Spacecraft attitude trajectory planning method and device for differential charging of heterogeneous surfaces

Abstract

The application discloses a spacecraft heterogeneous surface differential charging attitude trajectory planning method and device, relates to the spacecraft attitude control technical field, and can efficiently output the attitude trajectory by combining the model with the physical model for rapid screening and accurate review in the planning stage, and considering charging safety and multiple constraints. The method comprises the following steps: in the offline training stage, a physical constraint multi-task graph neural network agent model is trained; in the attitude planning application stage, multiple candidate attitude trajectories satisfying basic path constraints are generated; the physical constraint multi-task graph neural network agent model is used for charging risk evaluation and sorting of the multiple candidate attitude trajectories, and a preset number of candidate attitude trajectories are selected as a to-be-reviewed trajectory set; the surface charging physical model is called for numerical review for the to-be-reviewed trajectory set, and an attitude trajectory satisfying multiple constraints is output.

Description

Technical Field

[0001] This application relates to the field of spacecraft attitude control technology, and in particular to an attitude trajectory planning method and apparatus for differential charging of heterogeneous surfaces of spacecraft. Background Technology

[0002] When spacecraft operate in the space plasma environment, their outer surfaces are subjected to the combined effects of various currents, including electrons, ions, photoelectrons, and secondary electrons. Different surfaces form different charging equilibrium states due to differences in material properties, electrical characteristics, solar illumination conditions, and space orientation, resulting in differential potentials between the surface and the structural ground or between adjacent surfaces. When the differential potential is too large, it may induce electrostatic discharge, causing serious interference or damage to solar cell arrays, thermal control materials, sensors, and electronic equipment. During attitude maneuvers, the normal direction of each surface, the solar incidence angle, local solar illumination and shadow conditions, and self-shading relationships all change. In addition, the surface potential has dynamic response and charge memory effect, which means that even if the initial attitude is exactly the same as the target attitude, different intermediate attitude paths and maneuver speeds may lead to drastically different peak differential potentials throughout the process. Therefore, how to effectively predict and reduce differential charging risks in attitude maneuver planning has become a critical problem that urgently needs to be solved.

[0003] Existing technologies address the above problems primarily from three aspects: The first category is numerical analysis methods for spacecraft surface charging. These methods establish numerical models based on the spacecraft's three-dimensional structure, surface materials, space plasma environment, and solar orientation. By inputting structural and material parameters, as well as electron, ion, sunlight, and environmental parameters, they calculate surface current balance or particle transport, outputting the surface potential, differential potential, and discharge risk for a given configuration and attitude. However, existing surface charging analysis methods treat the spacecraft's attitude or attitude history as externally known input, only used to evaluate the risk of a given trajectory. They do not directly generate attitude geometry paths and maneuver velocities based on charging prediction results. When there are many feasible intermediate trajectories for the same starting and ending attitude, high-overhead numerical integration or particle simulations need to be performed one by one, making it difficult to quickly screen trajectories with low differential potentials.

[0004] The second category is spacecraft attitude maneuver planning methods. These methods take initial attitude, target attitude, maneuver time, angular velocity and angular acceleration constraints, control torque, and load pointing constraints as inputs. They generate attitude trajectories using quaternion interpolation, optimal control, model predictive control, sampling planning, or intelligent optimization. Optimization objectives typically include shortest path, shortest time, minimum energy consumption, and avoidance of prohibited pointing regions. However, existing attitude maneuver planning primarily focuses on rigid body kinematics, dynamics, and mission constraints, failing to establish the dynamic charging state of heterogeneous surfaces or evaluate intermediate attitudes based on the material and electrical properties of each surface, initial state, and local irradiation history. This can lead to situations where the initial and final attitudes meet electrostatic safety requirements, but large transient differential potentials arise during intermediate maneuver phases.

[0005] The third category involves mitigating charging and discharging risks through irradiation angle offsetting or hardware-based methods. Examples include calculating the solar panel's offset angle relative to the sun based on on-orbit telemetry and power margin, or employing hardware protection measures such as conductive coatings, grounding, ultraviolet or electron emission devices, and plasma contactors. However, existing hardware protection schemes primarily target specific components, fixed orientations, or dedicated hardware, failing to address the challenge of reducing the maximum differential potential between multiple heterogeneous surfaces throughout the entire maneuvering process from any initial attitude to any target attitude using selectable attitude paths and velocity curves. Furthermore, fixed offset angles cannot fully utilize the control degree of freedom that allows for multiple continuous paths within the same starting and ending attitude.

[0006] In summary, existing technologies lack a closed-loop coupling mechanism between attitude trajectory generation and dynamic surface charging prediction, making it difficult to quickly select the optimal attitude trajectory with low differential charging risk throughout the entire process while satisfying kinematic and task constraints. Summary of the Invention

[0007] In view of this, this application provides an attitude trajectory planning method and apparatus for differential charging of heterogeneous surfaces of spacecraft. The main purpose is to solve the problem that the existing technology lacks a closed-loop coupling mechanism between attitude trajectory generation and dynamic surface charging prediction, making it difficult to quickly select the optimal attitude trajectory with low risk of differential charging throughout the entire process under the premise of satisfying kinematic and mission constraints.

[0008] According to the first aspect of this application, an attitude trajectory planning method for differential charging of heterogeneous surfaces of a spacecraft is provided, comprising: During the offline training phase, a physical charging physical model is used to generate supervision labels on diverse attitude trajectory samples to train a physical constraint multi-task graph neural network proxy model. The physical constraint multi-task graph neural network proxy model includes a heterogeneous surface message passing graph structure, which is constructed based on the heterogeneous surface units divided on the spacecraft surface as nodes, according to surface geometric adjacency relationships or preset information association rules. In the attitude planning application phase, multiple candidate attitude trajectories that satisfy the basic path constraints are generated based on the spacecraft's kinematic boundaries and attitude maneuver requirements. The charging risk assessment and sorting of the multiple candidate attitude trajectories are performed using the physical constraint multi-task graph neural network surrogate model, and a preset number of candidate attitude trajectories are selected as the set of trajectories to be reviewed. The surface charging physical model is called to numerically verify each trajectory in the set to be verified, and the attitude trajectory that satisfies multiple constraints is output. The multiple constraints include at least charging safety constraints, task constraints and actuator constraints.

[0009] According to a second aspect of this application, an attitude trajectory planning device for differential charging of heterogeneous surfaces of a spacecraft is provided, comprising: The training unit is used to generate supervision labels on diverse attitude trajectory samples using the surface charging physical model during the offline training phase, and to train the physical constraint multi-task graph neural network proxy model. The physical constraint multi-task graph neural network proxy model includes a heterogeneous surface message passing graph structure, which is constructed based on the heterogeneous surface units divided on the spacecraft surface as nodes, according to the surface geometric adjacency relationship or preset information association rules. The generation unit is used in the attitude planning application phase to generate multiple candidate attitude trajectories that satisfy the basic path constraints based on the spacecraft's kinematic boundaries and attitude maneuver requirements. The selection unit is used to perform charging risk assessment and sorting on the multiple candidate attitude trajectories using the physical constraint multi-task graph neural network surrogate model, and select a preset number of candidate attitude trajectories as a set of trajectories to be reviewed. The verification unit is used to call the surface charging physical model to verify each trajectory in the set to be verified, and output the attitude trajectory that satisfies multiple constraints; the multiple constraints include at least charging safety constraints, task constraints and actuator constraints.

[0010] According to a third aspect of this application, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the method described in the first aspect above.

[0011] According to a fourth aspect of this application, a readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect above.

[0012] By employing the above technical solution, the attitude trajectory planning method and apparatus for differential charging of heterogeneous surfaces of spacecraft provided in this application have the following advantages compared with the prior art: By training a physical constraint multi-task graph neural network surrogate model with a heterogeneous surface message passing graph structure using supervised labels generated on diverse attitude trajectory samples during the offline training phase using a surface charging physical model, and generating multiple candidate attitude trajectories based on spacecraft kinematic boundaries and attitude maneuver requirements during the attitude planning application phase, the surrogate model first performs charging risk assessment and sorts the candidate attitude trajectories to select the set of trajectories to be verified. Then, the surface charging physical model is called to verify each trajectory in the set of trajectories to be verified numerically. This forms a two-layer planning architecture that combines rapid screening by the surrogate model with accurate verification by the physical model. It effectively represents the spatial correlation characteristics between heterogeneous surfaces by using the graph structure constructed with heterogeneous surface units as nodes and based on surface geometric adjacency relationships or preset information association rules, while avoiding the huge computational overhead of directly performing physical integration on all candidate attitude trajectories. At the same time, numerical verification ensures that the final output attitude trajectory strictly meets charging safety constraints, task constraints, and actuator constraints, thus balancing attitude trajectory planning efficiency and result reliability.

[0013] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and in order to make the above and other objects, features and advantages of this application more easily understood, specific embodiments of this application are given below. Attached Figure Description

[0014] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart illustrating the attitude trajectory planning method for differential charging of a spacecraft heterogeneous surface in one embodiment of this application. Figure 2 This is a schematic diagram of the construction process of a heterogeneous surface message passing graph structure in one embodiment of this application; Figure 3 This is a schematic diagram illustrating the mapping process from physical partitioning to graph structure of heterogeneous surface units in one embodiment of this application; Figure 4 yes Figure 1 A flowchart illustrating a specific implementation method for step 102; Figure 5 yes Figure 1 A schematic diagram of a specific implementation method for step 103; Figure 6 This is a schematic diagram of the structure of a physically constrained multi-task graph neural network surrogate model in one embodiment of this application; Figure 7 This is a schematic flowchart of the calculation method for the effective irradiation factor in one embodiment of this application; Figure 8 yes Figure 1 A flowchart illustrating a specific implementation method for step 104; Figure 9 This is a schematic diagram of the attitude trajectory planning device for differential charging of heterogeneous surfaces of a spacecraft in one embodiment of this application; Figure 10 This is a schematic diagram of the device structure of a computer device provided in an embodiment of the present invention. Detailed Implementation

[0015] The invention will now be discussed with reference to several exemplary embodiments. It should be understood that these embodiments are described merely to enable those skilled in the art to better understand and thus implement the invention, and are not intended to imply any limitation on the scope of the invention.

[0016] As used herein, the term "comprising" and its variations are to be interpreted as open-ended terms meaning "including but not limited to". The term "based on" is to be interpreted as "at least partially based on". The terms "one embodiment" and "an embodiment" are to be interpreted as "at least one embodiment". The term "another embodiment" is to be interpreted as "at least one other embodiment".

[0017] Existing technologies primarily address spacecraft differential charging issues through three independent approaches: First, surface charging numerical analysis methods calculate potential and risk under a given attitude based on structural, material, and environmental parameters. However, these methods can only evaluate predetermined trajectories and cannot generate low-risk charging paths, and the process of simulating and screening each path is inefficient. Second, attitude maneuver planning methods generate trajectories that meet pointing and energy consumption requirements based on kinematic and control constraints. However, these methods do not consider the dynamic charging state of heterogeneous surfaces and local irradiation processes, making it difficult to avoid transient differential charging peaks during intermediate maneuvering phases. Third, hardware protection or irradiation biasing schemes reduce the risk of specific components through measures such as conductive coatings, grounding, plasma contactors, or fixed bias angles. However, these methods cannot utilize the control degrees of freedom of attitude paths and velocity curves to optimize the maximum differential potential between multiple surfaces throughout the entire process. Furthermore, existing technologies lack a closed-loop coupling mechanism between attitude trajectory generation and dynamic surface charging prediction, making it difficult to quickly select the optimal attitude trajectory with low differential charging risk throughout the entire process while satisfying kinematic and mission constraints.

[0018] To address this issue, this embodiment provides an attitude trajectory planning method for differential charging of heterogeneous surfaces on spacecraft, such as... Figure 1 As shown, it includes the following steps: 101. During the offline training phase, a surface charging physical model is used to generate supervision labels on diverse attitude trajectory samples to train a physical constraint multi-task graph neural network surrogate model.

[0019] In one specific embodiment of the present invention, the offline training phase aims to construct and train a surrogate model capable of rapidly acquiring risk assessment results for spacecraft surface charging. During the offline training phase, a high-precision surface charging physical model is first used to perform simulation calculations on a large number of diverse attitude trajectory samples, generating realistic labels for supervised learning. Subsequently, these labeled sample data are used to iteratively train the physically constrained multi-task graph neural network surrogate model, enabling it to learn the complex nonlinear mapping relationship between spacecraft attitude changes and surface charging states.

[0020] When generating diverse attitude trajectory samples, a sample set of attitude trajectories covering different maneuver durations, solar azimuths, and space environment parameters is generated through random sampling or stratified sampling. For each sample trajectory, a surface charging physical model is called to perform numerical integration to obtain the surface potential sequence and peak differential potential at each time point as the true label. Subsequently, these sample data with supervised labels are used to iteratively train a physically constrained multi-task graph neural network surrogate model, enabling the model to learn the mapping relationship between attitude changes and surface charging states. During the training process, physical constraints such as charge conservation are applied to improve generalization ability.

[0021] The physically constrained multi-task graph neural network surrogate model includes a heterogeneous surface message passing graph structure, which is constructed based on a reasonable division of the spacecraft's outer surface. The heterogeneous surface message passing graph structure uses the heterogeneous surface units of the spacecraft's surface division as nodes, and is constructed according to surface geometric adjacency relationships or preset information association rules.

[0022] Specifically, the outer surface of the spacecraft is divided into multiple heterogeneous surface units based on material properties, functional uses, or spatial partitioning. For example, regions with different conductivity and secondary electron emission characteristics, such as solar panels, thermal control multilayer insulation materials, metal antenna reflectors, and optical sensor shields, are divided into independent heterogeneous surface units. Each heterogeneous surface unit is mapped to a node in a graph structure, forming a complete set of nodes, ensuring that each node corresponds to a surface region with uniform electrical characteristics. After determining the node set, a message passing edge set and the corresponding graph adjacency matrix are constructed based on surface geometric adjacency relationships or preset information association rules. For geometric adjacency relationships, if two heterogeneous surface units are directly connected in the spacecraft's physical structure or have electrical overlap, a connection edge is established between the corresponding two nodes. For preset information association rules, if two surface units are not spatially adjacent but have significant plasma wake effects or photoelectron interactions, a connection edge is also established between the corresponding nodes. The values ​​of the elements in the graph adjacency matrix follow a binary rule: when there is any of the above-mentioned connection edges between any two nodes, the corresponding element value is set to 1; otherwise, it is set to 0. This forms a graph topology that can characterize the physical associations and information transmission paths between heterogeneous surfaces.

[0023] 102. In the attitude planning application phase, multiple candidate attitude trajectories that satisfy the basic path constraints are generated based on the spacecraft's kinematic boundaries and attitude maneuver requirements.

[0024] During the attitude planning application phase, attitude maneuvering commands are received from the ground mission planning system or autonomous mission management system. These commands specify basic requirements such as the initial attitude, target attitude, and maneuvering time window. Based on this, the spacecraft's own physical parameters are read to determine kinematic boundaries. These kinematic boundaries include constraints such as maximum angular velocity, maximum angular acceleration, and the range of attitude angle changes, ensuring that each generated candidate trajectory is within the capabilities of the actuators.

[0025] After defining the attitude maneuver requirements and spacecraft kinematic boundaries, starting from the initial attitude and ending at the target attitude, the attitude transfer path connecting the start and end points is calculated, generating multiple candidate attitude paths while satisfying the maximum angular velocity and maximum angular acceleration limits. During the generation of candidate attitude trajectories, it is necessary to ensure that the trajectories meet the basic path constraints. These basic path constraints refer to the fundamental geometric and kinematic conditions that must be followed when planning a path in attitude space. These constraints include ensuring the continuity of the trajectory in the time dimension to avoid attitude jumps, ensuring that the angular velocity and angular acceleration at each node of the trajectory do not exceed the kinematic boundaries, and ensuring that the trajectory completes the attitude transfer within the time window specified by the mission.

[0026] Specifically, in the process of generating candidate attitude trajectories, trajectory search algorithms can be used to explore the attitude space in various ways. For example, intermediate waypoints can be randomly sampled in the attitude space and connected to form different attitude transition paths, or multiple objective functions can be constructed with different weight combinations to solve for candidate trajectories with different performance indicators, and finally, a set of candidate attitude trajectories with differences in the attitude space can be output.

[0027] 103. The charging risk assessment and sorting of the multiple candidate attitude trajectories are performed using the physical constraint multi-task graph neural network surrogate model, and a preset number of candidate attitude trajectories are selected as the set of trajectories to be reviewed.

[0028] In this embodiment, the physical constraint multi-task graph neural network surrogate model integrates two parallel output heads: a peak prediction head and a potential trajectory prediction head. After forward computation, the surrogate model synchronously outputs the predicted peak differential potential and the predicted surface potential sequence for each candidate attitude trajectory. The predicted surface potential sequence reflects the continuous change of surface potential at key parts of the spacecraft over time during trajectory execution. It is mainly used to verify the consistency of the predicted peak differential potential. By checking the distribution of extreme points in the surface potential sequence against the theoretical boundaries of the physical constraint module, it verifies whether the predicted peak differential potential accurately exists and conforms to physical laws, thereby eliminating false peaks caused by model extrapolation errors and ensuring the reliability of the evaluation results.

[0029] After output verification, charging risk assessment is performed on multiple candidate attitude trajectories based on the predicted peak differential potential output by the physical constraint multi-task graph neural network surrogate model. Specifically, the predicted peak differential potential is mapped to a charging risk score; the higher the predicted peak differential potential, the higher the corresponding charging risk score, indicating a greater probability of surface discharge faults during trajectory execution. Subsequently, all candidate attitude trajectories are sorted in ascending order according to the charging risk scores, and a predetermined number of candidate attitude trajectories with the lowest charging risk scores are selected from the sorting results to form a set of trajectories to be reviewed. Each trajectory in this set of trajectories to be reviewed has undergone rapid charging risk screening at the surrogate model level, and its charging safety level is better than the overall average of the candidate attitude trajectory set.

[0030] 104. Call the surface charging physical model to numerically verify each trajectory in the set to be verified, and output the attitude trajectory that satisfies multiple constraints.

[0031] Understandably, physical constraint multi-task graph neural network surrogate models may produce erroneous peak judgments when training data coverage is insufficient or nonlinear extrapolation occurs. Relying on the output of the surrogate model cannot fully guarantee charging safety. Therefore, it is necessary to introduce a surface charging physical model for independent verification to eliminate the evaluation bias of the surrogate model.

[0032] In the specific numerical verification process, for each candidate attitude trajectory in the trajectory set to be verified, the local irradiation factor of all heterogeneous surfaces of the spacecraft is calculated based on the attitude information of each discrete moment of the trajectory, and an irradiation vector is formed. At the same time, the current potential of each surface is formed into a state vector. Then, the above state vector and irradiation vector, together with the set of surface material and electrical parameters, time-varying space environment parameters, and physical connection parameters between surfaces, are input into the state evolution function of the surface charging physical model to obtain the time-series distribution data of the potential evolution of all heterogeneous surfaces over time. Each component of this state evolution function corresponds to the potential change rate of each surface node or the potential value at the next moment. By performing stepwise numerical integration of these components along the trajectory time axis, the instantaneous potential state of all surfaces at each discrete moment of the entire trajectory is obtained, and then the peak differential potential is extracted through differential operation.

[0033] After obtaining the peak differential potential, a joint judgment of multiple constraints must be performed sequentially. These constraints include at least charging safety constraints, mission constraints, and actuator constraints. Regarding charging safety constraints, the precise peak differential potential is compared with the material breakdown threshold and safety margin; those exceeding the limits are eliminated. Regarding mission constraints, the attitude pointing accuracy and solar panel orientation angle throughout the entire process are checked; failure to meet these requirements at any point renders the process infeasible. Regarding actuator constraints, the angular velocity and angular acceleration requirements at each moment are verified to ensure they do not exceed the torque limit and speed saturation limit of the flywheel or thruster; exceeding these limits renders the project unfeasible.

[0034] The attitude trajectory planning method for differential charging of heterogeneous surfaces of spacecraft provided in this application training method is as follows: During the offline training phase, a physical constraint multi-task graph neural network surrogate model containing a heterogeneous surface message passing graph structure is trained by generating supervision labels on diverse attitude trajectory samples using a surface charging physical model. In the attitude planning application phase, multiple candidate attitude trajectories are generated based on the spacecraft's kinematic boundaries and attitude maneuver requirements. The surrogate model first performs a charging risk assessment and sorts the candidate trajectories to select a set of trajectories to be verified. Then, the surface charging physical model is called to numerically verify each trajectory in the set. This forms a two-layer planning architecture combining rapid surrogate model selection and precise physical model verification. It effectively represents the spatial association characteristics between heterogeneous surfaces using a graph structure constructed with heterogeneous surface units as nodes and based on surface geometric adjacency relationships or preset information association rules. It also avoids the huge computational overhead of directly performing physical integration on all candidate attitude trajectories. Simultaneously, numerical verification ensures that the final output attitude trajectory strictly meets charging safety constraints, task constraints, and actuator constraints, balancing attitude trajectory planning efficiency and result reliability.

[0035] In the process of physical modeling and intelligent evaluation of spacecraft surface charging, traditional methods often treat the spacecraft's outer surface as a homogeneous whole or perform only simple geometric discretization, making it difficult to accurately characterize the non-uniform charging behavior caused by differences in electrical properties and spatial coupling between different materials and functional regions. Therefore, it is necessary to construct a structured representation method that can explicitly express the physical connections and information interactions between heterogeneous surface units. Specifically, such as... Figure 2 As shown, the heterogeneous surface message passing graph structure is constructed through the following steps: 201. Divide the outer surface of the spacecraft into multiple heterogeneous surface units according to materials, functions or spatial partitions, and map each of the heterogeneous surface units as a graph node to form a node set.

[0036] 202. Based on the spatial association between the heterogeneous surface units corresponding to each graph node in the node set, construct a message passing edge set and the corresponding graph adjacency matrix.

[0037] 203. Based on the node set, the message passing edge set, and the corresponding graph adjacency matrix, construct a heterogeneous surface message passing graph structure.

[0038] In this embodiment, each heterogeneous surface unit is mapped as a node in a graph structure, and all nodes together constitute a node set. Further characterization of the spatial relationships between the heterogeneous surface units is needed to form a message passing edge set. In this embodiment, the message passing edge set is constructed based on surface geometric adjacency relationships or preset information association rules. Geometric adjacency relationships refer to two surface units being directly connected in physical space or having a significant electromagnetic coupling path; information association rules cover non-contact but physically meaningful coupling mechanisms such as line-of-sight visibility, overlapping areas of the plasma sheath, or wire connections.

[0039] Based on the message-passing edge set, a corresponding graph adjacency matrix is ​​further generated to provide a numerical topological description. The rows and columns of this graph adjacency matrix correspond to the graph nodes in the node set. The value rule for the elements in the graph adjacency matrix is: if any two graph nodes in the node set have a connecting edge in the message-passing edge set, the value of the corresponding element for both graph nodes is set to 1; otherwise, it is set to 0. This graph adjacency matrix not only serves as the structural basis for the message-passing mechanism in the graph neural network but can also be directly embedded in the state evolution function to constrain the local dependencies of potential updates, thereby ensuring that the surrogate model always respects the true physical connection topology of the spacecraft surface during training and inference.

[0040] Finally, the aforementioned node set, message-passing edge set, and graph adjacency matrix are integrated to form a complete heterogeneous surface message-passing graph structure. This structure preserves the individual attributes of each heterogeneous surface unit and encodes the coupling relationships between units through explicit topological connections. This structured representation improves the modeling fidelity of complex heterogeneous surface charging behavior without sacrificing computational efficiency, thereby supporting high-confidence attitude trajectory safety verification.

[0041] In practical applications, the mapping process from physical partitioning to graph structure for heterogeneous surface units can be referenced. Figure 3 As shown, Figure 3 The outer surface of the spacecraft is divided into multiple heterogeneous surface units with clearly defined physical boundaries. See the diagram. , Indicates the first Each heterogeneous surface element has a defined physical boundary. Each heterogeneous surface element is mapped to a graph node in a graph structure. See the diagram. , In the graph structure, the first Each graph node. All graph nodes together constitute a node set. Further construct a message passing edge set. Based on node set and message passing edge set Construct a message passing graph structure for heterogeneous surfaces and its adjacency matrix Message passing edge set This is equivalent to the binary computation topology of a graph neural network, used to specify which other nodes each graph node aggregates information from during feature updates. It can be constructed based on surface geometric adjacency, known influence relationships, or pre-defined information association rules, but does not include the specific numerical values ​​of the physical connection strength between surfaces. Adjacency matrix ,in, In practical implementation, it constitutes a set of nodes. The heterogeneous surface units can be divided according to material, function or spatial partitioning, or refined into surface elements according to the modeling accuracy requirements, so as to ensure the simplicity of the topology while taking into account the spatial resolution of the charging behavior of heterogeneous surfaces.

[0042] In the process of spacecraft attitude maneuver planning, to avoid the limitations of a single path or velocity profile that cannot simultaneously account for multiple constraints such as charging safety, mission functionality, and actuator physics, it is necessary to actively construct multiple candidate attitude trajectories with different geometric orientations and velocity distribution characteristics, while satisfying the basic kinematic boundaries. Specifically, such as Figure 4 As shown, step 102 above includes the following steps: 301. Generate multiple geometric trajectories based on the initial attitude and the target attitude.

[0043] 302. Divide each geometric trajectory into multiple path segments and assign a duration to each path segment. Under the condition that the total duration of attitude maneuver remains unchanged, differentiate the duration of each path segment to obtain multiple candidate attitude trajectories with different velocity distributions.

[0044] The geometric trajectory refers to a continuous transition path connecting the initial attitude and the target attitude in attitude space, describing the spatial direction of attitude change. The geometric trajectory includes at least: the shortest path generated based on quaternion spherical linear interpolation, connecting the initial attitude and the target attitude; and a detour path formed through one or more intermediate attitudes; intermediate attitudes refer to transitional attitude points artificially inserted between the start and end attitudes to allow the detour path to avoid the preset high differential charging risk irradiated attitude region.

[0045] Specifically, in the geometric trajectory generation stage, the shortest path connecting the initial and target attitudes is first generated based on quaternion spherical linear interpolation as a baseline candidate trajectory. Subsequently, to generate effective detour paths, diverse intermediate attitude generation strategies are employed: for situations where the boundaries of known risk areas are clear, heuristic sampling based on the sun's direction can be used to directly select intermediate attitudes within the safe illumination cone; for complex, multi-constraint environments, fast expanding random trees or their variants can be used for collision detection and path searching in the attitude space; if it is necessary to find the optimal avoidance point globally, intelligent algorithms such as genetic algorithms, particle swarm optimization, or Bayesian optimization can be applied to iteratively solve for the intermediate attitude with the goal of minimizing the charging risk index; alternatively, candidate point sets can be constructed through uniform sampling of unit quaternions or Euler angle grid sampling, and then the final intermediate attitude is determined through safety screening. The intermediate attitudes generated through the fusion of these multiple strategies can construct detour geometric trajectories with diverse shapes.

[0046] Based on the obtained multiple geometric trajectories, each trajectory is further parameterized in the time dimension, transforming it into a candidate attitude trajectory with executable characteristics. Specifically, each geometric trajectory is divided into multiple continuous path segments, and the duration of each path segment is differentiated while keeping the total attitude maneuver duration constant. By employing non-uniform time configuration strategies, such as extending the duration in high-risk segments to reduce angular velocity and shortening the time in safe segments to improve efficiency, the same geometric trajectory can generate a set of multiple candidate attitude trajectories with different velocity distribution characteristics.

[0047] Thus, the charging dynamics can be altered by rapidly traversing high-risk irradiation combinations and appropriately stopping in low-risk sections, while simultaneously satisfying the constraints of maximum angular velocity and actuator capability. This results in multiple candidate attitude trajectories with different velocity distributions, forming a diverse set of trajectories that balances geometric safety and dynamic feasibility.

[0048] In practical applications, each geometric path is divided into... The path segment is used to represent the segment index, and is the first path segment. Each segment is allocated a duration. In the total duration of attitude maneuvers Under the condition of constant time constraints, different velocity parameterizations can be formed by changing the duration of each segment. The specific time constraints of each segment can be expressed by the following formula: ; Due to the large number of candidate attitude trajectories and the excessive time required for high-precision physical simulation calculations, directly and accurately evaluating each trajectory individually is insufficient to meet the real-time requirements of engineering. Therefore, a rapid screening mechanism that combines computational efficiency and physical reliability is needed. This embodiment employs a physically constrained multi-task graph neural network surrogate model to assess and rank the charging risks of multiple candidate attitude trajectories. The aim is to achieve preliminary risk quantification and optimization of a large number of trajectories in a very short time by combining data-driven approaches with physical priors. Specifically, as... Figure 5 As shown, step 103 above includes the following steps: 401. Input the node temporal features, graph topology input, and global task features corresponding to each candidate attitude trajectory into the physical constraint multi-task graph neural network surrogate model.

[0049] 402. In the physical constraint multi-task graph neural network proxy model, forward reasoning is performed based on the node temporal features, graph topology input and global task features to output the charging risk index of each candidate attitude trajectory.

[0050] 403. Based on the predicted peak differential potential, the multiple candidate attitude trajectories are sorted according to the charging risk assessment, and a preset number of candidate attitude trajectories are selected as the set of trajectories to be reviewed.

[0051] The node temporal features include at least an effective illumination factor, used to characterize the dynamic illumination conditions of different regions on the spacecraft surface during attitude maneuvers; the graph topology input is an adjacency matrix of a heterogeneous surface message-passing graph structure, used to describe the electrical connections and charge conduction paths between different surface units of the spacecraft; and the global mission features include at least an attitude quaternion sequence, used to provide attitude evolution context information for the entire trajectory. These three types of features comprehensively characterize the trajectory's charging response characteristics from three dimensions: local environmental excitation, structural physical correlation, and global motion state.

[0052] In the specific model architecture and forward inference process, the physically constrained multi-task graph neural network surrogate model internally includes a graph message passing module, a timing coding module, a physical constraint module, a peak prediction head, and a potential trajectory prediction head. Based on the above three types of input features, it outputs charging risk indicators for each candidate attitude trajectory. The charging risk indicators include the predicted peak differential potential and the predicted surface potential sequence.

[0053] The graph message passing module aggregates node temporal features based on the adjacency matrix to obtain aggregated node features. These aggregated node features and node temporal features are then input into the temporal coding module, which extracts local irradiation history, surface charging state, and task time changes based on the effective irradiation factor to form dynamic features. The peak prediction head outputs the predicted peak differential potential for each candidate attitude trajectory based on the dynamic features. The potential trajectory prediction head outputs the predicted surface potential sequence corresponding to each candidate attitude trajectory based on the dynamic features. The physical constraint module applies physical conservation constraints based on the predicted surface potential sequence and the dynamic features to generate physical constraint verification results.

[0054] The structure of the specific physical constraint multi-task graph neural network surrogate model is referenced. Figure 6 As shown, the graph message passing module is based on the heterogeneous surface message passing graph structure. and its adjacency matrix The spatial dimension of the input node temporal features is aggregated to obtain aggregated node features. Subsequently, the aggregated node features and the original node temporal features are input into the temporal coding module. This temporal coding module, based on the effective irradiation factor, deeply extracts the local irradiation history, surface charging state evolution, and task time changes of each surface region, forming a multi-dimensional dynamic feature that integrates spatial topology and temporal evolution.

[0055] After acquiring multi-dimensional dynamic features, multi-task output is performed through two parallel prediction heads. The peak prediction head directly outputs the predicted peak differential potential of each candidate attitude trajectory based on the dynamic features. It is used to quickly assess the electrostatic discharge risk intensity under the worst-case scenario; the potential trajectory prediction head outputs the predicted surface potential sequence corresponding to each candidate attitude trajectory based on dynamic characteristics. This provides a complete profile of the potential's temporal evolution. Based on this, the physical constraint module further imposes multi-task consistency constraints on the peak prediction head and the potential trajectory prediction head. Since the predicted peak differential potential output by the peak prediction head and the predicted surface potential sequence output by the potential trajectory prediction head have a necessary mathematical and logical connection in physics, the physical constraint module further imposes multi-task consistency constraints on both. Through this joint constraint on the temporal coding layer and the prediction head, the physical constraint module fundamentally ensures the physical rationality and multi-task synergy of the surrogate model's prediction results.

[0056] In constructing a physically constrained multi-task graph neural network surrogate model, relying solely on data-driven error backpropagation can easily lead to a decline in the model's generalization ability outside the training set, and it cannot guarantee that the prediction results strictly adhere to underlying physical laws such as charge conservation and current balance. Therefore, it is necessary to design a multi-task composite loss function system that integrates data-driven and physical priors. By co-optimizing network parameters through multiple constraints, the model can be endowed with strict physical consistency and excellent extrapolation stability while ensuring prediction accuracy. In specific implementation, the total training loss of the physically constrained multi-task graph neural network surrogate model is composed of a weighted combination of multiple sub-loss terms, aiming to impose constraints on the network output from different dimensions.

[0057] To fully characterize the surface charging dynamic response of spacecraft under complex space environments and diverse attitude maneuvers, a high-quality, high-coverage training dataset needs to be constructed before training the physically constrained multi-task graph neural network surrogate model. Specifically, the surface charging physical model is used to generate supervision labels on diverse attitude trajectory samples, including the following steps: Random or stratified sampling is performed on attitude path, segment duration, total maneuver time, solar direction, space environment parameters, surface material and electrical parameters, initial potential conditions, and physical connection parameters between surfaces to generate diverse attitude trajectory samples. For each sample trajectory in the diverse attitude trajectory samples, the local irradiation history of each heterogeneous surface unit is calculated, and the true surface potential sequence label and the true peak differential potential label are obtained using the surface charging physical model as supervision labels; The local irradiation history, surface material and electrical parameters, time-varying spatial environment parameters, physical connection parameters between surfaces, and task time parameters are organized into graph temporal input samples, which are paired with the supervision labels to form graph temporal training samples for training the physical constraint multi-task graph neural network surrogate model.

[0058] In practice, attitude path sampling covers different combinations of rotation axes, rotation angles, and path curvatures; segment duration and total maneuver time sampling covers multiple timescales from rapid maneuvering to slow drift; solar direction and space environment parameters sampling covers different orbital positions, seasons, and space weather conditions; surface material and electrical parameters sampling covers parameter drift caused by material aging, contamination, and temperature changes; initial potential conditions sampling covers multiple initial states from complete discharge to partial charging; and surface physical connection parameters sampling covers different grounding topologies and leakage resistance configurations. Through this multi-dimensional joint sampling, it is ensured that the training samples fully cover various combinations of operating conditions that the spacecraft may encounter during on-orbit operation.

[0059] For each generated sample trajectory, the local irradiation history of each heterogeneous surface unit under that trajectory is further calculated, i.e., the time-varying geometric relationship of each surface receiving solar radiation and space plasma incident during maneuvering. Subsequently, this irradiation history, along with surface material and electrical parameters, time-varying space environment parameters, inter-surface physical connection parameters, and initial potential conditions, are input into the surface charging physics model. The true surface potential sequence label is obtained through numerical integration, and based on this, the true peak differential potential label on the risk monitoring surface pair set is calculated. These two types of labels respectively characterize the continuous evolution process of the surface potential and the worst charging state, together constituting the monitoring label of the sample trajectory.

[0060] Finally, the local illumination history, surface material and electrical parameters, time-varying space environment parameters, inter-surface physical connection parameters, and mission time parameters corresponding to each sample trajectory are organized into graph-time-series input samples according to a graph structure. In this graph structure, nodes represent heterogeneous surface units, edges represent physical connections or spatial coupling relationships between surfaces, and the attributes of nodes and edges evolve over time to reflect the excitation changes brought about by dynamic attitude maneuvers. Furthermore, the graph-time-series input samples are paired with corresponding supervision labels to form complete graph-time-series training samples, which are used to drive the training of the physically constrained multi-task graph neural network surrogate model. This training sample set not only preserves the spatial structure information of the spacecraft surface topology but also fully encodes the temporal dynamic characteristics of the charging process.

[0061] Specifically, in the process of training the physical constraint multi-task graph neural network surrogate model, multiple sub-loss terms are weighted and summed to obtain the total loss function. The parameters of the physical constraint multi-task graph neural network surrogate model are then updated based on this total loss function. Total Loss Function It can be expressed by the following formula: ; Loss for fitting potential trajectory Corresponding weights; potential trajectory fitting loss Used to force and constrain the predicted potential of all heterogeneous surfaces at all discrete time points. With surface charging physical model The provided high-fidelity labels are consistent and can be defined using the following formula: ; Peak fitting loss Corresponding weights; peak fitting loss This is specifically used to constrain the output of the peak prediction head. Peak labels calculated by the physical model This is consistent, and its definition can be expressed by the following formula: ; For dual-output consistency loss The corresponding weights; to eliminate potential conflicts between different output branches in a multi-task architecture, a dual-output consistency loss is introduced. This loss term is used to constrain the output of the peak prediction head. The prediction results calculated from the predicted potential trajectory To maintain consistency, its definition can be expressed by the following formula: ; For physical residual loss The corresponding weights are used; the predicted potentials are substituted into the state evolution relationship of the selected surface charging physical model to calculate the predicted residuals of the physical equations for each surface at a specified time, and the physical residual loss is constructed accordingly. The physical residual loss The state evolution relationship used to constrain the predicted potential to satisfy the selected surface charging physical model can be expressed by the following formula: ; in, For surface At any moment The physical equations predict the residuals; The total set of discrete moments The first in A discrete time point; Specifically, when calculating the predicted residuals of the physical equations, one can... As , the potential sequence Substituting the state evolution relationship into the selected surface charging physical model, we obtain the surface At any moment Physical equations predict residuals Used to represent a certain moment The mapping relationship between surface potential and the predicted residuals of the physical equations. At this point... This can be expressed by the following formula: ; Initial state constraint loss Corresponding weights; initial state constraint loss Predicted initial potentials used to enforce constraints on all surfaces With input initial potential Completely identical, its definition can be expressed by the following formula: ; For sorting loss The corresponding weights; as an optional supplement, the ranking loss. This is used to constrain the relative risk order of candidate trajectories, ensuring that the model prioritizes the correct ranking of low-risk trajectories during training. This term can be implemented using pairwise ranking loss, list ranking loss, or risk interval-based loss, depending on specific needs. This multi-task loss structure cleverly balances the high accuracy of direct peak regression with the strong interpretability of potential trajectory prediction, making the surrogate model's charging risk assessment in complex spatial environments both fast, efficient, rigorous, and reliable.

[0062] After completing the forward inference of the physical constraint multi-task graph neural network surrogate model and obtaining the predicted peak differential potential of each candidate attitude trajectory, the charging risk assessment and sorting of all candidate attitude trajectories are performed based on the predicted peak differential potential. Trajectories with lower predicted peak differential potentials are prioritized, and a subset of high-quality trajectories with relatively low charging risk is quickly identified. A preset number of candidate attitude trajectories are selected from the sorting results as the set of trajectories to be reviewed. This preset number can be flexibly configured according to actual engineering needs.

[0063] In practical applications, the input to a physically constrained multi-task graph neural network surrogate model consists of node temporal features, graph topology input, and global task features. Among these, node temporal features include effective illumination factors. Surface materials and electrical parameters Initial potential state Surface area Normal vector and at least one of the time parameters; the graph topology input is composed of Constructed adjacency matrix Global task features may include a sequence of attitude quaternions. Angular velocity sequence Sun direction Environmental parameters and total duration of attitude maneuvers At least one of them.

[0064] Specifically, such as Figure 7 As shown, the effective irradiance factor is calculated as follows: 501. For each candidate attitude trajectory, determine the rotation matrix based on the time-varying unit quaternion corresponding to the candidate attitude trajectory, which describes the attitude change of the spacecraft's body coordinate system relative to the inertial coordinate system.

[0065] 502. Use the rotation matrix to transform the unit outward normal vector of each heterogeneous surface unit in the body coordinate system to the inertial coordinate system.

[0066] 503. Calculate the dot product of the transformed unit external normal vector and the unit direction vector in the inertial coordinate system pointing from the spacecraft's center of mass to the sun. Combine this with the ground shadow coefficient and the surface self-shading coefficient to obtain the effective illumination factor of each heterogeneous surface unit.

[0067] 504. Arrange the effective irradiation factors according to time throughout the entire maneuvering time interval to obtain the local irradiation history of each heterogeneous surface unit.

[0068] In practice, for each candidate attitude trajectory, a corresponding rotation matrix is ​​calculated based on the time-varying unit quaternion describing the attitude change of the spacecraft's body coordinate system relative to the inertial coordinate system. This rotation matrix fully characterizes the spacecraft's spatial orientation at every moment and is a key mathematical tool for transforming fixed geometric quantities of the spacecraft body to the inertial reference system. Subsequently, this rotation matrix is ​​used to transform the predefined unit outward normal vectors of each heterogeneous surface element in the body coordinate system to the inertial coordinate system, enabling the originally fixed surface orientation information to reflect its actual pointing state in inertial space in real time.

[0069] After completing the coordinate transformation of the normal vector, the dot product between the transformed unit outward normal vector and the unit direction vector pointing from the spacecraft's center of mass to the sun in the inertial coordinate system is further calculated. This dot product essentially reflects the cosine of the angle of incidence of sunlight and is a fundamental geometric factor determining the intensity of solar radiation received by the surface. Based on this, the dot product result needs to be corrected by incorporating the ground shadow coefficient and the surface self-shading coefficient. Finally, the result of multiplying these three factors is the effective irradiance factor for each heterogeneous surface unit at the corresponding time.

[0070] The calculated effective illumination factors are arranged chronologically over the entire maneuvering time interval to form the local illumination history of each heterogeneous surface unit. This local illumination history records the dynamic illumination excitation changes experienced by each heterogeneous surface unit from the start to the end of the maneuver in a complete time series form. It includes both the continuous evolution of the illumination angle caused by attitude rotation and the effects of discrete events such as ground shadow entry / exit and abrupt self-occlusion.

[0071] In practical applications, for candidate pose trajectories ,by Representing the spacecraft's body coordinate system, with This indicates the fixed inertial reference coordinate system used by the mission planning system, for example, in the J2000 geocentric inertial coordinate system. To describe the body coordinate system Relative to the inertial coordinate system Time-varying unit quaternion of attitude, This is the rotation matrix that transforms a vector in the body coordinate system to the inertial coordinate system. Let the first... The unit outward normal vector of a heterogeneous surface element in the body coordinate system Transform to the inertial coordinate system to obtain the transformed unit outward normal vector. Specifically, it can be expressed by the following formula: ; Furthermore, let In the inertial coordinate system The vector representing the unit direction from the spacecraft's center of mass to the sun; based on the Earth's shadow coefficient. Surface self-shading coefficient Calculate the first Effective irradiance factor of a heterogeneous surface unit Specifically, it can be expressed by the following formula: ; in, and Both are three-dimensional unit vectors, and their dot product is... It is the cosine of the direction of the sun's incidence; and The value of is in the range of 0 to 1. Therefore, at any given time, It is a scalar value between 0 and 1. After being arranged chronologically over the entire maneuvering time interval, heterogeneous surface units are formed. The local irradiation history. This local irradiation history is used to indicate when the surface begins to be irradiated, the duration of irradiation, and the differences in irradiation between different heterogeneous surface units.

[0072] Although the physical constraint multi-task graph neural network surrogate model has significantly improved the physical reliability of predictions through residual constraints and multi-task consistency mechanisms, it is still essentially an approximate representation of the actual charging process and may still have local biases under extreme space environments or complex attitude maneuvers. It is necessary to introduce a high-fidelity surface charging physical model as a verification benchmark to accurately verify each trajectory in the set to be verified. Specifically, such as... Figure 8 As shown, step 104 above includes the following steps: 601. For each candidate attitude trajectory in the set of trajectories to be verified, input the local irradiation history, surface material and electrical parameters, time-varying spatial environment parameters, and physical connection parameters between surfaces corresponding to the candidate attitude trajectory into the surface charging physical model.

[0073] 602. Under a given initial potential, the surface potential sequence of the candidate attitude trajectory is obtained by numerical integration based on the differential evolution equation of the surface charging physical model.

[0074] 603. Based on the surface potential sequence, calculate the instantaneous differential potential timing between each heterogeneous surface unit pair, and select the maximum value of the instantaneous differential potential within the total duration of attitude maneuvering from the preset risk monitoring surface pair set as the peak differential potential.

[0075] 604. The candidate attitude trajectory that satisfies the preset charging safety threshold condition and the preset task constraint condition and actuator constraint condition during the attitude maneuvering process is taken as the output attitude trajectory that satisfies multiple constraints.

[0076] In this embodiment, the local illumination history, surface material and electrical parameters, time-varying spatial environment parameters, and physical connection parameters between surfaces together constitute the complete physical boundary conditions and initial potential state describing the charging dynamic process under this trajectory. Under the given initial potential conditions, the differential evolution equation established based on the surface charging physical model is numerically integrated to obtain the surface potential sequence of the candidate attitude trajectory throughout the entire maneuvering time interval. This surface potential sequence accurately characterizes the continuous evolution process of the potential of each heterogeneous surface unit over time with high temporal resolution, fully reflecting the nonlinear dynamic coupling effect between illumination changes, environmental disturbances, and charge transport.

[0077] Based on the obtained surface potential sequence, the instantaneous differential potential time series between each heterogeneous surface unit pair is further calculated. Then, on a pre-defined set of risk monitoring surface pairs, the maximum instantaneous differential potential within the total duration of attitude maneuvering is extracted as the peak differential potential. The risk monitoring surface pairs are pre-defined heterogeneous surface unit pairs that require differential potential calculation. These pairs typically consist of combinations of key heterogeneous surface units known to be prone to electrostatic discharge or functionally sensitive in engineering. Their selection is based on historical failure data, material compatibility analysis, and mission criticality assessment, ensuring that the review focuses on truly engineering-significant risk points rather than performing indiscriminate calculations on all surface combinations.

[0078] Finally, the peak differential potential of each candidate attitude trajectory is compared with a preset charging safety threshold, while simultaneously verifying whether its attitude maneuvering process meets preset task constraints and actuator constraints. Only when all three conditions are met simultaneously—peak differential potential below the safety threshold, maneuvering path meeting task objective requirements, and actuator torque and angular velocity not exceeding limits—is the candidate attitude trajectory recognized as satisfying multiple constraints and output. This multi-dimensional screening mechanism ensures that the final output attitude trajectory not only withstands high-fidelity model verification in terms of charging safety but also possesses practical executability within the scope of task feasibility and platform capabilities.

[0079] In practical applications, for any candidate attitude trajectory, the potentials of all heterogeneous surfaces are combined to form a state vector. The effective irradiation factors of each heterogeneous surface unit are combined to form an irradiation vector. The selected surface charging physics model takes the current potential state, local irradiation history, set of surface material and electrical parameters, time-varying spatial environment parameters, and set or matrix of physical connection parameters between surfaces as comprehensive inputs. The continuous evolution process of the surface potential over time is calculated through a state evolution function. Each component of this state evolution function corresponds to the potential change rate of different surface units. The specific state evolution function can be expressed by the following formula: ; in, It represents the collection of all surface materials and electrical parameters. Indicates time-varying spatial environment parameters, A set or matrix representing the electrical connections, leakage, charge exchange, or other physical coupling parameters between surfaces. The state evolution function for the selected surface charging physical model. The state evolution function is the first... Each component.

[0080] In terms of specific implementation, the surface charging physical model possesses high engineering adaptability and can be constructed using current balance equations, equivalent circuit state equations, particle or field numerical solution models, state models calibrated from experimental or telemetry data, or surrogate forms of any of the above models. During the offline training phase, this surface charging physical model generates a large amount of high-fidelity surface potential evolution data as supervision labels to drive the learning and optimization of the multi-task graph neural network surrogate model. In the online attitude planning phase, the surface charging physical model is used to numerically verify each candidate attitude trajectories after initial screening, forming a complete evaluation closed loop from rapid coarse screening to precise verification.

[0081] To quantify the risk of electrostatic discharge, the instantaneous differential potential and peak differential potential between surfaces are defined. The instantaneous differential potential between any two heterogeneous surfaces is determined by the surface potentials of both surfaces at the same moment. and The difference is obtained by subtraction and is used to characterize the local electric field strength and discharge tendency. Specific instantaneous differential potential. This can be expressed by the following formula: ; Based on this, the set is monitored on a pre-defined risk monitoring surface. The process iterates through the entire attitude maneuver time interval and extracts the maximum value of all instantaneous differential potentials as the peak differential potential. This indicator reflects the worst charging state during attitude maneuvering and serves as a criterion for determining whether a candidate trajectory meets the preset charging safety threshold. Specifically, the peak differential potential... This can be expressed by the following formula: ; in, For the surface pairs required for differential potential risk assessment, Not belonging to Instead of defining the edges, it is used to specify the heterogeneous surface pairs that participate in the calculation of differential potential indices.

[0082] In practical engineering applications of spacecraft attitude planning, different feasible trajectories exhibit significant differences in energy consumption, path smoothness, and risk margin. Without a unified optimization mechanism, the system may output a safe but suboptimal trajectory. Therefore, it is necessary to introduce a comprehensive evaluation function to perform multi-dimensional quantitative ranking of candidate trajectories that have passed physical verification, and combine this with an online rolling planning strategy to achieve closed-loop dynamic updates. Furthermore, after step 104, the method also includes the following steps: For the attitude trajectory that satisfies multiple constraints and is verified by the surface charging physical model, a comprehensive evaluation function is calculated, and the attitude trajectory that satisfies the multiple constraints and has the smallest comprehensive evaluation function is selected as the final output attitude trajectory. The comprehensive evaluation function includes the following evaluation terms: physically verified peak differential potential, attitude geometry path length, angular velocity cost or control energy cost, and penalty terms for violations of mission pointing constraints, maximum angular velocity constraints, control torque constraints, or power generation constraints. Each evaluation term is assigned a non-negative weight, which can be dynamically adjusted according to the current mission priority. For example, the pointing constraint penalty weight is increased in high-precision observation missions, and the power generation constraint penalty weight is increased during periods of energy scarcity. Finally, the attitude trajectory with the smallest comprehensive evaluation function value is selected as the output, ensuring that the selected trajectory achieves an optimal balance between safety, economy, and mission adaptability.

[0083] In practical implementation, for candidate trajectories that have been physically verified as safe, a differential potential including the physical verification peak potential is constructed. Attitude geometric path length Angular velocity vector or control cost and constraint penalty term Comprehensive evaluation function Among them, the physical verification peak differential potential directly reflects the charging risk level of the trajectory at the worst moment and is the core quantitative indicator of safety; the attitude geometry path length characterizes the spatial span and time consumption of the maneuver; the angular velocity vector or control cost describes the propellant consumption or flywheel load required to execute the trajectory; the constraint penalty term is used to quantify the degree of violation of hard constraints such as mission pointing accuracy, maximum angular velocity limit, control torque saturation, and power generation lower limit. Each evaluation item is multiplied by a non-negative weight coefficient, the value of which can be dynamically adjusted according to the current mission priority. The specific comprehensive evaluation function... It can be expressed by the following formula: ; in, to The non-negative weights for each evaluation item are: Let be the spacecraft's angular velocity vector. Penalty terms for violating mission objectives, maximum angular velocity, control torque, or power generation constraints. Select a comprehensive evaluation function that satisfies all hard constraints. The minimum trajectory is taken as the output.

[0084] To cope with real-time changes in space environment parameters, solar orientation, and surface potential, an online rolling planning mode is adopted. In this mode, each planning session only executes the first preset planning period of the final output attitude trajectory, rather than the complete trajectory. After the execution of this period, the latest solar orientation vector, measured space environment data, and surface potential telemetry information are immediately acquired. Using the spacecraft's actual attitude and measured surface potential at the current moment as new initial conditions, the entire process of candidate attitude trajectory generation, numerical verification of the surface charging physical model, and selection of the optimal trajectory based on a comprehensive evaluation function is retried.

[0085] In the actual operation of spacecraft attitude planning, although the physical constraint multi-task graph neural network surrogate model can provide rapid charging risk prediction, its prediction accuracy inevitably decays or experiences local failures due to the time-varying evolution of the space environment, the aging of surface materials, and the occurrence of unexperienced conditions. Therefore, it is necessary to establish an adaptive feedback and model correction mechanism based on error monitoring and uncertainty assessment during the physical verification stage, dynamically adjusting the search strategy and continuously evolving the surrogate model. Furthermore, during or after the numerical verification using the surface charging physical model, when the estimated surrogate prediction error, model uncertainty, or deviation between the surrogate prediction result and the physical verification result is detected to exceed a preset threshold, at least one of the following operations is performed: Increase the preset number of candidate attitude trajectories; Regenerate candidate attitude trajectories and add them to the set of trajectories to be reviewed; Reduce the weight of the corresponding candidate attitude trajectory in the charging risk assessment ranking; The current physical verification result is added as a new supervision label to the training sample, and the physical constraint multi-task graph neural network proxy model is incrementally updated.

[0086] In practice, when the estimated error of the surrogate prediction, model uncertainty, or deviation between the surrogate prediction result and the physical verification result exceeds a preset threshold, the candidate trajectory set expansion mechanism is first triggered. The system will directly increase the preset number of candidate attitude trajectories, or regenerate new candidate attitude trajectories and supplement them to the trajectory set to be verified. This operation aims to compensate for the risk of omission caused by the prediction deviation of the surrogate model in local areas by increasing the sample density and diversity of the search space, ensuring that the physical verification process can cover more potential safe and high-performance attitude trajectories.

[0087] For specific candidate attitude trajectories where the surrogate prediction results deviate significantly from the physical verification results or where the model uncertainty is high, the system proactively reduces their corresponding weights during the charging risk assessment ranking. This conservative strategy aims to suppress the interference of high-uncertainty or high-error trajectories on the final decision, preventing trajector model misjudgments from prioritizing trajectories with actual charging risks. By dynamically adjusting the ranking weights, the system can guide the final comprehensive evaluation and selection process towards trajectories with high physical verification confirmation and low prediction deviation without directly eliminating candidate trajectories, thereby enhancing the safety margin of the decision-making process.

[0088] Furthermore, to fundamentally address the issue of decreased prediction accuracy of the surrogate model under specific operating conditions, the system uses the high-fidelity results obtained from the current physical verification as new high-quality supervision labels, adding them to the original training sample set, and incrementally updating the physical constraint multi-task graph neural network surrogate model. This allows the surrogate model to continuously absorb new data generated during the physical verification stage and automatically correct its network weight biases under unknown or complex environmental parameters.

[0089] In the final decision-making stage of spacecraft attitude planning, simply pursuing the lowest charging risk or the shortest path often fails to meet the comprehensive requirements of complex missions. It is necessary to establish a multi-objective comprehensive evaluation system that integrates charging safety, maneuver efficiency, and mission constraint compliance. Through weighted optimization, a reasonable trade-off can be achieved among various performance indicators, ensuring that the output trajectory takes into account mission execution efficiency while guaranteeing absolute safety.

[0090] To further illustrate the implementation process of the above method, this embodiment presents a method using six surfaces for order reduction. The specific implementation of the model is described below. The material equilibrium potential, charging time constant, coupling parameters, and environmental range in this implementation are all proof-of-concept settings. The relevant performance data are derived from actual numerical simulations, model training, and inference, and do not represent the on-orbit test or flight evaluation results of a specific type of spacecraft.

[0091] In this specific implementation, the six nodes correspond to six surfaces with normal vectors of ±x-axis, ±y-axis, and ±z-axis, respectively. Message-passing edges are established for any two surfaces whose normal vectors are not opposite to each other, thus obtaining a graph structure containing 12 undirected edges. , its adjacency matrix Node feature aggregation for graph neural networks.

[0092] To simplify the proof of concept, this specific implementation method reduces the graph message passing topology and order. The physical and electrical coupling topology of the model and the risk monitoring surface use the same node pair range. Specifically, for any node pair... ,make When the electrical coupling adjacency flag is 1, the node pair is... The set of surface pairs required for differential potential risk assessment .in, This is only used to define the message passing range of a graph neural network. A set / matrix of physical couplings between surfaces The physical coupling adjacency identifier in the graph. The above topology consistency is only applicable to this specific implementation. In general technical solutions, graph message passing topology... Physical coupling adjacency identifier and risk monitoring surfaces The three can be constructed independently and are not restricted by each other.

[0093] This specific implementation divides the spacecraft into six heterogeneous surface units and employs a first-order reduction method. The state equation generates potential labels and constructs training physical residuals. Surface Target equilibrium potential under current irradiation conditions It is calculated using the square root interpolation between the equilibrium potential of full sunshine and the equilibrium potential of full shadow, and can be achieved through the following formula: ; in, and Surface Equivalent equilibrium potential under conditions of full sunlight and full shadow The effective irradiated factor.

[0094] Order reduction with definite physical dimensions The equations define the evolution of surface potential, including the surface's first-order equivalent charging time constant, the equivalent capacitance relative to the structural reference potential, the equivalent conductance between surfaces, and the electrical coupling adjacency identifier. Specifically... The equation is expressed by the following formula: ; in, For surface The equivalent capacitance relative to the structural reference potential; For surface The first-order equivalent charging time constant; For surface With surface The equivalent conductance between; The electrical coupling adjacency identifier used in this specific implementation is... Represents surface The potential evolution equation includes surface The coupling effect it produces; and Surface Potential and surface The potential.

[0095] To facilitate numerical calculations, a normalized electrical coupling coefficient is defined. Specific electrical coupling coefficient This can be expressed by the following formula: ; Further, divide the dimensional equation by the equivalent capacitance. The normalized order reduction method for numerical integration is then obtained. Equations, specifically The equation is expressed by the following formula: ; When training the physical constraint model, the predicted potential is substituted into the above normalization order reduction. The equation can be used to construct the physical residual terms used in this specific implementation. The physical residual term This can be expressed by the following formula: ; To simplify the data generation and model input in this specific implementation, for all samples that satisfy... All surfaces use uniformly normalized electrical coupling parameters Specific normalized electrical coupling parameters This can be expressed by the following formula: ; This unified parameter setting is only used for proof of concept in this specific implementation and does not restrict general technical solutions from adopting other surface charging physical models, different connection matrices, or non-uniform surface coupling parameters.

[0096] Furthermore, as a specific implementation of the above method, this application provides an attitude trajectory planning device for differential charging of heterogeneous surfaces of spacecraft, such as... Figure 9As shown, the device includes: a training unit 71, a generation unit 72, a selection unit 73, and a verification unit 74.

[0097] Training unit 71 is used to generate supervision labels on diverse attitude trajectory samples using the surface charging physical model during the offline training phase, and to train the physical constraint multi-task graph neural network proxy model. The physical constraint multi-task graph neural network proxy model includes a heterogeneous surface message passing graph structure, which is constructed based on the heterogeneous surface units divided on the spacecraft surface as nodes, according to the surface geometric adjacency relationship or preset information association rules. The generation unit 72 is used to generate multiple candidate attitude trajectories that satisfy the basic path constraints based on the spacecraft's kinematic boundaries and attitude maneuver requirements during the attitude planning application phase. Selection unit 73 is used to use the physical constraint multi-task graph neural network surrogate model to perform charging risk assessment and sorting of the multiple candidate attitude trajectories, and select a preset number of candidate attitude trajectories as a set of trajectories to be reviewed. The verification unit 74 is used to call the surface charging physical model to verify each trajectory in the set to be verified, and output the attitude trajectory that satisfies multiple constraints; the multiple constraints include at least charging safety constraints, task constraints and actuator constraints.

[0098] In specific application scenarios, within the aforementioned training unit, the heterogeneous surface message passing graph structure is constructed in the following manner: The outer surface of the spacecraft is divided into multiple heterogeneous surface units according to materials, functions or spatial partitions, and each of the heterogeneous surface units is mapped as a graph node to form a node set. Based on the spatial association relationship between the heterogeneous surface units corresponding to each graph node in the node set, a message passing edge set and a corresponding graph adjacency matrix are constructed. The message passing edge set is constructed according to the surface geometric adjacency relationship or a preset information association rule. The value rule of the elements in the graph adjacency matrix is ​​as follows: when there is a connecting edge between any two graph nodes in the node set in the message passing edge set, the value of the element corresponding to the two graph nodes is set to 1, otherwise it is set to 0. Based on the node set, the message passing edge set, and the corresponding graph adjacency matrix, a heterogeneous surface message passing graph structure is constructed.

[0099] In specific application scenarios, the generation unit is specifically used for: Multiple geometric trajectories are generated based on the initial attitude and the target attitude. The geometric trajectories include at least: the shortest path connecting the initial attitude and the target attitude, generated based on quaternion spherical linear interpolation; and a detour path formed through one or more intermediate attitudes. The intermediate attitudes are used to enable the detour path to avoid a preset high differential charging risk irradiated attitude region. Each geometric trajectory is divided into multiple path segments, and a duration is assigned to each path segment. Under the condition that the total duration of attitude maneuver remains unchanged, the duration of each path segment is differentiated to obtain multiple candidate attitude trajectories with different velocity distributions.

[0100] In specific application scenarios, the selection unit is specifically used for: The node temporal features, graph topology input, and global task features corresponding to each candidate attitude trajectory are input into the physically constrained multi-task graph neural network surrogate model; the node temporal features include at least the effective illumination factor; the graph topology input is the adjacency matrix of a heterogeneous surface message-passing graph structure; the global task features include at least the attitude quaternion sequence. In the physical constraint multi-task graph neural network proxy model, forward inference is performed based on the node temporal features, graph topology input and global task features to output the charging risk index of each candidate attitude trajectory. The charging risk index includes the predicted peak differential potential and the predicted surface potential sequence. The multiple candidate attitude trajectories are sorted by charging risk assessment based on the predicted peak differential potential, and a preset number of candidate attitude trajectories are selected as the set of trajectories to be reviewed.

[0101] In specific application scenarios, the physical constraint multi-task graph neural network proxy model in the selection unit includes a graph message passing module, a timing coding module, a physical constraint module, a peak prediction head, and a potential trajectory prediction head; The graph message passing module aggregates the node temporal features based on the adjacency matrix to obtain aggregated node features; the aggregated node features and the node temporal features are input together into the temporal coding module, and local irradiation history, surface charging state and task time changes are extracted based on the effective irradiation factor to form dynamic features; the peak prediction head outputs the predicted peak differential potential of each candidate attitude trajectory based on the dynamic features; the potential trajectory prediction head outputs the predicted surface potential sequence corresponding to each candidate attitude trajectory based on the dynamic features; the physical constraint module applies physical conservation constraints based on the predicted surface potential sequence and the dynamic features to generate physical constraint verification results.

[0102] In specific application scenarios, the effective irradiance factor in the selection unit is calculated in the following manner: For each candidate attitude trajectory, the rotation matrix is ​​determined based on the time-varying unit quaternion corresponding to the candidate attitude trajectory, which describes the attitude change of the spacecraft's body coordinate system relative to the inertial coordinate system. The rotation matrix is ​​used to transform the unit outward normal vector of each heterogeneous surface unit in the body coordinate system to the inertial coordinate system; The effective illumination factor of each heterogeneous surface unit is obtained by calculating the dot product of the transformed unit external normal vector and the unit direction vector from the spacecraft's center of mass to the sun in the inertial coordinate system, and combining the ground shadow coefficient and the surface self-shading coefficient. The effective irradiation factors are arranged chronologically over the entire maneuvering time interval to obtain the local irradiation history of each heterogeneous surface unit.

[0103] In specific application scenarios, the verification unit is specifically used for: For each candidate attitude trajectory in the set of trajectories to be verified, the local illumination history, surface material and electrical parameters, time-varying spatial environment parameters, and physical connection parameters between surfaces corresponding to the candidate attitude trajectory are input into the surface charging physical model. Given an initial potential, the surface potential sequence of the candidate attitude trajectory is obtained by numerical integration of the differential evolution equation based on the surface charging physical model. Based on the surface potential sequence, the instantaneous differential potential timing between each heterogeneous surface unit pair is calculated. From the preset risk monitoring surface pair set, the maximum value of the instantaneous differential potential within the total duration of attitude maneuvering is selected as the peak differential potential. The risk monitoring surface pair is a preset heterogeneous surface unit pair that needs to be calculated for differential potential. The candidate attitude trajectory that satisfies the preset charging safety threshold condition and the preset task constraint condition and actuator constraint condition during the attitude maneuvering process is used as the output attitude trajectory that satisfies multiple constraints.

[0104] In specific application scenarios, the device further includes: The calculation unit is used to, after calling the surface charging physical model to numerically verify each trajectory in the set to be verified and outputting attitude trajectories that satisfy multiple constraints, calculate a comprehensive evaluation function for the attitude trajectories that satisfy multiple constraints output by the surface charging physical model, and select the attitude trajectory that satisfies the multiple constraints and has the smallest comprehensive evaluation function as the final output attitude trajectory; the evaluation items of the comprehensive evaluation function include: peak differential potential after physical verification, attitude geometric path length, angular velocity cost or control energy cost, and penalty items set for violating mission pointing constraints, maximum angular velocity constraints, control torque constraints or power generation constraints; each evaluation item is configured with a non-negative weight; The execution unit is used to execute only the first preset planning period of the final output attitude trajectory in the online rolling planning mode, and after obtaining new solar direction, environmental information or surface potential telemetry data, to re-execute the process of generating the candidate attitude trajectory, numerical verification and selecting the final output attitude trajectory based on the comprehensive evaluation function, using the spacecraft attitude and surface potential after the first preset planning period as the new initial conditions.

[0105] In specific application scenarios, the generation of supervisory labels on diverse attitude trajectory samples using the surface charging physical model in the training unit includes: Random or stratified sampling is performed on attitude path, segment duration, total maneuver time, solar direction, space environment parameters, surface material and electrical parameters, initial potential conditions, and physical connection parameters between surfaces to generate diverse attitude trajectory samples. For each sample trajectory in the diverse attitude trajectory samples, the local irradiation history of each heterogeneous surface unit is calculated, and the true surface potential sequence label and the true peak differential potential label are obtained using the surface charging physical model as supervision labels; The local irradiation history, surface material and electrical parameters, time-varying spatial environment parameters, physical connection parameters between surfaces, and task time parameters are organized into graph temporal input samples, which are paired with the supervision labels to form graph temporal training samples for training the physical constraint multi-task graph neural network surrogate model.

[0106] It should be noted that other corresponding descriptions of the functional units involved in the attitude trajectory planning device for differential charging of heterogeneous surfaces of spacecraft provided in this embodiment can be found in the descriptions of the corresponding methods, and will not be repeated here.

[0107] Based on the above method, the present application also provides a storage medium storing a computer program that, when executed by a processor, implements the above-mentioned attitude trajectory planning method for differential charging of heterogeneous surfaces of spacecraft.

[0108] Based on this understanding, the technical solution of this application can be embodied in the form of a software product. The software product can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, or portable hard drive), and includes several instructions to cause a computer device (such as a personal computer, server, or network device) to execute the methods described in the various implementation scenarios of this application.

[0109] Based on the above method and the corresponding virtual device embodiments, in order to achieve the above objectives, this application embodiment also provides a physical device for attitude trajectory planning of differential charging on heterogeneous surfaces of spacecraft. Specifically, it can be a computer, smartphone, tablet computer, smartwatch, server, or network device, etc. The physical device includes a storage medium and a processor; the storage medium is used to store a computer program; the processor is used to execute the computer program to implement the above-mentioned attitude trajectory planning method for differential charging on heterogeneous surfaces of spacecraft.

[0110] Optionally, the physical device may also include a user interface, a network interface, a camera, radio frequency (RF) circuitry, sensors, audio circuitry, a Wi-Fi module, etc. The user interface may include a display screen, input units such as a keyboard, etc., and optional user interfaces may also include USB interfaces, card reader interfaces, etc. The network interface may optionally include standard wired interfaces, wireless interfaces (such as Wi-Fi interfaces), etc.

[0111] In an exemplary embodiment, see Figure 10 The aforementioned physical devices include a communication bus, a processor, a memory, and a communication interface. They may also include input / output interfaces and a display device. The various functional units can communicate with each other via the bus. The memory stores a computer program, and the processor executes the program stored in the memory to perform the attitude trajectory planning method for differential charging of heterogeneous surfaces of spacecraft as described in the above embodiments.

[0112] Those skilled in the art will understand that the physical device structure for attitude trajectory planning of differential charging on heterogeneous surfaces of spacecraft provided in this embodiment does not constitute a limitation on the physical device, and may include more or fewer components, or combine certain components, or have different component arrangements.

[0113] The storage medium may also include an operating system and a network communication module. The operating system is a program that manages the hardware and software resources of the physical device for attitude trajectory planning of the differential charging of the spacecraft's heterogeneous surface, supporting the operation of information processing programs and other software and / or programs. The network communication module is used to enable communication between the various components within the storage medium, as well as communication with other hardware and software in the information processing physical device.

[0114] Through the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary general-purpose hardware platform, or it can be implemented by hardware. By applying the technical solution of this application, compared with the existing methods, this application trains a physical constraint multi-task graph neural network surrogate model containing a heterogeneous surface message passing graph structure by generating supervision labels on diverse attitude trajectory samples using a surface charging physical model during the offline training phase. In the attitude planning application phase, after generating multiple candidate attitude trajectories based on the spacecraft's kinematic boundaries and attitude maneuver requirements, the surrogate model first performs a charging risk assessment and sorts the candidate attitude trajectories to select the set of trajectories to be verified. Then, the surface charging physical model is called to verify each trajectory in the set of trajectories to be verified numerically. This forms a two-layer planning architecture that combines rapid screening by the surrogate model with accurate verification by the physical model. It effectively represents the spatial association characteristics between heterogeneous surfaces by using a graph structure constructed with heterogeneous surface units as nodes and based on surface geometric adjacency relationships or preset information association rules. It also avoids the huge computational overhead caused by directly performing physical integration on all candidate attitude trajectories. At the same time, numerical verification ensures that the final output attitude trajectory strictly meets the charging safety constraints, task constraints, and actuator constraints, thus balancing the efficiency and reliability of attitude trajectory planning.

[0115] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of a preferred embodiment, and the modules or processes shown in the drawings are not necessarily essential for implementing this application. Those skilled in the art will understand that the modules in the apparatus of the embodiment can be distributed within the apparatus of the embodiment as described, or can be modified to be located in one or more apparatuses different from this embodiment. The modules of the above-described embodiment can be combined into one module, or further divided into multiple sub-modules.

[0116] The serial numbers in this application are for descriptive purposes only and do not represent the superiority or inferiority of any particular implementation scenario. The above disclosures are merely a few specific implementation scenarios of this application; however, this application is not limited thereto, and any variations conceived by those skilled in the art should fall within the protection scope of this application.

Claims

1. A method for attitude trajectory planning in differential charging of heterogeneous surfaces of spacecraft, characterized in that, include: During the offline training phase, a physical charging physical model is used to generate supervision labels on diverse attitude trajectory samples to train a physical constraint multi-task graph neural network proxy model. The physical constraint multi-task graph neural network proxy model includes a heterogeneous surface message passing graph structure, which is constructed based on the heterogeneous surface units divided on the spacecraft surface as nodes, according to surface geometric adjacency relationships or preset information association rules. In the attitude planning application phase, multiple candidate attitude trajectories that satisfy the basic path constraints are generated based on the spacecraft's kinematic boundaries and attitude maneuver requirements. The charging risk assessment and sorting of the multiple candidate attitude trajectories are performed using the physical constraint multi-task graph neural network surrogate model, and a preset number of candidate attitude trajectories are selected as the set of trajectories to be reviewed. The surface charging physical model is called to numerically verify each trajectory in the set to be verified, and the attitude trajectory that satisfies multiple constraints is output. The multiple constraints include at least charging safety constraints, task constraints and actuator constraints.

2. The method according to claim 1, characterized in that, The heterogeneous surface message passing graph structure is constructed in the following manner: The outer surface of the spacecraft is divided into multiple heterogeneous surface units according to materials, functions or spatial partitions, and each of the heterogeneous surface units is mapped as a graph node to form a node set. Based on the spatial association relationship between the heterogeneous surface units corresponding to each graph node in the node set, a message passing edge set and a corresponding graph adjacency matrix are constructed. The message passing edge set is constructed according to the surface geometric adjacency relationship or a preset information association rule. The value rule of the elements in the graph adjacency matrix is ​​as follows: when there is a connecting edge between any two graph nodes in the node set in the message passing edge set, the value of the element corresponding to the two graph nodes is set to 1, otherwise it is set to 0. Based on the node set, the message passing edge set, and the corresponding graph adjacency matrix, a heterogeneous surface message passing graph structure is constructed.

3. The method according to claim 1, characterized in that, Based on the spacecraft's kinematic boundaries and attitude maneuver requirements, multiple candidate attitude trajectories satisfying the basic path constraints are generated, including: Multiple geometric trajectories are generated based on the initial attitude and the target attitude. The geometric trajectories include at least: the shortest path connecting the initial attitude and the target attitude, generated based on quaternion spherical linear interpolation; and a detour path formed through one or more intermediate attitudes. The intermediate attitudes are used to enable the detour path to avoid a preset high differential charging risk irradiated attitude region. Each geometric trajectory is divided into multiple path segments, and a duration is assigned to each path segment. Under the condition that the total duration of attitude maneuver remains unchanged, the duration of each path segment is differentiated to obtain multiple candidate attitude trajectories with different velocity distributions.

4. The method according to claim 1, characterized in that, The charging risk assessment and ranking of the multiple candidate attitude trajectories is performed using the physical constraint multi-task graph neural network surrogate model, and a preset number of candidate attitude trajectories are selected as the set of trajectories to be reviewed, including: The node temporal features, graph topology input, and global task features corresponding to each candidate attitude trajectory are input into the physically constrained multi-task graph neural network surrogate model; the node temporal features include at least the effective illumination factor; the graph topology input is the adjacency matrix of a heterogeneous surface message-passing graph structure; the global task features include at least the attitude quaternion sequence. In the physical constraint multi-task graph neural network proxy model, forward inference is performed based on the node temporal features, graph topology input and global task features to output the charging risk index of each candidate attitude trajectory. The charging risk index includes the predicted peak differential potential and the predicted surface potential sequence. The multiple candidate attitude trajectories are sorted by charging risk assessment based on the predicted peak differential potential, and a preset number of candidate attitude trajectories are selected as the set of trajectories to be reviewed.

5. The method according to claim 4, characterized in that, The physical constraint multi-task graph neural network proxy model includes a graph message passing module, a timing coding module, a physical constraint module, a peak prediction head, and a potential trajectory prediction head. The graph message passing module aggregates the temporal features of the nodes based on the adjacency matrix to obtain aggregated node features; The aggregated node features and the node temporal features are input into the temporal coding module, and the local irradiation history, surface charging state and task time changes are extracted based on the effective irradiation factor to form dynamic features; The peak prediction head outputs the predicted peak differential potential of each candidate attitude trajectory based on the dynamic features; the potential trajectory prediction head outputs the predicted surface potential sequence corresponding to each candidate attitude trajectory based on the dynamic features; the physical constraint module applies physical conservation constraints based on the predicted surface potential sequence and the dynamic features to generate physical constraint verification results.

6. The method according to claim 5, characterized in that, The effective irradiance factor is calculated as follows: For each candidate attitude trajectory, the rotation matrix is ​​determined based on the time-varying unit quaternion corresponding to the candidate attitude trajectory, which describes the attitude change of the spacecraft's body coordinate system relative to the inertial coordinate system. The rotation matrix is ​​used to transform the unit outward normal vector of each heterogeneous surface unit in the body coordinate system to the inertial coordinate system; The effective illumination factor of each heterogeneous surface unit is obtained by calculating the dot product of the transformed unit external normal vector and the unit direction vector from the spacecraft's center of mass to the sun in the inertial coordinate system, and combining the ground shadow coefficient and the surface self-shading coefficient. The effective irradiation factors are arranged chronologically over the entire maneuvering time interval to obtain the local irradiation history of each heterogeneous surface unit.

7. The method according to any one of claims 1-6, characterized in that, The step of calling the surface charging physical model to numerically verify each trajectory in the set to be verified, and outputting attitude trajectories that satisfy multiple constraints, includes: For each candidate attitude trajectory in the set of trajectories to be verified, the local illumination history, surface material and electrical parameters, time-varying spatial environment parameters, and physical connection parameters between surfaces corresponding to the candidate attitude trajectory are input into the surface charging physical model. Given an initial potential, the surface potential sequence of the candidate attitude trajectory is obtained by numerical integration of the differential evolution equation based on the surface charging physical model. Based on the surface potential sequence, the instantaneous differential potential timing between each heterogeneous surface unit pair is calculated. From the preset risk monitoring surface pair set, the maximum value of the instantaneous differential potential within the total duration of attitude maneuvering is selected as the peak differential potential. The risk monitoring surface pair is a preset heterogeneous surface unit pair that needs to be calculated for differential potential. The candidate attitude trajectory that satisfies the preset charging safety threshold condition and the preset task constraint condition and actuator constraint condition during the attitude maneuvering process is used as the output attitude trajectory that satisfies multiple constraints.

8. The method according to claim 7, characterized in that, After numerically verifying each trajectory in the set to be verified by calling the surface charging physical model and outputting attitude trajectories that satisfy multiple constraints, the method further includes: For the attitude trajectory that satisfies multiple constraints and is verified by the surface charging physical model, a comprehensive evaluation function is calculated, and the attitude trajectory that satisfies the multiple constraints and has the smallest comprehensive evaluation function is selected as the final output attitude trajectory. The evaluation items of the comprehensive evaluation function include: peak differential potential verified by physics, attitude geometric path length, angular velocity cost or control energy cost, and penalty items set for violating mission orientation constraints, maximum angular velocity constraints, control torque constraints or power generation constraints. Each evaluation item is configured with a non-negative weight. In the online rolling planning mode, only the first preset planning period of the final output attitude trajectory is executed. After obtaining new solar direction, environmental information or surface potential telemetry data, the spacecraft attitude and surface potential after the first preset planning period are executed are used as new initial conditions to re-execute the process of generating candidate attitude trajectories, numerical verification, and selecting the final output attitude trajectory based on the comprehensive evaluation function.

9. The method according to any one of claims 1-6, characterized in that, The method of generating supervised labels on diverse attitude trajectory samples using a surface charging physical model includes: Random or hierarchical sampling is performed on attitude path, segment duration, total maneuver time, solar direction, time-varying spatial environment parameters, surface material and electrical parameters, initial potential conditions, and physical connection parameters between surfaces to generate diverse attitude trajectory samples. For each sample trajectory in the diverse attitude trajectory samples, the local irradiation history of each heterogeneous surface unit is calculated, and the true surface potential sequence label and the true peak differential potential label are obtained using the surface charging physical model as supervision labels; The local irradiation history, surface material and electrical parameters, time-varying spatial environment parameters, physical connection parameters between surfaces, and task time parameters are organized into graph temporal input samples, which are paired with the supervision labels to form graph temporal training samples for training the physical constraint multi-task graph neural network surrogate model.

10. An attitude trajectory planning device for differential charging of heterogeneous surfaces in spacecraft, characterized in that, include: The training unit is used to generate supervision labels on diverse attitude trajectory samples using the surface charging physical model during the offline training phase, and to train the physical constraint multi-task graph neural network proxy model. The physical constraint multi-task graph neural network proxy model includes a heterogeneous surface message passing graph structure, which is constructed based on the heterogeneous surface units divided on the spacecraft surface as nodes, according to the surface geometric adjacency relationship or preset information association rules. The generation unit is used in the attitude planning application phase to generate multiple candidate attitude trajectories that satisfy the basic path constraints based on the spacecraft's kinematic boundaries and attitude maneuver requirements. The selection unit is used to perform charging risk assessment and sorting on the multiple candidate attitude trajectories using the physical constraint multi-task graph neural network surrogate model, and select a preset number of candidate attitude trajectories as a set of trajectories to be reviewed. The verification unit is used to call the surface charging physical model to verify each trajectory in the set to be verified, and output the attitude trajectory that satisfies multiple constraints; the multiple constraints include at least charging safety constraints, task constraints and actuator constraints.

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