CN115583367B - Satellite cluster reconstruction control method based on distributed sequence convex optimization - Google Patents

Abstract

A satellite cluster reconstruction control method based on distributed sequence convex optimization belongs to the field of satellite cluster reconstruction control. The invention solves the problems that the existing control method has poor expandability, collision avoidance among discrete points is not considered, and infeasible solution of the feasible problem is caused by simple convex planning due to excessively conservative approximation of non-convex constraint. According to the method, through decoupling of satellite collision constraint in the satellite cluster, the problem complexity is reduced, the calculation efficiency is improved, and the optimal track can be found for the large-scale satellite cluster under the condition that collision avoidance and barrier avoidance and thrust amplitude constraint are met. The method can be applied to solving the large-scale satellite cluster reconstruction optimal control problem, has strong expansibility, simultaneously avoids the problem that the existing method can cause the simple convex planning to fall into the infeasible solution of the feasible problem due to the excessively conservative approximation of the non-convex constraint, and can ensure the collision avoidance between any two discrete points. The method can be applied to satellite cluster reconstruction control.

Description

A satellite cluster reconfiguration control method based on distributed sequential convex optimization

Technical Field

The present invention belongs to the field of satellite cluster reconstruction control, and in particular relates to a satellite cluster reconstruction control method based on distributed sequence convex optimization.

Background Art

Distributed spacecraft systems mainly include three structures: constellations, star clusters and formations. A satellite cluster refers to a distributed satellite system consisting of multiple spacecraft flying closely together to complete a common mission. It is composed of dozens or even hundreds of similar satellites, and each satellite has the ability to fly autonomously and can work together to achieve tasks such as collision avoidance, orbit reconstruction, and member updates.

For a cluster consisting of dozens or even hundreds of satellites, if all of them are based on manual ground control, the requirements for ground human resources are too high, a large amount of financial resources and equipment are consumed, and it is very likely that sudden unexpected situations cannot be handled in time, resulting in serious consequences such as collisions between satellites. If all satellites in the cluster have autonomous flight capabilities, the satellites can respond quickly and complete the given tasks through mutual cooperation. At the same time, during the mission execution, they can autonomously perform collision and obstacle avoidance operations without ground instructions, which will greatly improve the reliability and mission diversity of the cluster system.

Most of the traditional satellite control methods are aimed at small-scale satellite formation systems and are based on centralized control. One or several satellites are used as master satellites and other satellites are used as slave satellites. The master satellite is responsible for obtaining instructions from the ground and then assigning tasks to other slave satellites. The slave satellites work according to the instructions of the master satellite. Another method of centralized control is the ruler-follower method. Some satellites are designated as rulers to issue instructions, and other satellites act according to the instructions as followers. The response speed is slow and the execution efficiency is low. On the one hand, the satellites in the satellite cluster are very small and have limited computing power. This method requires too high computing power for the satellites, which can easily cause them to fail. On the other hand, since information only flows from the leader to the followers, if the leader satellite fails, it is easy to cause the entire satellite cluster to fail. Therefore, large-scale satellite cluster autonomous collaborative control systems with strong flexibility, high reliability and rapid response have received worldwide attention. The satellite cluster reconfiguration control problem refers to the control problem of satellites transferring from one set of orbits to another, in which the satellites remain relatively bounded, that is, the farthest cannot exceed the specified upper limit, and the closest is not less than the minimum safety distance. From this point of view, satellite formation is a special case of satellite cluster. The formation requires not only boundedness constraints, but also strict position relationship constraints. Therefore, satellite clusters can also use some control methods of formation flight without pursuing optimality.

The satellite cluster reconfiguration maneuver problem is a complex multi-objective optimization problem. Usually, the propellant consumption, orbit transfer time, satellite cluster fuel consumption balance, etc. are used as objectives to find the best reconfiguration strategy and maneuvering strategy to achieve a specific task. Problems related to formation reconfiguration have been widely studied. These include both continuous thrust and pulse thrust. Sarno proposed a new method for autonomous reconfiguration of distributed space systems based on genetic algorithms, which simplifies orbital transformation into a convex optimization problem. While optimizing the total fuel consumption, it ensures the safe guidance of the spacecraft formation to the desired state.

The reconfiguration problem for large satellite swarms is essentially a class of optimal control problems for multi-agent systems with nonlinear dynamics and nonconvex path constraints. There are many approaches to solving this class of problems, both indirect and direct. Due to the complex nonlinear dynamics of the spacecraft swarm, indirect methods require the derivation of first-order necessary conditions for optimality and require good initial guesses, making them difficult to use. Therefore, many optimal control problems are solved using direct methods, which parameterize the control space and sometimes even the state space to reduce the problem to a nonlinear optimization problem. Pseudospectral methods are well suited to handle nonlinear dynamics, but they become computationally intractable as the number of satellites increases, and they have not yet been implemented in real time. So far, nonlinear solvers have been fast enough to be implemented onboard for well-posed problems, but are not well suited for multi-agent problems. Mixed integer linear programming (MILP) can be used to enforce collision avoidance constraints and has been implemented in real time as well as for pre-planning trajectories.

Solving optimal control problems online relies on the current advances in information technology. Recently, convex optimization has been applied to multi-vehicle trajectory design, and convex programming problems can be reliably solved to the global optimum in polynomial time. More importantly, recent advances have shown that these problems can be solved in real time by general second-order cone programming solvers and customized solvers that exploit specific problem structures. Convex optimization has been used to find collision-free trajectories for formation reconstruction and robotic motion planning. However, simple convex programming can fall into infeasible solutions to feasible problems due to overly conservative approximations of non-convex constraints.

In summary, the number of spacecraft involved in the existing control methods is very small (only a dozen at most), and the scalability of the methods is poor when facing the reconstruction problem of large-scale satellite clusters. In addition, the overly conservative approximation of non-convex constraints by existing methods may cause simple convex programming to fall into infeasible solutions to feasible problems. At the same time, a large number of spacecraft makes collision avoidance a major challenge. Existing control methods do not consider the collision avoidance problem between discrete points when constructing convex optimization subproblems.

Summary of the invention

The purpose of the present invention is to solve the problems that the existing control methods have poor scalability, do not consider collision avoidance between discrete points, and cause simple convex programming to fall into infeasible solutions of feasible problems due to overly conservative approximation of non-convex constraints, and propose a satellite cluster reconstruction control method based on distributed sequential convex optimization.

The technical solution adopted by the present invention to solve the above technical problems is:

A satellite cluster reconstruction control method based on distributed sequential convex optimization, the method specifically comprising the following steps:

Step S1, establishing a non-convex control model for satellite cluster reconstruction control;

Step S2, convexifying the non-convex items in the non-convex control model established in step S1;

Step S3, establishing a convex optimization model based on a penalty function according to the convexification result of step S2;

Step S4, decoupling the convex optimization model established in step S3 to obtain a decoupled convex optimization model;

Step S5: Solve the penalty function-based convex optimization model and the decoupled convex optimization model, and output the optimal control sequence.

The beneficial effects of the present invention are:

The present invention proposes a distributed sequential convex optimization method based on L1 penalty function and sequential convex optimization theory. By decoupling the satellite collision constraints in the satellite cluster, the problem complexity is reduced, the computational efficiency is improved, and the optimal trajectory can be found for a large-scale satellite cluster under the constraints of collision avoidance and thrust amplitude. The present invention can be applied to solving the optimal control problem of large-scale satellite cluster reconstruction. The method has strong scalability and avoids the problem that the existing method will cause the simple convex programming to fall into an infeasible solution of the feasible problem due to the overly conservative approximation of non-convex constraints, and can ensure collision avoidance between any two discrete points.

Moreover, compared with the traditional centralized solution method, the decoupling of satellite collision avoidance constraints can greatly reduce the complexity of the problem, achieve parallel solution, and improve solution efficiency.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of a relative motion coordinate system;

FIG2 is a flow chart of a satellite cluster reconstruction control method based on distributed sequential convex optimization of the present invention.

DETAILED DESCRIPTION

Specific implementation method 1: This implementation method is described in conjunction with Figure 2. This implementation method is a satellite cluster reconstruction control method based on distributed sequential convex optimization, and the method specifically includes the following steps:

Step S1, establishing a non-convex optimal control model for large-scale (cluster consisting of dozens or even hundreds of satellites) satellite cluster reconstruction control;

Step S2, convexifying the non-convex items in the non-convex optimal control model established in step S1;

Step S3, establishing a convex optimization model based on a penalty function according to the convexification result of step S2;

Step S4, decoupling the convex optimization model established in step S3 to obtain a decoupled convex optimization model;

Step S5: Solve the penalty function-based convex optimization model and the decoupled convex optimization model, and output the optimal control sequence.

Specific implementation method 2: This implementation method is described in conjunction with Figure 1. The difference between this implementation method and specific implementation method 1 is that the specific process of step S1 is:

Step S11, establishing an inertial coordinate system (ECI) with the earth as the center and a LVLH coordinate system, and using the established coordinate systems to describe the relative motion dynamics equations of the satellite cluster;

The inertial coordinate system with the earth as the center is used to locate the master spacecraft or a virtual reference point called the master orbit, and the LVLH coordinate system describes the relative position relationship of the slave satellite with respect to the master satellite;

Step S12, establishing a non-convex optimal control model for satellite cluster reconstruction control, wherein the control model takes minimum fuel consumption as the optimization target, and takes dynamic constraints, collision avoidance constraints, two end constraints and thrust amplitude constraints as constraint conditions;

The non-convex optimal control model is:

Using equations (2) to (6) as constraints:

x _j (0)＝x _j,0 ,x _j (t _f )＝x _j,f j＝1,...,N (6)

Wherein, formula (1) is the cost function of the non-convex optimal control model, _tf is the total time of the reconstruction maneuver process, _uj (t) represents the acceleration vector applied to the three coordinate axes of satellite j in the LVLH coordinate system at time t, j = 1, 2, …, N, N is the number of cluster satellites, ||·|| _p represents the p-norm, p = 1;

ρ_j代表第j颗卫星相对于主星的位置矢量，上角标T代表转置，

为ρ_j的导数，

为x_j的一阶导数；f(·)代表从星无动力时相对于主星的动力学方程；Formula (2) is the dynamic equation of the slave satellite relative to the master satellite, that is, the dynamic constraint, B = [0 _3×3 , I _3×3 ] ^T , I _3×3 is the unit matrix, oev(t) is the six orbital elements of the master satellite that change with time, which is a known quantity, _xj (t) represents the position state information of the jth satellite at time t,

ρ _j represents the position vector of the jth satellite relative to the host satellite, and the superscript T represents the transpose.

is the derivative of ρ _j ,

is the first-order derivative of x _j ; f(·) represents the dynamic equation of the slave satellite relative to the master satellite when it is unpowered;

Given the relative position vector ρ _j and the primary star orbit element (oev), the relative velocity vector that satisfies the J2 invariant orbit condition can be obtained:

Formula (3) represents that the control quantity needs to satisfy the thruster maximum amplitude constraint, U _max is the thruster amplitude upper limit, ||·|| _q represents the q norm, q=∞;

Formula (4) represents the collision constraint between satellites, G = [I _3×3 ,0 _3×3 ] ^T , I _3×3 is the unit matrix, x _i (t) represents the position state information of the i-th satellite at time t, ||·|| ₂ represents the 2-norm, and R _col represents the minimum collision constraint distance between satellites;

Formula (5) is the collision avoidance constraint between the satellite and the obstacle, O represents the position state information set of all obstacles, O _i is the position state information of the i-th obstacle, x _j (t) represents the position state information of the j-th satellite at time t, and R _obs,l represents the minimum safe distance that the satellite needs to maintain with the l-th obstacle;

Equation (6) represents the initial and terminal constraints, xj _,0 represents the initial state of the j-th satellite, and _xj,f represents the terminal state of the j-th satellite.

The other steps and parameters are the same as those in the first embodiment.

Specific implementation method three: This implementation method is different from specific implementation methods one or two in that the specific process of step S2 is as follows:

Step S21: Convexify the dynamic constraints

According to the definition of convex optimization problems, the equality constraints in convex optimization problems must be affine. Therefore, the dynamic constraints are linearized according to the reference trajectory, and then the linearized dynamic constraints are discretized using the zero-order hold method;

Step S22: Convexify the collision avoidance constraints between the satellite and the obstacle at the discrete points

There are a large number of obstacles such as space debris in space. Therefore, it is necessary to consider the obstacle avoidance constraints between the satellite and the external obstacles. Assuming that the obstacle shape is spherical, the static obstacle collision avoidance constraints are convexified at all discrete points corresponding to the reference trajectory, as shown in the following formula:

代表第j颗卫星在第k步时的基准轨迹，K代表离散化过程中离散区间数，R_obs,l代表卫星需要与第l个障碍物保持的最小安全距离，||·||₂代表2范数；Wherein, Ο represents the set of position status information of all obstacles, Ο _l is the position status information of the lth obstacle, G = [I _3×3 ,0 _3×3 ] ^T , I _3×3 is the unit matrix, x _j [k] represents the position status information of the jth satellite at the kth step,

represents the reference trajectory of the jth satellite at the kth step, K represents the number of discrete intervals in the discretization process, R _obs,l represents the minimum safe distance that the satellite needs to maintain with the lth obstacle, and ||·|| ₂ represents the 2-norm;

Step S23: Add satellite and obstacle avoidance constraints within the time period between discrete points

In order to ensure that the obstacle avoidance constraint is satisfied between two discrete points, an obstacle avoidance constraint is added between the discrete points, as shown in the following formula:

代表第j颗卫星在第k-1步时的基准轨迹；in,

represents the reference trajectory of the jth satellite at the k-1th step;

Step S24: Convexify the collision avoidance constraints between satellites at discrete points

The original collision avoidance constraint requires that the distance between any two satellites is greater than the minimum safety distance, while the convexified constraint becomes that any two satellites cannot be simultaneously located in a strip area with a width of R _col at any discrete point k. The extension direction of this area is perpendicular to the line connecting the discrete reference points of the nominal trajectories of the two satellites, and the strip area changes with the change of the nominal trajectory reference point.

The convexified inter-satellite collision avoidance constraint is:

上角标T代表转置，

代表第i颗卫星在第k步时的基准轨迹。Among them, R _col represents the minimum collision constraint distance between satellites,

The superscript T stands for transpose.

Represents the reference trajectory of the i-th satellite at the k-th step.

是对实际轨迹x_j的初始猜测，并且用于凸化碰撞规避约束。基准轨迹越接近实际轨迹，则代表动力学方程线性化过程和碰撞规避约束凸化过程更精确。因此，碰撞轨迹约束为仿射形式且满足凸优化框架。These reference trajectories are known,

is the initial guess of the actual trajectory _xj and is used to convexify the collision avoidance constraint. The closer the reference trajectory is to the actual trajectory, the more accurate the linearization of the dynamic equations and the convexification of the collision avoidance constraint are. Therefore, the collision trajectory constraint is in affine form and satisfies the convex optimization framework.

The present invention arranges priorities according to satellite serial numbers, satellites with smaller serial numbers have higher priorities, and satellites with larger serial numbers need to avoid satellites with smaller serial numbers.

The other steps and parameters are the same as those in the first or second embodiment.

Specific implementation method 4: This implementation method is different from any one of the specific implementation methods 1 to 3 in that the convex optimization model based on the penalty function is:

Since the dynamics equation constraints and the inter-satellite collision avoidance constraints are convexified according to the reference trajectory, an approximate convex optimization subproblem is obtained. Therefore, in order to make the solution of the convex optimization subproblem effective, the reference trajectory needs to be as close to the actual state as possible. In order to ensure the accuracy of the convexification and the convergence of the sequence iteration, the trust region constraint is added when solving the sequence.

The L1 penalty function strategy is used to introduce constraints into the objective function as penalties. The L1 penalty function is also called the exact penalty method. If the penalty is multiplied by a very large coefficient, then the optimal solution to the original problem can be obtained by solving the unconstrained optimization problem only once.

代表卫星j在第iter次迭代的基准轨迹，x_j,iter[k]代表第j颗卫星在第iter次迭代的位置状态信息，||·||_∞代表∞范数，δ_iter为信赖域半径。Wherein, Δt is the discrete time step, h _l″ (X) = 0 is the l″th equality constraint, l″ = 1, ..., n _eq , n _eq is the number of equality constraints, g _l′ (X) ≤ 0 is the l′th inequality constraint, |g _l′ (X)| ⁺ = max(g _l′ (X), 0), l′ = 1, ..., n _ineq , n _ineq is the number of inequality constraints, ω _eq represents the penalty coefficient of the equality constraint, ω _ineq represents the penalty coefficient of the inequality constraint,

represents the reference trajectory of satellite j at the iter-th iteration, x _j,iter [k] represents the position state information of the j-th satellite at the iter-th iteration, ||·|| _∞ represents the ∞ norm, and δ _iter is the trust region radius.

The equality constraints include dynamic constraints and two-end constraints, and the inequality constraints include collision avoidance constraints between satellites and obstacles at discrete points, obstacle avoidance constraints between satellites and obstacles in the time period between discrete points, and collision avoidance constraints between satellites at discrete points.

The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

Specific implementation mode five: This implementation mode is different from any one of specific implementation modes one to four in that, in step S4, the decoupling of collision constraints between satellites at discrete points is achieved based on the idea of trajectory freezing, and a second safe distance R _safe is defined. If R _safe > R _col is satisfied, collision constraints are imposed on satellites whose distances are within the second safe distance in the previous iteration. Otherwise, collision constraints between satellites are not required in the next iteration.

As the number of iterations increases, the trajectory obtained in the previous iteration becomes closer and closer to the trajectory obtained in this iteration. It can be considered that all other satellites are fixed objects, and their trajectories are the same as in the previous iteration. It is only necessary to prevent collisions with these fixed satellites, and then the collision avoidance constraint can be considered to be satisfied.

The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

Specific implementation method 6: This implementation method is different from the specific implementation methods 1 to 5 in that the specific process of step S5 is as follows:

Step S51, initializing the reference trajectory, trust region and trust region reduction coefficient;

Step S52, solving the convex optimization model after decoupling the collision constraints between satellites for all satellites in parallel according to the initialized reference trajectory, which can greatly reduce the solution time, and use the obtained sequence solution as the reference trajectory for solving the convex optimization model based on the penalty function in the next stage;

Step S53: Each satellite solves the penalty function-based convex optimization model in parallel according to the reference trajectory to obtain its own optimal trajectory, and then uses the obtained optimal trajectory as its own reference trajectory in the next iteration, that is, updates the reference trajectory;

Step S54: If all satellites meet the convergence condition, the iteration stops and the optimal control sequence is directly output;

Step S55: If not all satellites meet the convergence condition, the control sequence of the satellites that meet the convergence condition remains unchanged and the solution is stopped. For the satellites that do not meet the convergence condition, the reference trajectory and the trust region are updated (the trust region is updated at each iteration according to the initialized trust region and the trust region reduction coefficient) and the iterative solution is continued until the convergence condition is met. The solution is terminated when all satellites meet the convergence condition and the optimal control sequence is output.

The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5.

Specific implementation method 7: This implementation method is different from any one of specific implementation methods 1 to 6 in that the dynamic equation of the slave satellite relative to the master satellite when it is unpowered is:

为ω_z的一阶导数，将从星相对于主星的位置矢量表示为ρ_j＝[x_j y_j z_j]^T，x_j、y_j和z_j为ρ_j中的元素，

为y_j的一阶导数，

为x_j的二阶导数，r代表主星位置矢量的模长，

为x_j的一阶导数，

为y_j的二阶导数，

为z_j的一阶导数，

为ω_x的一阶导数，

为z_j的二阶导数；Wherein, u _jx , u _jy , u _jz are the thrust accelerations acting on the three axes of the slave satellite, s _i = sin(i), s _θ = sin(θ), c _θ = cos(θ), c _i = cos(i), ω _x and ω _z represent the angular velocities of rotation of the LVLH coordinate system around the x-axis and z-axis, respectively.

is the first-order derivative of ω _z , and the position vector of the slave star relative to the master star is expressed as ρ _j = [x _j y _j z _j ] ^T , where x _j , y _j and z _j are elements in ρ _j ,

is the first-order derivative of y _j ,

is the second-order derivative of x _j , r represents the modulus of the primary star position vector,

is the first-order derivative of x _j ,

is the second-order derivative of y _j ,

is the first-order derivative of z _j ,

is the first-order derivative of ω _x ,

is the second-order derivative of z _j ;

η，η_j，ξ，ξ_j，r_j和r_jZ是为了简化势能项；The orbital elements used by the master star orbit are: the master star position vector modulus r, radial velocity magnitude v _x , orbital angular momentum h, orbital inclination i, ascending node right ascension Ω and latitude argument θ. These six parameters can completely determine the orbit of the master star in the ECI coordinate system. Once the position information of the master star is determined, the position and velocity vector of the slave star relative to the master star can be expressed as ρ _j = [x _j y _j z _j ] ^T ,

η, η _j , ξ, ξ _j , r _j and r _jZ are used to simplify the potential energy terms;

Wherein, μ represents the Earth's gravitational constant, μ=398600.4418, with the unit of km ³ /s ² , and k _J2 =2.633×10 ¹⁰ , with the unit of km ⁵ /s ² .

The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims (6)

1. A satellite cluster reconstruction control method based on distributed sequential convex optimization, characterized in that the method specifically comprises the following steps: Step S1, establishing a non-convex control model for satellite cluster reconstruction control; The specific process of step S1 is as follows: Step S11, establishing an inertial coordinate system with the earth as the center and a LVLH coordinate system, and using the established coordinate systems to describe the relative motion dynamics equations of the satellite cluster; Step S12, establishing a non-convex control model for satellite cluster reconstruction control, wherein the control model takes minimum fuel consumption as the optimization target, and takes dynamic constraints, collision avoidance constraints, two end constraints and thrust amplitude constraints as constraint conditions; The non-convex control model is:

Using equations (2) to (6) as constraints:

x _j (0)＝x _j,0 ,x _j (t _f )＝x _j,f j＝1,...,N (6) Wherein, formula (1) is the cost function of the non-convex control model, _tf is the total time of the reconstruction maneuver process, _uj (t) represents the acceleration vector applied to the three coordinate axes of satellite j in the LVLH coordinate system at time t, j = 1, 2, …, N, N is the number of satellites in the cluster, ||·|| _p represents the p-norm, p = 1; Formula (2) is the dynamic equation of the slave satellite relative to the master satellite, B = [0 _3×3 , I _3×3 ] ^T , I _3×3 is the unit matrix, oev(t) is the six orbital elements of the master satellite that change with time, x _j (t) represents the position state information of the jth satellite at time t,

ρ _j represents the position vector of the jth satellite relative to the host satellite, and the superscript T represents the transposition.

is the derivative of ρ _j ,

is the first-order derivative of x _j ; f(·) represents the dynamic equation of the slave satellite relative to the master satellite when it is unpowered; Formula (3) represents the maximum amplitude constraint of the thruster, U _max is the upper limit of the thruster amplitude, ||·|| _q represents the q norm, q = ∞; Formula (4) represents the collision constraint between satellites, G = [I _3×3 ,0 _3×3 ] ^T , I _3×3 is the unit matrix, x _i (t) represents the position state information of the i-th satellite at time t, ||·|| ₂ represents the 2-norm, and R _col represents the minimum collision constraint distance between satellites; Formula (5) is the collision avoidance constraint between the satellite and the obstacle, O represents the position state information set of all obstacles, O _i is the position state information of the i-th obstacle, x _j (t) represents the position state information of the j-th satellite at time t, and R _obs,l represents the minimum safe distance that the satellite needs to maintain with the l-th obstacle; Formula (6) represents the initial and terminal constraints, x _j,0 represents the initial state of the j-th satellite, and x _j,f represents the terminal state of the j-th satellite; Step S2, convexifying the non-convex items in the non-convex control model established in step S1; Step S3, establishing a convex optimization model based on a penalty function according to the convexification result of step S2; Step S4, decoupling the convex optimization model established in step S3 to obtain a decoupled convex optimization model; Step S5: Solve the penalty function-based convex optimization model and the decoupled convex optimization model, and output the optimal control sequence. 2. According to the satellite cluster reconstruction control method based on distributed sequential convex optimization according to claim 1, it is characterized in that the specific process of step S2 is: Step S21: Convexify the dynamic constraints The dynamic constraints are linearized according to the reference trajectory, and then the linearized dynamic constraints are discretized using the zero-order hold method; Step S22: Convexify the collision avoidance constraints between the satellite and the obstacle at the discrete points

Wherein, Ο represents the set of position status information of all obstacles, Ο _l is the position status information of the lth obstacle, G = [I _3×3 ,0 _3×3 ] ^T , I _3×3 is the unit matrix, x _j [k] represents the position status information of the jth satellite at the kth step,

represents the reference trajectory of the jth satellite at the kth step, K represents the number of discrete intervals in the discretization process, R _obs,l represents the minimum safe distance that the satellite needs to maintain with the lth obstacle, and ||·|| ₂ represents the 2-norm; Step S23: Add satellite and obstacle avoidance constraints within the time period between discrete points

in,

represents the reference trajectory of the jth satellite at the k-1th step; Step S24: Convexify the collision avoidance constraints between satellites at discrete points The convexified inter-satellite collision avoidance constraint is:

Among them, R _col represents the minimum collision constraint distance between satellites,

The superscript T stands for transpose.

Represents the reference trajectory of the i-th satellite at the k-th step. 3. According to claim 2, a satellite cluster reconstruction control method based on distributed sequential convex optimization is characterized in that the convex optimization model based on penalty function is:

Wherein, Δt is the discrete time step, h _l″ (X) = 0 is the l″th equality constraint, l″ = 1, ..., n _eq , n _eq is the number of equality constraints, g _l′ (X) ≤ 0 is the l′th inequality constraint, |g _l′ (X)| ⁺ = max(g _l′ (X), 0), l′ = 1, ..., n _ineq , n _ineq is the number of inequality constraints, ω _eq represents the penalty coefficient of the equality constraint, ω _ineq represents the penalty coefficient of the inequality constraint,

represents the reference trajectory of satellite j at the iter-th iteration, x _j,iter [k] represents the position state information of the j-th satellite at the iter-th iteration, ||·|| _∞ represents the ∞ norm, and δ _iter is the trust region radius. 4. A satellite cluster reconstruction control method based on distributed sequential convex optimization according to claim 3, characterized in that, in step S4, the decoupling of collision constraints between satellites at discrete points is realized based on the idea of trajectory freezing, and a second safe distance R _safe is defined. If R _safe > R _col is satisfied, collision constraints are imposed on satellites whose distance is within the second safe distance in the previous iteration, otherwise, collision constraints between satellites are not required in the next iteration. 5. The satellite cluster reconstruction control method based on distributed sequential convex optimization according to claim 4 is characterized in that the specific process of step S5 is: Step S51, initializing the reference trajectory, trust region and trust region reduction coefficient; Step S52, solving the convex optimization model after decoupling the collision constraints between satellites for all satellites in parallel according to the initialized reference trajectory, and using the obtained sequence solution as the reference trajectory for solving the convex optimization model based on the penalty function in the next stage; Step S53: Each satellite solves the penalty function-based convex optimization model in parallel according to the reference trajectory to obtain its own optimal trajectory, and then uses the obtained optimal trajectory as its own reference trajectory for the next iteration; Step S54: If all satellites meet the convergence condition, the iteration stops and the optimal control sequence is directly output; Step S55: If not all satellites meet the convergence condition, the control sequence of the satellites that meet the convergence condition remains unchanged and the solution is stopped. For the satellites that do not meet the convergence condition, the reference trajectory and trust region are updated and the iterative solution is continued until the convergence condition is met. The solution is terminated when all satellites meet the convergence condition, and the optimal control sequence is output. 6. According to the satellite cluster reconstruction control method based on distributed sequential convex optimization of claim 5, it is characterized in that the dynamic equation of the slave satellite relative to the master satellite when it is unpowered is:

Wherein, u _jx , u _jy , u _jz are the thrust accelerations acting on the three axes of the slave satellite, s _i = sin(i), s _θ = sin(θ), c _θ = cos(θ), c _i = cos(i), ω _x and ω _z represent the angular velocities of rotation of the LVLH coordinate system around the x-axis and z-axis, respectively.

is the first-order derivative of ω _z , and the position vector of the slave star relative to the master star is expressed as ρ _j = [x _j y _j z _j ] ^T , where x _j , y _j and z _j are elements in ρ _j ,

is the first-order derivative of y _j ,

is the second-order derivative of x _j , r represents the modulus of the primary star position vector,

is the first-order derivative of x _j ,

is the second-order derivative of y _j ,

is the first-order derivative of z _j ,

is the first-order derivative of ω _x ,

is the second-order derivative of z _j ;

Wherein, μ represents the Earth's gravitational constant, μ=398600.4418, with the unit of km ³ /s ² , and k _J2 =2.633×10 ¹⁰ , with the unit of km ⁵ /s ² .

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