Space target approaching method based on multi-target optimization and particle swarm optimization

Abstract

The invention discloses a space target approaching method based on multi-target optimization and a particle swarm optimization algorithm, and belongs to the technical field of spacecraft control, and the method comprises the steps: building a multi-target optimization model according to the demands of a space target approaching task; defining constraint conditions; designing a fitness function based on constraint conditions and task requirements; initializing a particle swarm: setting the scale of the particle swarm, and initializing the speed and position of particles; calculating a fitness function; updating a particle swarm: updating the speed and the position of each particle through an iteration process of a particle swarm optimization algorithm; evaluating the objective function; processing constraint conditions; iterating until a termination condition is met; and outputting an optimization result: after multiple iterations, outputting an optimal orbital transfer strategy corresponding to the global optimal position. The space target approaching method based on the multi-target optimization and the particle swarm optimization can improve the calculation efficiency, and is high in adaptability and high in precision.

Description

Technical Field

[0001] The present invention relates to the technical field of spacecraft control, and particularly to a method for approaching a space target based on multi-objective optimization and particle swarm algorithm. Background Art

[0002] In the space target approaching mission, accurately calculating the orbit transfer strategy of the spacecraft is the key to achieving effective approach and tracking of the target. Traditional calculation methods usually rely on complex mathematical models and empirical formulas, such as Hohmann transfer and Lambert transfer. These methods have obvious deficiencies in terms of calculation efficiency and adaptability. Hohmann transfer is one of the most commonly used orbit transfer methods, applicable to transferring from one circular orbit to another. It changes the orbit radius through two velocity pulses, and the pulse amounts can be obtained through the calculation formulas of the orbit radius and velocity. However, Hohmann transfer has a large approaching error for elliptical orbits and requires passing through a semi-elliptical orbit, resulting in a long transfer time and being unsuitable for time-sensitive tasks. In addition, Hohmann transfer is only applicable to the transfer between circular orbits with the same orbit plane. If the orbit inclination needs to be changed, additional orbit maneuvers are required.

[0003] Lambert transfer is mainly used to calculate the shortest-time transfer path between two points. By solving the Lambert problem, the velocity increments of the two pulses can be obtained. Although Lambert transfer performs well in time optimization, for complex multi-stage or multi-objective tasks, its flexibility and adaptability are poor, and the single-pulse amount is large, making it difficult to meet the task requirements under multiple constraints.

[0004] In recent years, intelligent optimization algorithms such as genetic algorithms and simulated annealing have been introduced into the field of orbit design to find better path planning solutions. These methods can explore solutions in a larger space, but usually face problems such as large computational amount and slow convergence speed. In addition, intelligent optimization algorithms are prone to falling into local optimal solutions, especially when dealing with complex multi-constraints, and it is difficult to guarantee global optimality. Summary of the Invention

[0005] The present invention aims to provide a method for approaching a space target based on multi-objective optimization and particle swarm algorithm to improve the calculation efficiency and accuracy, ensure that the spacecraft can quickly and accurately approach the target, and meet the requirements such as time and pulse limitations during the approaching process.

[0006] To achieve the above object, the technical solution of the present invention is:

[0007] A method for approaching a space target based on multi-objective optimization and particle swarm algorithm, comprising:

[0008] Establish a multi-objective optimization model according to the requirements of the space target approaching mission;

[0009] Define the constraints;

[0010] Design a fitness function based on the constraints and task requirements;

[0011] Initialize the particle swarm: Set the size of the particle swarm and initialize the velocity and position of the particles;

[0012] Calculate the fitness function;

[0013] Update the particle swarm: Update the velocity and position of each particle through the iterative process of the particle swarm optimization algorithm;

[0014] Evaluate the objective function;

[0015] Process the constraints;

[0016] Iterate until the termination condition is met;

[0017] Output the optimization result: After multiple iterations, output the optimal orbit transfer strategy corresponding to the globally optimal position.

[0018] In a specific embodiment, the multi-objective optimization model includes the following sub-objectives: fuel consumption F1, approach time F2, illumination condition F3, proximity to the target position accuracy F4, mission execution time F5, mission execution time interval F6.

[0019] In a specific embodiment, the objective function expression of the multi-objective optimization model is:

[0020] J = ω1minF1 + ω2minF2 + ω3F3 + ω4F4 + ω5F5 + ω6F6

[0021] Where ω1, ω2, ω2, ω3, ω4, ω5, ω6 are the weight coefficients of fuel consumption F1, approach time F2, illumination condition F3, proximity to the target position accuracy F4, mission execution time F5, mission execution time interval F6, respectively.

[0022] In a specific embodiment, the constraints include the following sub-constraints: time constraint, fuel constraint, illumination constraint, terminal constraint, dynamic constraint.

[0023] In a specific embodiment, the fitness function is

[0024] f = ω1minF1 + ω2minF2 + ω3F3 + ω4F4 + ω5F5 + ω6F6 + P1 + P2 +

[0025] P3 + P4,

[0026] Among them, P1 is the penalty value dynamically added after exceeding the time constraint, P2 is the penalty value dynamically added after exceeding the fuel constraint, P3 is the penalty value dynamically added after exceeding the illumination constraint, and P4 is the penalty value dynamically added after exceeding the terminal constraint.

[0027] In a specific embodiment, the penalty value is:

[0028]

[0029] In a specific embodiment, the space target approaching method based on multi-objective optimization and particle swarm algorithm further includes individual optimal initialization and global optimal initialization. Initialize the individual optimal position as the initial position of each particle, and initialize the global optimal position g best as the one with the minimum objective function value among the individual optimal positions of all particles.

[0030] In a specific embodiment, updating the particle swarm includes:

[0031] Velocity update: According to the velocity update formula of the particle swarm optimization algorithm, update the velocity vector of each particle. The expression is as follows:

[0032] v i (k + 1) = w·v i (k) + c1·r1·(p best,i ―x i (k)) + c2·r2·(g best ―x i (k))

[0033] Among them, w is the inertia weight, which controls the inertial motion of the particle; c1 is the learning factor representing the individual learning ability, and c2 is the learning factor representing the group learning ability; r1 and r2 are random numbers between [0, 1], which introduce randomness to enhance the global search ability of the algorithm; k represents the current iteration number; v i (k) represents the velocity vector of the i-th particle in the k-th iteration; v i (k + 1) represents the velocity vector of the i-th particle in the k + 1-th iteration; x i (k) represents the position vector of the i-th particle in the k-th iteration; p best,i is the individual optimal position of the i-th particle;

[0034] Position update: According to the updated velocity vector, update the position vector of each particle. The expression is as follows:

[0035] x i (k + 1) = x i (k) + v i (k + 1),

[0036] Among them, xi (k + 1) represents the position vector of the i-th particle in the (k + 1)-th iteration.

[0037] The present invention also provides a device, which includes: one or more processors; a memory for storing one or more programs, and when the one or more programs are executed by the one or more processors, the one or more processors are caused to execute the above-mentioned space target approaching method based on multi-objective optimization and particle swarm algorithm.

[0038] The present invention also provides a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the above-mentioned space target approaching method based on multi-objective optimization and particle swarm algorithm is implemented.

[0039] Beneficial effects: The space target approaching method of the present invention based on multi-objective optimization and particle swarm algorithm can achieve faster approaching than the Hohmann transfer orbit change method, and can save more fuel compared with the Lambert transfer method; it provides more orbit change methods for satellites to perform tasks to meet the task requirements; and has the following advantages:

[0040] Improve calculation efficiency: The particle swarm optimization algorithm has the characteristic of fast convergence and can find the optimal solution in a short time.

[0041] Strong adaptability: It can adapt to different space environments and target characteristics and has good robustness.

[0042] High precision: Through multi-objective optimization, the optimal approaching strategy can be found under the condition of meeting multiple constraint conditions.

[0043] To make the above features and advantages of the invention more obvious and understandable, specific embodiments are hereinafter given and described in detail in conjunction with the accompanying drawings as follows. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a flowchart of the space target approaching method of the present invention based on multi-objective optimization and particle swarm algorithm.

[0045] Figure 2 is Figure 1 The flowchart of step S6 in DETAILED DESCRIPTION OF THE EMBODIMENTS

[0046] To make the objectives and technical solutions of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the described embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

[0047] Figure 1 Flowchart of the space target approaching method based on multi-objective optimization and particle swarm algorithm of the present invention. Figure 1 As shown, the space target approaching method based on multi-objective optimization and particle swarm algorithm includes steps S1 to S10.

[0048] Step S1, establishing a multi-objective optimization model according to the requirements of the space target approach mission.

[0049] Furthermore, the multi-objective optimization model includes the following sub-objectives:

[0050] Fuel consumption F1: Minimize the amount of fuel required during the approach process. Fuel consumption F1 is expressed as the sum of speed pulses.

[0051] Approach time F2: Minimize the total time required to reach the target position from the initial position

[0052] Lighting condition F3: Maximize the proportion of time spent in a well-lit corridor during the approach process.

[0053] Approach target position accuracy F4: Minimize the final relative distance between the approaching spacecraft and the target spacecraft.

[0054] Task execution time F5: The total time required to execute the task, such as the minimum time required to execute a task.

[0055] Task execution time interval F6: satisfies the start time and end time restricted by task execution.

[0056] According to the above sub-objectives, the objective function of the multi-objective optimization model is determined as:

[0057] J=ω1minF1+ω2minF2+ω3F3+ω4F4+ω5F5+ω6F6

[0058] Wherein, ω1, ω2, ω3, ω4, ω5, ω6 are weight coefficients of fuel consumption F1, approach time F2, illumination condition F3, target position accuracy F4, task execution time F5, and task execution time interval F6, respectively. The sum of the weight coefficients is 1.

[0059] Optionally, the weight coefficient may be assigned according to the user's subjective wishes.

[0060] Optionally, the priority of each sub-goal may be determined according to task requirements, thereby determining each weight coefficient.

[0061] In a specific embodiment, when the target is far from the spacecraft, the top priority of the spacecraft is to approach the target while minimizing fuel consumption as much as possible and ensuring the successful execution of the mission. At this time, the priority ranking is the approaching target position accuracy F4, fuel consumption F1, approaching time F2, mission execution time F5, mission execution time interval F6, and illumination condition F3. The corresponding weights can be set in descending order according to the actual situation. For example, the corresponding weights can be assigned as ω4 = 0.32, ω1 = 0.3, ω2 = 0.15, ω5 = 0.1, ω6 = 0.08, ω3 = 0.05.

[0062] In a specific embodiment, when the target is close to the spacecraft and within the mission execution distance range, the top priority of the spacecraft is to ensure the mission execution time. At this time, the priority ranking is the mission execution time F5, mission execution time interval F6, fuel consumption F1, illumination condition F3, approaching target position accuracy F4, and approaching time F2. The corresponding weights can be set in descending order according to the actual situation. For example, the corresponding weights can be assigned as ω5 = 0.32, ω6 = 0.3, ω1 = 0.15, ω3 = 0.1, ω4 = 0.08, ω2 = 0.05.

[0063] Furthermore, the weight coefficients corresponding to each mission requirement can be set in advance. When using the space target approaching method based on multi-objective optimization and particle swarm algorithm of the present invention for space target approaching, the corresponding weight coefficients can be directly called according to the mission requirements and input into the multi-objective optimization model to construct the objective function.

[0064] Step S2, define the constraint conditions.

[0065] Furthermore, the constraint conditions include the following sub-constraints:

[0066] Time constraint: The start time and end time of approaching do not exceed the preset time range limit.

[0067] Fuel constraint: The magnitude of each velocity pulse does not exceed the preset maximum value.

[0068] Illumination constraint: The angle between the position vector of the spacecraft and the direction vector of the sun connection line of the target spacecraft during the approaching process does not exceed the preset maximum value.

[0069] Terminal constraint: At the end of approaching, the relative position and relative velocity of the spacecraft satisfy the preset terminal conditions.

[0070] Dynamic constraint: The space target and the spacecraft satisfy the orbital dynamics equation.

[0071] Step S3, design the fitness function based on the constraint conditions and mission requirements.

[0072] Among them, the fitness function is

[0073] f = ω1minF1 + ω2minF2 + ω3F3 + ω4F4 + ω5F5 + ω6F6 + P1 + P2 +

[0074] P3 + P4, where P1 is the penalty value dynamically added after exceeding the time constraint, P2 is the penalty value dynamically added after exceeding the fuel constraint, P3 is the penalty value dynamically added after exceeding the illumination constraint, and P4 is the penalty value dynamically added after exceeding the terminal constraint.

[0075] Due to the constraints of the spacecraft's maneuverability and illumination conditions, and being affected by the mission time and position limitations, it is absolutely not allowed outside the constraint range. For example, under the constraint of maneuverability, the maximum increment of speed will not exceed the maximum allowable value. Another example is that completing the mission beyond the specified end time can be considered a failure of the mission execution. Therefore, all infeasible solutions are directly rejected by the way of death penalty without exploring the infeasible region. Therefore, the defined penalty values are:

[0076]

[0077] Step S4, initialize the particle swarm: Set the scale of the particle swarm and initialize the velocity and position of the particles.

[0078] Among them, each particle represents a possible orbit transfer strategy, the position of the particle represents the orbit transfer parameters, and the velocity of the particle represents the change rate of the orbit transfer parameters.

[0079] Furthermore, setting the scale of the particle swarm includes setting the number of particles as i.

[0080] Furthermore, step S4 includes particle representation, specifically including representing each particle as a solution vector containing the key parameters in the approach mission, including the number of velocity pulses and the moment, magnitude, and direction of each pulse. For example, the position vector x of the i-th particle i = [t i1 , Δv i1 , θ i1 , t i2 , Δv i2 , θ i2 , ……, t ij , Δv ij , θ ij , where j represents the number of velocity pulses, t ij represents the moment of the j-th velocity pulse of the i-th particle, Δv ij represents the magnitude of the j-th velocity pulse of the i-th particle, and θ ij represents the direction of the j-th velocity pulse of the i-th particle.

[0081] Further, initialize the velocity of the particles, specifically including initializing the velocity vector v of the particles i1 randomly, and its range is set according to the physical constraints of the task. For example, the range of the velocity pulse magnitude can be set to [0, Δv max , and the direction range is [0, 2π], where Δv max is the maximum value of the velocity pulse.

[0082] Further, initialize the positions of the particles, specifically including initializing the position vector x of the i-th particle i randomly within the feasible solution space to ensure that the time constraint and fuel constraint are satisfied.

[0083] Further, step S4 also includes individual best initialization and global best initialization, specifically including initializing the individual best position as the initial position of each particle, and initializing the global best position g best as the one with the minimum objective function value among the individual best positions of all particles.

[0084] Step S5, calculate the fitness function.

[0085] More specifically, the fitness function is used to evaluate the quality of the orbit transfer strategy represented by each particle.

[0086] Step S6, update the particle swarm: update the velocity and position of each particle through the iterative process of the particle swarm optimization algorithm.

[0087] Further, referring to Figure 2 , step S6 specifically includes:

[0088] Step S61, velocity update: update the velocity vector of each particle according to the velocity update formula of the particle swarm optimization algorithm, and the expression is as follows:

[0089] v i (k + 1) = w·v i (k) + c1·r1·(p best,i ―x i (k)) + c2r2·(g best ―x i (k))

[0090] where w is the inertia weight, which controls the inertial motion of the particles; c1 is the learning factor representing the individual learning ability, c2 is the learning factor representing the group learning ability; r1 and r2 are random numbers between [0, 1], which introduce randomness to enhance the global search ability of the algorithm; k represents the current iteration number; v i (k) represents the velocity vector of the i-th particle in the k-th iteration; v i(k + 1) represents the velocity vector of the i-th particle in the (k + 1)-th iteration; x i (k) represents the position vector of the i-th particle in the k-th iteration; p best,i is the individual optimal position of the i-th particle.

[0091] Step S62, position update: According to the updated velocity vector, update the position vector of each particle, and the expression is as follows:

[0092] x i (k + 1) = x i (k) + v i (k + 1),

[0093] where x i (k + 1) represents the position vector of the i-th particle in the (k + 1)-th iteration.

[0094] Furthermore, step S6 further includes performing a boundary check on the updated position to ensure that the constraint conditions are satisfied. If it exceeds the boundary, adjust the position of the particle to the boundary or randomly generate it again.

[0095] Step S7, evaluate the objective function.

[0096] More specifically, calculate the value of the objective function according to the formula in step S1 for the position vector of each current particle.

[0097] Step S8, handle the constraint conditions.

[0098] For particles that do not satisfy the constraint conditions, use penalty values or repair strategies. For example, for particles that exceed the fuel constraint, increase their penalty values to increase the fitness function; for particles that do not satisfy the illumination constraint, adjust the velocity pulse time or direction to make them satisfy the illumination conditions as much as possible.

[0099] Step S9, iterate until the termination condition is satisfied.

[0100] More specifically, determine whether the termination condition is satisfied. If the termination condition is satisfied, output the global optimal position g best and the corresponding value of the objective function; otherwise, return to step S4 to continue the iteration. Among them, the global optimal position g best is the one with the minimum value of the objective function among the individual optimal positions of all particles.

[0101] In a specific embodiment, the termination condition can be a preset maximum number of iterations K max , when the maximum number of iterations K max is reached, then output the global optimal position g best and the corresponding value of the objective function; otherwise, return to step S4 to continue the iteration.

[0102] In a specific embodiment, the termination condition may be the convergence of the value of the objective function, that is, in several consecutive iterations, the change in the global optimal position g best is less than a preset threshold ∈, then the termination condition is satisfied, and the global optimal position g best and the value of the corresponding objective function are output; otherwise, return to step S4 to continue the iteration.

[0103] Step S10, output the optimization result: After multiple iterations, output the global optimal position g best corresponding optimal orbit transfer strategy. Among them, the orbit transfer strategy includes parameters such as the number of pulses, the time of each orbit transfer, the velocity increment of each orbit transfer, the start time of task execution, the end time of task execution, etc.

[0104] Optionally, the space target approaching method based on multi-objective optimization and particle swarm algorithm of the present invention further includes, in practical applications, setting parameters such as the scale of the particle swarm, the number of iterations, the inertia weight, etc. according to specific task requirements, and setting constraint parameters such as the six orbital elements of the target and the spacecraft, the constraints of the spacecraft propulsion system, the payload capacity, the start time and end time of the task limit, the duration of task execution, etc.

[0105] Optionally, the space target approaching method based on multi-objective optimization and particle swarm algorithm of the present invention further includes verifying the optimization result through simulation software to ensure that the spacecraft can successfully approach the target according to the calculated orbit transfer strategy and can perform tasks for a specified time.

[0106] Optionally, the space target approaching method based on multi-objective optimization and particle swarm algorithm of the present invention further includes applying the optimization algorithm to an actual space target approaching task and adjusting the orbit transfer parameters of the spacecraft in real time to cope with the dynamically changing environment.

[0107] The present invention also provides a device, which includes: one or more processors; a memory for storing one or more programs, and when the one or more programs are executed by the one or more processors, the one or more processors execute the above-mentioned space target approaching method based on multi-objective optimization and particle swarm algorithm.

[0108] The present invention also provides a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the above-mentioned space target approaching method based on multi-objective optimization and particle swarm algorithm is implemented.

[0109] It should be understood that although the steps in the flowchart of the accompanying drawings are shown sequentially as indicated by the arrows, these steps are not necessarily executed sequentially in the order indicated by the arrows. Unless otherwise clearly stated in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, at least a part of the steps in the accompanying drawings may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed alternately or in turn with at least a part of other steps or sub-steps or stages of other steps.

[0110] Although the present invention has been disclosed as above by way of examples, it is not intended to limit the present invention. Any person having ordinary knowledge in the technical field to which the present invention pertains may make some modifications and refinements without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be subject to that defined by the appended patent application scope.

Claims

1. A space target approach method based on multi-objective optimization and particle swarm algorithm, characterized in that: include, According to the requirements of the space target approach mission, a multi-objective optimization model is established; Define constraints; Design fitness functions based on constraints and task requirements; Initialize particle swarm: set the size of particle swarm, initialize particle speed and position; Calculate the fitness function; Update particle swarm: Update the speed and position of each particle through the iterative process of particle swarm optimization algorithm; Evaluate the objective function; Dealing with constraints; Iterate until the termination condition is met; Output optimization results: After multiple iterations, the optimal track change strategy corresponding to the global optimal position is output.

2. The space target approach method based on multi-objective optimization and particle swarm algorithm as claimed in claim 1, characterized in that: The multi-objective optimization model includes the following sub-objectives: fuel consumption F1, approach time F2, lighting conditions F3, approach target position accuracy F4, task execution time F5, and task execution time interval F6.

3. The space target approach method based on multi-objective optimization and particle swarm algorithm as claimed in claim 2, characterized in that: The objective function expression of the multi-objective optimization model is: J=ω1minF1+ω2minF2+ω3F3+ω4F4+ω5F5+ω6F6 Where ω1, ω2, ω3, ω4, ω5, and ω6 are the weight coefficients of fuel consumption F1, approach time F2, illumination condition F3, target position accuracy F4, task execution time F5, and task execution time interval F6, respectively.

4. The space target approach method based on multi-objective optimization and particle swarm algorithm as claimed in claim 3, characterized in that: The constraint conditions include the following sub-constraints: time constraint, fuel constraint, light constraint, terminal constraint, and dynamic constraint.

5. The space target approach method based on multi-objective optimization and particle swarm algorithm as claimed in claim 4, characterized in that: Also included is that the fitness function is f=ω1minF1+ω2minF2+ω3F3+ω4F4+ω5F5+ω6F6+P1+P2+ P3+P4, Among them, P1 is the penalty value dynamically added after exceeding the time constraint, P2 is the penalty value dynamically added after exceeding the fuel constraint, P3 is the penalty value dynamically added after exceeding the light constraint, and P4 is the penalty value dynamically added after exceeding the terminal constraint.

6. The space target approach method based on multi-objective optimization and particle swarm algorithm as claimed in claim 5, characterized in that: The penalty values ​​are:

7. The space target approach method based on multi-objective optimization and particle swarm algorithm as claimed in claim 6, characterized in that: Individual optimal initialization and global optimal initialization, initializing the individual optimal position as the initial position of each particle, initializing the global optimal position g best It is the individual optimal position of all particles with the smallest objective function value.

8. The space target approach method based on multi-objective optimization and particle swarm algorithm as claimed in claim 7, characterized in that: Update the particle swarm, including: Speed ​​update: According to the speed update formula of the particle swarm optimization algorithm, the speed vector of each particle is updated. The expression is as follows: v i (k+1)=w·v i (k)+c1·r1·(p best,i ―x i (k))+c2·r2·(g best ―x i (k)) Where w is the inertia weight, which controls the inertial motion of the particle; c1 is the learning factor representing the individual learning ability, and c2 is the learning factor representing the group learning ability; r1 and r2 are random numbers between [0,1], which introduce randomness to enhance the global search ability of the algorithm; k represents the current number of iterations; v i (k) represents the velocity vector of the i-th particle in the k-th iteration; v i (k+1) represents the velocity vector of the i-th particle in the k+1-th iteration; x i (k) represents the position vector of the i-th particle in the k-th iteration; p best,i is the individual optimal position of the i-th particle; Position update: Update the position vector of each particle according to the updated velocity vector. The expression is as follows: x i (k+1)=x i (k)+v i (k+1), Among them, x i (k+1) represents the position vector of the i-th particle in the k+1-th iteration.

9. A device, characterized in that: The device includes: one or more processors; and a memory for storing one or more programs. When the one or more programs are executed by the one or more processors, the one or more processors execute the space target approach method based on multi-objective optimization and particle swarm algorithm as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the space target approach method based on multi-objective optimization and particle swarm algorithm as described in any one of claims 1 to 8 is implemented.

Images