A dynamic programming-game hybrid method for solving satellite cooperative mission scheduling

Abstract

The application discloses a dynamic programming-game hybrid method for solving satellite cooperative task scheduling, introduces a sequence constraint interval dynamic programming and an elite asynchronous updating mechanism on the basis of a traditional game theory cooperative method; a complex single-satellite best response problem is converted into a path optimization problem with side swing maneuver and illumination constraints through the sequence constraint dynamic programming, so that a task sequence with the maximum marginal contribution is obtained to improve the quality of local decision, and the algorithm has the ability to process complex space-time constraints; through the elite node strategy updating mechanism, system shock caused by multi-agent cooperative conflict is greatly reduced to improve the algorithm convergence speed, and the distributed network is more effectively guided to converge to a high-quality Nash equilibrium state; compared with a traditional greedy strategy or a heuristic algorithm, the method has better global optimization performance, the algorithm has faster convergence speed and stronger stability, and the cooperative scheme planned by the method has higher system total income and fewer resource conflicts.

Description

Technical Field

[0001] This invention belongs to the field of satellite mission planning and distributed intelligent optimization technology, specifically involving a dynamic programming-game hybrid method for solving satellite collaborative mission scheduling. Background Technology

[0002] Multi-imaging satellite collaborative mission scheduling is an important research direction in the aerospace field. Satellite mission scheduling requires autonomously coordinating the allocation of observation tasks and windows among multiple imaging satellites under constraints such as orbit and payload, in order to maximize system-level mission benefits. The main problems to be solved include: (1) satisfying complex engineering constraints such as satellite orbit, side angle, illumination, resolution constraints and satellite conversion constraints to ensure mission execution feasibility; (2) realizing satellite autonomous decision-making and coordination in a distributed architecture without central control, avoiding overlapping or omissions in mission allocation; (3) ensuring that the algorithm converges to an efficient Nash equilibrium, improving overall mission benefits while reducing communication overhead and computational complexity. Therefore, when planning, it is necessary to consider not only mission priority, observation window effectiveness, and constraint satisfaction, but also the optimal mission scheduling problem among satellites.

[0003] Multi-satellite mission scheduling is a problem that is based on a feasible schedule and continuously optimized to achieve optimal mission scheduling. This invention uses a distributed cooperative scheduling method combining weighted interval dynamic programming and potential game theory to ensure optimal mission scheduling among satellites while meeting all relevant constraints. Summary of the Invention

[0004] The purpose of this invention is to provide a dynamic programming-game theory hybrid method for solving satellite collaborative mission scheduling. This method can quickly calculate the observation scheme that maximizes the system benefits for multiple imaging satellites in a decentralized control architecture, ensuring that each satellite achieves efficient collaboration and conflict resolution under strict physical constraints.

[0005] To achieve the above objectives, this invention provides the following technical solution: a dynamic programming-game theory hybrid method for solving satellite collaborative task scheduling, with the following specific steps: Preparation: The orbital dynamic parameters (such as yaw conversion speed, minimum startup time), payload parameters (such as resolution, illumination requirements), and the set of tasks to be observed (including visible time windows, original scores, and observation frequency) of all satellites participating in the scheduling are known. Let the number of satellites participating in the scheduling be... The heterogeneous satellite types involved in the scheduling include OPT optical satellites and SAR radar remote sensing satellites. The number of target missions to be observed is [number missing]. The maximum operating time for a single satellite within a single orbit is set as follows: The safe buffer time for attitude transition calculation is The maximum number of iterations for the game theory algorithm is set to... ; Step 1: Read the satellite parameter set, which includes sensor type. SAR / OPT Imaging resolution Minimum boot time and the minimum illumination requirements for optical satellites. Read the observation task set, including the required resolution for the task. Task effective time window interval The task requires observation frequency And the original reward score of the task Read the over-the-top visibility window (hereinafter referred to as window) dataset corresponding to the satellite, which contains the target's mission. ID Window interval for satellite-visible missions Side swing angle and window solar altitude angle ; Step 2: Construct a constraint filter and perform a feasibility check on each window for the following constraints: verify whether the window time meets the minimum satellite startup time. ; Verify if there is any overlap between the window time period and the task requirement time period; Verify the lateral swing angle. Solar altitude angle Imaging resolution Does the physical constraint meet the constraint index? The set of windows that meet the constraints is denoted as the feasibility window set. ; Step 3: Based on the set of feasible windows Construct an adjacency matrix If satellite With satellite If there is at least one common observable task, then the two are defined as neighboring nodes. Step 4: From the feasibility window set Satellites were selected from the middle All executable tasks, and the original profit score Input a dynamic programming function, without considering inter-satellite coordination, for each satellite by Using weights, an interval dynamic programming algorithm with sequence constraints is used to solve for the optimal scheduling sequence for a single satellite, generating an initial sequence set. ,in Indicates the first i The mission execution sequence of a satellite in the t-th iteration; Step 5: Enter the multi-round iteration process, let the current iteration round be... t The maximum number of iterations is In each iteration, perform steps six through ten. Step Six: For each satellite Through the adjacency matrix Obtain the indices of all its neighbors, and use these to deduce its position in the previous sequence set. The task selection status in the data, and statistics for each task. Number of times observed by neighbors Based on the frequency of task requirements Calculate satellite For each window m marginal contribution revenue ; Step 7: Use the marginal contribution revenue from Step 6 Replace all satellites in the previous loop The score is then used to input the new score into the dynamic programming function. Under the premise of satisfying all physical constraints (such as lateral transition time and duty cycle constraints), a new strategy that maximizes local utility is calculated. ; Step 8: Calculate the utility increment resulting from switching the satellite to the new strategy, i.e., the regret value. ; Step Nine: To avoid conflicts caused by multiple agents simultaneously vying for high-priority tasks, an asynchronous update mechanism is adopted; Satellite Regret value Regret value with all its neighbors Compare; only when When the criteria for "elite node" are met, a sequence update is performed on the satellite, i.e. Otherwise, keep the original sequence unchanged, i.e. ; Step 10: Calculate the number of satellites used to update the strategy in this iteration. And the system's global situation function value, i.e., the global total gain. ;like (equivalent to) (or reaching the maximum number of iterations) If the system converges to the Nash equilibrium point, the loop stops; otherwise, the iteration loop continues. Step 11: Output the final joint scheduling sequence set generated after the t-th iteration. and its corresponding total system revenue. .

[0006] Preferably, the formula for checking the minimum power-on time in step two is: (1) In the above formula, , These are the start and end times of the window, respectively. The left side of the equation is the window time plus a 1-second buffer time, and the right side is the minimum power-on time for the satellite. The window validation formula is: (2) In the above formula The effective window range for the task. For satellite-visible missions; Side swing angle The verification formula is: (3) In the above formula and These are the minimum and maximum side-swing angle limits for the satellite, respectively. Solar elevation angle of optical satellites The verification formula is: (4) This is the minimum solar altitude angle requirement for optical satellites; Imaging resolution Verification formula: (5) In the above formula Resolution required for the task.

[0007] Preferably, the elements in the adjacency matrix in step three Defined as: (6) in M i , M j Satellites observable task set; adjacency matrix elements in express There is competition between them, and vice versa.

[0008] Preferably, the dynamic programming part of the interval dynamic programming algorithm with sequence constraints in steps four and seven is executed according to the following sub-steps: S1: Read the currently selected satellite The dynamic parameters are obtained, and the yaw transition time calculated in step one is read. And the maximum boot time limit within a 90-minute interval. Simultaneously set a safety buffer time. =1 s The goal is to enhance the robustness of the algorithm while avoiding the impact of errors caused by computational inaccuracies on the execution process. S2: Extract the set of feasible windows from step two. The window data in the middle, which corresponds to each window m The key attribute representation method is as follows: Start Time End time Side swing angle And the original reward score (weight) for the task. ; S3: Calculate all feasible windows based on their start time. Sort the windows in ascending order, and denote the resulting window sequence combination as follows: ,in For the first m There are 10 windows, and the total number of windows is 1. M； S4: Define an array The purpose is to force the selection of the first [item] while satisfying timing and physical constraints. m The maximum total reward score accumulated by the path when an observation window is used as the end of the current task sequence; Define For the first m The index of the predecessor node of each window on the optimal path; when initializing the state array, for all ,make , ; S5: First, set the outer loop, setting the loop parameter... m from Traversal to , indicating the current target task; the inner loop is set to Reverse traversal to Set a counter As a precursor task check count, when At this time, the inner loop is forcibly exited, thereby reducing the algorithm complexity through a pruning strategy. It is the dynamic programming pruning threshold; S6: Perform a conversion time constraint check for each group. First calculate its own time interval. and the change in lateral sway angle Then, the following judgment is made: If If the condition is determined to be physically overlapping and does not meet the constraints, skip it; otherwise, calculate... Corresponding conversion time If the conditions are met Then determine the task. n As m The precursor mission is feasible; in, Corresponding conversion time The calculation formula is: (7) In the above formula It is the settling time after the conversion. It is the angular velocity of the satellite's side-slip conversion; S7: Select the set of predecessor tasks deemed feasible in S6, variables Store the historical maximum return, iterate through the elements in the set, and if the current predecessor... n satisfy Then update the current maximum predecessor benefit. and Best Front-Drive Index Finally, all The maximum benefit of the forerunner is corresponding to ; S8: When the inner loop ends, update the current task's cumulative maximum reward based on the currently recorded maximum predecessor reward. ;then the outer loop variable Increment the value and continue calculating the state of the next task until the outer loop has traversed all tasks. One window; S9: Traversal DP Find the index of the maximum value in the array .from Beginning, with For the index, recursively backtrack the predecessor node until... Store the window index corresponding to the backtracking path into the candidate set. ; S10: Map tasks to a fixed 90-minute (5400-second) time interval based on their start time. In, based on the start time Calculate the time interval index ; S11: Index Iterate through all non-empty intervals and calculate the value of each interval. Total execution time of the selected task If a certain interval Then, starting from the last task in that interval, tasks are removed sequentially in reverse order until... This ensures that the maximum operating time of the satellite within a 90-minute interval does not exceed [the specified limit]. ; S12: Mark the final task set after processing in S11 as selected, and sum the scores of each interval to obtain the total score. The optimal response of the satellite in this iteration is denoted as... , a This is the observation window that is marked as selected.

[0009] Preferably, in step six, for each window m marginal revenue The calculation formula is as follows: (8) In the above formula, This represents the current number of observations. The cumulative reward function for a task represents the cumulative reward for that task. l Observed by the whole system The total value after that, The calculation formula is as follows: (9) In the above formula, For the required number of observations, This represents the original score reward for the task.

[0010] Preferably, the regret value in step eight The calculation formula is: (10) In the above formula, For the first i The sequence of satellites in the 1st t The total marginal utility at the next iteration is calculated using the following formula: (11) In the above formula, For window m The corresponding boundary benefits of the current satellite.

[0011] Preferably, in step nine, the update formula for "elite nodes" is as follows: (12) In the above formula, Indicates the first t Satellite after round of iteration i The final strategy adopted and For satellite and The regret value corresponding to the sequence, For satellite The corresponding set of neighbor indexes.

[0012] Preferably, in step ten, the formula for calculating the global situation function is: (13) in L This represents the total number of tasks in the entire system. This indicates the task being performed during this iteration. lThe maximum number of observations, summed by the cumulative rewards of all tasks, gives the overall situation function. .

[0013] Compared with the prior art, the beneficial effects of the present invention are: This invention proposes a distributed multi-satellite collaborative task scheduling method based on an exact potential game model and a sequence-constrained interval dynamic programming algorithm. This method decomposes the global collaborative optimization problem into a distributed local game by introducing exact potential game theory, significantly reducing the computational dependence and communication bandwidth pressure on centralized ground stations. It effectively achieves data isolation between different satellite entities, improving system operational security and the confidentiality of core parameters. Simultaneously, the algorithm combines sequence-constrained interval dynamic programming with pruning strategies to achieve optimal solutions for single-satellite decisions under strict compliance with complex engineering physical constraints such as transition time and duty cycle. Pruning also simplifies the program complexity. Furthermore, by utilizing dynamic utility evaluation based on marginal contribution and an asynchronous policy update mechanism based on maximum regret, it effectively resolves resource contention conflicts among multiple satellites for high-value tasks, avoiding policy oscillations and deadlocks. This allows the system to quickly converge to Nash equilibrium under a decentralized control architecture, demonstrating superior global optimization performance, convergence stability, and overall system benefit compared to traditional centralized algorithms. Attached Figure Description

[0014] Figure 1 It is the iterative convergence curve of the overall potential game-dynamic programming algorithm.

[0015] Figure 2 This is a bar chart showing the final benefit contribution of each satellite.

[0016] Figure 3 This is a diagram illustrating the effective decision-making coverage of the top 20% of high-value tasks.

[0017] Figure 4 This is the overall execution flowchart of the overall potential game-dynamic programming algorithm.

[0018] Figure 5 This is the execution flowchart of the sequence-constrained interval dynamic programming algorithm. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Preparation: Multi-satellite collaborative mission scheduling and planning for a heterogeneous satellite constellation. Experimental data is sourced from the "Tianzhi Cup Artificial Intelligence Challenge" open platform, and the data is publicly available for download. The simulation scenario includes the number of satellite nodes. This includes 10 optical satellites ( Opt ) and 10 synthetic aperture radar satellites ( SAR Number of tasks to be observed. The conversion time corresponding to the yaw conversion angle of each satellite is as follows: Figure 4 As shown. The remaining parameter values ​​are as follows: maximum number of iterations. Dynamic programming pruning threshold Simulation planning total time Mapping window time interval Maximum boot time The observation time is obtained by reading satellite data. Let the maximum side-swing angle of the satellite be... Minimum solar altitude angle required Imaging resolution requirements Obtained by reading satellite data. Set the converted stabilization time. Satellite side-slip conversion angular velocity .

[0021] Step 1: Import satellite visibility data, mission parameter set, and satellite parameter set. Mark heterogeneous characteristics: For optical satellites, set... Then only when the condition is satisfied For radar remote sensing (SAR) satellites, the entire day is considered a valid time period.

[0022] Step 2: For each window, determine whether it is a feasible window. Constraint verification is performed in the following sub-steps: Sub-step 1: Read the and Substitute formula (1) to verify whether the verification window time meets the minimum satellite startup time. ; Sub-step two: Read the , Substitute formula (2) to verify whether there is an overlap between the window time period and the task requirement time period; Sub-step 3: Verify the lateral swing angle Does it meet the following requirements: (14) Sub-step 4: Verify the solar elevation angle of the optical satellite Does it meet the following requirements: (15) Sub-step five: Read the and Substitute into formula (5) to check whether the imaging resolution meets the requirements.

[0023] Sub-step 6: Select the set of windows that meet the constraints and write them into the feasibility window set. .

[0024] Step 3: Based on the set of feasible windows Construct an adjacency matrix, where elements Calculate using formula (6) and fill in the information. If the satellite... With satellite If there is at least one common observable task, then the two are defined as neighboring nodes.

[0025] Step 4: Place the satellite Original Reward Score for the Task The weights are input into the dynamic programming function, which is then used to generate an initial set of sequences. The execution sub-steps of the dynamic programming function are as follows: Sub-step 1: Read satellite data The dynamic parameters, including the maximum on-time limit within a 90-minute interval. Wait. Also, set a safety buffer time. Read the feasibility window set from step two. Each window m Key attribute: Start time End time Side swing angle And the original reward score (weight) for the task. .

[0026] Sub-step 2: Sort all valid windows by start time Sort the windows in ascending order. The resulting combination of sorted window sequences is denoted as... ,in M This represents the total number of windows. , Perform initialization, that is, for all ,make , .

[0027] Sub-step 3: Loop parameter initialization, setting loop parameters for the outer loop. m from Traversal to Inner loop settings loop parameters Reverse traversal to .

[0028] Sub-step 4: In the inner loop, set the counter. As a precursor task, check the count; when At that time, force the exit from the inner backtracking loop. For each group First calculate relatively Time gap and the change in lateral sway angle Then calculate. corresponding And make the following judgment: If Skip; otherwise, if the condition is met. Then determine the task. n This is a feasible task.

[0029] In this process, the conversion time corresponding to the lateral sway angle is calculated by substituting the set values. : (16) Sub-step 5: Select a set of feasible tasks, iterate through the feasible elements in the set, and if the current predecessor... n satisfy Then update the current maximum predecessor benefit. and Best Front-Drive Index In order to obtain the maximum benefit of the precursor. .

[0030] Sub-step 6: When the inner loop ends, update the current task's cumulative maximum reward. Subsequently Incrementing until all iterations are completed. One task, loop ends.

[0031] Sub-step 7: Traversal DP Find the index of the maximum value in the array .from Beginning, with Recursively search for the predecessor node forward for the index until... Store the window indices corresponding to the recursive path into the candidate set. .

[0032] Sub-step 8: Based on start time Calculate the time interval index Iterate through all non-empty intervals and calculate the total execution time of the selected tasks within each interval. : (17) If a certain interval Then, tasks are removed in reverse order until... .

[0033] Sub-step nine: Select the final set of tasks marked as feasible after processing in sub-step eight, and summarize the final total score. The optimal response sequence combination for this satellite in this iteration is: .

[0034] Step 5: Perform game iteration, let the current iteration round be... t The maximum number of iterations is In each iteration, perform the following sub-steps: Sub-step 1: For each satellite Through the adjacency matrix Get all its neighbor nodes in the previous strategy The task selection status within the task. Statistics for each task. Number of times observed by neighbors Based on the frequency of task requirements The satellite is calculated using formulas (8) and (9). Observation mission marginal contribution revenue .

[0035] Sub-step 2: Calculate the regret value using formula (10) .satellite Regret value Regret value with all its neighbors Comparison. Regarding satellites. The "elite node" sequence is updated according to formula (12).

[0036] Sub-step 3: Calculate the number of satellites used to update the strategy in this iteration. and the system's overall situation function value .like or reaching the maximum number of iterations. If the iteration stops, then stop the iteration loop; otherwise, increment t and continue iterating.

[0037] Step 6: Output the final joint scheduling sequence set generated after the t-th iteration. and its corresponding total system revenue. Output its iteration process parameters, the final score of each satellite, and the effective decision coverage after checking the execution of the task.

[0038] Figure 1The graph illustrates the overall convergence characteristics of the algorithm during the iterative process, where the horizontal axis represents the number of game iterations and the vertical axis represents the total system payoff. As shown in the graph, the initial total system utility is 1420, subsequently exhibiting a significant upward trend, rapidly reaching a peak around the 18th generation and then stabilizing at 1582. This fully verifies the precise local optimization mechanism of the sequence-constrained dynamic programming algorithm, ensuring that a single policy update maximizes the marginal payoff increment, thereby driving the overall situation function to rapidly approach the optimal solution. Simultaneously, the asynchronous update strategy based on "elite selection" effectively suppresses system oscillations, achieving rapid and stable convergence of the distributed network to a high-quality Nash equilibrium state.

[0039] Figure 2 The figure illustrates the distribution of individual contributions of a heterogeneous satellite constellation after the iterative convergence of the potential game. The horizontal axis represents satellite nodes of different payload types, and the vertical axis represents the final cumulative score of a single satellite. The figure shows that all participating satellite nodes achieved effective task allocation, and... SAR Because satellites possess all-weather observation capabilities, their average contribution is slightly higher than that of satellites constrained by illumination. OPT The satellites demonstrate the algorithm's accurate perception and adaptive capabilities to heterogeneous physical constraints. They also show that the distributed negotiation mechanism based on potential game theory can effectively avoid resource idleness and excessive task concentration. Through iterative interaction of local optimal responses, it maximizes global resource utilization and synergistically improves the overall efficiency of the constellation.

[0040] Figure 3 The map shows the effective decision coverage of the top 20% of high-value tasks. The algorithm achieved 86.9% effective decision coverage (green) in the core geographic area, with only 13.1% of tasks (red) not being processed due to physical visibility or hard constraints. This verifies the algorithm's strong task capture capability and coverage breadth across a wide spatial range. In the map, the green hollow circles represent "conflict optimization" tasks, distributed at the edges of high-density task areas. This indicates that when faced with strong spatiotemporal resource competition among high-value tasks, the algorithm did not simply generate deadlock, but instead, based on the gain judgment of the overall situation function, made "proactive abandonment" decisions to obtain the optimal solution for overall scheduling benefits. Meanwhile, the green solid circles marking "captured" tasks densely cover high-value target clusters such as East Asia and the west coast of North America, indicating that most high-value tasks have been captured and allocated by the algorithm. These coverage results further demonstrate that the algorithm can accurately identify high-value tasks and achieve effective execution of high-priority tasks under complex constraints.

[0041] Figure 4 and Figure 5 The execution flowcharts for the overall system and the sequence-constrained interval dynamic programming algorithm are shown.

[0042] Although embodiments of the invention have been shown and described in detail above, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A dynamic programming-game theory hybrid method for solving satellite cooperative mission scheduling, characterized in that, The specific steps are as follows: Preparation: The orbital dynamic parameters, payload parameters, and the set of tasks to be observed for all satellites participating in the scheduling are known; assuming the number of satellites participating in the scheduling is... The heterogeneous satellite types involved in the scheduling include OPT optical satellites and SAR radar remote sensing satellites. The number of target missions to be observed is [number missing]. The maximum operating time for a single satellite within a single orbit is set as follows: The safe buffer time for attitude transition calculation is ; Set the maximum number of iterations for the game theory algorithm to be ; Step 1: Read the satellite parameter set, which includes sensor type. SAR / OPT Imaging resolution Minimum boot time and the minimum illumination requirements for optical satellites. ; Read the observation task set, including the task resolution requirements. Task effective time window interval The task requires observation frequency And the original reward score of the task Read the over-the-top visibility window (hereinafter referred to as window) dataset corresponding to the satellite, which contains the target's mission. ID Window interval for satellite-visible missions Side swing angle and window solar altitude angle ; Step 2: Construct a constraint filter and perform a feasibility check on each window for the following constraints: verify whether the window time meets the minimum satellite startup time. ; Verify if there is any overlap between the window time period and the task requirement time period; Verify the lateral swing angle. Solar altitude angle Imaging resolution Does the physical constraint meet the constraint index? The set of windows that meet the constraints is denoted as the feasibility window set. ; Step 3: Based on the set of feasible windows Construct an adjacency matrix If satellite With satellite If there is at least one common observable task, then the two are defined as neighboring nodes. Step 4: From the feasibility window set Satellites were selected from the middle All executable tasks, and the original profit score Input a dynamic programming function, without considering inter-satellite coordination, for each satellite by Using weights, an interval dynamic programming algorithm with sequence constraints is used to solve for the optimal scheduling sequence for a single satellite, generating an initial sequence set. ,in Indicates the first i The mission execution sequence of a satellite in the t-th iteration; Step 5: Enter the multi-round iteration process, let the current iteration round be... t The maximum number of iterations is In each iteration, perform steps six through ten. Step Six: For each satellite Through the adjacency matrix Obtain the indices of all its neighbors, and use these to deduce its position in the previous sequence set. The task selection status in the data, and statistics for each task. Number of times observed by neighbors Based on the frequency of task requirements Calculate satellite For each window m marginal contribution revenue ; Step 7: Use the marginal contribution revenue from Step 6 Replace all satellites in the previous loop The score is then used as input for the dynamic programming function. Under the premise of satisfying all physical constraints, a new strategy that maximizes local utility is calculated. ; Step 8: Calculate the utility increment resulting from switching the satellite to the new strategy, i.e., the regret value. ; Step Nine: To avoid conflicts caused by multiple agents simultaneously vying for high-priority tasks, an asynchronous update mechanism is adopted; Satellite Regret value Regret value with all its neighbors Compare; only when When the criteria for "elite node" are met, a sequence update is performed on the satellite, i.e. Otherwise, keep the original sequence unchanged, i.e. ; Step 10: Calculate the number of satellites used to update the strategy in this iteration. And the system's global situation function value, i.e., the global total gain. ;like (equivalent to) (or reaching the maximum number of iterations) If the system converges to the Nash equilibrium point, the loop stops; otherwise, the iteration loop continues. Step 11: Output the final joint scheduling sequence set generated after the t-th iteration. and its corresponding total system revenue. .

2. The dynamic programming-game theory hybrid method for solving satellite cooperative mission scheduling according to claim 1, characterized in that, The formula for checking the minimum boot time in step two is: (1) In the above formula, , These are the start and end times of the window, respectively. The left side of the equation is the window time plus a 1-second buffer time, and the right side is the minimum power-on time for the satellite. The window validation formula is: (2) In the above formula The effective window range for the task. For satellite-visible missions; Side swing angle The verification formula is: (3) In the above formula and These are the minimum and maximum side-swing angle limits for the satellite, respectively. Solar elevation angle of optical satellites The verification formula is: (4) This is the minimum solar altitude angle requirement for optical satellites; Imaging resolution Verification formula: (5) In the above formula Resolution required for the task.

3. The dynamic programming-game theory hybrid method for solving satellite cooperative mission scheduling according to claim 1, characterized in that, Elements in the adjacency matrix in step three Defined as: (6) in M i , M j Satellites observable task set; adjacency matrix elements in express There is competition between them, and vice versa.

4. The dynamic programming-game theory hybrid method for solving satellite cooperative mission scheduling according to claim 1, characterized in that, The dynamic programming part of the interval dynamic programming algorithm with sequence constraints in steps four and seven is executed as follows: S1: Read the currently selected satellite The dynamic parameters are obtained, and the yaw transition time calculated in step one is read. And the maximum boot time limit within a 90-minute interval. ; Simultaneously set a safety buffer time. =1 s The goal is to enhance the robustness of the algorithm while avoiding the impact of errors caused by computational inaccuracies on the execution process. S2: Extract the set of feasible windows from step two. The window data in the middle, which corresponds to each window m The key attribute representation method is as follows: Start Time End time Side swing angle And the original reward score (weight) for the task. ; S3: Calculate all feasible windows based on their start time. Sort the windows in ascending order, and denote the resulting window sequence combination as follows: ,in For the first m There are 10 windows, and the total number of windows is 1. M； S4: Define an array The purpose is to force the selection of the first [item] while satisfying timing and physical constraints. m The maximum total reward score accumulated by the path when an observation window is used as the end of the current task sequence; Define For the first m The index of the predecessor node of each window on the optimal path; when initializing the state array, for all ,make , ; S5: First, set the outer loop, setting the loop parameter... m from Traversal to , indicating the current target task; the inner loop is set to Reverse traversal to Set a counter As a precursor task check count, when At this time, the inner loop is forcibly exited, thereby reducing the algorithm complexity through a pruning strategy. It is the dynamic programming pruning threshold; S6: Perform a conversion time constraint check for each group. First calculate its own time interval. and the change in lateral sway angle Then, the following judgment is made: If If the condition is determined to be physically overlapping and does not meet the constraints, skip it; otherwise, calculate... Corresponding conversion time If the conditions are met Then determine the task. n As m The precursor mission is feasible; in, Corresponding conversion time The calculation formula is: (7) In the above formula It is the settling time after the conversion. It is the angular velocity of the satellite's side-slip conversion; S7: Select the set of predecessor tasks deemed feasible in S6, variables Store the historical maximum return, iterate through the elements in the set, and if the current predecessor... n satisfy Then update the current maximum predecessor benefit. and Best Front-Drive Index Finally, all The maximum benefit of the forerunner is corresponding to ; S8: When the inner loop ends, update the current task's cumulative maximum reward based on the currently recorded maximum predecessor reward. ;then the outer loop variable Increment the value and continue calculating the state of the next task until the outer loop has traversed all tasks. One window; S9: Traversal DP Find the index of the maximum value in the array .from Beginning, with For the index, recursively backtrack the predecessor node until... Store the window index corresponding to the backtracking path into the candidate set. ; S10: Map tasks to a fixed 90-minute (5400-second) time interval based on their start time. In, based on the start time Calculate the time interval index ; S11: Index Iterate through all non-empty intervals and calculate the value of each interval. Total execution time of the selected task If a certain interval Then, starting from the last task in that interval, tasks are removed sequentially in reverse order until... This ensures that the maximum operating time of the satellite within a 90-minute interval does not exceed [the specified limit]. ; S12: Mark the final task set after processing in S11 as selected, and sum the scores of each interval to obtain the total score. The optimal response of the satellite in this iteration is denoted as... , a This is the observation window that is marked as selected.

5. The dynamic programming-game theory hybrid method for solving satellite cooperative mission scheduling according to claim 1, characterized in that, In step six, for each window m marginal revenue The calculation formula is as follows: (8) In the above formula, This represents the current number of observations. The cumulative reward function for a task represents the cumulative reward for that task. l Observed by the whole system The total value after that, The calculation formula is as follows: (9) In the above formula, For the required number of observations, This represents the original score reward for the task.

6. The dynamic programming-game theory hybrid method for solving satellite cooperative mission scheduling according to claim 1, characterized in that, Regret value in step eight The calculation formula is: (10) In the above formula, For the first i The sequence of satellites in the 1st t The total marginal utility at the next iteration is calculated using the following formula: (11) In the above formula, For window m The corresponding boundary benefits of the current satellite.

7. The dynamic programming-game theory hybrid method for solving satellite cooperative mission scheduling according to claim 1, characterized in that, In step nine, the update formula for "elite nodes" is as follows: (12) In the above formula, Indicates the first t Satellite after round of iteration i The final strategy adopted and For satellite and The regret value corresponding to the sequence, For satellite The corresponding set of neighbor indexes.

8. The dynamic programming-game theory hybrid method for solving satellite cooperative mission scheduling according to claim 1, characterized in that, In step ten, the formula for calculating the global situation function is: (13) in L This represents the total number of tasks in the entire system. This indicates the task being performed during this iteration. l The maximum number of observations, summed by the cumulative rewards of all tasks, gives the overall situation function. .

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