Satellite cluster orbit game real-time task allocation and fast trajectory collaborative optimization method

Abstract

The application provides a satellite cluster orbit game real-time task allocation and rapid trajectory cooperative optimization method, and relates to the technical field of satellite pursuit and evasion game. The application determines the allocation relationship between the target and the satellite based on a distributed bidding mechanism, generates a task allocation scheme; constructs an optimal control problem with the minimum interception time as the target based on the task allocation scheme, establishes an accurate penalty function to solve the shortest interception time; and updates the task allocation scheme based on the shortest interception time and generates an optimal interception trajectory. The application overcomes the performance suboptimality problem of the traditional phased processing through the closed-loop coupling of task allocation and trajectory planning. The application uses control parameterization and an accurate penalty function method to convert a complex dynamic optimization problem into a nonlinear programming problem, significantly reduces the solution complexity, and improves the calculation efficiency; the distributed auction algorithm based on the consistency protocol does not require a central node, only relies on local communication, avoids single point failure, and has strong robustness.

Description

Technical Field

[0001] This invention belongs to the field of satellite pursuit and escape game technology, specifically involving a method for real-time task allocation and rapid trajectory collaborative optimization in satellite cluster orbit game. Background Technology

[0002] With the increasing demands for intelligent upgrades to satellite systems and collaborative space missions, modern aerospace engineering is accelerating its transformation towards a modular and networked distributed satellite system architecture. Satellite constellations, through multi-node collaborative operation, exhibit significant advantages in on-orbit reconfiguration capabilities and fault tolerance, gradually becoming a research hotspot in fields such as deep space exploration and Earth observation. The constellation collaborative scheduling problem for dynamic mission scenarios can typically be modeled as an integer programming model under multi-objective constraints. Its core lies in optimizing the spatiotemporal matching relationship between multi-satellite resources and heterogeneous missions, while simultaneously satisfying complex conditions such as inter-satellite communication delays, payload switching energy consumption, attitude maneuver constraints, and mission priorities. Current research needs to overcome key technical challenges such as online mission planning algorithms under limited onboard computing resources, the design of multi-satellite information interaction mechanisms, and dynamic replanning under uncertain environments. This is of significant research value for improving the on-orbit autonomous decision-making capabilities of satellite constellations.

[0003] In the field of task allocation in satellite game swarm intelligence systems, existing methods can be divided into two main paradigms: centralized and distributed. Centralized methods rely on a central controller for global optimization (such as genetic algorithms and simulated annealing). While they can guarantee the theoretical optimal solution, they suffer from inherent drawbacks such as high communication bandwidth pressure and a high risk of single-point failure. Distributed methods, on the other hand, achieve collaboration through local communication and autonomous decision-making, and have become a research hotspot in recent years. The core of distributed methods lies in utilizing multi-agent systems to achieve autonomous task processing. Among the many implementation paths, auction algorithms are favored due to their excellent scalability. Their theoretical foundation has evolved from early bidding models to mature decentralized collaborative protocols (such as the work of Bertsekas, Zavlanos, and others).

[0004] Time optimality is a crucial indicator for satellite mission allocation, and existing research explores this issue at multiple levels, focusing on numerical algorithm design and theoretical compatibility. Indirect methods, by constructing extended Hamiltonian functions to analyze time-optimal conditions, can obtain theoretically optimal solutions, but they suffer from inherent drawbacks such as poor numerical stability and high sensitivity to initial conditions in high-dimensional nonlinear systems. Some methods partially alleviate this problem through pseudospectral discretization and slack variable techniques. Direct methods, relying on discretization strategies such as control parameterization and pseudospectral collocation, explicitly incorporate time variables into the optimization space, combining sequential convex optimization or mixed-integer programming frameworks to achieve online solutions while considering terminal constraints. For complex dynamic environments, heuristic algorithms (such as the improved Raccoon Optimization algorithm) overcome local extrema limitations through global search strategies, and their parallel computing characteristics significantly improve decision-making efficiency in multi-satellite collaborative scenarios. Some methods, based on multi-agent deep reinforcement learning (MA-DRL) frameworks, further enhance the distributed routing adaptability of low-Earth orbit constellations in dynamic topologies through an "offline training-online deployment" mechanism.

[0005] The core challenges currently facing satellite orbital game theory are concentrated in three aspects: First, the fragmented processing of task allocation and trajectory planning leads to suboptimal system performance, and there is an urgent need to build a unified collaborative optimization framework; Second, many-to-many distributed task allocation needs to balance fairness and efficiency in uncertain communication environments, and traditional auction mechanisms are difficult to adapt to dynamically changing priorities; Third, complex trajectory constraints (such as two-body dynamics, fuel constraints, and collision avoidance) limit the real-time performance and computational efficiency of traditional path planning algorithms. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the core innovation of this invention lies in proposing a real-time task allocation and rapid trajectory collaborative optimization method based on satellite cluster orbital game theory. First, an enhanced robust auction mechanism is used to achieve efficient autonomous allocation of inter-satellite tasks, effectively addressing the dynamic priority problem. Then, an optimal control model is constructed based on the allocation results, aiming to minimize terminal time. A control parameterization-precise penalty function method is employed to efficiently solve the trajectory optimization problem under complex constraints. This invention achieves closed-loop coupling and real-time interaction between the task allocation and trajectory planning layers, overcoming the inherent limitations of traditional staged processing.

[0007] This invention provides a method for real-time task allocation and rapid trajectory collaborative optimization in satellite constellation orbit game, comprising the following steps:

[0008] A mathematical programming model for satellite cluster orbital game is constructed based on multiple satellites and multiple targets, and a global objective function is established.

[0009] The allocation relationship between targets and satellites is determined based on a distributed auction mechanism, and a task allocation scheme is generated.

[0010] Based on the task allocation scheme, an optimal control problem is constructed with the goal of minimizing the interception time. An exact penalty function is established to solve for the shortest interception time.

[0011] Under the constraint of the global objective function, the task allocation scheme is updated based on the shortest interception time, and the optimal interception trajectory is generated according to the updated task allocation scheme.

[0012] Furthermore, based on a mathematical programming model for orbital game theory involving multiple satellites and multiple targets, the specific method for establishing the global objective function is as follows:

[0013] The serial numbers of multiple satellites are set as follows: Establish a satellite collection ,in, The total number of satellites; obtain the payload type, dynamic equations, and maximum flight duration for each satellite;

[0014] Set the sequence numbers of multiple targets as follows: Establish a target set ,in, For the total number of targets; obtain the risk level, required intercept payload type, and required number of satellites for each target;

[0015] Generate a high-level mission allocation strategy based on the allocation relationship between satellites and targets. ,in, Indicates satellite and target The allocation relationship between them, when satellites Assigned to interception target When, set Otherwise set ;

[0016] The trajectory control strategy for each satellite intercepting its corresponding target is set as a control function that satisfies the satellite's dynamic equations and thrust constraints. ;

[0017] A global objective function is established to satisfy the trajectory generation strategy and minimize the risk removal cost of all satellite interception targets. As shown in the formula below:

[0018] ;

[0019] in, For satellite Intercept target The cost of removing the risk For satellite To the target Minimum arrival time For the goal Risk level;

[0020] Set constraints for the global objective function, including the number of targets intercepted by each satellite, the number of satellites simultaneously participating in the interception of the same target, payload matching constraints, and the maximum range of each satellite.

[0021] Furthermore, the specific method for determining the allocation relationship between targets and satellites based on the distributed auction mechanism is as follows:

[0022] Initialize the cost matrix Among them, satellite prediction is based on a simplified unconstrained relative kinematics model. To the target Minimum arrival time The estimated value, calculate the satellite Intercept target Risk removal cost If satellite Load type and target The required intercept payload type does not match or the satellite Reach the destination Minimum arrival time Beyond satellite The maximum flight time is used to set a risk removal cost. It is positive infinity;

[0023] During communication time At that time, each satellite is configured to target... The state vector includes the bidding vector and the vector with the highest bid and largest index; the target... The satellite with the largest bid vector will be assigned.

[0024] For allocation to satellites Allocated targets ,satellite During communication time Receive all neighboring satellites The state vector during communication time Internal iterative satellite updates During communication time The state vector; in each iteration, based on the price increase mechanism on the satellite For the assigned targets Add a preset positive number to the bidding vector. Obtain satellite During communication time The bidding vector;

[0025] When neighboring satellites For the assigned targets The bidding vector is not less than the satellite For the assigned targets When bidding on the target vector, the allocated target will be... Assigned to neighboring satellites According to communication time Bidding vector and target returns Calculate the net value for each objective. Select the target with the largest net value Assigned to satellite ;

[0026] When communication time When the state vectors of all satellites cease to be updated, the auction is considered to have converged; based on communication time... The highest bidder with the largest sequence number generates the task allocation scheme, which includes each satellite and its corresponding interception target.

[0027] Furthermore, update the satellite During communication time The specific method for using state vectors is as follows:

[0028] For each target , will satellite Bidding vector Bidding vector with all neighboring satellites Compare and select satellites The largest bid vector among all neighboring satellites is used as the satellite's bid vector. During communication time Bidding vector ;

[0029] If satellite The largest bid vector among all neighboring satellites is the bid vector of the neighboring satellites. The bidding vector will then be the satellite During communication time The vector with the highest bid and the largest index The serial number is updated to that of the neighboring satellite. The serial number;

[0030] If satellite The largest bid vector among all neighboring satellites is the satellite's bid vector. The bidding vector will then be the satellite During communication time The vector with the highest bid and the largest index As communication time The vector with the highest bid and the largest index ;

[0031] If satellite Bidding vector neighboring satellites If the bidding vectors are equal and the largest, then compare the satellites. and neighboring satellites The vector with the largest sequence number and the highest bid is selected as the satellite. Communication time The vector with the highest bid and the largest index .

[0032] Furthermore, the specific method for constructing an optimal control problem based on the task allocation scheme with the objective of minimizing interception time is as follows:

[0033] Total flight time of satellite interception target Establish objective function Given the constraints, solve for the optimal control law. and optimal interception time , so that the objective function Minimization; the constraints include the satellite's state equation, initial position constraints, terminal position constraints, anti-exposure path constraints, terminal velocity constraints, and thrust amplitude constraints.

[0034] Furthermore, the specific method for establishing an accurate penalty function to solve for the shortest interception time is as follows:

[0035] The total flight time interval of the satellite interception target Divided into Subintervals, the objective function Transform into a finite-dimensional nonlinear objective function ,in, For static decision variables; map constraints to virtual time domain constraints.

[0036] Based on the anti-exposure path constraints, terminal location constraints, and terminal speed constraints, an accurate penalty function is established. The exact penalty function satisfies the virtual time domain constraints; among which, For external penalty parameters, As an auxiliary variable;

[0037] By determining auxiliary variables The precise penalty function Transform into minimizing the augmented objective function ;

[0038] Construct the Hamiltonian function and use a numerical optimizer to minimize the augmented objective function. By performing iterative solutions, the optimal interception time can be obtained. .

[0039] Furthermore, based on the anti-exposure path constraints, terminal location constraints, and terminal speed constraints, a precise penalty function is established. The specific method is as follows:

[0040] Overvalue integral for setting the violation of the anti-exposure path constraint ;

[0041] The overall violation overvalue integral of the terminal position and terminal velocity constraints of the satellite. ;

[0042] The overvalue integral of the violation of the anti-exposure path constraint. The overall violation of the terminal position constraint and the terminal velocity constraint by the overvalue integral Substituting the finite-dimensional nonlinear objective function To obtain the exact penalty function .

[0043] Furthermore, the task allocation scheme is updated based on the shortest interception time, specifically as follows:

[0044] Use optimal interception time Replace satellite predictions based on simplified unconstrained relative kinematics models. To the target Minimum arrival time The estimated value is used to update the initial cost matrix; based on the updated initial cost matrix, the task allocation scheme is updated, and it is determined whether the updated task allocation scheme has changed; if the updated task allocation scheme has changed, the task allocation scheme is generated iteratively, and the shortest interception time is solved based on the generated task allocation scheme, until the task allocation scheme generated in two consecutive iterations does not change.

[0045] If the task allocation scheme generated in two consecutive iterations does not change, the optimal interception trajectory is generated based on the task allocation scheme generated in the last iteration.

[0046] The beneficial effects of adopting the above technical solution are as follows: The real-time task allocation and rapid trajectory collaborative optimization method for satellite cluster orbit game provided by this invention overcomes the suboptimal performance problem of traditional staged processing by achieving closed-loop coupling between task allocation and trajectory planning, and can obtain a globally superior collaborative strategy; by using control parameterization and the exact penalty function method, the complex dynamic optimization problem is transformed into a nonlinear programming problem, which significantly reduces the solution complexity and improves computational efficiency; the distributed auction algorithm based on the consensus protocol does not require a central node and only relies on local communication, avoiding single points of failure and exhibiting strong robustness. Compared with existing methods, this invention demonstrates significant advantages and innovative potential in terms of uniformity, computational efficiency, dynamic environment adaptability, and optimization performance. Attached Figure Description

[0047] Figure 1 Flowchart of the method for real-time task allocation and rapid trajectory collaborative optimization in satellite cluster orbit game provided in Embodiment 1 of the present invention;

[0048] Figure 2 The interception trajectory diagram of the satellite interception target provided in Embodiment 1 of the present invention;

[0049] Figure 3 The relative distance variation curve between the satellite and the target provided in Embodiment 1 of the present invention;

[0050] Figure 4 The illumination constraint angle variation diagram provided in Embodiment 1 of the present invention;

[0051] Figure 5 The relative velocity change curve between the satellite and the target provided in Embodiment 1 of the present invention;

[0052] Figure 6 The satellite thrust variation diagram provided in Embodiment 1 of the present invention;

[0053] Figure 7 A schematic diagram of the initial positions of the satellite and the target provided in Embodiment 1 of the present invention;

[0054] Figure 8 The satellite mission allocation result diagram provided in Embodiment 1 of the present invention. Detailed Implementation

[0055] The specific implementation methods of this application will be further described in detail below with reference to the accompanying drawings and embodiments.

[0056] Example 1:

[0057] A method for real-time task allocation and rapid trajectory collaborative optimization in satellite constellation orbit game, such as Figure 1 As shown, it includes the following steps:

[0058] Step 1: Construct a mathematical programming model for satellite cluster orbital game based on multiple satellites and multiple targets, and establish a global objective function;

[0059] Set up satellite set Including serial number of Each satellite, acquire information from each satellite. Payload type, dynamic model and long flight time .

[0060] Set target set Including serial number of One goal, obtain each goal Risk level Required interception payload type and required number of satellites .

[0061] Generate a high-level mission allocation strategy based on the allocation relationship between satellites and targets. ,in Indicates the allocation relationship, when satellite Assigned to target When, set Otherwise set .

[0062] Set the underlying trajectory control strategy for satellites with assigned targets. Set up satellite The underlying trajectory control strategy is a control function that satisfies the dynamic equations and thrust constraints. In order to achieve the goal Interception;

[0063] A global objective function is set with the overall risk level and interception time as the target. As shown in the formula below:

[0064] ;

[0065] in, For satellite Intercept target The cost of removing the risk.

[0066] The constraints of the global objective function are set, including the number of targets intercepted by each satellite, the number of satellites simultaneously participating in the interception of the same target, payload matching constraints, and the maximum range of each satellite. In this embodiment, each satellite is configured to intercept only one target.

[0067] Step 2: Determine the allocation relationship between targets and satellites based on the distributed auction mechanism, and generate a task allocation scheme;

[0068] The distributed auction mechanism includes an initialization phase, a distributed auction phase, a task redistribution phase, and an iterative convergence phase.

[0069] During the initialization phase, the risk removal cost for each satellite intercepting each target is calculated. Intercept target Risk removal cost , For satellite To the target The minimum arrival time is determined by the trajectory optimization problem. During the initialization phase, a simplified unconstrained relative kinematics model (such as the ratio of relative straight-line distance to the average flight speed of the satellite) is used to estimate the arrival time for each satellite. Reach each enemy target initial minimum time This is used as an unconstrained estimate to obtain an initial cost matrix. If satellite and target Payload mismatch or satellite To the target Minimum arrival time Beyond satellite For maximum flight time, satellites are configured. Intercept target Risk removal cost It is positive infinity.

[0070] During the distributed auction phase, a state vector is defined, including the bidding vector for each satellite and the vector for the satellite with the highest bid and largest sequence number; The bidding vector is ,satellite The vector with the highest bid and the largest index is .

[0071] satellite During communication time Receive all neighboring satellites Bidding vector The vector with the highest bid and the largest index Update satellite During communication time The corresponding vector is obtained by the following method:

[0072] For each target, the satellite Bidding vector Bidding vector with all neighboring satellites Perform an element-by-element comparison and select the largest bid vector as the satellite. During communication time Bidding vector .

[0073] Simultaneously, the communication time is updated based on the comparison results of the bidding vectors. The vector with the highest bid and the largest index If satellite The largest bid vector among all neighboring satellites originates from the neighboring satellites. Then the communication time The vector with the highest bid and the largest index The serial number is updated to that of the neighboring satellite. The sequence number; if the maximum bid vector originates from the satellite. itself, then the communication time The vector with the highest bid and the largest index As communication time The vector with the highest bid and the largest index If satellite Bidding vector If the bidding vector is equal to that of a neighboring satellite, then compare the satellites. and neighboring satellites The sequence number is used to select the vector with the largest sequence number and the highest bid, and the vector with the largest sequence number is selected as the communication time. The vector with the highest bid and the largest index .

[0074] During the mission reassignment phase, when the satellite Other satellite pairs with higher serial numbers were discovered and assigned to satellites. goal The bidding vector is no less than that of satellites. When determining the bidding vector, the communication time is re-established based on the stored data. Bidding vector and target returns Establish the maximum net asset value target ( (Target) for satellite Newly allocated targets .

[0075] During the iterative convergence phase, to ensure effective preemption of new tasks and break the bidding deadlock, this embodiment introduces a bidding increment mechanism on the satellite. Based on the bidding vector for the target, add a preset positive number. Obtain satellite During communication time The new bidding vector, with its incrementing mechanism, ensures a monotonically increasing bidding vector, thus guaranteeing that the distributed allocation process will converge after a finite number of iterations. When the communication time... Bidding vectors for all satellites The vector with the highest bid and the largest index When no further updates occur, the auction is considered to have converged.

[0076] Based on communication time The vector with the highest bid and the largest index Generate a globally consistent task allocation scheme, including interception tasks for each satellite.

[0077] Step 3: Based on the task allocation scheme, construct an optimal control problem with the goal of minimizing the interception time, and establish an exact penalty function to solve for the shortest interception time;

[0078] This embodiment addresses the task allocation scheme by constructing an optimal control problem with the objective of minimizing the interception time. A control parameterization method is used to discretize the continuous control input into finite-dimensional parameters, and an exact penalty function method is introduced to handle constraints. The optimal interception trajectory and its corresponding shortest interception time are then solved. The constraint modeling of the optimal control problem is as follows:

[0079] The equations of motion for the satellite relative to the Hill coordinate system are established as follows:

[0080] ;

[0081] in, , , This provides the thrust input for the satellite in the radial, track, and normal directions within the Hill coordinate system. Here are the radial coordinates of the satellite in the Hill coordinate system. Here are the satellite's trajectory coordinates in the Hill coordinate system. These are the normal coordinates of the satellite in the Hill coordinate system. for The first derivative, for The second derivative, for The first derivative, for The first derivative, for The second derivative, For the quality of the satellite, This is the average velocity of the satellite's main orbit, i.e., the orbital angular velocity; The gravitational constant, This represents the orbital radius of the satellite.

[0082] The relative motion dynamics equations of the satellite in the Hill coordinate system are transformed into matrix form to obtain the state equations, as shown in the following formula:

[0083] ;

[0084] in, This is the satellite's relative state vector. To control the input, The state matrix, The input matrix is ​​shown in the following formula:

[0085] ;

[0086] ;

[0087] in, It is a 3×3 identity matrix.

[0088] Establish constraints for satellite approaching the target, including:

[0089] To avoid direct physical collision between the satellite and the target, the satellite's terminal position constraint is established, as shown in the following formula:

[0090] ;

[0091] in, This represents the satellite's final position relative to the target. The maximum distance between the satellite and the target; satellite terminal position constraints. Indicates the satellite's interception time Precisely parked at a point centered on the target with a radius of [missing information]. On the safe sphere.

[0092] To ensure stable flight and effective sensor pointing, the satellite's terminal velocity constraint is established, as shown in the following formula:

[0093] ;

[0094] in, For the satellite during the interception time Relative to the target's terminal velocity, The maximum threshold for terminal velocity; terminal velocity constraints for satellites. Indicates the satellite's interception time The terminal velocity relative to the target is suppressed to the maximum permissible terminal velocity threshold. Within the range.

[0095] During the satellite's approach to the target, to prevent premature exposure to the target's field of view, the satellite needs to be positioned in the path of direct sunlight. Therefore, throughout the entire flight period... Inside, the angle between the line of sight of the target pointing towards the satellite and the direction of sunlight. It must not exceed the safety threshold. .set up The direction vector of sunlight at any given time is a constant vector. The line-of-sight vector pointing from the target to the satellite is the relative position vector. According to the dot product rule of spatial vectors, the included angle... The cosine value can be expressed as:

[0096] ;

[0097] Based on this, the anti-exposure path constraint conditions for the satellite relative to the target are established, as shown in the following formula:

[0098] ;

[0099] Limited by the actual performance of the satellite's onboard engines, the three-axis thrust acceleration vector output by the satellite during its approach to the target is limited. It must be strictly limited by the physical envelope. The thrust amplitude constraint condition for the satellite is established as shown in the following formula:

[0100] ;

[0101] in, This is the maximum thrust constraint for the satellite.

[0102] Based on the satellite's relative motion dynamics equations in the Hill coordinate system and the constraints of the satellite's approach to the target, an optimal control problem is constructed with the objective of minimizing the interception time, and the optimal control law is sought. and optimal interception time , so that the objective function Minimization is achieved as shown in the following formula:

[0103] ;

[0104] And it also satisfies the constraint condition of the satellite approaching the target, as shown in the following formula:

[0105] ;

[0106] in, This is the satellite's initial position.

[0107] The idea behind the control variable parameterization method is to discretize the continuous control input in the time domain and approximate the original continuous control curve using a set of finite-dimensional basis functions or piecewise constants, thereby transforming the solution of the unknown function into the solution of a finite number of scalar parameters. In this embodiment, the total flight time interval of the satellite intercepting the target is... Divided into Several sub-intervals. The set of time nodes is defined as follows: , , , , They are the 1st, 2nd, and 3rd respectively. , Subintervals satisfying:

[0108] ;

[0109] This embodiment uses an equidistant time grid as an example, setting the duration of each sub-interval to be... In any number Sub-intervals Inside, the thrust control vector of the forced satellite is kept constant, that is:

[0110] ;

[0111] in, For the first The constant thrust parameter vector within each subinterval for Direction control parameter values, for Direction control parameter values, for Direction control parameter values, It is a three-dimensional set of real numbers.

[0112] After parameterization of the control variables, the infinite-dimensional function space variables that originally needed optimization were... It was successfully dimensionality reduced and equivalently replaced by a finite-dimensional static decision parameter vector sequence. , for The set of real numbers.

[0113] At this point, the satellite's thrust amplitude constraint condition This is then transformed into an algebraic inequality constraint on each discrete parameter, as shown in the following formula:

[0114] ;

[0115] Since the optimization objective of this embodiment is to find the optimal interception time... The integral domain of interception time It is a dynamically changing, unknown boundary. To solve this problem, time compression is introduced, making... Interception time The original time domain Mapped to the virtual time domain Then the state equation transforms into:

[0116] ;

[0117] Original infinite-dimensional optimal control problem Transforming it into a finite-dimensional nonlinear programming problem, its mathematical model is as follows:

[0118] ;

[0119] in, These are static decision variables.

[0120] Simultaneously satisfying the mapping to the virtual time domain Constraints on the satellite's approach to the target:

[0121] ;

[0122] The specific method for handling constraints based on the exact penalty function method is as follows:

[0123] By embedding the anti-exposure path constraints, terminal location constraints, and terminal velocity constraints into the cost function, the continuous inequality path constraints are transformed into an optimization problem that is easy to solve.

[0124] First, define the violation overdue integral for the anti-exposure lighting constraint. for:

[0125] ;

[0126] in, To prevent the exposure of the illumination constraint function, As an auxiliary variable, For a fixed scaling constant, Let be a given positive real number.

[0127] Secondly, the overall violation threshold for setting the satellite's terminal position constraints and terminal velocity constraints is determined. for:

[0128] ;

[0129] Through the above construction, the original finite-dimensional nonlinear objective function The function is augmented to an exact penalty function, as shown in the following formula:

[0130] ;

[0131] in, For external penalty parameters, All are positive real numbers. The exact penalty function is obtained through... Amplify the penalties for constraint violations, and simultaneously... Force auxiliary variables During the optimization process, it gradually approaches zero, thereby minimizing the augmented cost function. At the same time, it ensures that all physical constraints are strictly satisfied.

[0132] Given auxiliary variables Under the condition of, the exact penalty function Transform into minimizing the augmented objective function As shown in the formula below:

[0133] ;

[0134] in, For the cost of the terminal, For integral cost, terminal cost Including interception time The overall violation of the satellite's terminal position constraints and terminal velocity constraints. :

[0135] ;

[0136] Integer Cost Including penalty terms for continuous path lighting constraints:

[0137] ;

[0138] To solve for the optimal interception time Establish a minimum augmented objective function The mapping relationship between the equations and the state equations. To this end, adjoint variables are introduced. The Hamiltonian function is constructed as shown in the following formula:

[0139] ;

[0140] Adjoint vector The dynamic evolution satisfies the adjoint equation:

[0141] ;

[0142] The terminal transverse condition of the adjoint equation is shown in the following formula:

[0143] ;

[0144] Based on the Hamiltonian function, a numerical optimizer is used to minimize the augmented objective function. By performing iterative solutions, the optimal interception time can be obtained. .

[0145] Step 4: Under the constraint of the global objective function, update the task allocation scheme based on the shortest interception time, and generate the optimal interception trajectory according to the updated task allocation scheme;

[0146] In this embodiment, the shortest interception time obtained in step 3 is fed back to step 2, and the optimal interception time is used. Replace satellite predictions based on simplified unconstrained relative kinematics models. To the target Minimum arrival time The estimated value is used to update the initial cost matrix; based on the updated initial cost matrix, the task allocation scheme is updated, and it is determined whether the updated task allocation scheme has changed; if the updated task allocation scheme has changed, the task allocation scheme is generated iteratively, and the shortest interception time is solved based on the generated task allocation scheme, until the task allocation scheme generated in two consecutive iterations does not change.

[0147] If the task allocation scheme generated in two consecutive iterations does not change, the optimal interception trajectory is generated based on the last generated task allocation scheme, thereby achieving closed-loop coupling and collaborative optimization of task allocation and trajectory optimization.

[0148] To verify the effectiveness of the above method, this embodiment selects the initial exposure state as the method in interception verification step 3, wherein the sunlight direction vector is set as... The initial angle between the line connecting the satellite and the target and the solar illumination vector is approximately 101°. Since the safe concealment zone is defined as a 0°-30° illumination cone, the satellite is initially fully exposed to the target's field of view. To meet concealment requirements, the precise penalty function mechanism in the cost function is significantly activated, causing the satellite to abandon the time-optimal straight-line interception strategy. Simulation results show that to satisfy continuous path constraints, the optimal interception time increases to nearly 1500 seconds. Please refer to [link / reference]. Figures 2 to 5 ,in, Figure 2 This is a trajectory diagram of the satellite interception target. Figure 3 This is a graph showing the change in the relative distance between the satellite and the target. Figure 4 This is a diagram showing the change in the lighting constraint angle. Figure 5 This is the curve showing the relative velocity change between the satellite and the target. Combining the three-dimensional intercept trajectory with the illumination angle change curve, it can be clearly observed that the satellite performed a significant non-coplanar maneuver after takeoff, forcibly suppressing the line-of-sight illumination angle from the initial 101° and pulling it into the safe and feasible region of 30°, and then gliding close to the 30° boundary during the subsequent long-duration flight. Please refer to... Figure 6 , Figure 6 The diagram shows the satellite thrust variation, with the thruster maintaining a saturated output of 0.2 m / s² almost throughout the entire process. Simultaneously, at the terminal moment, it still precisely meets the hard constraints of a safe parking distance of 1 km and a matching velocity of 0.5 m / s. This embodiment fully verifies that the algorithm, under extremely unfavorable initial geometric conditions, can autonomously plan a complex tactical evasion trajectory involving concealment followed by approximation, demonstrating the ability of the hybrid solution architecture to solve high-dimensional non-convex path constraints.

[0149] This embodiment sets up a real-time task allocation and rapid trajectory collaborative optimization method for orbital game among 10 satellites and 5 target verification satellites. The risk level of target 1 is set to level 4, the risk levels of targets 2 and 4 to level 3, the risk level of target 3 to level 5, and the risk level of target 5 to level 1. Please refer to [link to relevant documentation]. Figures 7 to 8 , Figure 7 This is an initial position map of 10 satellites. Figure 8 The task allocation results based on the above parameter settings are presented. These results closely match the preset attack and defense scenarios, verifying the effectiveness and rationality of the model under complex constraints. Specifically: Target 1 has a higher risk level and is intercepted collaboratively by two satellites with corresponding payloads, Satellite 2 and Satellite 4; Target 3 has the highest risk level and is intercepted collaboratively by three satellites with corresponding payloads, Satellite 8, Satellite 9, and Satellite 10, reflecting the principle that high-value targets require more resource investment; Target 2 is intercepted by a single satellite, Satellite 7; Target 4 is intercepted by a single satellite, Satellite 3; Target 5 has the lowest risk level and is intercepted collaboratively by two satellites with corresponding payloads, Satellite 5 and Satellite 6.

[0150] In summary, the method in this embodiment constructs a two-layer collaborative optimization framework for the task allocation and trajectory planning problem in satellite cluster orbital game. This embodiment models the multi-satellite, multi-target allocation problem, which includes payload matching, risk level, and range constraints, as a distributed auction mechanism. It also models the trajectory planning problem, which includes dynamic constraints, thrust saturation constraints, illumination constraints, and terminal constraints, as an optimal control problem. Relying on a distributed auction algorithm based on a consensus protocol and a control parameterization-precise penalty function method, each satellite independently completes the collaborative optimization of target allocation and interception trajectory under conditions relying only on local communication. The method in this embodiment guides multiple satellites to spontaneously form a tacit task allocation and efficient trajectory planning strategy, thereby effectively minimizing the overall risk-weighted interception time of the system while satisfying complex constraints.

[0151] Example 2:

[0152] This embodiment proposes an electronic device, including: one or more processors, and a memory, wherein the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors execute the satellite cluster orbit game real-time task allocation and fast trajectory collaborative optimization method.

[0153] The electronic device can be a mobile phone, computer, or tablet computer, etc., and includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, implements the real-time task allocation and rapid trajectory collaborative optimization method for satellite cluster orbit game as described in the embodiments. It is understood that the electronic device may also include input / output (I / O) interfaces and communication components.

[0154] The processor is used to execute all or part of the steps in the satellite cluster orbit game real-time task allocation and rapid trajectory collaborative optimization method as described in the above embodiments. The memory is used to store various types of data, which may include, for example, instructions for any application or method in the electronic device, as well as application-related data.

[0155] The processor can be implemented as an Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), controller, microcontroller, microprocessor, or other electronic components, and is used to execute the satellite cluster orbit game real-time task allocation and fast trajectory collaborative optimization method described in the above embodiments.

[0156] Example 3:

[0157] This embodiment proposes a computer-readable storage medium that stores executable instructions. When these instructions are executed, if they are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0158] The computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the satellite cluster orbit game real-time task allocation and fast trajectory collaborative optimization method described in the various embodiments of this application.

[0159] The aforementioned storage media include: flash memory, hard disks, multimedia cards, card-type memory (e.g., SD (Secure Digital Memory Card) or DX (Memory Data Register, MDR) memory), random access memory (RAM), static random-access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic storage, disks, optical discs, servers, APP (Application) app stores, and other media capable of storing program verification codes. These media store computer programs, which, when executed by a processor, can implement the various steps of the aforementioned satellite cluster orbit game real-time task allocation and rapid trajectory collaborative optimization method.

[0160] Example 4:

[0161] This embodiment proposes a computer program product, including a computer program or instructions, which, when executed by a processor, implements the aforementioned method for real-time task allocation and rapid trajectory collaborative optimization in satellite cluster orbital game.

[0162] Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a computer program product.

[0163] The various embodiments in this application are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0164] The scope of protection of this application is not limited to the embodiments described above. Obviously, those skilled in the art can make various modifications and variations to this disclosure without departing from the scope and spirit of this disclosure. If such modifications and variations fall within the scope of this disclosure and its equivalents, then the intent of this disclosure also includes these modifications and variations.

Claims

1. A method for real-time task allocation and rapid trajectory collaborative optimization in satellite swarm orbit game, characterized in that, Includes the following steps: A mathematical programming model for satellite cluster orbital game is constructed based on multiple satellites and multiple targets, and a global objective function is established. The allocation relationship between targets and satellites is determined based on a distributed auction mechanism, and a task allocation scheme is generated. Based on the task allocation scheme, an optimal control problem is constructed with the goal of minimizing the interception time. An exact penalty function is established to solve for the shortest interception time. Under the constraint of the global objective function, the task allocation scheme is updated based on the shortest interception time, and the optimal interception trajectory is generated according to the updated task allocation scheme.

2. The method for real-time task allocation and rapid trajectory collaborative optimization in satellite cluster orbit game according to claim 1, characterized in that, A mathematical programming model for satellite cluster orbital game based on multiple satellites and multiple targets is constructed. The specific method for establishing the global objective function is as follows: The serial numbers of multiple satellites are set as follows: Establish a satellite collection ,in, The total number of satellites; obtain the payload type, dynamic equations, and maximum flight duration for each satellite; Set the sequence numbers of multiple targets as follows: Establish a target set ,in, For the total number of targets; obtain the risk level, required intercept payload type, and required number of satellites for each target; Generate a high-level mission allocation strategy based on the allocation relationship between satellites and targets. ,in, Indicates satellite and target The allocation relationship between them, when satellites Assigned to interception target When, set Otherwise set ; The trajectory control strategy for each satellite intercepting its corresponding target is set as a control function that satisfies the satellite's dynamic equations and thrust constraints. ; A global objective function is established to satisfy the trajectory generation strategy and minimize the risk removal cost of all satellite interception targets. As shown in the formula below: ； in, For satellite Intercept target The cost of removing the risk For satellite To the target Minimum arrival time For the goal Risk level; Set constraints for the global objective function, including the number of targets intercepted by each satellite, the number of satellites simultaneously participating in the interception of the same target, payload matching constraints, and the maximum range of each satellite.

3. The method for real-time task allocation and rapid trajectory collaborative optimization in satellite cluster orbit game according to claim 1, characterized in that, The specific method for determining the allocation relationship between targets and satellites based on a distributed auction mechanism is as follows: Initialize the cost matrix Among them, satellite prediction is based on a simplified unconstrained relative kinematics model. To the target Minimum arrival time The estimated value, calculate the satellite Intercept target Risk removal cost If satellite Load type and target The required intercept payload type does not match or the satellite Reach the destination Minimum arrival time Beyond satellite The maximum flight time is used to set a risk removal cost. It is positive infinity; During communication time At that time, each satellite is configured to target... The state vector includes the bidding vector and the vector with the highest bid and largest index; the target... The satellite with the largest bid vector will be assigned. For allocation to satellites Allocated targets ,satellite During communication time Receive all neighboring satellites The state vector during communication time Internal iterative satellite updates During communication time The state vector; in each iteration, based on the price increase mechanism on the satellite For the assigned targets Add a preset positive number to the bidding vector. Obtain satellite During communication time The bidding vector; When neighboring satellites For the assigned targets The bidding vector is not less than the satellite For the assigned targets When bidding on the target vector, the allocated target will be... Assigned to neighboring satellites According to communication time Bidding vector and target returns Calculate the net value for each objective. Select the target with the largest net value Assigned to satellite ; When communication time When the state vectors of all satellites cease to be updated, the auction is considered to have converged; based on communication time... The highest bidder with the largest sequence number generates the task allocation scheme, which includes each satellite and its corresponding interception target.

4. The method for real-time task allocation and rapid trajectory collaborative optimization in satellite cluster orbit game according to claim 3, characterized in that, Update satellite During communication time The specific method for using state vectors is as follows: For each target , will satellite Bidding vector Bidding vector with all neighboring satellites Compare and select satellites The largest bid vector among all neighboring satellites is used as the satellite's bid vector. During communication time Bidding vector ; If satellite The largest bid vector among all neighboring satellites is the bid vector of the neighboring satellites. The bidding vector will then be the satellite During communication time The vector with the highest bid and the largest index The serial number is updated to that of the neighboring satellite. The serial number; If satellite The largest bid vector among all neighboring satellites is the satellite's bid vector. The bidding vector will then be the satellite During communication time The vector with the highest bid and the largest index As communication time The vector with the highest bid and the largest index ; If satellite Bidding vector neighboring satellites If the bidding vectors are equal and the largest, then compare the satellites. and neighboring satellites The vector with the largest sequence number and the highest bid is selected as the satellite. Communication time The vector with the highest bid and the largest index .

5. The method for real-time task allocation and rapid trajectory collaborative optimization in satellite cluster orbit game according to claim 1, characterized in that, The specific method for constructing an optimal control problem based on a task allocation scheme with the objective of minimizing interception time is as follows: Total flight time of satellite interception target Establish objective function Given the constraints, solve for the optimal control law. and optimal interception time , so that the objective function Minimization; the constraints include the satellite's state equation, initial position constraints, terminal position constraints, anti-exposure path constraints, terminal velocity constraints, and thrust amplitude constraints.

6. The method for real-time task allocation and rapid trajectory collaborative optimization in satellite cluster orbit game according to claim 1, characterized in that, The specific method for establishing an exact penalty function to solve for the shortest interception time is as follows: The total flight time interval of the satellite interception target Divided into Subintervals, the objective function Transform into a finite-dimensional nonlinear objective function ,in, For static decision variables; map constraints to virtual time domain constraints. Based on the anti-exposure path constraints, terminal location constraints, and terminal speed constraints, an accurate penalty function is established. The exact penalty function satisfies the virtual time domain constraints; among which, For external penalty parameters, As an auxiliary variable; By determining auxiliary variables The precise penalty function Transform into minimizing the augmented objective function ; Construct the Hamiltonian function and use a numerical optimizer to minimize the augmented objective function. By performing iterative solutions, the optimal interception time can be obtained. .

7. The method for real-time task allocation and rapid trajectory collaborative optimization in satellite cluster orbit game according to claim 6, characterized in that, Based on the anti-exposure path constraints, terminal location constraints, and terminal speed constraints, an accurate penalty function is established. The specific method is as follows: Overvalue integral for setting the violation of the anti-exposure path constraint ; The overall violation overvalue integral of the terminal position and terminal velocity constraints of the satellite. ; The overvalue integral of the violation of the anti-exposure path constraint. The overall violation of the terminal position constraint and the terminal velocity constraint by the overvalue integral Substituting the finite-dimensional nonlinear objective function To obtain the exact penalty function .

8. The method for real-time task allocation and rapid trajectory collaborative optimization in satellite cluster orbit game according to claim 3, characterized in that, The task allocation scheme is updated based on the shortest interception time. The specific method is as follows: Use optimal interception time Replace satellite predictions based on simplified unconstrained relative kinematics models. To the target Minimum arrival time The estimated value is used to update the initial cost matrix; based on the updated initial cost matrix, the task allocation scheme is updated, and it is determined whether the updated task allocation scheme has changed. If the updated task allocation scheme changes, the task allocation scheme is generated iteratively, and the shortest interception time is solved based on the generated task allocation scheme, until the task allocation scheme generated in two consecutive iterations does not change. If the task allocation scheme generated in two consecutive iterations does not change, the optimal interception trajectory is generated based on the task allocation scheme generated in the last iteration.

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