Aerospace craft trajectory optimization and tracking control method based on aerodynamic force assistance

Abstract

The invention discloses an aerospace craft trajectory optimization and tracking control method based on aerodynamic force assistance, and relates to the technical field of aerospace craft control, and the method comprises the steps: firstly obtaining an aircraft state, environmental perception, constraint data and historical planning data, obtaining performance indexes through calculation, and dynamically adjusting the weight of each index in combination with constraint to balance importance; then, trajectory optimization is carried out by utilizing state data, environment data, weights and historical data to generate a current reference trajectory sequence and a corresponding control quantity sequence, a real-time control instruction is output according to a current state and a planning sequence through sliding mode tracking control processing, and finally whether a re-planning condition is met is judged; if so, updating the historical data through re-planning; otherwise, continuing to execute tracking control and outputting the control quantity; according to the invention, adaptive trajectory optimization and stable tracking can be realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of spacecraft control, in particular to a spacecraft trajectory optimization and tracking control method based on aerodynamic force assistance. BACKGROUND

[0002] As a core means of spacecraft orbit control, the aerodynamic-assisted orbit transfer technology can significantly reduce propellant consumption and improve mission efficiency by reasonably utilizing the aerodynamic force in the planetary atmosphere to achieve orbit transfer; in this technology system, the trajectory optimization part is responsible for generating a reference trajectory that meets multiple constraints, while the tracking control part ensures that the spacecraft accurately executes the trajectory, and the coordinated work of the two is the key foundation for achieving high-precision orbit transfer.

[0003] However, in actual flight, the atmospheric environment presents highly dynamic characteristics, including uneven spatial distribution of atmospheric density, real-time changes of heat flow constraints, and non-steady fluctuations of temperature field, etc. These variables pose a continuous challenge to trajectory optimization; the existing technical solution relies on a fixed weight multi-objective optimization strategy preset before the task, which cannot dynamically adjust the priority of each performance indicator according to real-time working conditions; when the spacecraft encounters sudden atmospheric disturbances or thermal environment mutations, the fixed weight mechanism may lead to excessive conservatism in heat flow control, while being too aggressive in speed deviation or dynamic pressure management, thereby disrupting the overall performance balance; for example, in areas of sudden increase in atmospheric density, the fixed weight may not be able to timely increase the weight of the heat flow constraint, leaving the spacecraft at risk of thermal protection failure; while in areas of sudden decrease in density, the lack of overload weight may lead to a decrease in structural safety margin.

[0004] More critically, when the actual flight state deviates from the reference trajectory due to atmospheric disturbances, the tracking error continues to accumulate, and the system still mechanically follows the original trajectory, resulting in the spacecraft being unable to timely avoid safety hazards such as heat flow or overload overruns, and also unable to capture performance optimization opportunities brought by changes in atmospheric conditions; this fragmented control architecture forms a response fault between the trajectory optimization layer and the tracking control layer, making it difficult to dynamically coordinate economic and safety needs in complex and variable flight environments.

[0005] In view of the above problems, the existing technology needs to be improved. SUMMARY

[0006] In view of the deficiencies in the prior art, the present application provides a spacecraft trajectory optimization and tracking control method based on aerodynamic force assistance.

[0007] In order to achieve the above purpose, the technical solution of the present application is as follows:

[0008] In a first aspect, the present application discloses a spacecraft trajectory optimization and tracking control method based on aerodynamic force assistance, comprising the following steps:

[0009] acquire aircraft state data, environment perception data, constraint data and historical planning data, the constraint data including heat flow upper limit, overload upper limit and dynamic pressure upper limit, the historical planning data including historical reference trajectory sequence and corresponding historical control quantity sequence;

[0010] According to the aircraft state data and the environment perception data, a plurality of performance indicators are obtained through feature calculation, the performance indicators including characteristic speed deviation, heat flow value, overload value and dynamic pressure value;

[0011] According to the performance indicators and the constraint data, weights of the performance indicators are obtained through dynamic weight adjustment processing, the weights being used to balance the relative importance of the performance indicators;

[0012] According to the aircraft state data, the environment perception data, the weights and the historical planning data, a current reference trajectory sequence and a corresponding current control quantity sequence are generated through trajectory optimization processing; the current control quantity sequence being a series of control instructions calculated in advance within a current planning time period;

[0013] According to the aircraft state data, the current reference trajectory sequence and the current control quantity sequence, a real-time control quantity is obtained through sliding mode tracking control processing, the real-time control quantity being a single control instruction to be executed at the current time;

[0014] determine whether the current time reaches a preset period or the performance indicators exceed corresponding constraint upper limits:

[0015] Yes, the reference trajectory sequence and the control quantity sequence are updated as new historical planning data through re-planning processing according to the environment perception data and the current reference trajectory sequence and the current control quantity sequence;

[0016] Otherwise, output the control quantity to the actuator and continue to execute the tracking control.

[0017] In a second aspect, the present application discloses a spacecraft trajectory optimization and tracking control system based on aerodynamic force assistance, comprising:

[0018] The data acquisition module is used for acquiring aircraft state data, environment perception data, constraint data and historical planning data; the constraint data including heat flow upper limit, overload upper limit and dynamic pressure upper limit, the historical planning data including historical reference trajectory sequence and corresponding historical control quantity sequence;

[0019] The feature calculation module is used for obtaining a plurality of performance indicators through feature calculation according to the aircraft state data and the environment perception data, the performance indicators including characteristic speed deviation, heat flow value, overload value and dynamic pressure value;

[0020] The weight adjustment module is used to obtain the weight of each performance indicator through dynamic weight adjustment based on the performance indicators and constraint data. The weight is used to balance the relative importance of the performance indicators.

[0021] The trajectory optimization module is used to generate the current reference trajectory sequence and the corresponding current control quantity sequence through trajectory optimization processing based on aircraft status data, environmental perception data, weights, and historical planning data; the current control quantity sequence is a series of control commands pre-calculated within the current planning time period;

[0022] The tracking control module is used to obtain real-time control quantities through sliding mode tracking control processing based on the aircraft status data, the current reference trajectory sequence, and the current control quantity sequence. The real-time control quantity is the single control command that needs to be executed at the current moment.

[0023] The decision module is used to determine whether the current time has reached the preset period or whether the performance index has exceeded the corresponding constraint limit;

[0024] The replanning module is used to update the reference trajectory sequence and control sequence as new historical planning data based on the environmental perception data and the current reference trajectory sequence and the current control quantity sequence when the decision module determines that it is correct.

[0025] The output module is used to output real-time control quantities to the actuator and continue to perform tracking control when the decision module determines that the decision is negative.

[0026] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0027] 1. By calculating the relative deviations of each performance index from the upper limit of the constraint in real time and dynamically adjusting the weight coefficients in combination with the rate of change of the environment, the trajectory optimization process can automatically balance the priority of each target according to the actual flight environment. This overcomes the problem that the traditional fixed weight strategy cannot respond in time when the environment changes suddenly, which leads to heat flow or overload exceeding the limit. It significantly improves the system's adaptability and safety in complex atmospheric environments.

[0028] 2. By closely integrating trajectory optimization with sliding mode tracking control, the system determines whether to trigger replanning by tracking deviations in real time, and actively updates the reference trajectory and control sequence when performance indicators exceed limits or the environment changes abruptly. This mechanism effectively solves the problem of deviation accumulation caused by the disconnect between the optimization layer and the tracking layer in traditional methods, achieves a dynamic balance between trajectory economy and safety, and enhances the overall control accuracy and robustness of the system under disturbance environments.

[0029] 3. Based on sliding mode tracking control, the historical position deviation sequence is analyzed by autoregressive model to predict the compensation control quantity at future time and superimpose it into the real-time control command. This mechanism can proactively correct the trajectory deviation caused by environmental disturbances, effectively suppress the accumulation of deviation within the replanning interval, and significantly improve the accuracy of trajectory tracking and the control response speed of the system in dynamic environments.

[0030] 4. By fusing sensor measurements, theoretical atmospheric models, and state equation calculations, key environmental parameters such as atmospheric density are weighted and corrected. Combined with temperature measurements, aerodynamic parameters such as heat flux, lift, and drag are corrected in real time. This improves the accuracy of the models used in trajectory optimization and tracking control, making them more reflective of the real flight environment, thereby ensuring the effectiveness of trajectory planning and tracking control and the reliability of the mission. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is an overall block diagram of the method in Embodiment 1 of the present invention;

[0033] Figure 2 This is a flowchart illustrating the overall execution process of the method in Embodiment 1 of the present invention.

[0034] Figure 3 This is an overall block diagram of the system in Embodiment 2 of the present invention. Detailed Implementation

[0035] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] Application Overview: In aerodynamic-assisted orbit transfer technology, trajectory optimization and tracking control are core components for achieving precise orbit transfer, and their performance directly affects the reliability and efficiency of flight missions. Existing technologies generally employ fixed-weight multi-objective optimization strategies. The weight parameters of this strategy are preset before mission execution and remain constant throughout the mission, failing to adjust in real-time according to changes in the dynamic flight environment. Environmental variables such as uneven atmospheric density distribution and time-varying heat flux constraints cause dynamic shifts in the priority requirements of various performance indicators, which static weight allocation mechanisms struggle to adapt to. Consequently, the optimization process may exhibit an overly conservative tendency in indicators such as characteristic velocity deviation, while also demonstrating a risk accumulation effect in key indicators such as heat flux or overload values. Furthermore, when this optimization strategy is combined with open-loop or simple closed-loop tracking control, the system lacks the ability to actively respond to environmental disturbances, causing the deviation between the actual flight state and the reference trajectory to continuously widen, making it difficult to maintain the dynamic balance between trajectory economy and safety.

[0037] For example, during an aerodynamically assisted orbital transfer mission, the spacecraft encountered abnormal fluctuations in local atmospheric density, and the real-time density values ​​reported by environmental perception data deviated significantly from the preset model. The fixed-weight optimization strategy failed to dynamically increase the weight priority based on the situation where the heat flux value was approaching the safety limit, and the generated reference trajectory still required the spacecraft to maintain a high angle of attack to optimize the velocity deviation index. At the same time, the tracking and control system executed commands based on historical planning data and could not perceive the real-time evolution of the heat flux risk, resulting in a gradual accumulation of control deviations. In this scenario, the spacecraft's thermal protection system continuously endured thermal loads close to its design limits, and the overload value also approached the safety threshold simultaneously, significantly affecting the overall stability of the system.

[0038] If the aforementioned problems are not addressed, the aircraft will be unable to effectively coordinate the synergistic mechanism of trajectory optimization and tracking control in dynamic flight environments. The trajectory optimization results will continuously deviate from actual operating conditions due to a lack of environmental adaptability, and the cumulative effect of tracking control deviations will further amplify system risks. Consequently, the aircraft may frequently find itself in critical states under constraints such as heat flux, overload, and dynamic pressure, significantly reducing mission reliability. In the long term, this deficiency will limit the applicability of aerodynamic-assisted orbital transfer technology in complex atmospheric environments and hinder its effectiveness improvement.

[0039] Example 1:

[0040] like Figures 1-2 As shown, the aerodynamically assisted spacecraft trajectory optimization and tracking control method includes the following steps:

[0041] Step S1: Acquire aircraft status data, environmental perception data, constraint data, and historical planning data. The constraint data includes upper limits for heat flux, overload, and dynamic pressure. The historical planning data includes historical reference trajectory sequences and corresponding historical control quantity sequences.

[0042] Furthermore, the aircraft's state data is acquired through an integrated navigation system, including a Global Positioning System (GPS) receiver and an Inertial Measurement Unit (IMU), to collect raw state data of the aircraft in real time. This data includes the position vector, velocity vector, and attitude angles in a geocentric inertial coordinate system, where the position vector is represented as... The velocity vector is represented as Attitude angles include roll angle. Pitch angle and yaw angle To ensure consistency in subsequent trajectory optimization and tracking control processing, this raw data needs to be transformed into the aircraft's position coordinate system, which is based on the Earth's center and aligned with the aircraft's center of mass. This transformation is achieved by applying a predefined transformation matrix calculated based on the aircraft's longitude and latitude.

[0043] Specifically, longitude Defined as the aircraft position coordinate system The projection of the axis onto the equatorial plane and the geocentric coordinate system Angle between axes, latitude Defined as The angle between the axis and the equatorial plane. Transformation matrix. Represented as:

[0044]

[0045] By left-multiplying by the transformation matrix, the position vector is transformed into... The velocity vector is converted to Thus, the position vector in a unified coordinate system is obtained. and velocity vector Attitude angle data is not transformed and is directly used for subsequent control calculations to ensure the accuracy of the aircraft's attitude information. This process ensures that all state data is processed in a unified reference frame, providing consistent input for subsequent multi-objective performance index calculations and trajectory optimization.

[0046] Furthermore, environmental perception data is obtained in real time by atmospheric sensors collecting environmental parameters around the aircraft, including atmospheric density measurements, temperature measurements, and pressure measurements. First, a theoretical density value is calculated based on a theoretical atmospheric density model with exponential decay. This model describes the relationship between atmospheric density and altitude, and the specific formula is as follows:

[0047]

[0048] in, This represents the atmospheric density calculated based on a theoretical model. This represents the standard atmospheric density at sea level. Represents the reciprocal of sea level elevation. This represents the distance from the Earth's center to the ground of the aircraft (calculated using the magnitude of the position vector). This represents the average radius of the Earth at sea level. Simultaneously, the consistency of the measured values ​​is verified using the ideal gas law. The density value of the law is calculated from the pressure and temperature measurements using the following formula:

[0049]

[0050] in, This represents the atmospheric density calculated based on the equation of state. Indicates the pressure measurement value. Indicates the temperature measurement value. This represents the gas constant. Next, data fusion correction is performed, combining sensor measurements, theoretical model values, and state equation values ​​using a weighted average method to obtain the corrected atmospheric density, as shown in the formula:

[0051]

[0052] in, This represents the corrected atmospheric density. , , This represents the weighting coefficients, which are dynamically adjusted based on sensor accuracy, model reliability, and flight conditions, and satisfy... .

[0053] Furthermore, constraint data is obtained from mission planning or design specifications, including upper limits for heat flux, overload, and dynamic pressure, which are predefined based on the aircraft's structural safety limits and mission requirements. For example, the upper limit for heat flux is determined by the maximum tolerance of the aircraft's thermal protection system, the upper limit for overload is set based on the aircraft's structural strength and crew tolerance, while the upper limit for dynamic pressure is derived from aerodynamic load limits. These constraint data serve as hard boundaries to ensure that trajectory optimization does not violate safety constraints.

[0054] Meanwhile, historical planning data is read from the results of the previous optimization run, including a reference trajectory sequence and a control sequence. The reference trajectory sequence consists of a series of position and velocity vectors corresponding to timestamps, while the control sequence includes control variables such as lift coefficient and tilt angle. Historical data is updated through a periodic storage mechanism; after each trajectory optimization or replanning is completed, the newly generated trajectory and control sequence are written to storage, replacing the old data.

[0055] Step S2: Based on the aircraft status data and environmental perception data, multiple performance indicators are obtained through feature calculation. The performance indicators include characteristic velocity deviation, heat flux value, overload value and dynamic pressure value.

[0056] Furthermore, the feature calculation process includes:

[0057] Based on the velocity vector and the preset target orbit velocity vector, the characteristic velocity deviation is calculated through the vector magnitude difference.

[0058] The heat flux value is calculated using the stagnation point heat flux model based on atmospheric density measurements, temperature measurements, and velocity magnitude.

[0059] The overload value is calculated by the ratio of aerodynamic force and gravity, wherein the aerodynamic force is calculated based on atmospheric density measurement, velocity magnitude and aerodynamic coefficient, and the gravity is calculated based on the position vector.

[0060] The dynamic pressure value is calculated by square product of atmospheric density measurement and velocity magnitude.

[0061] Specifically, firstly, the characteristic velocity deviation is obtained by calculating the magnitude difference between the current velocity vector and the target orbit velocity vector. The current velocity vector is derived from coordinate system transformation, while the target orbit velocity vector is determined based on the orbital dynamics model. For example, for a circular orbit, its magnitude is calculated from the Earth's gravitational constant and the target orbit radius. Next, the heat flux value is calculated using a stagnation point heat flux model. This model incorporates corrected atmospheric density and velocity magnitude, and uses temperature measurements to correct the heat flux calculation coefficients, reflecting the actual temperature's influence on heat flux. Then, the overload value is calculated as the ratio of aerodynamic forces to gravity. Aerodynamic forces include lift and drag, calculated based on corrected atmospheric density, velocity magnitude, and temperature-dependent lift and drag coefficients, while gravity is determined by the Earth's gravitational constant and geocentric distance. Finally, the dynamic pressure value is calculated as half the square product of the corrected atmospheric density and velocity magnitude, directly reflecting the aerodynamic load intensity.

[0062] The following formula is used in the calculation of heat flux:

[0063]

[0064] in, Indicates the heat flux value. This represents the heat flux calculation coefficient related to temperature (corrected by temperature measurements). This represents the corrected atmospheric density. This represents the magnitude of the velocity (calculated from the magnitude of the velocity vector). This represents the density index (with a value of 0.5). This represents the speed index (with a value of 3.15).

[0065] The following formula is used in the overload value calculation:

[0066]

[0067] in, Indicates the overload value. Represents aerodynamic lift (from the formula) calculate, Indicates the reference area of ​​the aircraft. (This represents the temperature-dependent lift coefficient). Represents aerodynamic drag (from the formula) calculate, This represents the zero-lift drag coefficient related to temperature. (This represents the temperature-dependent induced drag factor). Indicates the mass of the aircraft. Represents the local gravitational acceleration (from the formula) calculate, Represents the Earth's gravitational constant. (Indicates the distance from the Earth's center).

[0068] The characteristic velocity deviation is calculated using the following formula:

[0069]

[0070] in, Indicates characteristic velocity deviation. Represents the current velocity vector. This represents the target orbital velocity vector.

[0071] The dynamic pressure value is calculated using the following formula:

[0072]

[0073] in, This indicates the dynamic pressure value.

[0074] Furthermore, temperature measurements are used to correct coefficients in the heat flux calculation model; for example, heat flux calculation coefficients are adjusted using temperature compensation formulas.

[0075]

[0076] in, This represents the heat flux calculation coefficient related to temperature. Represents the heat flux coefficient at standard temperature. This represents the temperature correction factor. This indicates the current temperature measurement value. This represents the standard temperature. The corrected atmospheric density and temperature compensation coefficient are used directly in the heat flux calculation to ensure the system adapts to actual atmospheric conditions.

[0077] Step S3: Based on the performance indicators and constraint data, obtain the weights of each performance indicator through dynamic weight adjustment. The weights are used to balance the relative importance of the performance indicators.

[0078] Furthermore, the dynamic weight adjustment process includes: adjusting the weights of each performance indicator through a linear combination based on the relative deviation between the performance indicator and the corresponding upper limit of the constraint, as well as the environmental change rate; wherein, the environmental change rate is calculated based on the time series changes of atmospheric density measurements and temperature measurements.

[0079] Specifically, the dynamic weight adjustment process is based on characteristic velocity deviation, heat flux value, overload value, dynamic pressure value, and environmental change rate. It adjusts the multi-objective optimization weights by calculating the relative deviation of each performance index from the corresponding constraint upper limit and combining the comprehensive influence of the environmental change rate using a linear combination method.

[0080] First, the rate of environmental change is calculated by the time series changes in atmospheric density and temperature measurements. The rate of change in atmospheric density is obtained by dividing the difference between the current and previous atmospheric density by the time interval, and the rate of change in temperature is obtained by dividing the difference between the current and previous temperature by the time interval. These rates of change are then weighted and combined to reflect the overall environmental fluctuations.

[0081] Next, for each optimization objective, including characteristic velocity deviation, heat flux value, overload value and dynamic pressure value, the relative deviation between it and the preset constraint upper limit is calculated. This deviation is expressed as the absolute difference between the current index value and the upper limit value divided by the upper limit value, thereby quantifying the degree of closeness between the performance index and the safety boundary.

[0082] Then, the relative deviation and the rate of change of the environment are input into the weight adjustment function, which generates the adjusted weights by linearly combining the benchmark weights, the static deviation term, and the dynamic change term. The static deviation term is based on the product of the relative deviation and the sensitivity coefficient, and the dynamic change term is based on the product of the rate of change of the environment and the sensitivity coefficient.

[0083] Finally, the multi-objective optimization weights are output for trajectory optimization processing, ensuring that the weights adapt to environmental conditions and performance status, thereby balancing the priority of each optimization objective in a dynamic environment.

[0084] The following formula is used in calculating the rate of environmental change:

[0085]

[0086] in, Indicates the rate of environmental change. Represents the rate of change of atmospheric density (in terms of the atmospheric density at the current moment). Atmospheric density compared to the previous moment The difference divided by the time interval calculate, Represents the rate of temperature change (in terms of the current temperature). Temperature compared to the previous moment The difference divided by the time interval calculate, This represents the temperature change weighting coefficient (used to adjust the relative importance of temperature change in the rate of environmental change).

[0087] The following formula is used in the weight adjustment:

[0088]

[0089] in, The weight represents the i-th optimization objective (e.g., the corresponding characteristic velocity deviation, heat flux value, overload value, or dynamic pressure value). This represents the baseline weight of the i-th objective. This represents the static deviation sensitivity coefficient of the i-th target. Represents the relative deviation of the i-th target (calculated as) ,in This is the current performance metric value. (This corresponds to the upper limit of the constraint). This represents the sensitivity coefficient to dynamic changes of the i-th target. It represents the absolute value of the rate of environmental change.

[0090] Step S3: Based on the aircraft status data, environmental perception data, weights, and historical planning data, generate the current reference trajectory sequence and the corresponding current control quantity sequence through trajectory optimization processing; the current control quantity sequence is a series of control commands pre-calculated within the current planning time period;

[0091] Furthermore, the trajectory optimization process uses the Gaussian pseudospectral method, which includes: mapping the time interval of the current planning period to a standard interval, and discretizing state variables and control variables at collocation points. The state variables include the position vector and velocity vector in the aircraft state data, and the control variables include the lift coefficient and inclination angle. Based on the state variables, control variables, and aerodynamic parameters, algebraic constraints are established based on the orbital dynamics model. A performance index function is constructed based on performance indices and weights, and the current reference trajectory sequence and current control variable sequence are generated by solving nonlinear programming.

[0092] Specifically, the trajectory optimization calculation process is based on the position and velocity vectors in a unified coordinate system, the corrected atmospheric density, the multi-objective optimization weights, and historical planning data. The continuous trajectory optimization problem is transformed into a nonlinear programming problem through the Gaussian pseudospectral method.

[0093] First, a time-domain transformation is performed to map the actual flight time interval to a standard interval, providing a standardized processing basis for subsequent numerical calculations. Next, the state and control variables are discretized. At selected collocation points, Lagrange interpolation polynomials are used to approximate the state and control variables, establishing a discretized system model.

[0094] Establishing algebraic constraints based on the orbital dynamics model involves transforming continuous differential equation constraints into collocational algebraic equation constraints using differential approximation matrices. Specifically, the orbital dynamics model describes the motion of the aircraft under aerodynamic assistance, including the differential relationships of the rate of change of velocity, the rate of change of flight path angle, and the rate of change of geocentric distance. The discretized form of these dynamic constraints at collocational points ensures the physical feasibility of the trajectory.

[0095] While establishing constraints, a performance index function is constructed based on multi-objective optimization weights. This function comprehensively considers the weighted sum of characteristic velocity deviation, heat flux, overload, and dynamic pressure. The performance index function and algebraic constraints together constitute a complete nonlinear programming problem. Finally, the problem is numerically solved using a nonlinear programming solver, generating a reference trajectory sequence and a control quantity sequence that satisfy all constraints.

[0096] In time-domain transformation, the following formula is used:

[0097]

[0098] in, This represents the transformed standard time variable. Indicates actual time. This indicates the initial time for trajectory optimization. This indicates the terminal time for trajectory optimization.

[0099] In the discretization of state variables, the following approximation is used:

[0100]

[0101] in, This represents a vector of state variables (including velocity, flight path angle, and distance from the Earth's center). This represents the i-th collocation point. This represents the corresponding Lagrange basis function. This indicates the total number of points.

[0102] The orbital dynamics model is a three-degree-of-freedom dynamics model, including differential equations for the rate of change of velocity, the rate of change of flight path angle, and the rate of change of geocentric distance; the three-degree-of-freedom dynamics model is represented by the following set of differential equations:

[0103]

[0104] in, Represents the rate of change of velocity. Indicates aerodynamic drag. Indicates the mass of the aircraft. Represents the Earth's gravitational constant. Indicates the flight path angle. Indicates the distance from the Earth's center. Indicates the rate of change of the flight path angle. Indicates aerodynamic lift. This represents the rate of change of distance from the Earth's center.

[0105] The algebraic form of the dynamic constraints is as follows:

[0106]

[0107] in, The elements of the differential approximation matrix represent the derivative values ​​of the basis functions at the collocation points; Indicates the control variables at the collocation points The value; This represents the right-hand function of the dynamic equations, the specific form of which is determined by the orbital dynamics model.

[0108] The discrete form of the performance index function is:

[0109]

[0110] in, Indicates comprehensive performance indicators, The weights representing the characteristic velocity deviation, Indicates characteristic velocity deviation. The weights representing the heat flux values, Indicates the heat flux value. The weight representing the overload value, Indicates the overload value. The weight representing the dynamic pressure value, This indicates the dynamic pressure value.

[0111] Discretization of state and control variables ensures computational feasibility, algebraic constraints guarantee the physical rationality of the trajectory, performance index functions guide the optimization direction, and finally, a practical trajectory scheme is obtained through numerical solution.

[0112] Step S4: Based on the aircraft status data, the current reference trajectory sequence, and the current control quantity sequence, obtain the real-time control quantity through sliding mode tracking control processing. The real-time control quantity is the single control command that needs to be executed at the current moment.

[0113] Furthermore, the sliding mode tracking control process includes: calculating the position deviation vector and velocity deviation vector based on the deviations of the position vector and velocity vector from the current reference trajectory sequence; constructing a sliding surface based on the position deviation vector and velocity deviation vector; and calculating the real-time control quantity based on the sliding surface and the current control quantity sequence through equivalent control and switching control.

[0114] Specifically, the sliding mode tracking control process is based on the deviation of the position and velocity vectors in a unified coordinate system from the reference trajectory sequence. It generates aircraft control commands by constructing a sliding mode surface and designing control laws.

[0115] First, calculate the position deviation vector and the velocity deviation vector. The position deviation vector is obtained by subtracting the current position vector from the reference position vector at the corresponding moment in the reference trajectory sequence. The velocity deviation vector is obtained by subtracting the current velocity vector from the reference velocity vector at the corresponding moment in the reference trajectory sequence.

[0116] Next, a sliding surface is constructed based on the position deviation vector and the velocity deviation vector. The sliding surface is designed as a linear combination of the velocity deviation vector and the position deviation vector, where the position deviation vector is weighted by a positive definite diagonal matrix.

[0117] The final control quantity is then calculated by combining equivalent control and switching control. The equivalent control is derived by setting the sliding surface derivative to zero and is used to maintain the motion of the system on the sliding surface. The switching control is designed based on the sliding surface function and is used to suppress system disturbances and ensure tracking robustness.

[0118] The final output control quantity is sent directly to the aircraft actuator to achieve the trajectory tracking control objective.

[0119] The following formula is used in the design of sliding surfaces:

[0120]

[0121] in, Represents the sliding surface vector. Represents the velocity deviation vector. Represents the position deviation vector. This represents a positive definite diagonal matrix, whose diagonal elements are sliding mode parameters used to adjust the weight of positional deviations in the sliding surface.

[0122] The following formula is used in the calculation of the control law:

[0123]

[0124] in, This represents the total control quantity. Indicates the equivalent control quantity. This indicates the switching control quantity.

[0125] The equivalent control quantity is obtained by solving the sliding surface derivative equation. The specific derivation process is as follows: First, calculate the derivative of the sliding surface. ,in , Then, the system dynamics equations are substituted and set to zero to obtain the equivalent control quantity.

[0126] The switching control quantity is designed using a saturation function form:

[0127]

[0128] in, Indicates the switching gain matrix. Represents a saturation function. This represents the boundary layer thickness parameter, used to mitigate and control chattering.

[0129] The entire sliding mode tracking control process forms a complete feedback control loop through continuous deviation calculation, sliding surface construction, and control law solution, ensuring tracking accuracy and system robustness.

[0130] Step S5: Determine whether the current time has reached the preset period or whether the performance index has exceeded the corresponding constraint limit: If yes, update the reference trajectory sequence and control quantity sequence as new historical planning data through replanning based on the environmental perception data, the current reference trajectory sequence and the current control quantity sequence; otherwise, output the control quantity to the actuator and continue to execute tracking control.

[0131] Specifically, the data judgment phase determines whether to trigger replanning based on multiple conditions, including current time, heat flux value, overload value, dynamic pressure value, position deviation vector, velocity deviation vector, and environmental change rate.

[0132] First, periodic trigger checks are performed to see if the time interval between the current time and the last planned time has reached a preset period value, which is pre-set based on task requirements and computing resources. Simultaneously, event trigger checks are performed, including checks for performance metrics exceeding limits, tracking deviation exceeding limits, and sudden environmental changes.

[0133] The performance index over-limit judgment checks whether the heat flux value exceeds the upper limit of heat flux, whether the overload value exceeds the upper limit of overload, and whether the dynamic pressure value exceeds the upper limit of dynamic pressure. The tracking deviation over-limit judgment checks whether the magnitude of the position deviation vector and the magnitude of the velocity deviation vector exceed the corresponding position deviation threshold and velocity deviation threshold, respectively. The environmental change judgment checks whether the environmental change rate exceeds the preset environmental change threshold. The environmental change rate reflects the comprehensive change of atmospheric density and temperature.

[0134] When the periodic trigger condition or any event trigger condition is met, the replanning subprocess is initiated.

[0135] In the replanning sub-process, the model is first updated. Current environmental perception data, including atmospheric density and temperature measurements, and historical planning data, including reference trajectory sequences and control variable sequences, are used as input. A new initial guess state is generated through interpolation. Linear interpolation is performed using the trajectory point sequences from the historical planning data to provide initial conditions for trajectory re-optimization. Next, trajectory re-optimization is performed. Based on the updated environmental parameters and the initial guess state, a new reference trajectory sequence and control variable sequence are generated using the same multi-objective optimization method as the initial trajectory optimization. Finally, historical data is updated. The newly generated reference trajectory sequence and control variable sequence are stored as historical planning data, overwriting the original historical data, ensuring that subsequent planning is based on the latest trajectory information.

[0136] The following formula is used to generate the initial guess state:

[0137]

[0138] in, This represents the initial guess state. Represents the interpolation function. Represents a historical reference trajectory sequence. This represents a historical control quantity sequence.

[0139] Therefore, this method, through deep coupling of environmental perception data and real-time performance evaluation, enables trajectory optimization and tracking control to form a collaborative response mechanism, effectively solving the problem of insufficient adaptive capability in dynamic flight environments. Dynamic weight adjustment ensures that the priority of each performance indicator is adjusted in real time according to environmental changes, avoiding optimization bias caused by fixed weight strategies; replanning actively updates the trajectory when performance indicators approach the constraint limit, preventing the system from continuing to operate in dangerous conditions; the overall closed-loop design dynamically integrates data streams, achieving a real-time balance between trajectory economy and safety, overcoming the limitations of traditional static optimization methods in scenarios such as atmospheric density fluctuations.

[0140] In some of the embodiments described above in this application, a deviation prediction and compensation mechanism for sliding mode tracking is proposed to predict future position deviation trends and perform forward compensation. However, in this process, the sliding mode tracking control only relies on the deviation at the current moment for feedback adjustment and cannot use historical deviation data to identify the evolution pattern under dynamic environmental disturbances. This leads to the continuous accumulation of position deviation within the replanning interval, which in turn causes the risk of a decrease in trajectory tracking accuracy or even exceeding the safety threshold.

[0141] In response, this application further proposes a deviation prediction and compensation mechanism for sliding mode tracking: the position deviation vector is calculated based on the position vector and the current reference trajectory sequence; the position deviation vector is stored in the historical deviation sequence, and the compensation control quantity for future moments is obtained by processing the historical deviation sequence through an autoregressive model; the compensation control quantity is superimposed on the real-time control quantity to form the final control command.

[0142] In practical applications, the position deviation vector refers to the vector difference between the actual position of the aircraft and the position of the reference trajectory. It can be calculated using Euclidean distance or Manhattan distance to capture instantaneous errors in trajectory tracking in real time, avoiding prediction distortion caused by relying on outdated data. The historical deviation sequence can be understood as a set of position deviation vectors stored in chronological order. It can be implemented using a circular buffer or queue data structure to fully record the dynamic evolution of the deviation, providing sufficient time-series data support for the prediction model. Specifically, the autoregressive model is a statistical model that predicts future values ​​based on historical data. It can employ an autoregressive moving average model (…). This is achieved using ARMA (Advanced Partial Memory) or Long Short-Term Memory (LSTM) networks, aiming to extract periodic or trend patterns under environmental disturbances from historical deviations, overcoming the limitation of traditional feedback control that only responds to current deviations. In practical applications, the compensation control quantity refers to the predictive control command used to correct future deviations. It can be generated in proportional-integral form or based on model predictive control, with the aim of predicting the impact of environmental disturbances in advance and shortening the delay of control response. The final control command can be understood as the combined output of the real-time control quantity and the compensation control quantity. It can be implemented using vector addition or weighted summation, with the aim of ensuring that the control strategy responds to both the real-time state and future trends.

[0143] The proposed solution calculates the position deviation vector in real time and stores it in a historical deviation sequence. An autoregressive model is then used to analyze the historical deviation data to predict the compensation control quantity for future moments. This compensation quantity is then superimposed on the real-time control quantity, thus ensuring that the current control command already includes correction for future deviations. This mechanism enables the system to make proactive adjustments based on the evolution of historical deviations, effectively suppressing the accumulation of position deviations caused by environmental disturbances within the replanning interval, and significantly improving the accuracy and stability of trajectory tracking.

[0144] Through the above technical solution, this application effectively reduces the cumulative effect of position deviation in dynamic flight environment, avoids the risk of trajectory tracking accuracy decline and exceeding safety threshold, and thus maintains the reliability of trajectory tracking under complex conditions such as atmospheric density fluctuation.

[0145] Furthermore, the formula for calculating the compensation control quantity is:

[0146]

[0147] in, Indicates supplementary control quantity. Represents the prediction gain coefficient. Represents the autoregressive coefficient. Represents the historical position deviation vector. This indicates the order of the autoregressive model.

[0148] Among them, supplementary control quantity This refers to the predictive compensation vector superimposed on the real-time control quantity. It can be represented in three-dimensional vector form, specifically as an adjustment of the lift coefficient or tilt angle. Its purpose is to actively correct trajectory tracking deviations through a feedforward compensation mechanism; predictive gain coefficient. This can be understood as a proportional coefficient that adjusts the magnitude of the compensation, which can be implemented using a scalar or diagonal matrix. Specifically, it can be adjusted online based on the aircraft's dynamic characteristics, with the aim of balancing the compensation intensity to avoid control oscillations; autoregressive coefficient. Specifically, it involves assigning weighting coefficients to deviations at different historical time points. These coefficients can be fixed values ​​or updated in real time using a recursive least squares algorithm. The purpose is to optimize the contribution of historical data to the current prediction; historical position deviation vector. It can be understood as the positional deviation over the past k moments, which can be calculated by the navigation system. Specifically, it can be a deviation vector of geocentric distance, longitude, and latitude. Its purpose is to provide time-related historical information to capture the evolution pattern of the deviation. The order m of the autoregressive model refers to the number of historical data points considered by the model. It can be set to an integer from 3 to 5. Specifically, it can be dynamically selected based on computing resources and the rate of change of the environment. Its purpose is to balance prediction accuracy and computational complexity.

[0149] Specifically, the proposed solution involves inputting the historical position deviation vector into an autoregressive model to calculate the compensation control quantity, which is then superimposed on the real-time control quantity of the sliding mode tracking control. The system first calculates the position deviation vector based on the position vector and the current reference trajectory sequence, storing it in a historical deviation sequence. Subsequently, based on the historical deviation sequence, the system generates the compensation control quantity for future moments through autoregressive model processing. Finally, this compensation control quantity is superimposed on the real-time control quantity obtained from sliding mode tracking control to form the final control command. This mechanism enables the system to proactively capture trajectory deviation trends caused by atmospheric disturbances, generating compensation commands in advance during sudden environmental changes, avoiding the accumulation of deviations due to prediction lag. Simultaneously, the dynamic adjustment of the prediction gain coefficient ensures that the compensation intensity adapts to the real-time response characteristics of the aircraft, thereby establishing a dynamic feedback channel between trajectory optimization and tracking control.

[0150] Through the above scheme, this application can generate accurate compensation commands based on the quantitative analysis of historical deviation data under complex flight conditions such as sudden changes in atmospheric density or fluctuations in thermal environment, effectively suppressing the cumulative effect of tracking error and improving the robustness and stability of trajectory tracking control in dynamic environments.

[0151] Example 2:

[0152] like Figure 3 As shown, the aerodynamic-assisted spacecraft trajectory optimization and tracking control system includes: a data acquisition module, used to acquire spacecraft status data, environmental perception data, constraint data, and historical planning data; the constraint data includes upper limits for heat flux, overload, and dynamic pressure, and the historical planning data includes historical reference trajectory sequences and corresponding historical control quantity sequences;

[0153] The feature calculation module is used to obtain multiple performance indicators through feature calculation based on aircraft status data and environmental perception data. The performance indicators include characteristic velocity deviation, heat flux value, overload value and dynamic pressure value.

[0154] The weight adjustment module is used to obtain the weight of each performance indicator through dynamic weight adjustment based on the performance indicators and constraint data. The weight is used to balance the relative importance of the performance indicators.

[0155] The trajectory optimization module is used to generate the current reference trajectory sequence and the corresponding current control quantity sequence through trajectory optimization processing based on aircraft status data, environmental perception data, weights, and historical planning data; the current control quantity sequence is a series of control commands pre-calculated within the current planning time period;

[0156] The tracking control module is used to obtain real-time control quantities through sliding mode tracking control processing based on the aircraft status data, the current reference trajectory sequence, and the current control quantity sequence. The real-time control quantity is the single control command that needs to be executed at the current moment.

[0157] The decision module is used to determine whether the current time has reached the preset period or whether the performance index has exceeded the corresponding constraint limit;

[0158] The replanning module is used to update the reference trajectory sequence and control sequence as new historical planning data based on the environmental perception data and the current reference trajectory sequence and the current control quantity sequence when the decision module determines that it is correct.

[0159] The output module is used to output real-time control quantities to the actuator and continue to perform tracking control when the decision module determines that the decision is negative.

[0160] The above description is merely an example and illustration of the structure of the present invention. Those skilled in the art can make various modifications or additions to the specific embodiments described, or use similar methods to replace them, as long as they do not deviate from the structure of the invention or exceed the scope defined in the claims, all of which should fall within the protection scope of the present invention.

[0161] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0162] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to any specific implementation. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for trajectory optimization and tracking control of a space vehicle based on aerodynamic force assistance, characterized in that, The method comprises the following steps: acquiring aircraft state data, environment perception data, constraint data, and historical planning data, the constraint data including a heat flow upper limit, an overload upper limit, and a dynamic pressure upper limit, and the historical planning data including a historical reference trajectory sequence and a corresponding historical control quantity sequence; calculating a plurality of performance indicators according to the aircraft state data and the environment perception data, the performance indicators including a characteristic velocity deviation, a heat flow value, an overload value, and a dynamic pressure value; adjusting the weights of the performance indicators according to the performance indicators and the constraint data through a dynamic weight adjustment process, the weights being used to balance the relative importance of the performance indicators; generating a current reference trajectory sequence and a corresponding current control quantity sequence through a trajectory optimization process according to the aircraft state data, the environment perception data, the weights, and the historical planning data, the current control quantity sequence being a series of control instructions calculated in advance within a current planning time period; obtaining a real-time control quantity through a sliding mode tracking control process according to the aircraft state data, the current reference trajectory sequence, and the current control quantity sequence, the real-time control quantity being a single control instruction to be executed at the current time; determining whether the current time reaches a preset period or the performance indicators exceed the corresponding constraint upper limits: if yes, updating the reference trajectory sequence and the control quantity sequence as new historical planning data through a re-planning process according to the environment perception data and the current reference trajectory sequence and the current control quantity sequence; otherwise, outputting the control quantity to an execution mechanism and continuing to execute the tracking control.

2. The method according to claim 1, wherein: the aircraft state data includes a position vector, a velocity vector, and an attitude angle, and the environment perception data includes an atmospheric density measurement value and a temperature measurement value; the process of the characteristic calculation includes: calculating a characteristic velocity deviation through a vector modulus difference calculation according to the velocity vector and a preset target orbit velocity vector; calculating a heat flow value through a stagnation point heat flow model calculation according to the atmospheric density measurement value, the temperature measurement value, and the velocity magnitude; calculating an overload value through a ratio calculation according to the aerodynamic force and the gravity, wherein the aerodynamic force is calculated based on the atmospheric density measurement value, the velocity magnitude, and the aerodynamic coefficient, and the gravity is calculated based on the position vector; calculating a dynamic pressure value through a square product calculation according to the atmospheric density measurement value and the velocity magnitude; the heat flow value calculation adopts the following formula: wherein represents a heat flow value, represents a temperature-dependent heat flow calculation coefficient, represents an atmospheric density measurement value, represents a speed magnitude, represents a density index, represents a speed index.

3. The method of trajectory optimization and tracking control for a space vehicle based on aerodynamic force assistance according to claim 2, characterized in that: the dynamic weight adjustment process includes: adjusting the weights of the performance indicators through a linear combination method according to the relative deviations of the performance indicators and the corresponding constraint upper limits, and an environment change rate; wherein the environment change rate is calculated based on the time series change amount of the atmospheric density measurement value and the temperature measurement value.

4. The method of trajectory optimization and tracking control for a space vehicle based on aerodynamic force assistance according to claim 3, characterized in that: the trajectory optimization process uses a Gauss pseudospectral method, including: mapping the time interval of the current planning time period to a standard interval, and discretizing state variables and control variables on the collocation points, wherein the state variables include the position vector and the velocity vector in the aircraft state data, and the control variables include a lift coefficient and a tilt angle; establishing an algebraic constraint based on an orbit dynamics model according to the state variable and the control variable and aerodynamic parameters; constructing a performance index function according to the performance index and the weight, and generating a current reference trajectory sequence and a current control variable sequence through nonlinear programming solving; the performance index function adopts the following formula: wherein denotes a comprehensive performance indicator, denotes a weight of the characteristic speed deviation, denotes a characteristic speed deviation, denotes a weight of the heat flow value, denotes a heat flow value, denotes a weight of the overload value, denotes an overload value, denotes a weight of the dynamic pressure value, denotes a dynamic pressure value.

5. The method according to claim 4, characterized in that: the orbit dynamics model is a three-degree-of-freedom dynamics model, including differential equations of velocity variation rate, flight path angle variation rate and geocentric distance variation rate; the three-degree-of-freedom dynamics model adopts the following differential equation set: wherein, denotes a rate of change of velocity, denotes aerodynamic drag, denotes an aircraft mass, denotes the earth gravitational constant, denotes a flight path angle, denotes a geocentric distance, denotes a rate of change of flight path angle, denotes aerodynamic lift, denotes a rate of change of geocentric distance; the aerodynamic drag is calculated according to the drag coefficient in the aerodynamic parameters, the atmospheric density measurement value and the speed size; the aerodynamic lift is calculated according to the lift coefficient in the aerodynamic parameters, the atmospheric density measurement value in the environment perception data and the speed size.

6. The method of trajectory optimization and tracking control for a space vehicle based on aerodynamic force assistance according to claim 5, characterized in that: The sliding mode tracking control process includes: calculating a position deviation vector and a speed deviation vector according to the deviation of the position vector and the speed vector from the current reference trajectory sequence; constructing a sliding surface according to the position deviation vector and the speed deviation vector; calculating a real-time control variable through equivalent control and switching control according to the sliding surface and the current control variable sequence; the sliding surface is calculated by the following formula: wherein, denotes a synovial membrane facing vector, denotes a velocity deviation vector, denotes a position deviation vector, denotes a positive definite diagonal matrix.

7. The method of trajectory optimization and tracking control for a space vehicle based on aerodynamic force assistance according to claim 6, characterized in that: The process of the re-planning process includes: updating the aerodynamic parameters of the orbit dynamics model according to the atmospheric density measurement value and the temperature measurement value in the environment perception data; generating an initial guess sequence through interpolation processing according to the current reference trajectory sequence and the current control variable sequence; performing a trajectory optimization process to generate an updated reference trajectory sequence and a control variable sequence according to the updated aerodynamic parameters and the initial guess sequence; replacing the original historical planning data with the updated reference trajectory sequence and the control variable sequence.

8. The method of trajectory optimization and tracking control for a space vehicle based on aerodynamic force assistance according to claim 7, characterized in that: It also includes a deviation prediction compensation mechanism for sliding mode tracking: calculating a position deviation vector according to the position vector and the current reference trajectory sequence; storing the position deviation vector into a historical deviation sequence, and obtaining a compensation control variable at a future time through autoregressive model processing according to the historical deviation sequence; superimposing the compensation control variable into the real-time control variable to form a final control instruction.

9. The method of trajectory optimization and tracking control for a space vehicle based on aerodynamic force assistance according to claim 8, characterized in that: The calculation formula of the compensation control variable is: wherein, denotes a supplementary control quantity, denotes a prediction gain coefficient, denotes an autoregressive coefficient, denotes a historical position bias vector, denotes an order of the autoregressive model.

10. A system for trajectory optimization and tracking control of a space vehicle based on aerodynamic force assistance, characterized in that, It includes: a data acquisition module for acquiring aircraft state data, environment perception data, constraint data and historical planning data; the constraint data includes a heat flow upper limit, an overload upper limit and a dynamic pressure upper limit, and the historical planning data includes a historical reference trajectory sequence and a corresponding historical control variable sequence; a feature calculation module for calculating a plurality of performance indexes through feature calculation according to the aircraft state data and the environment perception data, the performance indexes including a characteristic speed deviation, a heat flow value, an overload value and a dynamic pressure value; a weight adjustment module for obtaining the weight of each performance index through dynamic weight adjustment processing according to the performance indexes and the constraint data, the weight being used to balance the relative importance of the performance indexes. a trajectory optimization module, configured to generate a current reference trajectory sequence and a corresponding current control quantity sequence by a trajectory optimization process according to the aircraft state data, the environment perception data, the weights, and the historical planning data; the current control quantity sequence being a series of control instructions calculated in advance within a current planning time period; a tracking control module, configured to obtain a real-time control quantity by a sliding mode tracking control process according to the aircraft state data, the current reference trajectory sequence, and the current control quantity sequence; the real-time control quantity being a single control instruction to be executed at a current time; a decision module, configured to determine whether a current time reaches a preset period or whether the performance index exceeds a corresponding upper limit of a constraint; a re-planning module, configured to update a reference trajectory sequence and a control quantity sequence as new historical planning data by a re-planning process according to the environment perception data and the current reference trajectory sequence and the current control quantity sequence when the decision module determines that the current time reaches the preset period or the performance index exceeds the corresponding upper limit of the constraint; an output module, configured to output the real-time control quantity to an execution mechanism and continue to execute tracking control when the decision module determines that the current time does not reach the preset period or the performance index does not exceed the corresponding upper limit of the constraint.

Images