Low-orbit constellation multi-drift orbit collaborative deployment method and system based on multi-strategy adaptive optimization

Abstract

The invention discloses a low orbit constellation multi-drift orbit collaborative deployment method and system based on multi-strategy adaptive optimization. Dividing satellites which are launched at a time into a direct deployment batch, a medium drift orbit deployment batch and a low drift orbit deployment batch according to the target orbit parameters and the number of the satellites; an integrated optimization model of carrier rocket performance, drift orbit design, satellite thrust maneuver and in-plane phase separation is constructed, initial separation height, low drift orbit height and medium drift orbit height are taken as decision variables, and minimization of total deployment time, minimization of total fuel consumption and maximization of carrier rocket utilization rate are taken as targets. A Pareto optimal solution set is obtained by adopting a multi-strategy adaptive non-dominated sorting genetic algorithm, and an optimal deployment scheme is selected through a sorting method based on an ideal solution, so that parallel collaborative deployment of multiple drift orbits is realized, the constellation networking period is remarkably shortened, the fuel consumption is reduced, and the single-time launching carrying efficiency and the overall constellation networking benefit are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of satellite constellation deployment technology, and in particular to a method and system for collaborative deployment of low Earth orbit constellations with multiple drift orbits based on multi-strategy adaptive optimization. Background Technology

[0002] The rapid development of the Low Earth Orbit (LEO) constellation has placed extremely high demands on satellite deployment efficiency. Deploying dozens of satellites to multiple different orbital planes in a single launch can significantly reduce launch costs and shorten the constellation deployment cycle. In large-scale constellation deployment missions, multiple factors need to be comprehensively considered, including launch vehicle performance constraints, orbital plane separation strategies, satellite thrust maneuverability, and fuel consumption. Adopting a reasonable deployment strategy can significantly improve the economy and timeliness of constellation deployment.

[0003] Existing deployment methods based on a single drift orbit employ a sequential deployment approach, where all satellites remain in the same drift orbit for varying durations to achieve orbital separation. This results in deployment cycles that can last for months or even years. Furthermore, due to the strong coupling between launch vehicle capability and separation altitude, and the interplay between drift orbit design and satellite maneuvering strategies, optimizing a single component is unlikely to yield a globally optimal solution. Simultaneously, considering the complex multi-objective conflicts between deployment time, fuel consumption, and launch efficiency, traditional optimization methods struggle to obtain high-quality Pareto optimal solutions within a reasonable timeframe. Therefore, more efficient multi-objective optimization algorithms are needed to achieve better overall performance.

[0004] Current research on constellation deployment optimization mainly employs serial deployment with a single drift orbit. The optimization model fails to integrate multiple factors such as launch capacity, drift orbit design, satellite maneuvering, and phase separation. Furthermore, standard multi-objective evolutionary algorithms suffer from poor convergence and low solution quality when dealing with strongly constrained high-dimensional problems. An effective methodology has yet to be established for global optimization design in scenarios of rapid deployment of large-scale constellations. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for collaborative deployment of multiple drift orbits of low-Earth orbit constellations based on multi-strategy adaptive optimization, so as to solve the problems of long deployment time, high fuel consumption, low deployment efficiency and lack of global optimization design in the prior art.

[0006] To achieve the above objectives, this invention provides a method for collaborative deployment of multiple drift orbits in a low-Earth orbit constellation based on multi-strategy adaptive optimization, comprising the following steps:

[0007] Step 1: Based on the target constellation parameters, divide the satellites to be deployed into three batches: direct deployment batch, medium drift orbit deployment batch, and low drift orbit deployment batch;

[0008] Step 2: Establish an integrated optimization model, wherein the decision variables of the model include the initial separation height, the low drift trajectory height, and the medium drift trajectory height;

[0009] Step 3: Set optimization objectives, including minimizing deployment time, minimizing fuel consumption, and maximizing capacity utilization;

[0010] Step 4: Solve the optimization model using a multi-objective optimization algorithm to obtain the Pareto optimal solution set;

[0011] Step 5: Select the optimal solution from the Pareto optimal solution set and execute the deployment.

[0012] Preferably, in step 1, the satellites in the direct deployment batch climb directly from the initial separation orbit to the target working orbit; the satellites in the medium drift orbit deployment batch first climb to the medium drift orbit and stay there, then use J2 perturbation to adjust the right ascension of the ascending node before climbing to the target working orbit; the satellites in the low drift orbit deployment batch first climb to the low drift orbit and stay there, then use J2 perturbation to adjust the right ascension of the ascending node before climbing to the target working orbit.

[0013] Preferably, in step 2, establishing the integrated optimization model specifically includes: a launch vehicle capability model to calculate the maximum effective payload corresponding to the initial separation altitude; an ascending node right ascension drift model to calculate the ascending node right ascension drift rate and dwell time corresponding to different drift orbit altitudes; an orbital maneuver model to calculate the time and fuel consumption required for the satellite to transfer between orbits; and a phase separation model to calculate the time and fuel consumption required for the satellite to adjust its phase within the orbital plane.

[0014] Preferably, in the ascending node right ascension drift model, the formula for calculating the ascending node right ascension drift rate is:

[0015]

[0016] Where J2 is the Earth's second-order zonal harmonic coefficient, R E Let be the Earth's equatorial radius, μ be the Earth's gravitational constant, i be the orbital inclination, and a be the semi-major axis of the orbit. The formula for calculating the dwell time in a low-drift orbit is:

[0017]

[0018] Where ΔΩ is the difference in right ascension between the target ascending nodes. For the right ascension drift rate of the ascending node of the low drift orbit, The right ascension drift rate of the ascending node of the target working orbit.

[0019] Preferably, in the track maneuvering model, the formula for calculating the track climb time is:

[0020]

[0021] Where m0 is the initial mass of the satellite, For the thruster mass flow rate, F t Δv is the thrust, λ is the correction factor, and Δv is the thrust. climb This represents the speed increment required for track climbing.

[0022] Preferably, in step 3, the objective function for optimization is:

[0023] Minimize total fuel consumption:

[0024] Minimize deployment time: f2(X) = max T(X);

[0025] Maximize capacity utilization:

[0026] Where, X = [h sep h low h mid ] T h is the decision variable. sep h is the initial separation height. low For low drift track height, h mid The height of the drift track.

[0027] Preferably, in step 4, a non-dominated sorting genetic algorithm based on multi-strategy adaptive algorithm is used to solve the problem. The algorithm includes the following steps:

[0028] Step 41: Introduce a dynamic switching mechanism between the adaptive differential evolution operator and the simulated binary crossover and polynomial mutation operators;

[0029] Step 42: Use a dynamic penalty function strategy to handle constraints;

[0030] Step 43: Introduce an adaptive reference point adjustment mechanism to dynamically adjust the distribution of reference points.

[0031] Preferably, in step 41, the operator switching probability is:

[0032]

[0033] Where p0 is the initial probability, t is the current iteration number, and G max This represents the maximum number of iterations.

[0034] Preferably, step 5, which uses the approximation of the ideal solution sorting method to select the optimal solution, specifically includes the following steps:

[0035] Step 51: Construct and normalize the decision matrix;

[0036] Step 52: Set weights and determine positive and negative ideal solutions according to task requirements;

[0037] Step 53: Calculate the relative similarity of each scheme and select the scheme with the highest similarity.

[0038] Preferably, in step 53, the relative similarity of the solutions is as follows:

[0039]

[0040] in, Let be the Euclidean distance from the solution to the positive ideal solution. The Euclidean distance from the proposed solution to the negative ideal solution is used to select the solution with the highest relative proximity as the optimal deployment solution.

[0041] This invention also provides a low-Earth orbit constellation multi-drift orbit collaborative deployment system based on multi-strategy adaptive optimization, comprising: a batch division module, used to divide the satellites to be deployed into direct deployment batches, medium-drift orbit deployment batches, and low-drift orbit deployment batches according to the target constellation parameters; a model building module, used to build an integrated optimization model including the initial separation altitude, low-drift orbit altitude, and medium-drift orbit altitude; an objective setting module, used to set optimization objectives of minimizing deployment time, minimizing fuel consumption, and maximizing payload utilization; an optimization solution module, used to solve the optimization model using a multi-objective optimization algorithm to obtain a Pareto optimal solution set; and a scheme decision module, used to select the optimal scheme from the Pareto optimal solution set and generate deployment instructions.

[0042] The beneficial effects of this invention are as follows: It significantly shortens deployment time by introducing multiple drift orbits to allow deployment processes on different orbital planes to proceed in parallel, reducing the total deployment time by more than 15% compared to a single drift orbit serial deployment method; it effectively saves fuel consumption by primarily utilizing natural orbital perturbations to achieve orbital plane separation, avoiding energy-intensive high-angle orbital maneuvers, and balancing fuel consumption between orbital ascent and drift waiting through global optimization; it improves deployment efficiency and economy by tightly coupling rocket carrying capacity with separation altitude and drift orbit design through an integrated optimization model, maximizing the number of satellites that can be carried in a single launch while meeting the requirements of rapid deployment and low fuel consumption; and it provides a systematic global optimization scheme, offering a systematic design method from modeling and optimization to decision-making, capable of globally weighing multiple complex factors and outputting a Pareto optimal solution set for decision-makers to choose from. Attached Figure Description

[0043] Figure 1 This is a block diagram illustrating the operation of the present invention.

[0044] Figure 2 This is a schematic diagram illustrating the satellite constellation deployment strategy based on multiple drift orbits provided by the present invention.

[0045] Figure 3 This is a flowchart of the non-dominated sorting genetic algorithm based on multi-strategy adaptive algorithm used in this invention. Detailed Implementation

[0046] like Figure 1 As shown, a method for collaborative deployment of multiple drift orbits in a low-Earth orbit constellation based on multi-strategy adaptive optimization includes the following steps:

[0047] Step 1: Based on the target constellation parameters, divide the satellites to be deployed into three batches: direct deployment batch, medium-drift orbit deployment batch, and low-drift orbit deployment batch; specifically including the following steps:

[0048] Step 11: Obtain the orbital parameters of the target constellation, including the target working orbit altitude, orbital inclination, number of orbital planes, and number of satellites in each orbital plane.

[0049] Step 12: Divide the satellites to be deployed into at least three batches based on the number of orbital planes, with each batch corresponding to a specific drift orbit strategy. Satellites in the direct deployment batch will climb directly from the initial separation orbit to the target working orbit; satellites in the medium drift orbit deployment batch will first climb to the medium drift orbit and stay there, then use the J2 perturbation to adjust the right ascension of the ascending node before climbing to the target working orbit; satellites in the low drift orbit deployment batch will first climb to the low drift orbit and stay there, then use the J2 perturbation to adjust the right ascension of the ascending node before climbing to the target working orbit.

[0050] Step 2: Establish an integrated optimization model, wherein the decision variables of the model include the initial separation height, the low drift trajectory height, and the medium drift trajectory height; specifically including:

[0051] (a) Launch vehicle capability model, calculating the maximum payload corresponding to the initial separation altitude. The launch vehicle's payload capacity is closely related to the satellite's initial separation altitude; the higher the separation altitude, the lower the payload capacity.

[0052] (b) Ascending node right ascension drift model: Calculate the drift rate and dwell time of the ascending node right ascension at different drift orbital altitudes. In near-Earth orbit, the long-term drift of the ascending node right ascension caused by the Earth's oblateness J2 perturbation is the main influence, and its drift rate can be approximated by the following formula:

[0053]

[0054] Where J2 is the Earth's second-order zonal harmonic coefficient, R E Let be the Earth's equatorial radius, μ be the Earth's gravitational constant, i be the orbital inclination, and a be the orbital semi-major axis; the formula for calculating the dwell time in a low-drift orbit is:

[0055]

[0056] Where ΔΩ is the difference in right ascension between the target ascending nodes. For the right ascension drift rate of the ascending node of the low drift orbit, Let be the right ascension drift rate of the ascending node of the target working orbit. Similarly, the dwell time of the drifting batch can be calculated.

[0057] (c) Orbital maneuvering model: Calculates the time and fuel consumption required for the satellite to move between different orbits. The formula for calculating orbital climb time is:

[0058]

[0059] Where m0 is the initial mass of the satellite, For the thruster mass flow rate, F t Δv is the thrust, λ is the correction factor, and Δv is the thrust. climb This represents the speed increment required for track climbing.

[0060] (d) Phase separation model, calculates the time and fuel consumption required for satellite phase adjustment within the orbital plane.

[0061] Step 3: Set optimization objectives, including minimizing deployment time, minimizing fuel consumption, and maximizing capacity utilization; specifically including the following steps:

[0062] Step 31: Define the objective function to minimize total fuel consumption, and calculate the total mass of propellant consumed by all satellites during all orbital maneuvers:

[0063]

[0064] Where, Δm i,j (X) represents the total fuel consumption of the j-th satellite in the i-th orbital plane.

[0065] Step 32: Define the objective function to minimize the total deployment time of the constellation, taking the total time spent by the last satellite to be deployed out of all satellites:

[0066] f2(X) = maxT(X);

[0067] Step 33: Define the objective function for maximizing launch vehicle utilization, which is the ratio of the total mass of the satellite in a single launch to the maximum effective payload of the launch vehicle at that separation altitude:

[0068]

[0069] Where, X = [h sep h low h mid ] T h is the decision variable. sep h is the initial separation height. lowFor low drift track height, h mid The altitude is the mid-drift orbit. Q represents the total number of satellites, in meters. sat For single-star dry weight, M payload This is the rocket's maximum effective payload.

[0070] Step 4: Solve the optimization model using a multi-objective optimization algorithm to obtain the Pareto optimal solution set; specifically including the following steps:

[0071] Step 41: Introduce a dynamic switching mechanism between the adaptive differential evolution operator and the simulated binary crossover and polynomial mutation operators. Set the operator switching probability that varies with the number of iterations:

[0072]

[0073] Where p0 is the initial probability, t is the current iteration number, and G max This represents the maximum number of iterations. In the early stages of evolution, the algorithm tends to use simulated binary crossover / polynomial mutation operators, which have strong global exploration capabilities. As the evolution progresses, the algorithm gradually increases the proportion of adaptive differential evolution operators, which have strong local convergence capabilities.

[0074] Step 42: Apply a dynamic penalty function strategy to handle constraints. A dynamic penalty strategy of early relaxation followed by later tightening is used to apply dynamic penalty terms to the objective function of infeasible individuals:

[0075] F j′ (X)=F j (X)+P(t)·CV(X)

[0076] The penalty factor P(t) increases linearly with the number of iterations t. The penalty is smaller in the early stages of evolution and increases in the later stages, forcing the population to converge quickly to the feasible region.

[0077] Step 43: Introduce an adaptive reference point adjustment mechanism to dynamically adjust the distribution of reference points. The algorithm periodically checks the crowding and improvement status of the solutions associated with each reference point, dynamically inserts new reference points in regions where the solution distribution is sparse and the improvement is significant, and removes redundant reference points in regions where there has been no improvement for a long time or where the solution is too crowded.

[0078] Reference Figure 3 A multi-strategy adaptive non-dominated sorting genetic algorithm is used to search for the Pareto optimal front through iterative evolution, starting from an initial reference point and population. In each generation, the algorithm performs selection, crossover, and mutation operations to generate offspring, then merges the parent and offspring generations for non-dominated sorting and reference point association. Finally, an elite retention strategy is used to select the next generation. Through this improved strategy, a set of Pareto optimal solutions is obtained, representing the optimal trade-off between deployment time, fuel consumption, and carrying capacity under different preferences.

[0079] Step 5: Select the optimal solution from the Pareto optimal solution set and execute the deployment; specifically, this includes the following steps:

[0080] Step 51: Construct and normalize the decision matrix. Assume the Pareto solution set contains m candidate solutions, each with n objective function values, forming an m×n decision matrix. Since the three objectives have different dimensions, the decision matrix first needs to be vector normalized.

[0081] Step 52: Set weights and determine positive and negative ideal solutions according to task requirements. Set a weight vector W = [w1, w2, w3] for the three objectives, and determine the positive and negative ideal solutions based on the weighted normalized matrix.

[0082] Step 53: Calculate the relative proximity of each solution and select the solution with the highest proximity. For each candidate solution, calculate its Euclidean distance to both the positive and negative ideal solutions, and then calculate the relative proximity of each solution:

[0083]

[0084] in, Let be the Euclidean distance from the solution to the positive ideal solution. Let be the Euclidean distance from the proposed solution to the negative ideal solution. Select the solution with the highest relative proximity as the optimal deployment solution and generate deployment instructions for execution.

[0085] like Figure 1 and Figure 2 As shown, a multi-strategy adaptive optimization-based method for the coordinated deployment of multiple drift orbits in a low-Earth orbit constellation includes a three-drift orbit parallel deployment strategy, an integrated optimization modeling method, and a multi-strategy adaptive non-dominated sorting genetic algorithm solution method. The three-drift orbit parallel deployment strategy divides all satellites launched in a single launch into three batches, achieving parallel deployment under three modes: direct climb, medium-drift orbit residence, and low-drift orbit residence. It utilizes the difference in right ascension drift rates at the ascending nodes of different orbital altitudes to achieve rapid orbital plane separation. The integrated optimization modeling method couples and models multiple factors such as launch vehicle performance constraints, drift orbit altitude design, satellite orbital maneuvers, and phase separation, using the initial separation altitude, low-drift orbit altitude, and medium-drift orbit altitude as decision variables, while simultaneously optimizing three objectives: deployment time, fuel consumption, and launch vehicle utilization.

[0086] The three-drift orbit parallel deployment strategy consists of an integrated optimization modeling method and a solution method based on a multi-strategy adaptive non-dominated sorting genetic algorithm. The integrated optimization modeling method constructs a launch vehicle capability model, an ascending node right ascension drift model caused by J2 perturbation, a low-thrust orbit climb model, and an in-plane phase adjustment model. It uses the altitudes of the three drift orbits as decision variables for global optimization, calculating the deployment time and fuel consumption for each batch of satellites, thus providing the objective function calculation basis for the multi-strategy adaptive non-dominated sorting genetic algorithm. The multi-strategy adaptive non-dominated sorting genetic algorithm solution method employs a dynamic switching mechanism between adaptive differential evolution operators and simulated binary crossover / polynomial mutation operators. It emphasizes global search in the early stages of evolution and strengthens local convergence in the later stages. It handles constraints through a dynamic penalty function and uses an adaptive reference point adjustment mechanism to ensure the uniformity of the solution set distribution, ultimately obtaining a Pareto optimal solution set.

[0087] The multi-strategy adaptive non-dominated sorting genetic algorithm solution consists of an adaptive operator switching mechanism, a dynamic constraint handling mechanism, an adaptive reference point adjustment mechanism, and an approximation-ideal-solution sorting method. Specifically, the adaptive operator switching mechanism dynamically adjusts the probability of using the adaptive differential evolution operator and the simulated binary crossover / polynomial mutation operator based on the number of iterations, balancing global exploration and local development capabilities. The dynamic constraint handling mechanism employs an early-loose, later-tight penalty strategy to guide the population to gradually converge to the feasible region. The adaptive reference point adjustment mechanism periodically checks the distribution of solutions, inserting new reference points in sparse regions and removing redundant reference points in crowded regions. The approximation-ideal-solution sorting method selects the best solution from the Pareto optimal solution set as the final deployment decision. This method can significantly shorten the total deployment time in the multi-drift orbit collaborative deployment process, reduce fuel consumption, and improve payload utilization.

Claims

1. A method for collaborative deployment of multiple drift orbits in a low-Earth orbit constellation based on multi-strategy adaptive optimization, characterized in that, Includes the following steps: Step 1: Based on the target constellation parameters, divide the satellites to be deployed into three batches: direct deployment batch, medium drift orbit deployment batch, and low drift orbit deployment batch; Step 2: Establish an integrated optimization model, wherein the decision variables of the model include the initial separation height, the low drift trajectory height, and the medium drift trajectory height; Step 3: Set optimization objectives, including minimizing deployment time, minimizing fuel consumption, and maximizing capacity utilization; Step 4: Solve the optimization model using a multi-objective optimization algorithm to obtain the Pareto optimal solution set; Step 5: Select the optimal solution from the Pareto optimal solution set and execute the deployment.

2. The method according to claim 1, characterized in that, In step 1, the satellites in the direct deployment batch climb directly from the initial separation orbit to the target working orbit; the satellites in the mid-drift orbit deployment batch first climb to the mid-drift orbit and stay there, then use J2 perturbation to adjust the right ascension of the ascending node before climbing to the target working orbit. Satellites deployed in batches to low-drift orbits first climb to a low-drift orbit and remain there. Then, using the J2 perturbation to adjust the right ascension of the ascending node, they climb to the target working orbit.

3. The method according to claim 1 or 2, characterized in that, Step 2, establishing the integrated optimization model specifically includes: a launch vehicle capability model to calculate the maximum payload corresponding to the initial separation altitude; an ascending node right ascension drift model to calculate the ascending node right ascension drift rate and dwell time corresponding to different drift orbit altitudes; an orbital maneuver model to calculate the time and fuel consumption required for the satellite to transfer between orbits; and a phase separation model to calculate the time and fuel consumption required for the satellite to adjust its phase within the orbital plane.

4. The method according to claim 3, characterized in that, In the ascending node right ascension drift model, the formula for calculating the ascending node right ascension drift rate is: Where J2 is the Earth's second-order zonal harmonic coefficient, R E Let be the Earth's equatorial radius, μ be the Earth's gravitational constant, i be the orbital inclination, and a be the orbital semi-major axis; the formula for calculating the dwell time in a low-drift orbit is: Where ΔΩ is the difference in right ascension between the target ascending nodes. For the right ascension drift rate of the ascending node of the low drift orbit, The right ascension drift rate of the ascending node of the target working orbit.

5. The method according to claim 3, characterized in that, In the aforementioned orbital maneuvering model, the formula for calculating the orbital climb time is: Where m0 is the initial mass of the satellite, For the thruster mass flow rate, F t Δv is the thrust, λ is the correction factor, and Δv is the thrust. climb This represents the speed increment required for track climbing.

6. The method according to claim 1, characterized in that, In step 3, the objective function to be optimized is: Minimize total fuel consumption: Minimize deployment time: f2(X) = maxT(X); Maximize capacity utilization: Where, X = [h sep h low h mid T is the decision variable, h sep h is the initial separation height. low For low drift track height, h mid The height of the drift track.

7. The method according to claim 1, characterized in that, In step 4, a non-dominated sorting genetic algorithm based on multi-strategy adaptive algorithm is used to solve the problem. The algorithm includes the following steps: Step 41: Introduce a dynamic switching mechanism between the adaptive differential evolution operator and the simulated binary crossover and polynomial mutation operators; Step 42: Use a dynamic penalty function strategy to handle constraints; Step 43: Introduce an adaptive reference point adjustment mechanism to dynamically adjust the distribution of reference points.

8. The method according to claim 7, characterized in that, In step 41, the operator switching probability is: Where p0 is the initial probability, t is the current iteration number, and G max This represents the maximum number of iterations.

9. The method according to claim 1, characterized in that, Step 5, which uses the approximation of the ideal solution sorting method to select the optimal solution, specifically includes the following steps: Step 51: Construct and normalize the decision matrix; Step 52: Set weights and determine positive and negative ideal solutions according to task requirements; Step 53: Calculate the relative similarity of each scheme and select the scheme with the highest similarity.

10. A method for collaborative deployment of multiple drift orbits in a low-Earth orbit constellation based on multi-strategy adaptive optimization, characterized in that, include: The batch division module is used to divide the satellites to be deployed into direct deployment batches, medium drift orbit deployment batches, and low drift orbit deployment batches according to the target constellation parameters; The model building module is used to build an integrated optimization model that includes the initial separation altitude, low drift trajectory altitude, and medium drift trajectory altitude; the target setting module is used to set optimization targets that minimize deployment time, minimize fuel consumption, and maximize payload utilization. The optimization solution module is used to solve the optimization model using a multi-objective optimization algorithm to obtain a Pareto optimal solution set; the scheme decision module is used to select the optimal scheme from the Pareto optimal solution set and generate deployment instructions.

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