angular velocity of the target aircraft; is the position vector of the target aircraft; a is the semi-major axis of the cluster center orbit, and e is the eccentricity of the cluster center orbit; make u=[T x ,T y ,T z ,T] T , then the relative motion equation corresponding to formula (1) can be written in the following matrix form: in, 4. The sequential convex optimization method for distributed multi-spacecraft migration maneuvers according to claim 3, characterized in that: The implementation method of step 2 is: According to the control method of the cluster spacecraft, the thrust component constraints need to be met, namely: ||T||=T (5) T min ≤T≤T max (6) In this cluster spacecraft migration maneuver trajectory optimization problem, we hope to obtain the fuel-optimal migration maneuver process and minimize the spacecraft fuel consumption as much as possible. Therefore, the performance index of the optimization problem is set as: J=-m(t f ) (7) Since the departure time of the cluster spacecraft is known, the state of the spacecraft at the initial time and the state of the migration maneuver target position are both determined, so the corresponding initial and final state parameters are: Where t0 and t f are the start and end times respectively; at the same time, the initial mass of the cluster spacecraft satisfies m(t0)=m0, and the terminal mass of the cluster spacecraft satisfies m(t f ) No constraints; The collision constraints for cluster spacecraft migration maneuver planning are: where r min For the minimum safe distance to avoid collision, subscripts i and j represent two different cluster spacecraft respectively; The constraints corresponding to equations (5), (6), and (10) need to be considered throughout the entire migration process. Equations (5)-(10) are the constraints and performance indicators of the migration optimization problem. Based on the constraints and performance indicators in equations (5)-(10), the following optimization model for the large-scale cluster migration problem is established:

5. The sequential convex optimization method for distributed multi-spacecraft migration maneuvers according to claim 4, characterized in that: The implementation method of step three is: The control quantity in the dynamic equation (2) belongs to the affine form, and only the thrust coefficient matrix B belongs to the nonlinear expression. In the sequence iteration process, the control coefficient matrix is directly calculated by the state obtained by the previous iteration, so there is no need for convexification. Let X k is a solution of the kth iteration in the continuous approximation process, then in the k+1th iteration process, the dynamic equation is expressed as: By transforming the dynamic equation (2) into equation (12), the linearization of the dynamics is achieved, thereby ensuring the convexity of the dynamic equation. In addition, the nonlinear constraint function of the thrust vector in equation (1) is non-convex, so it needs to be transformed into a convex constraint. The equal sign in the equation is relaxed to an inequality sign, and the problem is equivalent. After being transformed into an inequality sign, the constraint has the form of a cone constraint, that is, it is transformed into a convex constraint, which is: ||T||≤T (13) By transforming Equation (12) and Equation (13), the convex relaxation of the inequality of nonlinear equality constraints is achieved; Since the collision constraints between spacecraft are non-convex constraints and the collision constraints are coupled with each other, they need to be convexified and decoupled. i (t) sequence, the optimal r obtained by each iteration i (t) serves as the initial value for the next iteration The linear, decoupled collision constraint expression is obtained: And the credible interval constraints: Among them, ε r is the confidence interval boundary value. Adding the constraint corresponding to Equation (15) can ensure the effectiveness of linear decoupling and the convergence of the problem. According to Equations (12)-(15), for the i-th spacecraft in the cluster, the decoupled cluster migration maneuver trajectory sequence convex optimization problem model is as follows: The problem variables in Equation (16) are only related to the state quantity X of the i-th spacecraft. i and the control quantity u i Compared with Equation (11), the problem variable dimension is smaller and the solution speed is faster; Equation (16) also belongs to a time-varying continuous optimization problem, which is further converted into a discrete optimization problem using numerical integration.

6. The method for sequential convex optimization of multi-spacecraft distributed migration maneuvers according to claim 5, characterized in that: The implementation method of step 4 is: Given the time interval of cluster migration maneuver process [t0,t f ], the number of numerical integration points is M+1, and the state vector and control variable of the sth numerical integration point are respectively denoted as X s 、u s ; Then the linearized dynamic numerical integration is: Where Δt=(t f -t0) / M is the time interval of numerical integration, I is the identity matrix of the same type as A, and the subscript s represents the expression of the corresponding variable / matrix calculated at the s-th numerical integration point; Since the approximation of nonlinear terms is involved before and after the transformation, the convex subproblem is not equivalent to the original problem. The optimal cluster migration maneuver trajectory is obtained by performing sequential convex optimization approximation on it in order to iteratively solve it.

7. The sequential convex optimization method for distributed multi-spacecraft migration maneuvers according to claim 6, characterized in that: The process of sequential convex optimization is as follows: First, let k = 0; since mass is the only nonlinear state variable in dynamics, we only need to give a guess value m for the initial mass profile. 0 ; The m given here is 0 Allows a straight line from the initial value to the guessed final value; Then, for the (k+1)th iteration, solve the N decoupled sub-problems corresponding to Equation (16) in parallel, and select the solution X of the kth iteration k As the guess of the initial value of the state vector, the solution is {X k+1 ,u k+1 }; Check whether the convergence conditions are met: Where is the accuracy requirement. When the above inequality is met, it is equivalent to iterative convergence, that is, the distributed migration planning maneuver solution of cluster spacecraft is realized; By using formulas (16) and (17) and combining the termination condition of formula (18), the optimal solution X is obtained quickly in a limited number of steps using sequential convex optimization. * =X k+1 That is the optimized cluster spacecraft migration maneuver flight trajectory, u * =u k+1 That is the corresponding optimal thrust parameter.

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