A Distributed Model Predictive Path Planning Method for Intelligent Spacecraft Clusters

Abstract

This invention provides a distributed model predictive path planning method for intelligent spacecraft swarms, comprising the following steps: determining the target orbital parameters and initial orbital parameters of each spacecraft in the swarm based on the swarm's path planning objectives; establishing a spacecraft dynamics model and using state vectors to describe the spacecraft's motion state and trajectory information; determining the constraints for each spacecraft's path planning; constructing a model predictive controller for each spacecraft; optimizing the controller parameters using the Metropolis-Hastington sampling algorithm; setting the sampling period and discretizing the spacecraft orbital dynamics model; using the discretized spacecraft orbital dynamics model as the predictive model; using the target orbital parameters as the control objective; and combining the constraints, performing model predictive control on the trajectory of each spacecraft. This invention solves the problem of online real-time trajectory generation for spacecraft swarms, reduces computational load, and improves controller robustness.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft path planning technology, and specifically relates to a method for predictive path planning using a distributed model for intelligent spacecraft clusters. Background Technology

[0002] Driven by the continuous demands of space applications and the advancement of aerospace technology, on the one hand, the scope of human exploration and development of space resources has gradually expanded from orbital space to deep space domains such as the Moon and Mars, and inward to the near space between traditional aviation and aerospace, making space activities face a more complex environment; on the other hand, the methods by which spacecraft perform missions are also constantly evolving, from independent implementation by a single entity to collaborative completion by multiple entities, further increasing the difficulty of control. Spacecraft trajectory planning, for a given flight mission, considers factors such as the spacecraft's dynamic characteristics and constraints to design a flight trajectory that starts from the initial state and ends when the terminal conditions are met, and has practical physical feasibility. Spacecraft trajectory planning can maximize the overall system efficiency. Mission trajectory planning and control best reflect the characteristics of spacecraft and are key to reducing the risk of spacecraft missions in complex environments and improving mission operational reliability and benefits. In fact, trajectory planning and control are important issues throughout the entire life cycle of a spacecraft system, playing an irreplaceable role in scheme demonstration and design, as well as the flight mission operation phase.

[0003] Spacecraft trajectory design often requires optimizing performance indicators such as fuel / energy consumption and mission duration while satisfying complex constraints such as mission environment and spacecraft physical performance. This type of optimal trajectory planning problem can typically be described as a constrained nonlinear optimal control problem. Spacecraft trajectory planning and control is characterized by high dimensionality of state variables, numerous constraints, strong coupling, and high uncertainty, posing significant challenges in both theory and technical implementation. The main challenges facing spacecraft trajectory planning and control are as follows: First, the system dynamics model is generally high-dimensional and strongly nonlinear, easily leading to increased computational complexity and reduced planning efficiency, while also increasing the difficulty of controller design; second, there are numerous constraints involving multiple aspects such as spacecraft performance, mission environment, and system safety; third, there are many planning elements that need to be considered, and these elements are interconnected, not only between state variables but also between control inputs, indicators / constraints, and state variables; fourth, the increased system complexity and uncertainty further increase the requirements for the robustness of the planning results and the robustness of the trajectory control algorithm.

[0004] Traditional spacecraft trajectory planning is mathematically described as a constrained nonlinear control problem. Advances in control theory and computer technology have spurred various numerical methods for solving optimal control problems, broadly categorized into indirect and direct methods. Direct methods discretize the original continuous optimal control problem, transforming it into a high-dimensional nonlinear parameter optimization problem. Indirect methods, based on Pontryagin's extremum principle, transform the constrained optimal control problem into a two-point boundary value problem satisfying the necessary first-order optimality condition, and then numerically solve the target function to obtain the optimal control. Commonly used optimal control methods require optimization over the entire time domain, generally only handling linearized models and relatively simple constraints, resulting in very high computational complexity. Because optimal control overemphasizes optimality, it suffers from drawbacks such as difficulty in solving nonlinear cases with complex constraints and the need for precise system model description. Therefore, optimal control methods typically involve high computational cost, slow convergence, and a tendency to converge to local optima. Recent algorithms using artificial intelligence algorithms such as particle swarm optimization can address these issues to some extent, but real-time trajectory planning remains unreliable.

[0005] Model predictive control (MDC) is an emerging and powerful advanced process control technique. MDC based on rolling time-domain optimization is grounded in iterative, finite-time rolling optimization of the controlled entity model. Within a time window, the state of the controlled entity is sampled, and for a very short future rolling time domain, a cost-minimizing control strategy (numerical minimization calculus) is computed. Specifically, online or on-the-fly computation is used to explore the state trajectory evolving from the current state, and the cost-minimizing strategy before the time window is computed using the Euler-Lagrange equations. The control strategy only implements the first step; then, the system state is sampled again, and a new control strategy is computed from the new state, predicting a new state path. While this method is not necessarily optimal, the simplification in the model and time domain significantly improves its real-time performance compared to optimal control methods.

[0006] The design of the cost function for traditional model predictive control requires a set of appropriate parameters. Parameter design usually relies on the experience of the controller designer. However, the performance of the controller depends to a large extent on the controller parameters, which poses a great challenge to parameter design.

[0007] Current spacecraft swarm algorithms require a central node to obtain the initial states of all spacecraft and calculate the trajectories of all spacecraft from the starting point to the destination in one go. This is computationally intensive and lacks robustness. Most existing spacecraft swarm path planning algorithms employ optimal control algorithms, which are computationally intensive, have slow convergence speeds, and are prone to converging to local optima. Existing model predictive control algorithms applied to spacecraft rely on manual adjustment of the objective function parameters, and there is currently no intelligent method for automatically tuning these parameters. Summary of the Invention

[0008] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a distributed model prediction path planning method for intelligent spacecraft clusters, which reduces the computational load of spacecraft cluster path planning and effectively improves the computational accuracy and stability.

[0009] The technical solution of this invention is:

[0010] A distributed model prediction path planning method for intelligent spacecraft clusters includes the following steps:

[0011] (1) Determine the reference trajectory of each spacecraft in the cluster from its initial orbit to its target orbit based on the path planning objective of the spacecraft cluster;

[0012] (2) Assuming that each spacecraft is only considered in terms of weight and not shape, and is only subject to the control force generated by the gravity of the central celestial body and its propulsion device, and that the central celestial body is an ideal central gravitational body, a spacecraft dynamics model is established, and the motion state and trajectory information of the spacecraft are described by state vectors.

[0013] (3) Determine the constraints of the path planning of each spacecraft, including determining the set of feasible state vectors of each spacecraft based on the position boundary constraints of each spacecraft, determining the set of feasible control quantities of each spacecraft based on the fuel limit carried by each spacecraft, and the safe distance constraints between each spacecraft and other spacecraft in the spacecraft cluster.

[0014] (4) Construct model predictive controllers for each spacecraft, set the sampling period and discretize the spacecraft orbital dynamics model, use the discretized spacecraft orbital dynamics model as the predictive model, take the reference trajectory as the control target, and combine the constraints to perform model predictive control for each spacecraft.

[0015] Preferably, the step of performing model predictive control on each spacecraft separately involves: setting a prediction time domain and a control time domain; at each sampling time, obtaining the current state vector of the spacecraft; predicting the trajectory of the spacecraft in the prediction time domain based on the control quantity and prediction model in the control time domain; establishing a model predictive control optimization equation in the prediction time domain by combining the reference trajectory and constraints in the prediction time domain; solving the optimization equation to obtain the optimal control quantity sequence in the control time domain; and applying the first control quantity in the sequence to the spacecraft.

[0016] Preferably, the model predictive control optimization equation is specifically as follows:

[0017]

[0018] stx i,k + =f(x) i,k )

[0019] x i,k ∈X i

[0020] u i,k ∈U i

[0021] s(x i,k )-s(x j,k )≥R safe for j∈N i

[0022] Where, x i,k Let x represent the state vector of spacecraft i after k sampling periods. i,k,r Let u represent the expected state vector of spacecraft i after k sampling periods. i,k Let x represent the control quantity of spacecraft i after k sampling periods, where N represents the number of sampling periods included in the prediction time domain. i + =f(x) i X represents a discretized spacecraft dynamics model. i U represents the set of feasible state vectors for spacecraft i. i Let s(x) represent the set of feasible control variables for spacecraft i. i,k ),s(x j,k R represents the position information of spacecraft i and j after k sampling periods. safe N represents the minimum safe distance. i This indicates that the distance to spacecraft i is less than the warning threshold R. warn The assembly of spacecraft, R warn >R safe The positive semidefinite matrices Q, P, R are the controller parameters of the model predictive controller.

[0023] Preferably, the controller parameters of the model prediction controller are determined in the following manner:

[0024] Different controller parameters are randomly generated and simulations are carried out. Under different controller parameter conditions, the model predicts the controller to control the spacecraft to track the reference trajectory, obtains the cumulative error between the simulated trajectory and the reference trajectory, and obtains the probability distribution between the controller parameters and the cumulative error.

[0025] The Metropolis-Hastington algorithm is used to sample from the probability distribution to determine the controller parameters.

[0026] Preferably, the step of sampling from the probability distribution using the Metropolis-Hastington algorithm to determine the controller parameters specifically includes:

[0027] (11) Select an initial state ω0 and let the number of iterations t = 0;

[0028] (12) Assume the current state ω t Transition to candidate state ω' t The candidate state ω' is determined according to the following expression, following a Gaussian distribution. t Probability of acceptance:

[0029]

[0030] d(ω)=exp(-m(ω))

[0031] Where m(ω) represents the cumulative error of the model predictive controller under the controller parameters corresponding to this state;

[0032] (13) Generate a random number u from a uniform distribution in [0,1].

[0033] If u≤α, then accept the candidate state and update ω. t+1 =ω' t ,

[0034] If u > α, then reject the candidate state and maintain the original state ω. t+1 =ω t ;

[0035] (14) Let t = t + 1, repeat steps (102) and (103) until the number of iterations t reaches the preset number, and take the controller parameters corresponding to the state with the minimum cumulative error as the final controller parameters of the model prediction controller.

[0036] Preferably, the spacecraft dynamics model is as follows:

[0037]

[0038]

[0039] Where r is the position vector from the Earth's center to the spacecraft, a represents the control force acceleration vector, t represents time, μ is the gravitational constant, and F... max To control the force amplitude, I sp Let g be the specific impulse of the engine, and g0 be the gravitational acceleration at sea level.

[0040] Preferably, the position boundary constraints of each spacecraft are achieved by limiting the range of values ​​for orbital elements, specifically including:

[0041] Set the range of values ​​for the semi-major axis to [a min ,a max ]; Set the eccentricity range to [e min ,e max The orbital inclination angle ranges from [i] to [i]. min i max The right ascension of the ascending node ranges from [0, 180°], the argument of perigee ranges from [-180°, 180°], and the true anomaly ranges from [0, 360°].

[0042] Preferably, the state vector is composed of the spacecraft's position vector and velocity vector.

[0043] Preferably, the state vector is composed of the spacecraft's Kepler orbital parameters.

[0044] The advantages of this invention compared to the prior art are:

[0045] (1) This invention adopts a distributed model predictive control algorithm. The spacecraft only needs to obtain information from neighboring spacecraft to calculate the optimal control law. Compared with the traditional centralized control, distributed control has better scalability, robustness and adaptability. At the same time, the control algorithm adopts a rolling optimization strategy to perform optimization calculations online, which has low computational cost and good dynamic performance.

[0046] (2) This invention uses the Metropolis-Hastington algorithm to estimate the model and predict the optimal control parameters of the controller, eliminating the need for manual tuning of the control parameters and improving the ease of use of the controller; at the same time, the optimal control parameters obtained by this algorithm are a function of the spacecraft state, and the controller can dynamically adjust the parameters under different motion states to achieve optimal performance. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0048] Figure 2 This is a block diagram of the method of the present invention;

[0049] Figure 3 This is a schematic diagram of the spacecraft cluster path planning of the present invention;

[0050] Figure 4 This is a schematic diagram of the coordinate system modeling in an embodiment of the present invention. Detailed Implementation

[0051] The features and advantages of the present invention will become clearer and more explicit through the following detailed description.

[0052] The contents not described in detail in this specification are common knowledge to those skilled in the art.

[0053] like Figures 1 to 2 As shown, this embodiment discloses a distributed model predictive path planning method for intelligent spacecraft clusters. It generates trajectories online based on distributed model predictive control and optimizes the model predictive controller parameters using the Metropolis-Hastington sampling algorithm, including:

[0054] Step 101: Establish a model for the spacecraft trajectory planning problem, and use state vectors to describe the spacecraft's motion state and orbital information.

[0055] In this embodiment, as Figure 4 As shown, to facilitate modeling the spacecraft, three coordinate systems are established: a geocentric inertial coordinate system, a geocentric orbital coordinate system, and a spacecraft orbital coordinate system. The geocentric inertial coordinate system uses the Earth's center of mass as its origin. The x-axis points from the Earth's center of mass along the intersection of the ecliptic plane and the equatorial plane to the vernal equinox. The z-axis points from the Earth's center of mass along the Earth's rotation axis to the north. The y-axis follows the right-hand screw rule with the x and z axes. The geocentric orbital coordinate system uses the Earth's center of mass as its origin. The x-axis points from the Earth's center of mass along the orbital plane to the perigee. The y-axis points from the Earth's center of mass along the semi-major axis to the true anomaly angle. The z-axis points from the Earth's center of mass along the angular momentum vector. It also follows the right-hand screw rule with the x and y axes. The orbital coordinate system of the spacecraft has the spacecraft's center of mass as its origin. The x-axis points from the spacecraft's center of mass along the orbital plane toward the nose of the spacecraft. The y-axis points from the spacecraft's center of mass along the spacecraft's motion and is perpendicular to the x-axis. The z-axis points from the spacecraft's center of mass along the normal direction of the orbital plane and satisfies the right-hand screw rule with the x-axis and y-axis.

[0056] Preferably, the state vector includes a set of position vectors r and velocity vectors or a set of Keplerian orbital parameters. Position and velocity information and Keplerian orbital parameter information can be interconverted to obtain spacecraft motion information and spacecraft orbital characteristics. Keplerian orbital parameters are described by a set of vectors [aei Ω ω θ], where a is the semi-major axis, e is the eccentricity, i is the orbital inclination, Ω is the right ascension of the ascending node, ω is the argument of perigee, and θ is the true anomaly.

[0057] Step 102: Assuming that only the weight of the spacecraft is considered and its shape is ignored, and that it is only subject to the control force generated by the central gravity and its propulsion device, and that the central celestial body is an ideal central gravitational body, establish the spacecraft dynamics equations.

[0058] As a further preferred technical solution, based on the aforementioned assumptions, the dynamic equations of the spacecraft's non-Kepler motion are as follows:

[0059]

[0060] Where r is the position vector from the Earth's center to the spacecraft, a represents the control force acceleration vector, t represents time, and μ is the gravitational constant;

[0061] Under finite continuous thrust, the differential equation for the mass change of the spacecraft is as follows:

[0062]

[0063] Among them, F max I represents the engine thrust amplitude. sp Let F be the engine's specific impulse, measured in seconds, and g0 be the gravitational acceleration at sea level. Since engine thrust is often not adjustable, it is generally set to F. max It is a constant value.

[0064] In this embodiment, as Figure 3 As shown, the type and mass of the spacecraft are determined. By establishing dynamic equations and differential equations of mass change under finite continuous thrust for each spacecraft, the change in the motion state of the spacecraft under the action of a specified thrust generated by the propulsion device can be determined.

[0065] Step 103: Determine the spacecraft position boundary constraints by limiting the range of values ​​for each orbital element.

[0066] It should be noted that the specific numerical range of each orbital element is set to the range of the semi-major axis of the orbital parameters as [a min ,a max To avoid singular values ​​in orbital dynamics models based on classical orbital elements when the eccentricity e or orbital inclination i is zero or small, an eccentricity constraint range [e] is set for spacecraft. min ,e max The orbital inclination angle ranges from [i] to [i]. min i max The right ascension of the ascending node ranges from [0, 180°], the argument of perigee ranges from [-180°, 180°], and the true anomaly ranges from [0, 360°].

[0067] Step 104: Determine the spacecraft's energy boundary value based on the spacecraft's fuel carrying capacity.

[0068] It should be noted that the thrust required during the orbital maneuvering swarm flight of the spacecraft is provided by fuel combustion, and the range of usable energy for the spacecraft is determined based on the fuel capacity of the spacecraft.

[0069] E≤E max

[0070] Where E represents the spacecraft's available energy, E max It represents all the energy that the spacecraft can provide from burning fuel.

[0071] In this embodiment, the fuel conversion rate is determined according to the spacecraft type, the total available energy is determined according to the initial fuel type and mass, the spacecraft energy boundary value is further obtained, and the energy required by the spacecraft is limited to within the energy boundary value.

[0072] Step 105: Construct a network topology diagram of the spacecraft cluster and establish spacecraft space security constraints.

[0073] As a further preferred technical solution, a spacecraft distance warning threshold R is set. warn The warning threshold R warn It should be greater than the minimum safe distance.

[0074] Furthermore, during the spacecraft's movement, when the distance between the spacecraft and other surrounding spacecraft is less than the warning threshold R... warn At the same time, they establish mutual communication and periodically broadcast their own position information, which is then taken into account in subsequent trajectory generation. The constraints are expressed as follows:

[0075] s(x i )-s(x j )≥R safe for j∈N i

[0076] Where s(x) i ),s(x j ) represents the spacecraft's position information, R safe N represents the minimum safe distance. i This indicates that the distance to spacecraft i is less than the warning threshold R. warn A collection of spacecraft.

[0077] Step 106: Determine the target orbit parameters based on the set path planning objectives, and determine the initial orbit parameters for each spacecraft.

[0078] In this embodiment, the parameter selection is shown in the table below.

[0079] Table 1 Initial and target orbital parameters of the spacecraft cluster in the embodiments of the present invention

[0080] parameter Aircraft 1 Aircraft 2 Aircraft 1 Aircraft 4 Target orbit semi-long shaft 14000 13000 11000 10000 12000 Eccentricity 0.2 0.13 0.15 0.19 0.14 track inclination 0.16 0.25 0.15 0.22 0.20 Right ascension of ascending node 1.00 1.00 1.00 1.00 1.00 Perimeter Argument 0.10 0.10 0.10 0.10 0.10 True near point angle 3.00 0 1.00 0.70 - quality 1000 1000 1000 1000 -

[0081] Step 107: At each sampling time, the Metropolis-Hastington algorithm is used to sample and optimize the parameters.

[0082] In this embodiment, step 107 may specifically include the following sub-steps:

[0083] Sub-step 1071: Parameter initialization. Select the initial state ω0 according to the parameters in step 106, and set time t = 0.

[0084] Sub-step 1072: Select the initial parameter distribution and assume the transition model t(ω) t+1 ,ω t It follows a Gaussian distribution.

[0085] Sub-step 1073 calculates the probability that the new distribution is accepted as follows:

[0086]

[0087] Where the scoring function d(ω) t In this embodiment, the following definitions apply.

[0088] d(ω)=exp(-m(ω))

[0089] Where m(ω) represents the cumulative error metric accumulated by the controller during trajectory planning, and the error for each measurement can be obtained from state estimation.

[0090] Sub-step 1074: Generate a random number u from a uniform distribution in [0,1]. If u ≤ α, then accept the state and update ω. t+1 If u > α, then accept the state and maintain the original state;

[0091] Sub-step 1075: Let t = t + 1, and repeat the above process.

[0092] Step 108: Solve the trajectory optimization problem online using distributed model predictive control based on the sampling information.

[0093] As a further preferred technical solution, after each sampling, a distributed model is established using the dynamic equations of the discretized spacecraft to solve the predictive control optimization problem. The specific control requirements are as follows:

[0094]

[0095] stx i,k + =f(x) i,k )

[0096] x i,k ∈Xi

[0097] u i,k ∈U i

[0098] s(x i,k )-s(x j,k )≥R safe for j∈N i

[0099] Where x i,k Let x represent the state of spacecraft i at step k. i,k,r U represents the reference state of spacecraft i at step k. i,k Let x represent the input of spacecraft i at step k. i + =f(x) i X represents the discrete state transition equation of the spacecraft. i and U i This represents the feasible states and input set of the spacecraft. The positive semi-definite matrices Q, P, and R are the parameters of the cost function for model predictive control.

[0100] Step 109: Numerically solve the optimization equations of the model predictive control, obtain the control sequence, and apply the first output to the spacecraft.

[0101] In this embodiment, the equations of the model predictive controller described in step 108 are solved, and the output control quantity is applied to the spacecraft in the manner of generating thrust through the propulsion device, thereby planning the trajectory of the spacecraft in real time online.

[0102] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

[0103] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. An intelligent spacecraft swarm distributed model predictive path planning method, characterized in that, The method comprises the following steps: (1) determining reference trajectories of each spacecraft in the cluster from initial orbits to target orbits according to path planning objectives of the spacecraft cluster; (2) assuming that each spacecraft only considers weight and does not consider shape, is only subjected to central celestial body gravity and control force generated by a propulsion device, and the central celestial body is an ideal central gravity body, establishing a spacecraft dynamics model, and adopting a state vector to describe motion states and trajectory information of the spacecraft; (3) determining constraint conditions of path planning of each spacecraft, including determining a feasible state vector set of each spacecraft according to position boundary constraints of each spacecraft, determining a feasible control amount set of each spacecraft according to fuel limits carried by each spacecraft, and determining safety distance constraints of each spacecraft and other spacecraft in the spacecraft cluster; (4) respectively constructing a model predictive controller of each spacecraft, setting a sampling period, discretizing the spacecraft orbit dynamics model, taking the discretized spacecraft orbit dynamics model as a prediction model, taking the reference trajectory as a control target, and combining the constraint conditions to perform model predictive control on each spacecraft respectively; The model predictive control on each spacecraft respectively specifically comprises: setting a prediction time domain and a control time domain, acquiring a current state vector of the spacecraft at each sampling time, predicting a trajectory of the spacecraft in the prediction time domain according to control amounts in the control time domain and the prediction model, combining the reference trajectory in the prediction time domain and the constraint conditions to establish a model predictive control optimization equation in the prediction time domain, solving the optimization equation to obtain an optimal control amount sequence in the control time domain, and applying a first control amount in the sequence to the spacecraft; The model predictive control optimization equation specifically comprises: x i,k ∈X i u i,k ∈U i s(x i,k )-s(x j,k )≥R safe ,for j∈N i where x i,k represents the state vector of spacecraft i after k sampling periods, x i,k,r represents the expected state vector of spacecraft i after k sampling periods, u i,k represents the control amount of spacecraft i after k sampling periods, N represents the number of sampling periods contained in the prediction horizon, x i + = f(x i ) represents the discretized spacecraft dynamics model, X i represents the feasible state vector set of spacecraft i, U i represents the feasible control amount set of spacecraft i, s(x i,k ), s(x j,k ) represents the position information of spacecraft i, j after k sampling periods, R safe represents the minimum safety distance, N i represents the spacecraft set whose distance to spacecraft i is less than the alert threshold R warn , R warn > R safe , the semi-positive definite matrix Q, P, R is the controller parameter of the model predictive controller.

2. The intelligent spacecraft swarm distributed model predictive path planning method of claim 1, wherein, Controller parameters of the model predictive controller are determined in the following manner: Different controller parameters are randomly generated and simulation is carried out, the spacecraft is controlled to track the reference trajectory under different controller parameters by using the model predictive controller, cumulative errors of simulation trajectories and the reference trajectory are acquired, a probability distribution between the controller parameters and the cumulative errors is obtained; Controller parameters are determined by sampling the probability distribution by using a Metropolis-Hastings algorithm.

3. The intelligent spacecraft swarm distributed model predictive path planning method of claim 2, wherein, The determination of the controller parameters by sampling the probability distribution by using the Metropolis-Hastings algorithm specifically comprises: (11) selecting an initial state ω0 and letting an iteration number t = 0; (12) Assume current state ω t Transition to candidate state ω ‘ t Satisfies Gaussian distribution, determine candidate state ω according to the following expression ‘ t Probability of being accepted: d(ω) = exp(-m(ω)) Wherein, m(ω) represents a cumulative error of the model predictive controller under the controller parameters corresponding to the state; (13) generating a random number u from a uniform distribution of [0, 1], If u < a, accept the candidate state and update w t+1 = w ‘ t , If u > a, reject the candidate state and keep the original state ω t+1 = ω t ; (14) letting t = t + 1, repeating steps (102) and (103) until the iteration number t reaches a preset number, and taking the controller parameters corresponding to a state with the minimum cumulative error as the final controller parameters of the model predictive controller.

4. The intelligent spacecraft swarm distributed model predictive path planning method of claim 3, wherein, The spacecraft dynamics model specifically comprises: where r is the position vector from the center of the Earth to the spacecraft, a represents the control force acceleration vector, t represents time, μ is the gravitational constant, F max is the control force magnitude, I sp is the specific impulse of the engine, and g0is the sea level gravitational acceleration.

5. The intelligent spacecraft swarm distributed model predictive path planning method of claim 4, wherein, The position boundary constraints of each spacecraft are achieved by limiting value ranges of orbit elements, and specifically comprise: The value range of the semi-major axis is [a min ,a max ]; the value range of the eccentricity is [e min ,e max ], the value range of the orbital inclination is [i min ,i max ], the value range of the longitude of the ascending node is [0, 180°], the value range of the argument of the perigee is [-180°, 180°], and the value range of the true anomaly is [0, 360°].

6. The method according to any one of claims 1-5, wherein, The state vector is composed of a position vector and a velocity vector of the spacecraft.

7. The method according to any one of claims 1-5, wherein, The state vector is composed of Kepler orbit parameters of the spacecraft.

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