Hypersonic vehicle reentry trajectory optimization method and system based on safety margin and feasibility collaborative guidance mechanism

Abstract

The application discloses a hypersonic vehicle reentry trajectory optimization method and system based on a safety margin and feasibility collaborative guidance mechanism, constructs a multi-objective optimization model including flight time, integral heat load and track angle smoothness based on a reentry trajectory optimization constraint system and a reentry trajectory state sequence, and calculates hierarchical constraint violation, comprehensive hard constraint violation and minimum no-fly zone safety margin; utilizes a decomposed multi-objective differential evolution algorithm to decompose the multi-objective optimization model into multiple sub-problems, introduces a hard constraint feasible proportion and a no-fly zone safety proportion to optimize an adaptive epsilon constraint threshold and differential evolution scaling factors and crossover probability based on an SMFG collaborative optimization mechanism, generates offspring and executes neighborhood replacement, maintains a feasible non-dominated solution set and selects a recommended reentry trajectory. Compared with the prior art, the application improves the feasible trajectory generation capability of the vehicle reentry trajectory under complex no-fly zone constraint conditions, improves the no-fly zone avoidance safety and the multi-objective solution set quality.

Description

Technical Field

[0001] This invention belongs to the field of hypersonic vehicle trajectory planning and intelligent optimization control technology, and involves multi-objective optimization of reentry trajectory, path constraint processing in no-fly zones and evolutionary optimization algorithms. In particular, it relates to a method and system for optimizing the reentry trajectory of hypersonic vehicles based on a collaborative guidance mechanism of safety margin and feasibility. Background Technology

[0002] Hypersonic vehicle reentry trajectory optimization is a core issue in mission planning and guidance control. During reentry, the vehicle must maneuver under conditions of high speed, drastic atmospheric parameter changes, and strong aerodynamic coupling, while simultaneously satisfying multiple strongly coupled constraints such as heat flux, dynamic pressure, overload, terminal accuracy, control boundaries, and no-fly zone avoidance. As the number of no-fly zones increases or the safe buffer distance expands, the feasible domain tends to become narrower and more fragmented, and trajectory search faces difficulties such as scarce feasible solutions, close boundary conditions, and local clustering, significantly increasing the difficulty of solving the problem.

[0003] Among existing methods, direct methods, indirect methods, and sequential convex optimization achieve high accuracy when the model is continuous and the initial values ​​are good. However, under strong constraints such as multiple no-fly zones, they are easily affected by the initial values ​​and the non-convexity of the feasible region, making convergence difficult. Evolutionary algorithms are more adaptable due to their ability to perform population search and random perturbation. Among them, decomposition-based multi-objective evolutionary methods are widely used due to their balance between efficiency and scalability. However, their design focuses on objective convergence and distribution maintenance, and does not give sufficient consideration to the priority of physical constraints.

[0004] Specific shortcomings are as follows: First, fixed penalty functions or simple weighted violation rates ignore the dimensional differences and engineering significance of various constraints, easily masking violations of key constraints and resulting in the retention of individuals with better objectives but insufficient safety margins in the no-fly zone. Second, the safety distance in the no-fly zone is often only used for posterior verification, without real-time feedback of the population's safety status to the search process; feasibility adjustments often rely on a single violation rate or iterative algebra, lacking coordinated feedback on hard constraint convergence and spatial safety risks. A single feedback quantity cannot take into account both types of states: relying solely on hard constraint violation rates cannot identify whether an individual is close to the no-fly zone buffer boundary; relying solely on the safety status in the no-fly zone ignores the convergence of constraints such as terminal accuracy and dynamic pressure, potentially leading to excessive bias towards avoidance and weakening overall feasibility. Third, search parameters are often fixed or only change with the number of algebras, failing to utilize population feasibility and safety status information, resulting in insufficient perturbation when there are few feasible solutions and excessive perturbation when there are many feasible solutions, making dynamic adaptation difficult.

[0005] In summary, there is an urgent need to develop an optimization method for evaluating related constraints, no-fly zone safety status, population feasibility status, parameter adjustment, and neighborhood replacement within the same iterative closed loop. Summary of the Invention

[0006] Objective: To address the problems in existing technologies such as the easy mixing of multiple constraints, insufficient participation of no-fly zone safety margin in search adjustment, and lack of linkage between evolutionary parameters and population feasibility status, this invention provides a hypersonic vehicle reentry trajectory optimization method and system based on a collaborative guidance mechanism of safety margin and feasibility. Using the same constraint evaluation results of the same generation of population as a common data source, the invention separately calculates the feasibility ratio of hard constraints and the safety ratio of no-fly zones, and applies these two as dual feedback quantities to the adaptive ε-constraint threshold update, differential evolution parameter adjustment, and neighborhood candidate solution replacement processes. This improves the generation capability of feasible trajectories under complex multi-no-fly zone strong constraint conditions, the safety of no-fly zone avoidance, the quality of multi-objective solution sets, and the repeatability of output trajectories.

[0007] Technical solution: This invention discloses a method for optimizing the reentry trajectory of a hypersonic vehicle based on a coordinated guidance mechanism of safety margin and feasibility, comprising:

[0008] The system acquires the initial reentry state, desired terminal state, aircraft parameters, and no-fly zone data of the aircraft, and constructs a reentry trajectory optimization constraint system that includes process constraints, terminal constraints, control constraints, and no-fly zone constraints.

[0009] The continuous angle of attack profile and the continuous dip angle profile are discretized into finite-dimensional decision variables, and the candidate reentry trajectory state sequence is obtained based on the finite-dimensional decision variables and the reentry dynamics model.

[0010] Based on the candidate reentry trajectory state sequence and the reentry trajectory optimization constraint system, a multi-objective optimization model including flight time, integral thermal load and track angle smoothness is constructed, and the hierarchical constraint violation degree, comprehensive hard constraint violation degree and minimum no-fly zone safety margin are calculated.

[0011] By leveraging the safety margin and feasibility collaborative guidance mechanism, a multi-objective differential evolution algorithm based on decomposition decomposes the multi-objective optimization model into multiple weighted Tchebycheff subproblems. Based on the same generation of population, the feasible proportion of hard constraints and the safe proportion of no-fly zones are calculated respectively, thereby updating the adaptive ε-constraint threshold, differential evolution scaling factor, and crossover probability. The updated adaptive ε-constraint threshold, differential evolution scaling factor, and crossover probability are used to generate offspring, and neighborhood replacement is performed to maintain the feasible non-dominated solution set.

[0012] Select a recommended reentry trajectory from the set of feasible non-dominated solutions.

[0013] Furthermore, the initial reentry state includes initial altitude, initial longitude, initial latitude, initial velocity, initial track angle, and initial heading angle; the desired terminal state includes terminal altitude, terminal longitude, terminal latitude, and terminal velocity; the aircraft physical properties and aerodynamic parameters include aircraft mass, aerodynamic reference area, nose radius of curvature, aerodynamic coefficient, and angle of attack and roll boundaries; the no-fly zone data includes the center latitude and longitude, physical radius, safe buffer distance, and effective altitude range of each no-fly zone.

[0014] Furthermore, the process constraints include heat flux, dynamic pressure, and overload constraints; the terminal constraints include allowable error constraints for terminal altitude, longitude, latitude, and velocity; the control constraints include boundary constraints for angle of attack, roll angle, and their rate of change; and the no-fly zone constraints include distance constraints between the candidate reentry trajectory and the physical boundary and safety buffer boundary of the no-fly zone.

[0015] Furthermore, the acquisition of the multi-objective optimization model and the hierarchical constraint violation degree, the comprehensive hard constraint violation degree, and the minimum no-fly zone safety margin includes:

[0016] The integrated thermal load of the multi-objective optimization model is obtained by numerical integration of the heat flow rate along the trajectory, and the smoothness of the track angle is obtained by integral of the square of the rate of change of the track angle. All three objectives are minimized.

[0017] The safety margin of the no-fly zone is determined based on the spherical distance between the candidate reentry trajectory sampling point and the center of the no-fly zone. For the first... No-fly zones and the first The safety margin for each trajectory sampling point is:

[0018] ;

[0019] in, This indicates that the k-th trajectory sampling point is relative to the k-th trajectory sampling point. The margin of the no-fly zone safety buffer boundary; the minimum no-fly zone safety margin of the candidate reentry trajectory is expressed as:

[0020] ;

[0021] The minimum value is taken for all no-fly zones and all trajectory sampling points to obtain the minimum no-fly zone safety margin for the candidate re-entry trajectory; the no-fly zone constraint violation degree is expressed as:

[0022] ;

[0023] in, For the first The trajectory sampling point up to the first The spherical distance from the center of the no-fly zone The physical radius of the no-fly zone. For a safe buffer distance, For safety margin normalization scale; A value not less than zero indicates that the candidate reentry trajectory satisfies all no-fly zone safety buffer constraints.

[0024] The layered constraint violation degree includes process constraint violation degree, terminal constraint violation degree, control constraint violation degree, and no-fly zone constraint violation degree. The process constraint violation degree consists of the normalized over-limit of heat flux, dynamic pressure, and overload; the terminal constraint violation degree consists of the normalized error over-limit of terminal altitude, longitude, latitude, and speed; the control constraint violation degree consists of the normalized over-limit of angle of attack, roll angle, and control change rate.

[0025] The overall hard constraint violation rate is a weighted sum of the normalized constraint violation rate, the terminal constraint violation rate, the control constraint violation rate, and the no-fly zone constraint violation rate.

[0026] Furthermore, the specific calculations for the feasible proportion of hard constraints and the safe proportion of no-fly zones are as follows:

[0027] In the During the iterative calculation process, the first The ratio of the number of feasible solutions in the population to the population size is used as the hard constraint feasibility ratio. , used to characterize the degree to which the current population enters the hard-constrained feasible region, the th The number of feasible solutions in the population is the number of individuals whose overall hard constraint violation is no greater than the feasible decision tolerance.

[0028] In the During the iterative calculation process, the ratio of the number of individuals with zero violations of the no-fly zone safety buffer to the population size is used as the no-fly zone safety risk ratio. , is used to characterize the degree to which the current population enters the feasible region of hard constraints.

[0029] Furthermore, the decomposition-based multi-objective differential evolution algorithm adaptively adapts during the iterative optimization process. The constraint threshold is first algebraically generated using the fundamental values ​​of the decaying basic constraints. Then adjust according to the feasible proportion of the hard constraints, and through The tightening speed of a single generation is limited as follows:

[0030] ;

[0031] ;

[0032] in, The threshold value of the basic constraint decays with the number of iterations. The lower limit of the threshold. As the initial threshold, The decay exponent, For the maximum number of iterations, Feasibility ratio correction coefficient used to adjust the threshold according to the feasible ratio of hard constraints This is the threshold smoothing coefficient, used to limit the tightening rate of the threshold between adjacent generations. hour, .

[0033] Furthermore, in the iterative optimization process, the differential evolution scaling factor and crossover probability of the decomposition-based multi-objective differential evolution algorithm are updated collaboratively using the hard constraint feasible ratio and the no-fly zone safe ratio, specifically as follows:

[0034] ;

[0035] in, For the first Differential evolution scaling factor This is a search intensity compensation item when the safety ratio of the no-fly zone is insufficient. , These are the upper and lower bounds of the differential evolution scaling factor;

[0036]

[0037] in, and These are compensation coefficients used to adjust the differential evolution scaling factor and crossover probability according to the safe wind ratio of the no-fly zone, with the lower and upper limits of the crossover probability being... , .

[0038] Furthermore, during neighborhood replacement, the following rules apply:

[0039] If at least one offspring or neighboring individual violates the no-fly zone safety buffer, the offspring with the smaller violation amount will be retained; otherwise... Feasible individuals take priority over Infeasible individuals; when both are When an individual is deemed infeasible, priority is given to retaining the one with the lower overall hard constraint violation. If the overall hard constraint violation is the same, priority is given to retaining the one with the lower sum of the normalized hierarchical constraint violations. When both are infeasible... When a feasible individual is selected, the Tchebycheff decomposition scalar value is calculated according to the corresponding weight vector and ideal point, and the smaller scalar value is retained first. When the difference between the decomposition scalar values ​​is within a given similar tolerance, the one with the smaller comprehensive hard constraint violation is retained first. If the comprehensive hard constraint violation is the same, the one with the smaller sum of normalized constraint violations is retained first.

[0040] Furthermore, when selecting a recommended reentry trajectory from the set of feasible non-dominated solutions, candidate solutions that fail to meet terminal constraints and no-fly zone safety buffer constraints are first screened out from the set of feasible non-dominated solutions. Then, TOPSIS is used to select a recommended reentry trajectory. At the same time, the recommended reentry trajectory is verified for continuity and checked against all constraints. If the check is passed, the recommended reentry trajectory, control profile, multi-objective optimization function value, no-fly zone safety margin, and constraint verification results are output. If the check is not passed, the candidate solution is removed and a new one is selected. If there are no qualified candidate solutions, the optimization search continues.

[0041] This invention also discloses a hypersonic vehicle reentry trajectory optimization system based on a safety margin and feasibility collaborative guidance mechanism, comprising a data acquisition module, a constraint system construction module, a trajectory generation and propagation module, a constraint evaluation module, an SMFG collaborative optimization module, and a decision selection module, to implement the aforementioned hypersonic vehicle reentry trajectory optimization method based on a safety margin and feasibility collaborative guidance mechanism; wherein,

[0042] The data acquisition module is used to acquire the initial reentry status of the aircraft, the desired terminal status, the aircraft parameters, and the no-fly zone data.

[0043] The constraint system construction module is used to construct a reentry trajectory optimization constraint system that includes process constraints, terminal constraints, control constraints, and no-fly zone constraints.

[0044] The trajectory generation and propagation module is used to discretize the continuous angle of attack profile and the continuous dip angle profile into finite-dimensional decision variables, and obtain the candidate reentry trajectory state sequence based on the decision variables and the reentry dynamics model.

[0045] The constraint evaluation module is used to construct a multi-objective optimization model that includes flight time, integral thermal load and track angle smoothness, and to calculate the hierarchical constraint violation degree, the comprehensive hard constraint violation degree and the minimum no-fly zone safety margin.

[0046] The SMFG collaborative optimization module is used to decompose the multi-objective optimization model into multiple weighted Tchebycheff subproblems based on the multi-objective differential evolution algorithm, using a safety margin and feasibility collaborative guidance mechanism. It calculates the hard constraint feasible proportion and the no-fly zone safe proportion based on the same generation population, thereby updating the adaptive ε constraint threshold, differential evolution scaling factor and crossover probability. It generates offspring using the updated adaptive ε constraint threshold, differential evolution scaling factor and crossover probability, and performs neighborhood replacement to maintain the feasible non-dominated solution set.

[0047] The decision selection module is used to select a recommended reentry trajectory from the set of feasible non-dominated solutions.

[0048] Beneficial effects

[0049] First, this invention transforms the no-fly zone safety margin from a posterior geometric verification quantity after optimization into a constraint guidance quantity participating in the optimization search. By directly incorporating the no-fly zone safety buffer violation quantity into the constraint evaluation, population safety ratio statistics, and neighborhood replacement process, this invention can avoid candidate trajectories with better objective functions but insufficient no-fly zone safety margins being preferentially retained in neighborhood replacement, thereby reducing the risk of candidate trajectories approaching or intruding into the no-fly zone safety buffer boundary.

[0050] Second, this invention constructs a hard constraint feasibility ratio and a no-fly zone safety ratio based on the same constraint evaluation results of the same generation of population. The hard constraint feasibility ratio characterizes the degree to which the population enters the hard constraint feasible region, which is jointly constituted by the terminal constraint, process constraint, control constraint, and no-fly zone safety buffer constraint. The no-fly zone safety ratio characterizes the spatial safety status of the population satisfying the no-fly zone safety buffer constraint. These two ratios correspond to the constraint convergence state and the spatial safety risk state, respectively, overcoming the problem that a single feedback quantity cannot simultaneously reflect both overall feasibility and no-fly zone boundary risk.

[0051] Third, this invention enables the hard constraint feasible ratio and the no-fly zone safety ratio to act together in the same iteration process on the adaptive ε-constraint threshold, differential evolution scaling factor, crossover probability, and neighborhood candidate solution replacement process. Compared to feedback adjustment based solely on a single constraint violation degree, a single feasible ratio, or a single no-fly zone safety state, this invention allows the search process to both retain near-feasible solutions converging towards the overall feasible region and suppress boundary risk trajectories due to insufficient no-fly zone safety margin. It dynamically adjusts the search perturbation intensity according to population feasibility and no-fly zone safety state, simultaneously addressing both "insufficient overall feasibility" and "prominent no-fly zone boundary risk," thus creating a coupled feedback between safety margin and feasibility state.

[0052] Fourth, in the neighborhood replacement process, this invention prioritizes comparing the violation amount of the no-fly zone safety buffer, and then combines the ε-feasible state, the comprehensive hard constraint violation degree, the sum of the violations of each normalized constraint, and the Tchebycheff decomposition scalar value to retain candidate solutions. This replacement rule can avoid retaining trajectories with high safety risks based solely on the objective function value or the violation degree of a single aggregate constraint, giving the no-fly zone safety constraints a clear discrimination priority during the candidate solution update process.

[0053] Fifth, this invention performs continuity verification and full constraint review of the output trajectory through maintenance of feasible non-dominated solution sets, recommended trajectory selection, and result verification. For candidate trajectories that fail the review of terminal constraints, process constraints, control constraints, or no-fly zone safety buffer constraints, they are removed from the recommended candidate set, and the decision selection is re-executed. If no qualified candidate solution is found, the optimization search continues. This improves the engineering repeatability and constraint satisfaction reliability of the output reentry trajectory.

[0054] In summary, this invention does not simply juxtapose no-fly zone safety margin evaluation, ε-constraint processing, and differential evolution parameter adaptation. Instead, it uses the same constraint evaluation results from the same generation of population as a common data source to form a closed-loop collaborative mechanism that includes constraint evaluation, dual feedback generation, constraint threshold adjustment, search intensity adjustment, neighborhood candidate solution replacement, feasible non-dominated solution set maintenance, and result verification. This improves the feasibility generation capability, safety redundancy, multi-objective solution set quality, and result verifiability of hypersonic vehicle reentry trajectories under complex no-fly zone constraints. Attached Figure Description

[0055] Figure 1 This is a system structure block diagram of the present invention;

[0056] Figure 2 This is a schematic diagram of the three-dimensional reentry trajectory and multiple no-fly zone avoidance of the present invention;

[0057] Figure 3 This is a graph showing the change of the minimum no-fly zone safety margin over time according to the present invention.

[0058] Figure 4 This is a comparison chart of the ground trajectory avoidance of the present invention and different optimization methods;

[0059] Figure 5 This is a comparison chart of the minimum no-fly zone safety margin of the present invention and different optimization methods;

[0060] Figure 6 This is a comparison chart of the comprehensive performance indicators of the present invention and different optimization methods. Detailed Implementation

[0061] The specific technical solutions of the present invention will be further described in detail below with reference to specific embodiments. It should be understood that these embodiments are used to illustrate the technical solutions of the present invention and do not constitute a limitation on the scope of protection.

[0062] Example 1:

[0063] This invention discloses a method for optimizing the reentry trajectory of hypersonic vehicles based on a safety margin and feasibility collaborative guidance mechanism (SMFG collaborative mechanism). SMFG refers to the safety margin and feasibility collaborative guidance mechanism, which does not involve separate guidance for each vehicle. The constraints and differential evolution parameters are independently and adaptively adjusted, and this is not a simple parallel arrangement of multiple known algorithm modules. Instead, it uses the same constraint evaluation results from the same generation of the population as a common data source: the proportion of feasible hard constraints is statistically calculated based on the comprehensive hard constraint violation rate. The convergence state of the constraints is evaluated; the safety ratio of the no-fly zone is independently calculated based on the number of violations of the no-fly zone safety buffer. To evaluate space security risks. Hard constraints and feasible proportions act on adaptive... The threshold and differential evolution parameters are the basic terms. The safety ratio of the no-fly zone acts as an independent risk feedback to the differential evolution search intensity. The updated threshold and search parameters further act on the generation of offspring and neighborhood replacement. The non-dominated solution, verified by complete dynamics and hard constraints, is then passed to the decision selection and result verification process, thus forming a unified closed-loop data link of constraint evaluation, dual feedback generation, constraint convergence control, search intensity control, candidate solution replacement and result verification.

[0064] This invention discloses a method for optimizing the reentry trajectory of a hypersonic vehicle based on the SMFG cooperative mechanism, comprising the following steps:

[0065] Step 1: Obtain the initial reentry state, desired terminal state, aircraft parameters, and no-fly zone data of the aircraft, and construct a reentry trajectory optimization constraint system that includes process constraints, terminal constraints, control constraints, and no-fly zone constraints.

[0066] The initial reentry state includes initial altitude, initial longitude, initial latitude, initial velocity, initial track angle, and initial heading angle; the desired terminal state includes terminal altitude, terminal longitude, terminal latitude, and terminal velocity; the aircraft's physical and aerodynamic parameters include aircraft mass, aerodynamic reference area, nose radius of curvature, aerodynamic coefficients, and angle of attack and roll boundaries; the no-fly zone data includes the center latitude and longitude, physical radius, safe buffer distance, and effective altitude range of each no-fly zone.

[0067] Process constraints include heat flux, dynamic pressure, and overload constraints; terminal constraints include allowable error constraints for terminal altitude, longitude, latitude, and velocity; control constraints include boundary constraints for angle of attack, roll angle, and their rate of change; and no-fly zone constraints include distance constraints between the candidate reentry trajectory and the physical boundaries and safety buffer zones of the no-fly zone.

[0068] Step 2: Discretize the continuous angle of attack profile and the continuous dip angle profile into finite-dimensional decision variables, and obtain the candidate reentry trajectory state sequence based on the finite-dimensional decision variables and the reentry dynamics model.

[0069] A piecewise control profile discretization method is adopted to transform the continuous-time reentry control optimization problem into a finite-dimensional parameter optimization problem. Terminal time, piecewise angle-of-attack nodes, and piecewise tilt angle nodes are composed of finite-dimensional decision variables. Let the control profile be divided into... The decision variable is determined by the terminal time. The value of each angle of attack node and It consists of tilt angle node values. Adjacent nodes are generated using continuous interpolation. and After generation, upper and lower bound repair is performed to ensure that the control variables initially meet the boundary conditions.

[0070]

[0071] In the formula, For flight time, To control the number of sections in the profile, For the first Angle of attack parameters, For the first Segment tilt angle parameters. To obtain the complete reentry trajectory state based on the candidate control profile, numerical propagation is performed using the aircraft state vector and control vector as inputs. The aircraft state vector and control vector are expressed as follows:

[0072]

[0073] in, , , , , and These are altitude, longitude, latitude, speed, track angle, and heading angle, respectively.

[0074]

[0075] The fourth-order Runge-Kutta method is used based on the reentry dynamics equations. Perform numerical integration. These are the physical, aerodynamic, and environmental parameters of the aircraft.

[0076] For step size Δt, its update form is:

[0077]

[0078] in, to This is the slope term of a fourth-order Runge-Kutta process. It outputs the altitude, latitude, longitude, speed, track angle, heading angle, angle of attack, and roll angle at each sampling time, and simultaneously calculates the heat flux, dynamic pressure, and overload.

[0079] Step 3: Based on the candidate reentry trajectory state sequence and the reentry trajectory optimization constraint system, construct a multi-objective optimization model including flight time, integral thermal load and track angle smoothness, and calculate the hierarchical constraint violation degree, the comprehensive hard constraint violation degree and the minimum no-fly zone safety margin.

[0080] After candidate trajectory propagation is completed, the reentry trajectory optimization process needs to simultaneously consider flight speed, thermal protection load, and trajectory smoothness. Therefore, a multi-objective optimization function is constructed, with flight time, integral thermal load, and track angle smoothness as the three objectives to be minimized:

[0081]

[0082] in, For flight time, For integral thermal load, For track angle smoothness;

[0083] Calculate flight time Integral thermal load and track angle smoothness Three objectives. The integral thermal load is calculated using numerical integration of the heat flow rate along the trajectory; the track angle smoothness is calculated using the integral of the square of the track angle change rate.

[0084]

[0085] in, For heat flow rate, Used to characterize the cumulative thermal load on an aircraft throughout the reentry process;

[0086]

[0087] in, The rate of change of the track angle, Used to characterize the smoothness of candidate reentry trajectories.

[0088] Because the no-fly zone safety buffer constraints, terminal constraints, process constraints, and control constraints have different physical meanings and processing priorities, directly using a single penalty function for mixed evaluation can easily mask violations of key constraints. Therefore, the constraint evaluation results are normalized for each of the no-fly zone safety buffer constraints, terminal constraints, process constraints, and control constraints, and a hierarchical constraint violation degree is constructed:

[0089]

[0090] in, For terminal constraint violation degree, For process constraint violation degree, To limit violations of no-fly zones, To control the degree of constraint violation.

[0091] To obtain scalar constraint evaluation results in population statistics, ε feasibility judgment, and feasibility file access, the four types of normalized violation degrees are further weighted and synthesized into a comprehensive hard constraint violation degree:

[0092]

[0093] Among them, the hierarchical constraint violation degree is used to preserve different physical meanings and processing priorities, while the comprehensive hard constraint violation degree is used to calculate the feasible state of the population. Feasibility and feasibility documentation access.

[0094] To determine whether a candidate trajectory intrudes into the no-fly zone's safety buffer zone, it is necessary to first calculate the spherical distance on the Earth's surface between each trajectory sampling point and the center of each no-fly zone. For the... A no-fly zone, the center of which is at latitude and longitude of [missing information]. Candidate trajectory number The latitude and longitude of each sampling point are The spherical distance is:

[0095]

[0096] in, For Earth's reference radius, For the latitude and longitude of the trajectory sampling points, For the first The latitude and longitude of the center of the no-fly zone.

[0097] After obtaining the spherical distance, both the physical radius of the no-fly zone and the safety buffer distance are subtracted to obtain the safety margin of the trajectory sampling point relative to the safety buffer boundary:

[0098]

[0099] in, Indicates the first The trajectory sampling point is relative to the first The margin of the safety buffer boundary of a no-fly zone;

[0100] Since a candidate trajectory is considered to have violated the no-fly zone constraint if it enters any no-fly zone safety buffer area at any sampling point, the minimum safety margin is taken for all no-fly zones and all sampling points:

[0101]

[0102] This yields the minimum no-fly zone safety margin for the candidate reentry trajectory, see [reference]. Figure 5 A comparison chart of the minimum no-fly zone safety margin of the present invention and different optimization methods.

[0103] When the minimum no-fly zone safety margin is negative, it indicates that the candidate trajectory has encroached upon the no-fly zone safety buffer zone. To ensure that this violation is included in a unified constraint evaluation system, it is normalized to the no-fly zone safety buffer constraint violation degree:

[0104]

[0105] in, The physical radius of the no-fly zone. For a safe buffer distance, This serves as a normalized scale for the safety margin. By directly incorporating the safety buffer distance into the margin calculation, the no-fly zone safety margin is not an additional indicator after optimization, but rather a search quantity that participates in constraint evaluation, population safety ratio calculation, and neighborhood replacement. The no-fly zone safety buffer violation also serves as an independent priority metric for neighborhood replacement, and therefore will not be masked by smaller violation rates of other constraints or smaller objective function values.

[0106] Process constraint violation Composed of normalized excesses of heat flux, dynamic pressure, and overload; terminal constraint violation degree Composed of the normalized error exceeding the limit for terminal altitude, longitude, latitude, and speed; control constraint violation degree. It consists of the normalized exceedance values ​​for angle of attack, roll angle, and control rate of change. Each normalized exceedance value adopts... or Calculation, where This is the corresponding normalization scale.

[0107] Step 4: Utilizing the safety margin and feasibility collaborative guidance mechanism, the multi-objective optimization model is decomposed into multiple weighted Tchebycheff subproblems based on the decomposition multi-objective differential evolution algorithm. The hard constraint feasible proportion and no-fly zone safe proportion are calculated based on the same generation population, thereby updating the adaptive ε constraint threshold, differential evolution scaling factor and crossover probability. Offspring are generated using the updated adaptive ε constraint threshold, differential evolution scaling factor and crossover probability, and neighborhood replacement is performed to maintain the feasible non-dominated solution set.

[0108] A decomposition-based multi-objective optimization framework is adopted to decompose the three-objective problem of the aforementioned multi-objective optimization model into multiple weighted Tchebycheff subproblems, and offspring generation and replacement are performed through neighborhood. During initialization, a weight vector, neighborhood index, population, and ideal point are generated, and the initial threshold is obtained from the quantile of the hard constraint violation degree of the initial population. The three subproblems evolve synchronously, and each generation of the population consists of the current best solutions to all the subproblems. The final set is the approximate Pareto optimal solution set.

[0109] To simultaneously describe the extent to which the population enters the hard-constrained feasible region and the extent to which the no-fly zone safety buffer constraint is satisfied, in the first... In this generation, the number of individuals whose statistically comprehensive hard constraint violation degree is no greater than the feasible judgment tolerance is determined. Calculate the feasible proportion of hard constraints The number of individuals with zero violations of the no-fly zone safety buffer zone was counted. Calculate the safety ratio of no-fly zones Both methods use the evaluation results of the same generation of the population, and do not require an additional manually given coordination function.

[0110]

[0111] in, For the first The number of individuals that satisfy the hard constraints and are feasible to determine. For population size, Indicates the first The hard constraint feasible proportion of the current population is used to characterize the extent to which the current population enters the hard constraint feasible region.

[0112]

[0113] in, For the first The number of individuals who violated the safety buffer zone of the no-fly zone was not present. Used to characterize the degree to which the current population meets the safety buffer constraints of the no-fly zone.

[0114] To preserve near-feasible solutions in the early stages of the search and gradually tighten feasibility criteria in the later stages, adaptive... The constraint threshold is first algebraically generated to generate the basic decay value. :

[0115]

[0116] in, The threshold value of the basic constraint decays with the number of iterations. The lower limit of the threshold. This is the initial threshold.

[0117] When the proportion of feasible hard constraints in the population is low, it indicates that the population has not yet fully entered the feasible region. At this time, by... Appropriately relax the threshold; at the same time, limit the tightening speed of the threshold between adjacent generations by using the previous generation's threshold, thus obtaining an adaptive... Constraint threshold. Specifically, when season ;when Time, adaptive The constraint threshold is derived recursively according to the following formula:

[0118]

[0119] Therefore, when the feasibility ratio is low, it is permissible to retain near-feasible individuals whose constraint violation rate continues to decrease, and gradually shift to strict feasibility search as the feasibility ratio increases.

[0120] Differential evolution parameters are used to control the intensity of perturbation during offspring search. If the differential evolution scaling factor and crossover probability are set solely based on the number of iterations or fixed parameters, it is difficult to respond promptly to the feasibility status of the population and the safety risks of no-fly zones. Therefore, this invention also introduces a hard constraint on the feasible ratio. Safety ratio of no-fly zones The differential evolution scaling factor and crossover probability are updated jointly by the hard constraint feasible ratio and the no-fly zone safe ratio. The basic terms follow... Increase and decrease; when At low temperatures, through Increase security risk compensation to enhance the exploration of secure areas:

[0121]

[0122] in, For the first Differential evolution scaling factor This is a search intensity compensation item when the safety ratio of the no-fly zone is insufficient.

[0123]

[0124] For the The individual problem involves selecting three distinct individuals from their neighborhood or the entire population. , and Generate difference mutation vector , and then Perform binomial crossover, followed by polynomial mutation and control node boundary repair to obtain offspring. .right A complete trajectory propagation and constraint evaluation were re-performed.

[0125] During neighbor replacement, the comparison of no-fly zone safety buffer violations is performed sequentially. The process involves comparing feasibility, comprehensive hard constraint violation rates, and Tchebycheff decomposition scalars. This order prioritizes no-fly zone safety and constraint feasibility before the objective function converges. Specifically, if at least one offspring or neighboring individual violates the no-fly zone safety buffer, the violation rate is compared first; if no safety buffer violation requires priority, the comparison is made relative to the objective function. The feasible state. Feasible individuals take priority over Infeasible individuals; both are When not feasible, prioritize retaining the one with the lower overall hard constraint violation rate; both are... When feasible, compare the scalar values ​​of the Tchebycheff decompositions of the corresponding subproblems. If the differences in scalar values ​​are within a given tolerance, then determine the outcome by the sum of the combined hard constraint violation and the normalized violation.

[0126]

[0127] Each candidate solution after evaluation is simultaneously written into the candidate file. This order prevents individuals with better objective function values ​​but insufficient safety buffers from entering the neighborhood simply because their decomposition scalar is small.

[0128] Before outputting the feasible non-dominated solution set, hard constraint determination, terminal constraint determination, and no-fly zone safety buffer determination are re-performed on the solutions in the archive, retaining only the non-dominated solutions that satisfy all hard constraints under complete dynamic conditions. Near-feasible solutions can be used in the search process, but are not output as the final feasible result.

[0129] Step 5: Select a recommended reentry trajectory from the set of feasible non-dominated solutions.

[0130] When selecting a recommended reentry trajectory from the set of feasible non-dominated solutions, candidate solutions that fail to meet terminal constraints and no-fly zone safety buffer constraints are first screened out from the set of feasible non-dominated solutions. Then, TOPSIS is used to select a recommended reentry trajectory. At the same time, the recommended reentry trajectory is continuously verified and fully constrained. If the verification is passed, the recommended reentry trajectory, control profile, multi-objective optimization function value, no-fly zone safety margin, and constraint verification results are output. If the verification is not passed, the candidate solution is removed and a new one is selected. If there are no qualified candidate solutions, the optimization search continues.

[0131] TOPSIS is only used for posterior trade-off selection within the set of feasible non-dominated solutions that have already passed hard constraint screening, and does not participate in the aforementioned evolutionary search process. The decision selection module first performs terminal feasibility and no-fly zone safety buffer screening, and then uses TOPSIS to select recommended trajectories. For cost-oriented objectives, their vector normalization, weighting, ideal distance, and proximity are:

[0132]

[0133] in, For the first The first candidate solution The numerical values ​​of the target after vector norm normalization.

[0134]

[0135] in, For the first The weight of each objective, This represents the corresponding weighted normalized value. In one specific implementation, the target weights can be [0.40, 0.40, 0.20], corresponding to flight time, integral thermal load, and track angle smoothness, respectively. In other embodiments, the target weights can be adjusted according to the mission's emphasis on speed, thermal protection, and track smoothness, while maintaining that each target weight is non-negative and the sum of the weights is 1. For candidate solutions that have passed the hard constraints, the no-fly zone safety margin, terminal residual error, and control smoothness can also be used as secondary ranking factors for the recommended trajectory, but this does not change the three-objective optimization problem, nor does it allow secondary ranking to allow candidate solutions that have not passed the hard constraints to enter the recommended set.

[0136] Since all three objectives in this embodiment are cost-related objectives, the positive ideal point is taken as the minimum value of each column, and the negative ideal point is taken as the maximum value of each column:

[0137]

[0138] After determining the positive and negative ideal points, calculate the Euclidean distances from the candidate solutions to the positive and negative ideal points respectively:

[0139]

[0140] in, For the first The Euclidean distance from each candidate solution to the positive ideal point.

[0141]

[0142] in, For the first The Euclidean distance from each candidate solution to the negative ideal point.

[0143] Finally, the closeness is calculated based on the degree to which candidate solutions simultaneously approach the positive ideal point and move away from the negative ideal point:

[0144]

[0145] in, and The first For each objective, the positive and negative ideal values ​​are considered, and the candidate solution with the highest degree of similarity is selected. TOPSIS only ranks feasible non-dominated solutions that have passed the hard constraint screening, and does not replace constraint verification with decision ranking.

[0146] Example 2:

[0147] This invention also discloses a hypersonic vehicle reentry trajectory optimization system based on a safety margin and feasibility collaborative guidance mechanism (SMFG collaborative mechanism), see [link to relevant documentation]. Figure 1Corresponding to the method in Example 1, it includes a data acquisition module, a constraint system construction module, a reentry trajectory optimization module (including a trajectory generation and propagation module, a constraint evaluation module, an SMFG collaborative optimization module, and a decision selection module), a result verification module, and an output device.

[0148] The data acquisition module includes an initial state data acquisition unit, a terminal expected state data acquisition unit, an aircraft data acquisition unit, and a no-fly zone data acquisition unit; the constraint system construction module includes a process constraint construction unit, a terminal constraint construction unit, a control constraint construction unit, and a no-fly zone constraint construction unit.

[0149] The initial state data acquisition unit in the data acquisition device reads the initial altitude, initial longitude, initial latitude, initial speed, initial track angle, and initial heading angle of the aircraft; the terminal expected state data acquisition unit reads the terminal altitude, terminal longitude, terminal latitude, and terminal speed; the aircraft data acquisition unit reads the aircraft mass, aerodynamic reference area, nose curvature radius, aerodynamic parameters, and allowable ranges for angle of attack and roll angle; the no-fly zone data acquisition unit reads the center latitude and longitude, physical radius, safe buffer distance, and effective altitude range of each no-fly zone.

[0150] The process constraint building unit in the constraint system construction module sets the upper limits of heat flux, dynamic pressure, and overload; the terminal constraint building unit sets the allowable errors of terminal altitude, longitude, latitude, and speed; the control constraint building unit sets the boundaries of angle of attack, tilt angle, and rate of change of adjacent control segments; the no-fly zone constraint building unit uses the sum of the physical radius of the no-fly zone and the safety buffer distance as the radius of the safety buffer boundary, and requires that all trajectory sampling points within the effective altitude range of the no-fly zone be located outside the corresponding safety buffer boundary.

[0151] The trajectory generation module discretizes the continuous angle of attack profile and continuous tilt angle profile into finite-dimensional decision variables. The trajectory propagation module obtains the candidate reentry trajectory state sequence based on the decision variables and the reentry dynamics model. The constraint evaluation module calculates the multi-objective optimization function value, hierarchical constraint violation degree, comprehensive hard constraint violation degree, and no-fly zone safety margin.

[0152] The SMFG collaborative optimization module is set within a multi-objective evolutionary optimization framework based on a decomposition strategy. It is configured to: based on the same constraint evaluation results of the current generation of the population, calculate the feasible proportion of hard constraints according to the comprehensive hard constraint violation degree, and independently calculate the safe proportion of the no-fly zone according to the no-fly zone safety buffer violation amount, forming dual feedback quantities that respectively characterize the constraint convergence state and the space safety risk state. The feasible proportion of hard constraints and the safe proportion of the no-fly zone are calculated separately from the same constraint evaluation results of the same generation of the population, and simultaneously participate in the adaptive ε-constraint threshold update, differential evolution parameter adjustment, and neighborhood replacement discrimination during the same iteration, thus coupling the constraint convergence state and the space safety risk state. The adaptive ε-constraint threshold is updated using the feasible proportion of hard constraints to control the convergence of the population from the near-feasible region to the strictly feasible region. The differential evolution scaling factor and crossover probability are collaboratively updated using the feasible proportion of hard constraints and the safe proportion of the no-fly zone to control the intensity of search perturbation. Offspring are generated using the updated adaptive ε-constraint threshold, differential evolution scaling factor, and crossover probability. During neighborhood replacement, the violation amount of the no-fly zone safety buffer is first compared. Then, based on the ε feasible state, the comprehensive hard constraint violation degree, the sum of the normalized constraint violation amounts, or the Tchebycheff decomposition scalar value are compared respectively. The non-dominated solutions that satisfy the complete dynamics and hard constraint verification are stored in the feasible non-dominated solution set. As a result, the no-fly zone safety margin is no longer just used as a posterior verification index, but is included in the constraint threshold adjustment, search intensity adjustment, and candidate solution replacement process together with the hard constraint feasible state.

[0153] The decision selection module is used to select a recommended reentry trajectory from the set of feasible non-dominated solutions.

[0154] The result verification module is used to verify the continuity of the recommended reentry trajectory and to review the process constraints, terminal constraints, control constraints, and no-fly zone safety buffer constraints.

[0155] The output device is used to output the recommended reentry trajectory, control profile, multi-objective optimization function value, no-fly zone safety margin, and constraint verification results that have passed the review.

[0156] Experimental verification:

[0157] In this embodiment, the SMFG cooperation parameters are consistent with the program implementation: lower bound of differential evolution scaling factor. 0.52, upper limit The lower bound of the crossover probability is 0.88. 0.68, upper limit The coefficient of 0.96 represents the compensation factor for the safety risk of the no-fly zone due to the scaling factor and the crossover probability. , The decay exponents are 0.08 and 0.06 respectively; the adaptive ε threshold. The feasible ratio correction factor is 2.2. The threshold smoothing coefficient for adjacent generations is 1.25. The lower limit of the threshold is 0.90. for Initial threshold Take the 0.90 quantile of the initial population's overall hard constraint violation rate and... The larger value in the above parameters is used to illustrate the reproducible settings of this embodiment. These settings can be adjusted in other tasks based on population size, constraint strength, and no-fly zone distribution.

[0158] To verify the comprehensive optimization performance of the system of this invention under complex no-fly zone constraints, the complete SMFG-MOEA / D-DE implementation of this invention was compared with NSGA-II and MOPSO under the same reentry mission environment, the same constraint evaluation criteria, the same hardware platform, the same programming environment, the same population size, the same maximum number of iterations, and the same termination criteria. The comparison metrics included the cumulative number of feasible candidate trajectories, the final number of feasible non-dominated solutions, common normalized HV, spacing, minimum no-fly zone safety margin, and CPU time.

[0159] Among them, "cumulative number of feasible candidate trajectories" represents the cumulative number of candidate trajectories that have entered the feasibility archive or passed the feasibility screening during the optimization process, reflecting the algorithm's ability to generate feasible candidate trajectories. "Final number of feasible non-dominated solutions" represents the number of non-dominated solutions retained after full hard constraint screening. "Minimum no-fly zone safety margin" represents the minimum margin of the recommended trajectory or the trajectory in the solution set relative to the no-fly zone safety buffer boundary. "CPU time" represents the running time required for the corresponding program to complete the optimization calculation. The number of candidate trajectories, number of non-dominated solutions, Spacing, minimum no-fly zone safety margin, and CPU time in Table 1 are read from the final consistency output result. The HV is then recalculated based on the complete set of feasible non-dominated targets saved by the three algorithms.

[0160] To ensure the comparability of HV values, the feasible non-dominated target sets of the three algorithms are merged, and a common minimum and maximum value for each target are determined. This common boundary is then used to perform minimum-maximum normalization on the target values ​​of each algorithm. The common reference point after normalization is set to (1.12, 1.12, 1.12). HV is estimated using random seeds 123 and 2,000,000 common Monte Carlo samples, and multiplied by the reference cube volume 1.12³. Therefore, in this embodiment, HV is a volume index under the common normalized target space, and its value is not required to be limited to the interval between 0 and 1. Spacing is used to evaluate the distribution spacing of the non-dominated solution set; the smaller the value, the more uniform the spacing of the solution set.

[0161] Table 1 Comparison of feasible solution sets and computational performance of different optimization methods

[0162] This invention system 7535 161 0.882554 0.022739 45.0549 4.0405 NSGA-II 1200 486 0.687236 0.004816 75.1192 45.0201 MOPSO 1200 368 0.695127 0.006036 77.9069 331.8808

[0163] Table 2. Verification results of the objectives and constraints of the recommended trajectories using different optimization methods.

[0164] This invention system 1438.8795 312.1576 <![CDATA[2.93711×10⁻ 4 ]]> 0.4691 0 NSGA-II 1435.7590 312.1258 <![CDATA[2.93214×10⁻ 4 ]]> 0.3102 0 MOPSO 1435.7927 312.1751 <![CDATA[2.88649×10⁻ 4 ]]> 0.3066 0

[0165] As shown in Tables 1 and 2, under the calculation caliber of common target normalized boundary, common reference point, and common Monte Carlo samples, the HV obtained by the system of the present invention is 0.882554, which is higher than 0.687236 for NSGA-II and 0.695127 for MOPSO, indicating that the system of the present invention has better comprehensive coverage capability in the common normalized target space. Meanwhile, the cumulative number of feasible candidate trajectories of the system of the present invention is 7535, which is higher than the two comparative algorithms, indicating that it can accumulate more feasible candidate trajectories under complex no-fly zone constraints; the CPU time is 4.0405 s, which is lower than NSGA-II and MOPSO, indicating that it has high operating efficiency in the program implementation and calculation environment set in this embodiment.

[0166] It should be noted that HV reflects the overall coverage quality of the non-dominated solution set in the common normalized target space, and does not monotonically correspond to the number of final feasible non-dominated solutions. In the process of neighborhood replacement, feasibility file maintenance, and result verification, the system of this invention employs strict screening of no-fly zone safety buffer constraints and all hard constraints. Some near-feasible solutions or candidate solutions with high boundary risks are eliminated. Therefore, the number of final feasible non-dominated solutions is less than that of NSGA-II and MOPSO, but the retained solutions have a higher overall coverage volume in the common target space.

[0167] Based on the recommended trajectory verification results, the hard constraint violation rates of all three algorithms are 0, indicating that their recommended trajectories meet the hard constraint requirements set in this embodiment. The minimum no-fly zone safety margin of the recommended trajectory of this invention is 45.0549 km, which is higher than the 40 km safety buffer distance requirement, indicating that its output trajectory meets the no-fly zone safety buffer constraint and retains a positive safety margin. NSGA-II and MOPSO have their own advantages in individual indicators such as minimum safety margin, flight time, or terminal error; therefore, this invention's system cannot be described as absolutely optimal in all individual indicators. The technical effects of this invention are mainly reflected in: improving the ability to accumulate feasible candidate trajectories, the comprehensive quality of the solution set under the common normalized target space, and computational efficiency, while satisfying all hard constraints and no-fly zone safety buffer constraints.

[0168] To further illustrate the role of each component in the present invention in the safety of the no-fly zone, mechanism-level diagnostics were performed on the standard MOEA / D-DE, hierarchical constraint violation degree, safety margin constraint, adaptive ε replacement, and complete SMFG mechanism. The results are shown in Table 3.

[0169] Table 3 Mechanism-level diagnostic results of SMFG synergistic mechanism

[0170] A0 Standard MOEA / D-DE 7600 259 25.0000 no A1 + Hierarchical constraint violation rate 6696 246 25.0000 no A2 + Safety Margin Constraints 6610 245 40.0185 yes A3 + Adaptive ε Replacement 6610 245 40.0185 yes A4 + Adaptive DE Complete SMFG 7535 161 45.0549 yes

[0171] Table 3 illustrates the changes in candidate pool diagnostics after the gradual addition of various SMFG mechanisms. A0 to A3 represent mechanism-level gating diagnoses within the same candidate pool, not identical budgetary, independent, repeated runs of the complete algorithm; A4 represents the complete SMFG-MOEA / D-DE results verified by eventual consistency. "Candidate File Count" indicates the number of candidate records retained or screened under the corresponding gating conditions, and is not equivalent to the number of final strictly feasible solutions obtained after independent algorithm runs. As hierarchical constraint violation, safety margin constraints, and adaptive ε-replacement are gradually added, gating conditions become stricter, and the candidate file count and post-gating non-dominated number may decrease. Therefore, this indicator does not require an increase in randomness but rather a monotonically increasing trend. Since A0 to A3 and A4 do not belong to the same category of identical budgetary independent run results, Table 3 does not compare their HV and Spacing, but mainly uses minimum safety margin and safety buffer satisfaction states to illustrate the role of each mechanism in handling no-fly zone safety constraints.

[0172] From the mechanism-level diagnostic results, after adding hierarchical constraint violation degree to A0 standard MOEA / D-DE and A1, the minimum no-fly zone safety margin is 25.0000 km, which does not meet the 40 km safety buffer requirement. This indicates that relying solely on standard decomposition evolution search or general hierarchical constraint evaluation may still retain candidate trajectories with insufficient no-fly zone safety margin. After adding safety margin constraints, the minimum no-fly zone safety margin of A2 increases to 40.0185 km and meets the 40 km safety buffer requirement. On this basis, after adding adaptive ε replacement, A3 maintains the safety buffer satisfaction state, indicating that safety margin constraints and ε feasibility replacement can jointly improve the screening stability of no-fly zone safety constraints. After further adding adaptive differential evolution parameters jointly adjusted by the hard constraint feasibility ratio and the no-fly zone safety ratio, the minimum no-fly zone safety margin of A4 increases to 45.0549 km, indicating that the complete SMFG mechanism can further increase the safety margin on the basis of meeting the safety buffer constraint.

[0173] The reentry trajectory optimization program in this embodiment can be a MATLAB program, a compiled executable program, or other programs capable of implementing the same computational flow, and stored in a hard disk, solid-state memory, read-only memory, random access memory, or other non-transitory computer-readable storage medium. When the processor reads and executes the program, it sequentially completes the following steps: task data acquisition, continuous control profile discretization, trajectory propagation, constraint evaluation, SMFG parameter update, neighborhood candidate solution replacement, feasible non-dominated solution set maintenance, TOPSIS recommended trajectory selection, and result verification.

[0174] This invention can be executed by a processor and applied to the generation, screening, and verification of reentry trajectories for specific hypersonic vehicles. It can be applied to hypersonic vehicle reentry mission planning, temporary no-fly zone avoidance, ballistic vehicle reentry corridor optimization, near-space vehicle autonomous trajectory design, and other flight mission planning scenarios with geographical safety buffer constraints, and has clear engineering applicability.

Claims

1. A method for optimizing the reentry trajectory of a hypersonic vehicle based on a coordinated guidance mechanism of safety margin and feasibility, characterized in that, include: The system acquires the initial reentry state, desired terminal state, aircraft parameters, and no-fly zone data of the aircraft, and constructs a reentry trajectory optimization constraint system that includes process constraints, terminal constraints, control constraints, and no-fly zone constraints. The continuous angle of attack profile and the continuous dip angle profile are discretized into finite-dimensional decision variables, and the candidate reentry trajectory state sequence is obtained based on the finite-dimensional decision variables and the reentry dynamics model. Based on the candidate reentry trajectory state sequence and the reentry trajectory optimization constraint system, a multi-objective optimization model including flight time, integral thermal load and track angle smoothness is constructed, and the hierarchical constraint violation degree, comprehensive hard constraint violation degree and minimum no-fly zone safety margin are calculated. By leveraging the safety margin and feasibility collaborative guidance mechanism, a multi-objective differential evolution algorithm based on decomposition decomposes the multi-objective optimization model into multiple weighted Tchebycheff subproblems. Based on the same generation of population, the feasible proportion of hard constraints and the safe proportion of no-fly zones are calculated respectively, thereby updating the adaptive ε-constraint threshold, differential evolution scaling factor, and crossover probability. The updated adaptive ε-constraint threshold, differential evolution scaling factor, and crossover probability are used to generate offspring, and neighborhood replacement is performed to maintain the feasible non-dominated solution set. Select a recommended reentry trajectory from the set of feasible non-dominated solutions.

2. The hypersonic vehicle reentry trajectory optimization method based on a safety margin and feasibility collaborative guidance mechanism as described in claim 1, characterized in that, The initial reentry state includes initial altitude, initial longitude, initial latitude, initial velocity, initial track angle, and initial heading angle; the desired terminal state includes terminal altitude, terminal longitude, terminal latitude, and terminal velocity; the aircraft physical properties and aerodynamic parameters include aircraft mass, aerodynamic reference area, nose radius of curvature, aerodynamic coefficient, and angle of attack and roll boundaries; the no-fly zone data includes the center latitude and longitude, physical radius, safe buffer distance, and effective altitude range of each no-fly zone.

3. The hypersonic vehicle reentry trajectory optimization method based on a safety margin and feasibility collaborative guidance mechanism as described in claim 1, characterized in that, The process constraints include heat flux, dynamic pressure, and overload constraints; the terminal constraints include allowable error constraints for terminal altitude, longitude, latitude, and velocity; the control constraints include boundary constraints for angle of attack, roll angle, and their rate of change; and the no-fly zone constraints include distance constraints between the candidate reentry trajectory and the physical boundary and safety buffer boundary of the no-fly zone.

4. The hypersonic vehicle reentry trajectory optimization method based on a safety margin and feasibility collaborative guidance mechanism as described in claim 1, characterized in that, The acquisition of the multi-objective optimization model and the hierarchical constraint violation degree, the comprehensive hard constraint violation degree, and the minimum no-fly zone safety margin includes: The integrated thermal load of the multi-objective optimization model is obtained by numerical integration of the heat flow rate along the trajectory, and the smoothness of the track angle is obtained by integral of the square of the rate of change of the track angle. All three objectives are minimized. The safety margin of the no-fly zone is determined based on the spherical distance between the candidate reentry trajectory sampling point and the center of the no-fly zone. For the first... No-fly zones and the first The safety margin for each trajectory sampling point is: ； in, This indicates that the k-th trajectory sampling point is relative to the k-th trajectory sampling point. The margin of the no-fly zone safety buffer boundary; the minimum no-fly zone safety margin of the candidate reentry trajectory is expressed as: ； The minimum value is taken for all no-fly zones and all trajectory sampling points to obtain the minimum no-fly zone safety margin for the candidate re-entry trajectory; the no-fly zone constraint violation degree is expressed as: ； in, For the first The trajectory sampling point up to the first The spherical distance from the center of the no-fly zone The physical radius of the no-fly zone. For a safe buffer distance, For safety margin normalization scale; A value not less than zero indicates that the candidate reentry trajectory satisfies all no-fly zone safety buffer constraints. The layered constraint violation degree includes process constraint violation degree, terminal constraint violation degree, control constraint violation degree, and no-fly zone constraint violation degree. The process constraint violation degree consists of the normalized over-limit of heat flux, dynamic pressure, and overload; the terminal constraint violation degree consists of the normalized error over-limit of terminal altitude, longitude, latitude, and speed; the control constraint violation degree consists of the normalized over-limit of angle of attack, roll angle, and control change rate. The overall hard constraint violation rate is a weighted sum of the normalized constraint violation rate, the terminal constraint violation rate, the control constraint violation rate, and the no-fly zone constraint violation rate.

5. The hypersonic vehicle reentry trajectory optimization method based on a safety margin and feasibility collaborative guidance mechanism according to claim 1, characterized in that, The specific calculations for the feasible proportion of hard constraints and the safe proportion of no-fly zones are as follows: In the During the iterative calculation process, the first The ratio of the number of feasible solutions in the population to the population size is used as the hard constraint feasibility ratio. , used to characterize the degree to which the current population enters the hard-constrained feasible region, the th The number of feasible solutions in the population is the number of individuals whose overall hard constraint violation is no greater than the feasible decision tolerance. In the During the iterative calculation process, the ratio of the number of individuals with zero violations of the no-fly zone safety buffer to the population size is used as the no-fly zone safety risk ratio. , is used to characterize the degree to which the current population enters the feasible region of hard constraints.

6. The hypersonic vehicle reentry trajectory optimization method based on a safety margin and feasibility collaborative guidance mechanism according to claim 5, characterized in that, The decomposition-based multi-objective differential evolution algorithm adapts during the iterative optimization process. The constraint threshold is first algebraically generated using the fundamental values ​​of the decaying basic constraints. Then adjust according to the feasible proportion of the hard constraints, and through The tightening speed of a single generation is limited as follows: ； ； in, The threshold value of the basic constraint decays with the number of iterations. The lower limit of the threshold. As the initial threshold, The decay exponent, For the maximum number of iterations, Feasibility ratio correction coefficient used to adjust the threshold according to the feasible ratio of hard constraints This is the threshold smoothing coefficient, used to limit the tightening rate of the threshold between adjacent generations. hour, .

7. The hypersonic vehicle reentry trajectory optimization method based on a safety margin and feasibility collaborative guidance mechanism according to claim 5, characterized in that, In the iterative optimization process, the differential evolution scaling factor and crossover probability of the decomposition-based multi-objective differential evolution algorithm are updated collaboratively using the hard constraint feasible ratio and the no-fly zone safe ratio, specifically as follows: ； in, For the first Differential evolution scaling factor This is a search intensity compensation item when the safety ratio of the no-fly zone is insufficient. , These are the upper and lower bounds of the differential evolution scaling factor; in, and These are compensation coefficients used to adjust the differential evolution scaling factor and crossover probability according to the safe wind ratio of the no-fly zone, with the lower and upper limits of the crossover probability being... , .

8. The hypersonic vehicle reentry trajectory optimization method based on a safety margin and feasibility collaborative guidance mechanism according to claim 1, characterized in that, When performing a neighborhood replacement, the following rules apply: If at least one offspring or neighboring individual violates the no-fly zone safety buffer, the offspring with the smaller violation amount will be retained; otherwise... Feasible individuals take priority over Infeasible individuals; when both are When an individual is deemed infeasible, priority is given to retaining the one with the lower overall hard constraint violation. If the overall hard constraint violation is the same, priority is given to retaining the one with the lower sum of the normalized hierarchical constraint violations. When both are infeasible... When a feasible individual is selected, the Tchebycheff decomposition scalar value is calculated according to the corresponding weight vector and ideal point, and the smaller scalar value is retained first. When the difference between the decomposition scalar values ​​is within a given similar tolerance, the one with the smaller comprehensive hard constraint violation is retained first. If the comprehensive hard constraint violation is the same, the one with the smaller sum of normalized constraint violations is retained first.

9. The hypersonic vehicle reentry trajectory optimization method based on a safety margin and feasibility collaborative guidance mechanism according to claim 1, characterized in that, When selecting a recommended reentry trajectory from the set of feasible non-dominated solutions, candidate solutions that fail to meet terminal constraints and no-fly zone safety buffer constraints are first screened out from the set of feasible non-dominated solutions. Then, TOPSIS is used to select a recommended reentry trajectory. At the same time, the recommended reentry trajectory is continuously verified and fully constrained. If the verification is passed, the recommended reentry trajectory, control profile, multi-objective optimization function value, no-fly zone safety margin, and constraint verification results are output. If the verification is not passed, the candidate solution is removed and a new one is selected. If there are no qualified candidate solutions, the optimization search continues.

10. A hypersonic vehicle reentry trajectory optimization system based on a safety margin and feasibility collaborative guidance mechanism, characterized in that, The system includes a data acquisition module, a constraint system construction module, a trajectory generation and propagation module, a constraint evaluation module, an SMFG collaborative optimization module, and a decision selection module, to implement the hypersonic vehicle reentry trajectory optimization method based on the safety margin and feasibility collaborative guidance mechanism as described in any one of claims 1 to 9; wherein, The data acquisition module is used to acquire the initial reentry status of the aircraft, the desired terminal status, the aircraft parameters, and the no-fly zone data. The constraint system construction module is used to construct a reentry trajectory optimization constraint system that includes process constraints, terminal constraints, control constraints, and no-fly zone constraints. The trajectory generation and propagation module is used to discretize the continuous angle of attack profile and the continuous dip angle profile into finite-dimensional decision variables, and obtain the candidate reentry trajectory state sequence based on the decision variables and the reentry dynamics model. The constraint evaluation module is used to construct a multi-objective optimization model that includes flight time, integral thermal load and track angle smoothness, and to calculate the hierarchical constraint violation degree, the comprehensive hard constraint violation degree and the minimum no-fly zone safety margin. The SMFG collaborative optimization module is used to decompose the multi-objective optimization model into multiple weighted Tchebycheff subproblems based on the multi-objective differential evolution algorithm, using a safety margin and feasibility collaborative guidance mechanism. It calculates the hard constraint feasible proportion and the no-fly zone safe proportion based on the same generation population, thereby updating the adaptive ε constraint threshold, differential evolution scaling factor and crossover probability. It generates offspring using the updated adaptive ε constraint threshold, differential evolution scaling factor and crossover probability, and performs neighborhood replacement to maintain the feasible non-dominated solution set. The decision selection module is used to select a recommended reentry trajectory from the set of feasible non-dominated solutions.

Images