A distance keeping game control framework and method for a maneuvering non-cooperative target

Abstract

The application belongs to the technical field of aerospace, and relates to a distance-keeping game control framework and method for a maneuvering non-cooperative target. The framework comprises a rolling control window, an event perception window arranged in each rolling control window, and an event triggering mechanism arranged in each event perception window. The event perception window predicts an orbit state through a two-body dynamics model, the event triggering mechanism calculates a relative distance between an active satellite and a target satellite at each discrete point according to an orbit prediction result, and judges whether the relative distance constraint is met. If the relative distance constraint is met, an impulse maneuver strategy of the active satellite as a decision output is calculated through a game strategy optimization algorithm. Simulation results show that the application can realize long-time distance keeping, and the success rate reaches 98% in a 12-hour maintenance task, which is increased by 308.3% compared with a traditional algorithm.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology, specifically relating to a distance-keeping game control framework and method for maneuvering non-cooperative targets. Background Technology

[0002] In recent years, with the development of space technology, space game theory has received extensive research from scholars both domestically and internationally. Among space games, the "chase and escape between two non-cooperative spacecraft" problem is a fundamental one. In this problem, the pursuing and escaping parties typically use relative distance as a performance indicator and engage in game theory competition by minimizing or maximizing this indicator. However, the game strategy of minimizing relative distance for the pursuing party is difficult to apply in some non-strongly adversarial space missions, such as long-term observation. Therefore, there is an urgent need for a game control method that can meet distance constraints and does not aim at terminal interception or rendezvous.

[0003] The incomplete information of non-cooperative targets in space leads to uncertainties and time delays in real-time state perception. This incompleteness causes error accumulation in relative position control, thus imposing stringent requirements on the robustness and adaptability of the control system. More seriously, when the target possesses autonomous maneuvering capabilities, its proactive approach / avoidance strategies accelerate the breach of constraint boundaries, transforming the robust control problem of maintaining a preset distance into a dynamic game with time-varying constraints. In existing methods, elliptical orbital design is widely used for distance maintenance missions between the host satellite and the target. The advantage of this method lies in its ability to achieve long-term stable relative distance control through periodic orbital dynamics once the target enters an elliptical orbit; however, its application is significantly limited, requiring the target to be in a near-circular orbit and lacking autonomous maneuvering capabilities.

[0004] Compared to traditional control methods, this invention proposes a rolling time-domain control framework that integrates a rolling control window and an event-triggered mechanism. This architecture effectively suppresses distance boundary breaches caused by target state uncertainty and non-cooperative maneuvering through rolling control; the event-triggered mechanism further improves the control system's response speed to disturbances; based on this, an optimization model is designed with the target constraint satisfaction time as the maximization performance index, which can effectively utilize impulse maneuvering capabilities to maximize the extension of the relative distance constraint satisfaction time window, ultimately generating a control strategy with strong robustness and real-time adaptability. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a distance-maintaining game control framework and method for maneuvering non-cooperative targets.

[0006] To achieve the objectives of this invention, the following technical solutions are adopted.

[0007] A distance-preservation game control framework for maneuvering non-cooperative targets includes a rolling control window with a fixed time step of time A, an event-aware window with a fixed time step of time B in each rolling control window, and an event triggering mechanism set in each event-aware window; wherein:

[0008] The event perception window takes the current orbital states of the active satellite and the target satellite as state variables as inputs, predicts the orbital states of the active satellite and the target satellite within a future time period C through a two-body dynamics model, and performs discrete point sampling with time D as the step size to obtain a discrete point sequence.

[0009] The event triggering mechanism calculates the relative distance between the active satellite and the target satellite at each discrete point in the discrete point sequence based on the orbit prediction results, and determines whether the relative distance meets the relative distance constraint. If the relative distance between the active satellite and the target satellite at the discrete point does not meet the relative distance constraint, the event triggering mechanism is satisfied, and the next rolling control window is entered in advance.

[0010] In a rolling control window, if the relative distance between the active satellite and the target satellite at a discrete point satisfies the relative distance constraint, the orbital states of the active satellite and the target satellite at the current moment are used as input state variables. The game-theoretic strategy optimization algorithm calculates the pulse maneuver strategy of the active satellite as the decision output. Specifically, the game-theoretic strategy optimization algorithm uses the pulse maneuver velocity vector of the active satellite as the optimization variable, predicts the orbital state based on the two-body dynamics model, constructs a comprehensive weighted performance index by calculating the constraint satisfaction time and terminal distance index, and obtains the optimal pulse maneuver time and velocity vector of the active satellite, i.e., the pulse maneuver strategy, through the particle swarm optimization algorithm.

[0011] Furthermore, the expression for the relative distance constraint is:

[0012] ;

[0013] In the formula: Given the minimum relative distance constraint between the active satellite and the target satellite, Given the maximum relative distance constraint between the active satellite and the target satellite, For distance determination margin, The relative distance between the active star and the target star at each discrete point.

[0014] Furthermore, the process of establishing the event triggering mechanism includes the following steps:

[0015] S31. Under each scrolling control window, set an event sensing window with a fixed time step of time Ts; in each event sensing window, check the current active star orbit status. Orbital state of the target star Duration is Orbit prediction;

[0016] S32, using time step By performing discrete point sampling, a sequence of discrete points is obtained:

[0017] ;

[0018] S33. Calculate the relative distance between the active satellite and the target satellite at each discrete point based on the orbit prediction results. Determine whether the relative distance between the active satellite and the target satellite at each discrete point satisfies the relative distance constraint:

[0019] ;

[0020] If the relative distance between the active satellite and the target satellite at a certain discrete point does not meet the relative distance constraint, then the event triggering mechanism is met, and the next rolling control window is entered in advance.

[0021] The orbit prediction result is as follows:

[0022] .

[0023] Furthermore, the game strategy optimization algorithm includes the following steps:

[0024] S41. The active satellite is configured to perform two pulse maneuvers in each rolling control window; therefore, these two maneuvers are modeled as optimization variables. The timing of the first pulse maneuver is set at the beginning of the rolling control window, and the waiting time for the second pulse maneuver is... ; two pulse maneuver velocity vectors Represented as:

[0025] ;

[0026] In the formula: For the magnitude of the speed increment, Let be the velocity direction angle, and let the subscript i be the pulse maneuver number. Then the optimization variable is... ;

[0027] S42. Based on the current active satellite orbit status. As input, based on the two-body dynamics model, the state of the active satellite after pulse maneuver is analyzed for a duration of... The forecast, also based on For input, the duration of the target satellite status is... Forecast;

[0028] S43, Using time step By performing discrete point sampling, a sequence of discrete points is obtained:

[0029] ,

[0030] S44. Calculate the relative distance between the active satellite and the target satellite at each discrete point based on the orbit prediction results. Among them, the orbital prediction results are as follows:

[0031] ;

[0032] S45. Calculate the constraint satisfaction time index according to the following formula. :

[0033] ;

[0034] Where: index The physical meaning is the total time it takes for the active star to satisfy the distance constraint. Here is the switching function representing the constraint satisfaction:

[0035] ,

[0036] S46, End Time The relative distance is denoted as Calculate the end distance index :

[0037] ,

[0038] The purpose of this indicator is to constrain the terminal moment of active satellites to be as close as possible to the center of the range constraint.

[0039] S47. The comprehensive weighted performance index is calculated as follows:

[0040] ,

[0041] In the formula: To comprehensively weight performance indicators, These are the weighting coefficients;

[0042] S48. The comprehensive weighted performance index is optimized by using the particle swarm optimization algorithm to calculate the optimal pulse maneuver time and pulse velocity vector of the active satellite, which are then used as the decision output.

[0043] A distance-keeping game control method for maneuvering non-cooperative targets utilizes the pulse maneuver strategy calculated by the aforementioned distance-keeping game control framework for maneuvering non-cooperative targets.

[0044] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0045] This invention proposes a distance-maintaining game control method for maneuvering non-cooperative targets. Through rolling time-domain control and heuristic policy optimization, it achieves dynamic maintenance of the safe boundary distance. Compared with traditional algorithms, this invention shows significant advantages in non-cooperative adversarial scenarios, with stronger perturbation robustness and real-time policy performance. In the 12-hour distance-maintaining scenario for maneuvering non-cooperative targets, the success rate of this invention is 308.3% higher than that of the traditional control and maintenance strategy based on Lambert maneuvers. Attached Figure Description

[0046] Figure 1 A flowchart of a distance-preserving game control method for maneuvering non-cooperative targets;

[0047] Figure 2 A schematic diagram of the game control framework for maintaining the distance;

[0048] Figure 3 A graph showing the velocity increment consumption variation for distance maintenance control of the active satellite in the test case.

[0049] Figure 4 This is a diagram showing the relative trajectory of the active star in the target star's orbital system during the test case.

[0050] Figure 5 This is a graph showing the relative distance between the active satellite and the target satellite in the test case.

[0051] Figure 6 This is a comparison chart showing the distance constraint satisfaction of the present invention and the traditional method in Monte Carlo simulation. Detailed Implementation

[0052] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0053] As an embodiment of the present invention, such as Figure 1 and Figure 2 As shown, a distance-preserving game control framework for maneuvering non-cooperative objectives includes time-based... A scrolling control window is set for a fixed time step, and within each scrolling control window, time... An event-aware window with a fixed time step and an event triggering mechanism set in each event-aware window; wherein:

[0054] The event perception window uses the current orbital states of the active and target satellites as input state variables, and employs a two-body dynamics model to predict the future orbital states of the active and target satellites over a given period of time. The orbital status within the orbit is predicted, and the prediction is performed in time steps. Discrete points are selected to obtain a discrete point sequence;

[0055] The event-triggered mechanism calculates the relative distance between the active satellite and the target satellite at each discrete point in the discrete point sequence based on orbit prediction results. It determines whether the relative distance meets the relative distance constraint. If the relative distance between the active satellite and the target satellite at the discrete point does not meet the relative distance constraint, the event triggering mechanism is satisfied, and the next scrolling control window is entered in advance.

[0056] In the rolling control window, if the relative distance between the active satellite and the target satellite at a discrete point satisfies the relative distance constraint, the orbital states of the active satellite and the target satellite at the current moment are used as input state variables. The game strategy optimization algorithm is used to calculate the pulse maneuver strategy of the active satellite as the decision output. Specifically, the game strategy optimization algorithm uses the pulse maneuver velocity vector of the active satellite as the optimization variable, predicts the orbital path based on the two-body dynamics model, constructs a comprehensive weighted performance index by calculating the constraint satisfaction time and terminal distance index, and obtains the optimal pulse maneuver time and velocity vector of the active satellite, i.e., the pulse maneuver strategy, through the particle swarm optimization algorithm.

[0057] As an embodiment of the present invention, the expression for the relative distance constraint is:

[0058]

[0059] In the formula: Given the minimum relative distance constraint between the active satellite and the target satellite, Given the maximum relative distance constraint between the active satellite and the target satellite, For distance determination margin, The relative distance between the active star and the target star at each discrete point.

[0060] As an embodiment of the present invention, such as Figure 1 and Figure 2 As shown, the process of establishing the event triggering mechanism includes the following steps:

[0061] S31. Under each scrolling control window, set an event sensing window with a fixed time step of time Ts; in each event sensing window, check the current active star orbit status. Orbital state of the target star Duration is Orbit prediction;

[0062] S32, using time step By performing discrete point sampling, a sequence of discrete points is obtained:

[0063] ;

[0064] S33. Calculate the relative distance between the active satellite and the target satellite at each discrete point based on the orbit prediction results. Determine whether the relative distance between the active satellite and the target satellite at each discrete point satisfies the relative distance constraint:

[0065] ;

[0066] If the relative distance between the active satellite and the target satellite at a certain discrete point does not meet the relative distance constraint, then the event triggering mechanism is met, and the next rolling control window is entered in advance.

[0067] The orbit prediction result is as follows:

[0068] .

[0069] As an embodiment of the present invention, such as Figure 2 As shown, the process of establishing the game strategy optimization algorithm includes the following steps:

[0070] S41. The active satellite is configured to perform two pulse maneuvers in each rolling control window; therefore, these two maneuvers are modeled as optimization variables. The timing of the first pulse maneuver is set at the beginning of the rolling control window, and the waiting time for the second pulse maneuver is... ; two pulse maneuver velocity vectors Represented as:

[0071] ;

[0072] In the formula: For the magnitude of the speed increment, Let be the velocity direction angle, and let the subscript i be the pulse maneuver number. Then the optimization variable is... ;

[0073] S42. Based on the current active satellite orbit status. As input, based on the two-body dynamics model, the state of the active satellite after pulse maneuver is analyzed for a duration of... The forecast, also based on For input, the duration of the target satellite status is... Forecast;

[0074] S43, Using time step By performing discrete point sampling, a sequence of discrete points is obtained:

[0075] ,

[0076] S44. Calculate the relative distance between the active satellite and the target satellite at each discrete point based on the orbit prediction results. ;

[0077] The orbit prediction result is as follows: ;

[0078] S45. Calculate the constraint satisfaction time index according to the following formula. :

[0079] ;

[0080] Where: index The physical meaning is the total time it takes for the active star to satisfy the distance constraint. Here is the switching function representing the constraint satisfaction:

[0081] ,

[0082] S46, End Time The relative distance is denoted as Calculate the end distance index :

[0083] ,

[0084] The purpose of this indicator is to constrain the terminal moment of active satellites to be as close as possible to the center of the range constraint.

[0085] S47. The comprehensive weighted performance index is calculated as follows:

[0086] ,

[0087] In the formula: To comprehensively weight performance indicators, These are the weighting coefficients;

[0088] S48. The comprehensive weighted performance index is optimized by using the particle swarm optimization algorithm to calculate the optimal pulse maneuver time and pulse velocity vector of the active satellite, which are then used as the decision output.

[0089] As an embodiment of the present invention, such as Figure 1 and Figure 2 As shown, a distance-keeping game control method for maneuvering non-cooperative targets utilizes a pulse maneuvering strategy calculated within a distance-keeping game control framework for maneuvering non-cooperative targets.

[0090] During the simulation, the target spacecraft was initially positioned in geosynchronous orbit with a position vector of [0; -42166.3; 0.001136] km and a velocity vector of [3.074582; 0; 0] km / s. The active satellite was located nearby at a relative distance of 30 km, with a position vector of [30; -42166.3; 0.001136] km and a velocity vector of [3.074582; 0; 0] km / s. Parameters were set as follows: Tc = 3600 s, Ts = 300 s. , =3600s, =30km, =50km, =3km, , Because the target possesses maneuverability, it is set to perform a random directional maneuver every hour, with a maximum pulse amplitude of 10 m / s. The active satellite's maneuverability is comparable to the target satellite's, with the same maximum pulse amplitude of 10 m / s. For this maneuvering target, the active satellite applies pulse maneuvers based on the method of this invention for distance maintenance control, keeping the relative distance between the two satellites between 20 km and 50 km. The simulation duration is 12 hours. The simulation results are as follows: Figures 3-6 As shown. Figure 3 The graph showing the change in speed increment consumption for distance maintenance control of the active satellite shows that after the target satellite maneuvers, the active satellite enters the control loop and performs two maneuvers per hour. Figure 4 This is a relative trajectory image of the active star in the target orbital system. Figure 5 The image shows the relative distance change between the active and target stars. It can be seen that the active star's trajectory remains within the safe distance constraint throughout. As the target star performs random maneuvers, the relative distance fluctuates, but always remains within the safe distance range. The method of this invention is compared with the traditional distance maintenance method based on Lambert maneuvers. 100 Monte Carlo simulations were performed with randomly generated initial states, each lasting 12 hours. The distance change comparison in the Monte Carlo simulations is shown below. Figure 6 As shown, the left figure shows the distance constraint satisfaction of the present invention, and the right figure shows the satisfaction of the traditional method. It can be seen that the traditional method violates the distance constraint in most cases, with a success rate of only 24%, while the success rate of the present invention is 98%, which is significantly better than the traditional method.

[0091] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A distance keeping game control framework for maneuvering non-cooperative targets, characterized in that: The distance keeping game control framework comprises a rolling control window set with a fixed time step A, an event-aware window set with a fixed time step B in each rolling control window, and an event trigger mechanism set in each event-aware window; wherein: The event-aware window inputs the orbit state of the active satellite and the target satellite at the current time as a state variable, predicts the orbit state of the active satellite and the target satellite in a future time C through a two-body dynamics model, and discretely takes points with a time step D to obtain a discrete point sequence; The event trigger mechanism calculates the relative distance between the active satellite and the target satellite at each discrete point in the discrete point sequence according to the orbit prediction result, and judges whether the relative distance satisfies the relative distance constraint; if the relative distance between the active satellite and the target satellite at the discrete point does not satisfy the relative distance constraint, the event trigger mechanism is satisfied, and the next rolling control window is entered in advance; The rolling control window, if the relative distance between the active satellite and the target satellite at the discrete point satisfies the relative distance constraint, inputs the orbit state of the active satellite and the target satellite at the current time as a state variable, and calculates the impulse maneuver strategy of the active satellite as a decision output through a game strategy optimization algorithm; wherein: the game strategy optimization algorithm takes the impulse maneuver velocity vector of the active satellite as an optimization variable, constructs a comprehensive weighted performance index by calculating the constraint satisfaction time and the terminal distance index based on the orbit state predicted by the two-body dynamics model, and obtains the optimal impulse maneuver time and velocity vector of the active star through the particle swarm optimization algorithm, i.e. the impulse maneuver strategy.

2. The range keeping game control framework for maneuvering non-cooperative targets according to claim 1, wherein: The expression of the relative distance constraint is: ； wherein: is the minimum relative distance constraint for a given active satellite and target satellite, is the maximum relative distance constraint for a given active satellite and target satellite, is the distance decision margin, is the relative distance of the active satellite and target satellite at each discrete point.

3. The range keeping game control framework for maneuvering non-cooperative targets according to claim 2, wherein: The establishment process of the event trigger mechanism comprises the following steps: S31, under each rolling control window, set an event-aware window with a fixed time step Ts; in each event-aware window, perform an orbit prediction with a time length of and a target star orbit state at the current time ​ S32, with a time step Discrete points are taken to obtain a sequence of discrete points: ； S33、According to the track prediction result, calculate the relative distance between the active satellite and the target satellite at each discrete point , determine whether each discrete point meets the relative distance constraint: ； If a certain discrete point does not satisfy the relative distance constraint, the event trigger mechanism is satisfied, and the next rolling control window is entered in advance; The orbit prediction result is: 。 4. The range keeping game control framework for maneuvering non-cooperative targets according to claim 3, wherein: The game strategy optimization algorithm comprises the following steps: S41, set the active satellite to make two impulsive maneuvers under each rolling control window, so model the two maneuvers as optimization variables; the first impulsive maneuver time is set at the beginning of the rolling control window, and the waiting time of the second impulsive maneuver is ; the velocity vectors of the two impulsive maneuvers are expressed as: ； wherein: is the velocity increment amplitude, is the velocity direction angle, the subscript i is the pulse maneuver sequence number, and the optimization variable ; S42, the active satellite orbit state at the current time For input, according to the two-body dynamics model, the state of the active satellite after impulse maneuver is predicted for a time length of , also taking as input, the state of the target satellite is predicted for a time length of ; S43, in time steps Discrete points are taken to obtain a sequence of discrete points: ， S44. Calculate the relative distance between the active star and the target star at each discrete point according to the orbit prediction result ; wherein the orbit prediction result is: ； S45, calculate the constraint satisfaction time indicator according to the following formula : ； where: index Physical meaning is the total time that the active star satisfies the distance constraint, is a switching function representing the constraint satisfaction: ， S46, end time The relative distance of , the end distance index : ， The purpose of the index is to constrain the active satellite to be as close as possible to the center position of the distance constraint at the end time; S47, the comprehensive weighted performance index is calculated as follows: ， In the formula: is a comprehensive weighted performance index, is a weight coefficient; S48, the particle swarm optimization algorithm is used to optimize the comprehensive weighted performance index, and the optimal impulse maneuver time and impulse velocity vector of the active satellite are calculated as the decision output.

5. A distance keeping game control method for a maneuvering non-cooperative target, characterized in that: The distance keeping game control method is controlled by the impulse maneuver strategy calculated by the distance keeping game control framework for maneuvering non-cooperative targets in claim 1.

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