Planning method for avoiding optimal reentry flight path in no-fly zone

Abstract

The invention belongs to the technical field of reentry flight path planning. The invention provides a no-fly zone avoidance optimal reentry flight path planning method. According to the embodiment of the invention, a variant high-speed three-degree-of-freedom motion model is established, and the variable system number is expanded into the control quantity; specific forms of process constraint, control quantity constraint, end point constraint, performance index constraint and no-fly zone constraint are given; and aiming at the constraint condition and the motion model, converting a trajectory optimization problem into a Bolaz type optimal control problem, and carrying out time domain transformation and optimal control solution on the Bolaz type optimal control problem based on an hp self-adaptive pseudo-spectral method. A no-fly zone is converted into path constraint, an hp self-adaptive pseudo-spectral method is introduced, the rapid convergence of an h method and the calculation sparsity of a p method are fully combined, and more reasonable collocation point distribution is achieved. The problem of optimal trajectory planning of the high-precision no-fly zone is solved.

Description

Technical Field

[0001] The disclosed embodiments relate to the technical field of re-entry flight trajectory planning, and in particular to an optimal re-entry flight trajectory planning method for avoiding a no-fly zone. Background Art

[0002] High-speed morphing aircraft can change its flight shape according to the flight state and given mission, thereby affecting the lift-to-drag ratio, and then changing the flight attitude of the aircraft, so that the aircraft always maintains the optimal flight state, and can meet the requirements of the aircraft to perform multiple tasks in a large flight envelope. As a necessary research content of high-speed technology, the optimal trajectory planning problem of aircraft occupies an extremely important position in the aerospace transportation system. In the study of optimal trajectory planning of the reentry phase of a morphing high-speed aircraft, when the aircraft passes through the atmosphere from orbit or suborbital altitude, the atmospheric environmental parameters such as atmospheric pressure, temperature, density and ionization change dramatically. The uncertainty and complexity of the atmospheric environmental parameters have a great impact on the aerodynamic characteristics of the aircraft, and the flight environment has strong uncertainty. In addition, due to the complex structure of the morphing aircraft, the high degree of integration of the fuselage, and the high coupling between the subsystems, most of its trajectory dynamics equations and kinematic equations have highly nonlinear and strongly constrained characteristics, which makes it more difficult to solve the trajectory of the aircraft. In addition, with the diversification of near-space flight missions, high-speed variant aircraft not only need to meet general process constraints and terminal constraints, but also need to meet the requirements of avoiding no-fly zones, such as avoiding geopolitically prohibited areas, various anti-missile systems and the establishment of aviation identification zones. Therefore, it is of great theoretical significance and engineering value to study the optimal reentry trajectory planning of aircraft under strong uncertainty, strong nonlinearity, strong constraints and no-fly zone constraints to ensure that the aircraft has the optimal trajectory and high landing point accuracy under the conditions of meeting multi-mission constraints and no-fly zone constraints.

[0003] At present, the methods for solving the trajectory of a spacecraft mainly include the direct method of directly optimizing the performance index and the indirect method of solving the problem by constructing a two-point boundary value problem for the optimal trajectory. Compared with the indirect method, the direct method has the advantages of easy convergence and high efficiency. With the rapid development of computing performance, the advantages of the direct method are gradually higher than those of the indirect method, and it is easier to implement in engineering. The pseudo-spectral method belongs to the direct method. The basic principle is to parameterize the constructed trajectory optimal control problem into an NLP (Non-Linear Programming) problem; perform numerical calculations on the converted NLP problem to obtain the optimal solution. Due to the strong nonlinearity and strong constraints of the reentry phase of the high-speed variant spacecraft, the converted NLP problem exhibits the characteristics of high nonlinearity, strong constraints, and many optimization variables. It is difficult to obtain satisfactory results using general numerical optimization methods.

[0004] Therefore, it is necessary to improve one or more problems existing in the above-mentioned related technical solutions.

[0005] It should be noted that this section is intended to provide background or context for the technical solutions of the present disclosure stated in the claims. The description herein is not admitted to be prior art by virtue of being included in this section. Summary of the invention

[0006] In order to avoid the shortcomings of the prior art, the present application provides a no-fly zone avoidance optimal reentry flight trajectory planning method to solve the problem that the prior art is difficult to adapt to the strong nonlinearity, strong constraints and strong uncertainty of the reentry phase of high-speed variant aircraft.

[0007] According to an embodiment of the present disclosure, a method for planning an optimal reentry flight trajectory for avoiding a no-fly zone is provided, the method comprising: Establish the three-degree-of-freedom dimensionless equations of the variant high-speed aircraft; Setting a constraint group; wherein the constraint group includes thermal flow constraint, dynamic pressure constraint, overload constraint, no-fly zone constraint, endpoint constraint, control quantity constraint and performance index constraint; Constructing a trajectory optimization problem, and converting the trajectory optimization problem into a Bolaz-type optimal control problem based on the three-degree-of-freedom dimensionless equation and the constraint group; The Bolaz-type optimal control problem is transformed in the time domain and solved for optimal control to obtain the optimal reentry flight trajectory planning result.

[0008] Furthermore, the three-degree-of-freedom dimensionless equation includes:

[0009] in, is the dimensionless distance from the center of the Earth, given by the radius of the Earth To make it dimensionless, for The differential of is the Earth's longitude, for The differential of is the Earth's latitude, for The differential of is the dimensionless velocity, given by the first cosmic velocity Dimensionless, , for The differential of is the track angle, for The differential of is the heading angle, for The differential of is the tilt angle; is the dimensionless lift acceleration; is the dimensionless drag acceleration; and:

[0010] in, is the distance from the center of the earth, is the aircraft speed, is the atmospheric density, is the reference area of ​​the aircraft, is the weight of the aircraft, is the dimensionless time, is the time, using the Schuler constant Dimensionless.

[0011] Furthermore, the heat flow constraint is:

[0012] in, is the first constant, for to the power of 0.5, for to the power of 3.15, is the maximum heat flux that the aircraft can withstand; The dynamic pressure constraint is:

[0013] in, is the maximum dynamic pressure that the aircraft can withstand; The overload constraints are:

[0014] in, The maximum overload that the aircraft can withstand; The no-fly zone constraints are:

[0015] in, is the number of no-fly zones, is the radius of each no-fly zone, is the distance from the aircraft to the center of each no-fly zone; The endpoint constraints are:

[0016] in, is the endpoint constraint state vector, , , , , and are the initial values ​​of the distance from the center of the earth, the initial values ​​of the longitude, the initial values ​​of the latitude, the initial values ​​of the speed, the initial values ​​of the track inclination and the initial values ​​of the yaw angle, is the endpoint constraint state vector, , and They are the end point value of the geocentric distance, the end point value of the longitude, and the end point value of the latitude; The control quantity constraint is:

[0017] in, is the minimum tilt angle, is the maximum tilt angle, is the coefficient of variation, is the minimum value of the variation coefficient, is the maximum value of the variation coefficient; The performance indicator constraints are:

[0018] in, is the maximum terminal velocity of the aircraft.

[0019] Furthermore, the cost function of the Bolaz type optimal control problem is:

[0020] The constraints are:

[0021] Among them, the state variable , is the initial time, is the terminal time, Represents dynamic constraints, control quantity , is the path constraint, is a boundary constraint.

[0022] Furthermore, the step of performing time domain transformation and optimal control solution on the Bolaz type optimal control problem to obtain the optimal reentry flight trajectory planning result includes: The time interval of the Bolaz type optimal control problem is divided into subintervals, and performing a time domain transform on each of the subintervals; Discretizing the cost function of the Bolaz-type optimal control problem after the time domain transformation using the hp adaptive pseudo-spectral method to obtain the maximum relative error of the k-th subinterval; If the maximum relative error of the kth subinterval is greater than a preset allowable error, the number of matching points is increased to obtain an increased number of matching points; The sub-intervals are refined according to the increased number of allocation points to obtain the optimal reentry flight trajectory planning result.

[0023] Furthermore, the time interval of the Bolaz type optimal control problem is divided into subintervals, and performing time domain transformation on each of the subintervals, comprising: use express grid points, using Indicates Sub-interval The number of points in the interval is calculated, and the following time domain transformation is performed on each interval:

[0024] The time interval Transformed to .

[0025] Furthermore, the expression of the increased allocation points is:

[0026] The increased number of points is rounded to obtain:

[0027] in, To increase the number of points, is the initial number of points in the kth subinterval, is the maximum relative error, For the allowable error, This is a rounding operation.

[0028] Furthermore, the step of subdividing the sub-intervals according to the number of the increased allocation points includes: According to the increased allocation points and the initial number of points in the kth subinterval , get the number of points required for the kth subinterval ; Set the maximum number of points in the sub-interval to , the minimum number of points in the subinterval is ; like , then increase the allocation points; like , then the interval is refined into refined molecular intervals, and the number of the refined molecular intervals is:

[0029] The initial value of the number of points in each subinterval is set to .

[0030] The technical solution provided by the embodiments of the present disclosure may have the following beneficial effects: In the embodiments of the present disclosure, the above-mentioned optimal reentry flight trajectory planning method for avoiding no-fly zones is used. On the one hand, first, a variant high-speed three-degree-of-freedom motion model is established, and the variant coefficient is expanded into a control quantity; secondly, the specific forms of process constraints, control quantity constraints, endpoint constraints, performance index constraints and no-fly zone constraints are given; finally, according to the constraints and motion model, the trajectory optimization problem is converted into a Bolaz-type optimal control problem, and the Bolaz-type optimal control problem is transformed in the time domain and solved for optimal control based on the hp adaptive pseudo-spectral method. On the other hand, while converting the no-fly zone into a path constraint, the hp adaptive pseudo-spectral method is introduced, which fully combines the rapid convergence of the h method and the computational sparsity of the p method, and has a more reasonable distribution of points. High-precision solution to the optimal trajectory planning problem of the no-fly zone is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The accompanying drawings herein are incorporated into the specification and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the specification are used to explain the principles of the present disclosure. Obviously, the accompanying drawings described below are only some embodiments of the present disclosure, and for ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without creative work.

[0032] Figure 1 A step diagram showing a method for planning an optimal reentry flight trajectory for avoiding a no-fly zone in an exemplary embodiment of the present disclosure; Figure 2 The longitude and latitude change curves and no-fly zone avoidance conditions of the optimal reentry flight trajectory planning method for avoiding no-fly zones proposed in this application and the traditional pseudo-spectral flight trajectory planning method are shown in Case 1; Figure 3 The height variation curves of the optimal reentry flight trajectory planning method for avoiding a no-fly zone proposed in this application and the traditional pseudo-spectral flight trajectory planning method in Case 1 are shown; Figure 4 The speed variation curves of the optimal reentry flight trajectory planning method for avoiding a no-fly zone proposed in this application and the traditional pseudo-spectral flight trajectory planning method in Case 1 are shown; Figure 5 The roll angle variation curve of the optimal reentry flight trajectory planning method for avoiding a no-fly zone proposed in this application in Case 1 is shown; Figure 6The change curve of the variable lift-to-drag ratio coefficient of the optimal reentry flight trajectory planning method for avoiding a no-fly zone proposed in this application in Case 1 is shown; Figure 7 The heat flux variation curve of the optimal reentry flight trajectory planning method for avoiding a no-fly zone proposed in this application in Case 1 is shown; Figure 8 The overload variation curve of the optimal reentry flight trajectory planning method for avoiding a no-fly zone proposed in this application in Case 1 is shown; Fig. 9 The dynamic pressure variation curve of the optimal reentry flight trajectory planning method for avoiding a no-fly zone proposed in this application in Case 1 is shown; Fig.10 The longitude and latitude change curves and no-fly zone avoidance conditions of the optimal reentry flight trajectory planning method for avoiding no-fly zones proposed in this application and the traditional pseudo-spectral flight trajectory planning method are shown in Case 2; Fig.11 The height variation curves of the optimal reentry flight trajectory planning method for avoiding a no-fly zone proposed in this application and the traditional pseudo-spectral flight trajectory planning method in Case 2 are shown; Fig.12 The speed variation curves of the optimal reentry flight trajectory planning method for avoiding a no-fly zone proposed in this application and the traditional pseudo-spectral flight trajectory planning method in Case 2 are shown; Fig.13 The roll angle variation curve of the optimal reentry flight trajectory planning method for avoiding a no-fly zone proposed in this application in Case 2 is shown; Fig.14 The change curve of the variable lift-to-drag ratio coefficient of the optimal reentry flight trajectory planning method for avoiding a no-fly zone proposed in this application in Case 2 is shown; Fig.15 The heat flux variation curve of the optimal reentry flight trajectory planning method for avoiding a no-fly zone proposed in this application in Case 2 is shown; Fig.16 The overload variation curve of the optimal reentry flight trajectory planning method for avoiding a no-fly zone proposed in this application in Case 2 is shown; Fig.17 The dynamic pressure variation curve of the optimal reentry flight trajectory planning method for avoiding a no-fly zone proposed in this application in Case 2 is shown. DETAILED DESCRIPTION

[0033] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that the disclosure will be more comprehensive and complete and to fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0034] In addition, the accompanying drawings are only schematic illustrations of the embodiments of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the figures represent the same or similar parts, and their repeated descriptions will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0035] This example implementation provides a method for planning an optimal reentry flight trajectory to avoid a no-fly zone. Figure 1 As shown in , the no-fly zone avoidance optimal reentry flight trajectory planning method may include: steps S101 to S104.

[0036] Step S101: establishing a three-degree-of-freedom dimensionless equation of a variant high-speed aircraft; Step S102: setting a constraint group; wherein the constraint group includes thermal flow constraint, dynamic pressure constraint, overload constraint, no-fly zone constraint, endpoint constraint, control amount constraint and performance index constraint; Step S103: constructing a trajectory optimization problem, and converting the trajectory optimization problem into a Bolaz-type optimal control problem based on the three-degree-of-freedom dimensionless equation and the constraint group; Step S104: performing time domain transformation and optimal control solution on the Bolaz type optimal control problem to obtain an optimal reentry flight trajectory planning result.

[0037] Through the above-mentioned optimal reentry flight trajectory planning method for avoiding no-fly zones, on the one hand, firstly, a variant high-speed three-degree-of-freedom motion model is established, and the variant coefficient is expanded into a control quantity; secondly, the specific forms of process constraints, control quantity constraints, endpoint constraints, performance index constraints and no-fly zone constraints are given; finally, according to the constraints and motion model, the trajectory optimization problem is converted into a Bolaz-type optimal control problem, and the Bolaz-type optimal control problem is transformed in the time domain and solved for optimal control based on the hp adaptive pseudo-spectral method. On the other hand, while converting the no-fly zone into a path constraint, the hp adaptive pseudo-spectral method is introduced, which fully combines the fast convergence of the h method and the computational sparsity of the p method, and has a more reasonable distribution of points. High-precision solution of the optimal trajectory planning problem of the no-fly zone is achieved.

[0038] Next, we will refer to Figures 1 to 17 Each step of the above-mentioned no-fly zone avoidance optimal re-entry flight trajectory planning method in this example implementation is described in more detail.

[0039] In step S101, the high-speed morphing aircraft targeted by the present application is a high-speed morphing aircraft with variable swept wings, which changes the aerodynamic parameters of the aircraft by changing the body, thereby changing the lift-to-drag ratio. The variation range of the variation coefficient is , Denotes the deformation coefficient. Different deformation coefficients correspond to different lift-to-drag ratios. Considering the changes in the aircraft configuration, the deformation coefficient is regarded as a control variable and is related to the angle of attack. , tilt angle Together they constitute the control quantity. In order to simplify the analysis, the following assumptions are made: (1) The unsteady aerodynamic force caused by the change of swept wing is not considered; (2) Assume that the instantaneous equilibrium condition is met, that is, the guidance control variables such as angle of attack, roll angle, and variation coefficient can be obtained in real time.

[0040] (3) The aerodynamic coefficients of traditional fixed-shape aircraft are related to the angle of attack and Mach number. The aerodynamic model of a morphing aircraft is related to the angle of attack and Mach number as well as the morphing coefficient. In order to simplify the trajectory planning steps, when the shape of the aircraft changes, it is assumed that the drag coefficient Unchanged, lift coefficient becomes .

[0041] First, the three-degree-of-freedom dimensionless equation of the variant high-speed aircraft is established as shown in (1): (1) In the formula, is the dimensionless distance from the center of the Earth, given by the radius of the Earth Make it dimensionless; and are the longitude and latitude of the Earth, both in radians; is the dimensionless velocity, given by the first cosmic velocity Dimensionless, where ; is the track angle; is the heading angle; is the tilt angle; and are the dimensionless lift acceleration and drag acceleration, respectively, given by the sea level gravity Dimensionless, we have: (2) In the formula, is the atmospheric density, which can be considered as a function of altitude, is the reference area of ​​the aircraft; is the weight of the aircraft, is the distance from the center of the earth, is the speed of the aircraft; the differential equations also imply the integral independent variable time , using the Schuler constant Dimensionless.

[0042] The control variable of the reentry process is usually only the angle of attack and roll angle In this application, the variation coefficient Also considered as a control variable, in addition, during the reentry flight trajectory, the angle of attack The value is a fixed value , so the control quantity is .

[0043] In step S102, the high-speed aircraft will be subject to complex aerodynamic and thermal effects during the flight. To ensure the normal flight of the aircraft, process constraints must be met, including stagnation point heat flux. Constraints, overloads Constraint, dynamic pressure To ensure that the aircraft can smoothly enter the final handover point, the terminal altitude and speed constraints must be met. In addition, the no-fly zone constraints must also be met.

[0044] By processing the various constraints during the flight, we can obtain: (1) Heat flow constraints (3) in, is a constant related to the aircraft itself, The maximum heat flux that the aircraft can withstand.

[0045] (2) Dynamic pressure constraint (4) in, It is the maximum dynamic pressure that the aircraft can withstand.

[0046] (3) Overload constraint (5) in, The maximum overload that the aircraft can withstand.

[0047] (4) No-fly zone restrictions The actual shape of the no-fly zone is changeable and irregular, but the irregular shape can be decomposed into multiple circular superpositions. Therefore, in order to simplify the design steps, it is assumed that there are multiple circular no-fly zones when planning the reentry trajectory, and the no-fly zone is regarded as an infinitely high cylinder. The aircraft trajectory can only avoid it from the left and right sides, without considering the situation of avoiding it from the top or bottom. Suppose the number of no-fly zones is The radius of the no-fly zones are , the distances from the aircraft to the center of the no-fly zone are , the no-fly zone constraint can be expressed as: (6) (5) Endpoint constraints (7) in , , , , , They are the initial values ​​of the distance from the center of the earth, longitude, latitude, speed, track inclination, and yaw angle. , , They are the end point values ​​of the geocentric distance, longitude, and latitude respectively.

[0048] in, , , , , and are the initial values ​​of the distance from the center of the earth, the initial values ​​of the longitude, the initial values ​​of the latitude, the initial values ​​of the speed, the initial values ​​of the track inclination and the initial values ​​of the yaw angle, , and They are the end point value of the geocentric distance, the end point value of the longitude, and the end point value of the latitude; (6) Control quantity constraints In order to prevent the aircraft controller from saturation, the control quantity needs to be constrained. The control quantity constraint is: (8) (7) Performance indicator constraints In order to improve the strike effectiveness of the aircraft, the performance index of this application is set as the maximum terminal speed of the high-speed aircraft , expressed as (9) In step 103, the optimal trajectory planning problem is transformed into finding the optimal control quantity and The objective function is maximized while satisfying multiple constraints (3) to (9). This problem is described as a general Bolza-type optimal control problem, and the state variables are defined as , so that the cost function is minimized: (10) The constraints are (11) In the formula, is the initial time, is the terminal time, Represents a dynamic constraint; represents the path constraint, Represents a boundary constraint.

[0049] In step 104, the time interval of the Bolza type problem is Divide into subintervals, using express grid points, Indicates Sub-interval The number of points in the interval is calculated, and the following time domain transformation is performed on each interval: (12) The time interval Transformed to .

[0050] This application selects the Radau pseudospectral method as the pseudospectral method of the hp adaptive strategy, because the Radau pseudospectral method uses Legendre-Gauss-Radau (LGR) collocation to discretize the optimal problem, and the optimal solution of the NLP problem satisfies the first-order necessary conditions of the original continuous-time optimal control problem, and the collocation contains (-1) points, which makes it easier to represent the interval connection of the multi-interval optimal control problem. The state variable of the continuous Bolza problem is approximately: (13) In the formula, , is the Lagrangian basis function, is the collocation point of LGR. According to the above discretization state, the cost function can be discretized as: (14) In the formula is the Gaussian weight, is the approximate value of the control quantity at the LGR collocation point. The path constraint, boundary constraint, and differential constraint of the optimal control problem are discretized at the LGR collocation point at the same time, and its differential-algebraic constraint is: (15) In the formula is the Radau pseudospectral differential matrix, which can be obtained by the following formula: (16) If the solution obtained by numerical method can accurately approximate the exact solution of the original problem, the differential-algebraic constraints must be satisfied at any point. The state error of the differential-algebraic constraints at the matching points can be used as an evaluation criterion for the quality of the numerical method. The absolute error, relative error and maximum relative error of the state quantity are given below.

[0051] (17) (18) (19) In the formula, the control quantity It is approximated by constructing an interpolation polynomial, as shown below: (20) According to the maximum relative error of the kth subinterval solved , set the allowable error to ,like , then the solution in the interval can be considered to have reached the preset accuracy. Otherwise, it is necessary to increase the number of points or refine the interval to improve the accuracy of the solution. The process of improving accuracy is given below: Assume that the maximum relative error of interval k , then the accuracy can be improved by increasing the number of matching points. The increased number of matching points should satisfy ,Right now (twenty one) In order to ensure that the number of matching points is an integer, the above formula is rounded up to: (twenty two) The number of points required for interval k can be obtained by formula (22): , set the maximum and minimum values ​​of the number of points in the sub-interval to and ,like , then increase the number of points. The interval is divided into smaller sub-intervals, and the number of sub-intervals is: (twenty three) The initial value of the number of points in each interval is set to .

[0052] In a specific embodiment, Case 1: The initial state parameters of the high-speed variant aircraft are: altitude ,longitude ,latitude ,speed , track angle and heading angle The terminal constraint is: Terminal longitude constraint , terminal latitude constraint and terminal height constraints The process constraints are: heat flow constraints , overload constraint and dynamic pressure constraints The control quantity constraint is: roll angle constraint and the variation coefficient constraint The no-fly zone constraints are: the center position of the circle , no-fly zone radius . Select the maximum final speed, that is , as the optimal performance indicator.

[0053] The simulation results are as follows Figures 2 to 9 As shown in FIG. 1 , the curve for flying around a no-fly zone is the method proposed in this application, and the curve for flying around a no-fly zone is the traditional pseudo-spectral method. It can be seen that by considering the no-fly zone as an additional constraint, the optimal reentry flight trajectory planning and no-fly zone avoidance of a high-speed variant aircraft can be achieved based on the hp adaptive pseudo-spectral method. Figure 2 and Figure 3 The longitude and latitude changes and altitude changes of the high-speed variant aircraft are shown respectively. The aircraft can avoid the no-fly zone while meeting the terminal constraints. Figure 4 The speed change curve of the aircraft is given. After successfully avoiding the no-fly zone, the final speed of the aircraft is 342.22m / s; the final speed of the aircraft that does not avoid the no-fly zone is 524.25m / s. This is because avoiding the no-fly zone will consume a certain amount of energy, resulting in a decrease in speed. Figure 5 and Figure 6 The control amount change curve is shown. It can be seen that the roll angle and the coefficient of variation All constraints are satisfied. Figures 7 to 9 The process constraint variation curves are given, including heat flux variation curve, overload variation curve and dynamic pressure variation curve, where the heat flux is , overloaded to , the dynamic pressure is , all satisfy the process constraints. Therefore, the method of the present application can successfully avoid the no-fly zone and complete the flight trajectory planning.

[0054] In a specific embodiment, Case 2: The initial state parameters of the high-speed variant aircraft are: altitude ,longitude ,latitude ,speed , track angle and heading angle The terminal constraint is: Terminal longitude constraint , terminal latitude constraint and terminal height constraints The process constraints are: heat flow constraints , overload constraint and dynamic pressure constraints The control quantity constraint is: roll angle constraint and the variation coefficient constraint . Select the maximum final speed, that is as the optimal performance indicator.

[0055] The simulation results are as follows Figure 10-Figure 17As shown in the figure, it can be seen that by changing the constraints, the hp adaptive pseudo-spectral method can still achieve the optimal reentry flight trajectory planning and no-fly zone avoidance of the high-speed variant aircraft, which has strong robustness. Fig.10 and Fig.11 It can be seen that the aircraft can meet the terminal constraints while completing the no-fly zone avoidance. Fig.12 It can be seen that after successfully avoiding the no-fly zone, the final speed of the aircraft is 392.42m / s; the final speed of the aircraft that did not avoid the no-fly zone is 485.27m / s. This is because avoiding the no-fly zone will consume a certain amount of energy, resulting in a decrease in speed. Fig.13 and Fig.14 Shows the control amount change curve, roll angle and the coefficient of variation All constraints are satisfied. Finally, Figure 15-17 The process constraint variation curves are given, including heat flux variation curve, overload variation curve and dynamic pressure variation curve, where the heat flux is , overloaded to , the dynamic pressure is , all satisfy the process constraints. Therefore, the method of the present application can successfully avoid the no-fly zone and complete the flight trajectory planning.

[0056] Through the above-mentioned optimal reentry flight trajectory planning method for avoiding no-fly zones, on the one hand, firstly, a variant high-speed three-degree-of-freedom motion model is established, and the variant coefficient is expanded into a control quantity; secondly, the specific forms of process constraints, control quantity constraints, endpoint constraints, performance index constraints and no-fly zone constraints are given; finally, according to the constraints and motion model, the trajectory optimization problem is converted into a Bolaz-type optimal control problem, and the Bolaz-type optimal control problem is transformed in the time domain and solved for optimal control based on the hp adaptive pseudo-spectral method. On the other hand, while converting the no-fly zone into a path constraint, the hp adaptive pseudo-spectral method is introduced, which fully combines the fast convergence of the h method and the computational sparsity of the p method, and has a more reasonable distribution of points. High-precision solution of the optimal trajectory planning problem of the no-fly zone is achieved.

[0057] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the embodiments of the present disclosure, the meaning of "multiple" is two or more, unless otherwise clearly and specifically defined.

[0058] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example" or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present disclosure. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification.

[0059] Those skilled in the art will readily appreciate other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. This application is intended to cover any modification, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary techniques in the art that are not disclosed in the present disclosure. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present disclosure are indicated by the appended claims.

Claims

1. A method for planning an optimal reentry flight trajectory to avoid a no-fly zone, characterized in that: The method includes: Establish the three-degree-of-freedom dimensionless equations of the variant high-speed aircraft; Setting a constraint group; wherein the constraint group includes thermal flow constraint, dynamic pressure constraint, overload constraint, no-fly zone constraint, endpoint constraint, control quantity constraint and performance index constraint; Constructing a trajectory optimization problem, and converting the trajectory optimization problem into a Bolaz-type optimal control problem based on the three-degree-of-freedom dimensionless equation and the constraint group; The Bolaz-type optimal control problem is transformed in the time domain and solved for optimal control to obtain the optimal reentry flight trajectory planning result.

2. The optimal reentry flight trajectory planning method for avoiding a no-fly zone according to claim 1, characterized in that: The three-degree-of-freedom dimensionless equation includes: in, is the dimensionless distance from the center of the Earth, given by the radius of the Earth To make it dimensionless, for The differential of is the Earth's longitude, for The differential of is the Earth's latitude, for The differential of is the dimensionless velocity, given by the first cosmic velocity Dimensionless, , for The differential of is the track angle, for The differential of is the heading angle, for The differential of is the tilt angle; is the dimensionless lift acceleration; is the dimensionless drag acceleration; and: in, is the distance from the center of the earth, is the aircraft speed, is the atmospheric density, is the reference area of ​​the aircraft, is the weight of the aircraft, is the dimensionless time, is the time, using the Schuler constant Dimensionless.

3. The optimal reentry flight trajectory planning method for avoiding a no-fly zone according to claim 2 is characterized in that: The heat flow constraint is: in, is the first constant, for to the power of 0.5, for to the power of 3.15, is the maximum heat flux that the aircraft can withstand; The dynamic pressure constraint is: in, is the maximum dynamic pressure that the aircraft can withstand; The overload constraints are: in, The maximum overload that the aircraft can withstand; The no-fly zone constraints are: in, is the number of no-fly zones, is the radius of each no-fly zone, is the distance from the aircraft to the center of each no-fly zone; The endpoint constraints are: in, is the endpoint constraint state vector, , , , , and are the initial values ​​of the distance from the center of the earth, the initial values ​​of the longitude, the initial values ​​of the latitude, the initial values ​​of the speed, the initial values ​​of the track inclination and the initial values ​​of the yaw angle, is the endpoint constraint state vector, , and They are the end point value of the geocentric distance, the end point value of the longitude, and the end point value of the latitude; The control quantity constraint is: in, is the minimum tilt angle, is the maximum tilt angle, is the coefficient of variation, is the minimum value of the variation coefficient, is the maximum value of the variation coefficient; The performance indicator constraints are: in, is the maximum terminal velocity of the aircraft.

4. The optimal reentry flight trajectory planning method for avoiding a no-fly zone according to claim 3 is characterized in that: The cost function of the Bolaz type optimal control problem is: The constraints are: Among them, the state variable , is the initial time, is the terminal time, Represents dynamic constraints, control quantity , is the path constraint, is a boundary constraint.

5. The optimal reentry flight trajectory planning method for avoiding a no-fly zone according to claim 4 is characterized in that: The step of performing time domain transformation and optimal control solution on the Bolaz type optimal control problem to obtain the optimal reentry flight trajectory planning result includes: The time interval of the Bolaz type optimal control problem is divided into subintervals, and performing a time domain transform on each of the subintervals; Discretizing the cost function of the Bolaz-type optimal control problem after the time domain transformation using the hp adaptive pseudo-spectral method to obtain the maximum relative error of the k-th subinterval; If the maximum relative error of the kth subinterval is greater than a preset allowable error, the number of matching points is increased to obtain an increased number of matching points; The sub-intervals are refined according to the increased number of allocation points to obtain the optimal reentry flight trajectory planning result.

6. The optimal reentry flight trajectory planning method for avoiding a no-fly zone according to claim 5, characterized in that: The time interval of the Bolaz type optimal control problem is divided into subintervals, and performing time domain transformation on each of the subintervals, comprising: use express grid points, using Indicates Sub-interval The number of points in the interval is calculated, and the following time domain transformation is performed on each interval: The time interval Transformed to .

7. The optimal reentry flight trajectory planning method for avoiding a no-fly zone according to claim 6, characterized in that: The expression of the increased allocation points is: The increased number of matching points is rounded to obtain: in, To increase the number of points, is the initial number of points in the kth subinterval, is the maximum relative error, For the allowable error, This is a rounding operation.

8. The method for planning optimal reentry flight trajectory to avoid a no-fly zone according to claim 7, characterized in that: The step of subdividing the sub-intervals according to the number of the increased allocation points includes: According to the increased allocation points and the initial number of points in the kth subinterval , get the number of points required for the kth subinterval ; Set the maximum number of points in the sub-interval to , the minimum number of points in the subinterval is ; like , then increase the allocation points; like , then the interval is refined into refined molecular intervals, and the number of the refined molecular intervals is: The initial value of the number of points in each subinterval is set to .

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