Dynamic projection method for multi-constraint flight path of aircraft

Abstract

The invention discloses a dynamic projection method for a multi-constraint flight path of an aircraft, and belongs to the field of flight path planning of aircrafts. According to the method, the problem that the projection distortion from the non-uniform surface curved surface to the flight path planning plane is large because the influence of the non-uniform shape of the earth on the flight path planning is not considered in the existing method is solved. According to the invention, an optimization problem is established according to the area deformation of a projection plane around the current latitude and longitude of an aircraft, and then the optimization problem is dynamically solved by adopting an improved exponential distribution optimization algorithm based on a chaos random sequence to obtain an optimal projection baseline. And then a projection model from the non-uniform surface curved surface to the flight path planning plane is established according to the solved projection base line, a projection scheme can be dynamically corrected according to the actual position of the aircraft, and the minimum projection distortion from the non-uniform surface curved surface to the flight path planning plane is realized. The method can be applied to dynamic projection of the flight path of the aircraft.

Description

Technical Field

[0001] The invention belongs to the field of aircraft trajectory planning, and in particular relates to a dynamic projection method for aircraft multi-constraint trajectories. Background Art

[0002] Aircraft are aircraft used for long-distance unmanned transportation or environmental monitoring in the future. They have the advantages of high speed, long range, large scope, multiple uses and modularity. This type of aircraft has a power propulsion system and a high lift-to-drag ratio shape, and can fly hundreds of kilometers under high-speed airborne delivery conditions. In long-distance and high-speed flight, conventional plane coordinate systems cannot be used, and the impact of the earth's non-uniform shape on trajectory planning must be considered, including the projection distortion from the non-uniform surface surface to the trajectory planning plane. However, the existing methods are mainly carried out in conventional plane coordinate systems or under preset projection planes, without considering the non-uniform shape or curvature of the earth under long-distance flight conditions, and without considering the dynamic adjustment of the projection baseline or projection scheme. The projection distortion from the non-uniform surface surface to the trajectory planning plane is large, and the adaptability to the flight airspace and longitude and latitude span is insufficient.

[0003] In summary, the existing methods do not consider the impact of the non-uniform shape of the earth on trajectory planning, resulting in large projection distortion from the non-uniform surface to the trajectory planning plane. Therefore, it is necessary to propose an improved trajectory planning plane projection scheme to solve the problem of large projection distortion. Summary of the invention

[0004] The purpose of the present invention is to solve the problem that the existing methods do not consider the influence of the non-uniform shape of the earth on trajectory planning, resulting in large projection distortion from the non-uniform surface to the trajectory planning plane, and a dynamic projection method for multi-constrained trajectories of aircraft is proposed by dynamically adjusting the projection baseline.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: a dynamic projection method for multi-constrained aircraft tracks, the method specifically comprising the following steps:

[0006] Step 1: Establish an optimization problem based on the area deformation generated by the projection plane around the current latitude and longitude of the aircraft;

[0007] The area deformation produced by the projection plane around the current latitude and longitude of the aircraft is:

[0008]

[0009] Among them, S d Indicates the area difference between the projected area and the actual area; Indicates the lower latitude limit of the area around the current latitude and longitude of the aircraft. Indicates the upper latitude limit of the area around the current latitude and longitude of the aircraft. represents the projection baseline, Indicates the current latitude of the aircraft;

[0010] Step 2: Use the improved exponential distribution optimization algorithm to solve the optimization problem established in step 1, and perform dynamic projection of the track based on the solution results.

[0011] Furthermore, the track model of the aircraft is:

[0012]

[0013] Among them, V represents the speed of the aircraft, γ represents the ballistic inclination angle of the aircraft, ψ represents the heading angle of the aircraft, h represents the height of the aircraft, R is the radius of the earth, and a ψ is the turning acceleration, G ψ represents the gravitational perturbation acceleration caused by the non-uniform shape, non-uniform mass distribution and rotation of the Earth, ψ′ is the derivative of ψ, yes The derivative of θ, θ represents the current longitude of the aircraft, and θ′ is the derivative of θ.

[0014] Furthermore, the establishment process of the optimization problem is:

[0015] Calculate area deformation about the projection baseline The derivative of

[0016]

[0017] Then the optimization problem is established as:

[0018]

[0019] Among them, u represents the variable to be optimized.

[0020] Furthermore, the specific process of step 2 is as follows:

[0021] Step 21: Initialize the population size to N and the population to x 1 :

[0022]

[0023] in, and are the projection baselines of the 1st, 2nd, …, Nth individuals in the initialization population respectively;

[0024] Step 22, initialize the number of iterations l = 1;

[0025] Step 23: Determine whether the number of iterations l is less than or equal to l max / 2, lmax is the maximum number of iterations;

[0026] If the number of iterations l is less than or equal to l max / 2, then execute step 24;

[0027] Otherwise, execute step 25;

[0028] Step 24: Calculate the fitness function value of each individual in the l-generation population respectively, sort the fitness function values ​​of each individual in the l-generation population from small to large, and record the individuals with the top three fitness function values ​​in the l-generation population as and

[0029] According to and Calculate the bootstrap solution According to x l , and the memoryless matrix y l Get the candidate population z of the lth iteration l , and according to the alternative population z l Get the updated population x l+1 and the updated memoryless matrix y l+1 ;

[0030] Then set l=l+1 and return to step 2 and 3;

[0031] Step 25: Calculate the fitness function value of each individual in the l-th generation population, sort the fitness function values ​​of each individual in the l-th generation population from small to large, and record the individuals with the top two fitness function values ​​in the l-th generation population as and

[0032] According to and x l Get the candidate population z of the lth iteration l , and according to the alternative population z l Get the updated population x l+1 ; Then execute step 26;

[0033] Step 26: Determine whether the current number of iterations is less than l max ;

[0034] If the current number of iterations is less than l max , then set l = l + 1, and return to step 2 and 3;

[0035] If the current number of iterations is equal to l max , then calculate the population x after the last iteration update l+1The fitness function value of each individual in the equation is calculated, and the individual corresponding to the minimum fitness function value is taken as the final solution.

[0036] Furthermore, according to and Calculate the bootstrap solution Specifically:

[0037]

[0038] in, It is a guided solution.

[0039] Furthermore, in step 24, according to x l , and the memoryless matrix y l Get the candidate population z of the lth iteration l , the specific process is:

[0040]

[0041] Among them, y l is the memoryless matrix of the lth iteration;

[0042]

[0043] in, is the variance, r1 is a random number between [-1,1], and r2 is a random number between [0,1];

[0044]

[0045] Among them, z l is the candidate matrix for the lth iteration.

[0046] Furthermore, the variance for:

[0047]

[0048] Furthermore, the alternative population z l Get the updated population x l+1 , specifically:

[0049]

[0050] in, is based on The calculated fitness function value, is based on The calculated fitness function value;

[0051] Then the updated population x l+1 for:

[0052]

[0053] According to the alternative population z l To update the memoryless matrix y l+1 :

[0054]

[0055] Further, in the step 25, according to and x l Get the candidate population z of the lth iteration l , and according to the alternative population z l Get the updated population x l+1 ; The specific process is:

[0056]

[0057] The subscript "mean" indicates the mean value, b1, b2, ..., b N It is a chaotic sequence generated based on random numbers;

[0058] Then update the population x by comparing the fitness function l+1 :

[0059]

[0060] in, is based on The calculated fitness function value, is based on The calculated fitness function value;

[0061]

[0062] Furthermore, the chaotic sequence generated based on random numbers is specifically:

[0063]

[0064] Where a and b1 are random numbers between [0,1].

[0065] The beneficial effects of the present invention are:

[0066] The present invention aims at the trajectory planning problem under long-distance flight conditions of aircraft. The present invention proposes an exponential distribution optimization algorithm based on an improved chaotic random sequence to dynamically solve the optimal projection baseline, and then establishes a projection model from the non-uniform surface to the trajectory planning plane according to the solved projection baseline. The projection scheme can be dynamically corrected according to the actual position of the aircraft to achieve minimized projection distortion from the non-uniform surface to the trajectory planning plane. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is to improve the dynamic projection scheme of the trajectory planning plane;

[0068] Figure 2 It is a flowchart of the improved exponential distribution optimization algorithm. DETAILED DESCRIPTION

[0069] Specific implementation method 1: This implementation method is a dynamic projection method for aircraft multi-constrained tracks, and the method specifically includes the following steps:

[0070] Step 1: Based on the projection plane around the current longitude and latitude of the aircraft (in the present invention, the current longitude and latitude refers to the longitude of θ and the latitude span of The area deformation generated by the area within the area) is used to establish an optimization problem;

[0071] The area deformation produced by the projection plane around the current latitude and longitude of the aircraft is:

[0072]

[0073] Among them, S d It indicates the area difference between the projected area and the actual area, reflecting the projection deformation; Indicates the lower latitude limit of the area around the current latitude and longitude of the aircraft. Indicates the upper latitude limit of the area around the current latitude and longitude of the aircraft. represents the projection baseline, Indicates the current latitude of the aircraft;

[0074] Step 2: Use the improved exponential distribution optimization algorithm to solve the optimization problem established in step 1, and perform dynamic projection of the track based on the solution results.

[0075] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that the track model of the aircraft is:

[0076]

[0077] Among them, V represents the speed of the aircraft, γ represents the ballistic inclination angle of the aircraft, ψ represents the heading angle of the aircraft, h represents the height of the aircraft, R is the radius of the earth, and a ψ is the turning acceleration, G ψ represents the gravitational perturbation acceleration caused by the non-uniform shape, non-uniform mass distribution and rotation of the Earth, ψ′ is the derivative of ψ, yes The derivative of θ, θ represents the current longitude of the aircraft, and θ′ is the derivative of θ.

[0078] The other steps and parameters are the same as those in the first embodiment.

[0079] According to the aircraft's track model, it can be seen that for the lateral motion of the aircraft, the longitude and latitude, ballistic inclination, heading angle and gravitational perturbation depth are coupled. Compared with studying the lateral motion law directly on the earth's curved surface, it is easier to complete the lateral trajectory design in a plane. Therefore, it is necessary to study the projection scheme that converts the three-dimensional motion problem into a two-dimensional plane for this problem. The commonly used Mercator projection method is used here. Mercator projection can realize the transformation from curved surface to plane, and the coordinates in the projection plane can be expressed as:

[0080]

[0081] in, represents the projection baseline, x and y are the horizontal and vertical coordinates in the projection plane. When , the origin of the coordinates in the projection plane is zero longitude and zero latitude.

[0082] like Figure 1 As shown in the figure, the conventional Mercator projection method considers the uniform spherical earth model and uses zero latitude as the baseline for projection, that is, the projection cylinder is selected based on the equatorial plane, and the projection cylinder is tangent to the earth at this time. Indicates that when When the projection plane is around the current latitude and longitude of the aircraft, it will produce an area deformation S d , then based on the area deformation S d Set up the optimization problem.

[0083] Specific implementation method three: This implementation method is different from specific implementation methods one or two in that the process of establishing the optimization problem is:

[0084] Calculate area deformation about the projection baseline The derivative of

[0085]

[0086] In order to minimize the distortion of the projection, it is necessary to So we need to base it on the latitude of the aircraft and the latitude span for aircraft detection or attack To continuously modify the baseline

[0087] Then the optimization problem is established as:

[0088]

[0089] Among them, u represents the variable to be optimized.

[0090] The other steps and parameters are the same as those in the first or second embodiment.

[0091] The multiple constraints in the present invention refer to constraints and

[0092] Specific implementation method four: Combination Figure 2 This embodiment is different from the first to third embodiments in that the specific process of step 2 is as follows:

[0093] Step 21: Initialize the population size to N and the population to x 1 :

[0094]

[0095] in, and are the projection baselines of the 1st, 2nd, …, Nth individuals in the initialization population respectively;

[0096] Step 22, initialize the number of iterations l = 1;

[0097] Step 23: Determine whether the number of iterations l is less than or equal to l max / 2, l max is the maximum number of iterations;

[0098] If the number of iterations l is less than or equal to l max / 2, then execute step 24;

[0099] Otherwise, execute step 25;

[0100] Step 24: Calculate the fitness function value of each individual in the first generation population (i.e. calculate ), after sorting the fitness function values ​​of each individual in the l-generation population from small to large, the individuals with the top three fitness function values ​​in the l-generation population are recorded as and

[0101] According to and Calculate the bootstrap solution According to x l , and the memoryless matrix y l Get the candidate population z of the lth iteration l , and according to the alternative population z l Get the updated population x l+1 and the updated memoryless matrix y l+1 ;

[0102] Then set l=l+1 and return to step 2 and 3;

[0103] Step 25: Calculate the fitness function value of each individual in the l-th generation population, sort the fitness function values ​​of each individual in the l-th generation population from small to large, and record the individuals with the top two fitness function values ​​in the l-th generation population as and

[0104] According to and x l Get the candidate population z of the lth iteration l , and according to the alternative population z l Get the updated population x l+1 ; Then execute step 26;

[0105] Step 26: Determine whether the current number of iterations is less than l max ;

[0106] If the current number of iterations is less than l max , then set l = l + 1, and return to step 2 and 3;

[0107] If the current number of iterations is equal to l max , then calculate the population x after the last iteration update l+1 The fitness function value of each individual in the equation is calculated, and the individual corresponding to the minimum fitness function value is taken as the final solution.

[0108] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0109] Specific implementation method 5: This implementation method is different from the specific implementation methods 1 to 4 in that the and Calculate the bootstrap solution Specifically:

[0110]

[0111] in, It is a guided solution.

[0112] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0113] Specific implementation method 6: This implementation method is different from the specific implementation methods 1 to 5 in that in step 24, according to x l , and the memoryless matrix y l Get the candidate population z of the lth iteration l , the specific process is:

[0114]

[0115] Among them, y l is the memoryless matrix of the lth iteration; when l = 1, y l =x l ;

[0116]

[0117] in, is the variance, r1 is a random number between [-1,1], and r2 is a random number between [0,1];

[0118]

[0119] Among them, z l is the candidate matrix for the lth iteration.

[0120] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5.

[0121] Specific implementation method 7: This implementation method is different from any one of the specific implementation methods 1 to 6 in that the variance for:

[0122]

[0123] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0124] Specific implementation eight: This implementation differs from one of the specific implementations one to seven in that the l Get the updated population x l+1 , specifically:

[0125]

[0126] in, is based on The calculated fitness function value, is based on The calculated fitness function value;

[0127] Then the updated population x l+1 for:

[0128]

[0129] According to the alternative population z l To update the memoryless matrix y l+1 :

[0130]

[0131] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0132] Specific implementation method 9: This implementation method is different from the specific implementation methods 1 to 8 in that in step 25, according to and x l Get the candidate population z of the lth iteration l , and according to the alternative population z l Get the updated population x l +1 ; The specific process is:

[0133]

[0134] The subscript "mean" indicates the mean value, b1, b2, ..., b N It is a chaotic sequence generated based on random numbers;

[0135] Then update the population x by comparing the fitness function l+1 :

[0136]

[0137] in, is based on The calculated fitness function value, is based on The calculated fitness function value;

[0138]

[0139] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0140] Specific implementation method 10: This implementation method is different from the specific implementation methods 1 to 9 in that the chaotic sequence generated based on random numbers is specifically:

[0141]

[0142] Where a and b1 are random numbers between [0,1].

[0143] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0144] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A dynamic projection method for aircraft multi-constrained trajectories, characterized in that: The method specifically comprises the following steps: Step 1: Establish an optimization problem based on the area deformation generated by the projection plane around the current latitude and longitude of the aircraft; The area deformation produced by the projection plane around the current latitude and longitude of the aircraft is: Among them, S d Indicates the area difference between the projected area and the actual area; Indicates the lower latitude limit of the area around the current latitude and longitude of the aircraft. Indicates the upper latitude limit of the area around the current latitude and longitude of the aircraft. represents the projection baseline, Indicates the current latitude of the aircraft; Step 2: Use the improved exponential distribution optimization algorithm to solve the optimization problem established in step 1, and perform dynamic projection of the track based on the solution results.

2. The method for dynamic projection of aircraft multi-constrained trajectories according to claim 1, characterized in that: The trajectory model of the aircraft is: Among them, V represents the speed of the aircraft, γ represents the ballistic inclination angle of the aircraft, ψ represents the heading angle of the aircraft, h represents the height of the aircraft, R is the radius of the earth, and a ψ is the turning acceleration, G ψ represents the gravitational perturbation acceleration caused by the non-uniform shape, non-uniform mass distribution and rotation of the Earth, ψ′ is the derivative of ψ, yes The derivative of θ, θ represents the current longitude of the aircraft, and θ′ is the derivative of θ.

3. The dynamic projection method for aircraft multi-constraint tracks according to claim 2, characterized in that: The establishment process of the optimization problem is: Calculate area deformation about the projection baseline The derivative of Then the optimization problem is established as: Among them, u represents the variable to be optimized.

4. The method for dynamic projection of aircraft multi-constrained tracks according to claim 3, characterized in that: The specific process of step 2 is as follows: Step 21: Initialize the population size to N and the population to x 1 : in, and are the projection baselines of the 1st, 2nd, …, Nth individuals in the initialization population respectively; Step 22, initialize the number of iterations l = 1; Step 23: Determine whether the number of iterations l is less than or equal to l max / 2, l max is the maximum number of iterations; If the number of iterations l is less than or equal to l max / 2, then execute step 24; Otherwise, execute step 25; Step 24: Calculate the fitness function value of each individual in the l-generation population respectively, sort the fitness function values ​​of each individual in the l-generation population from small to large, and record the individuals with the top three fitness function values ​​in the l-generation population as and According to and Calculate the bootstrap solution According to x l , and the memoryless matrix y l Get the candidate population z of the lth iteration l , and according to the alternative population z l Get the updated population x l+1 and the updated memoryless matrix y l+1 ; Then set l=l+1 and return to step 2 and 3; Step 25: Calculate the fitness function value of each individual in the l-th generation population, sort the fitness function values ​​of each individual in the l-th generation population from small to large, and record the individuals with the top two fitness function values ​​in the l-th generation population as and According to and x l Get the candidate population z of the lth iteration l , and according to the alternative population z l Get the updated population x l+1 ; Then execute step 26; Step 26: Determine whether the current number of iterations is less than l max ; If the current number of iterations is less than l max , then set l = l + 1, and return to step 2 and 3; If the current number of iterations is equal to l max , then calculate the population x after the last iteration update l+1 The fitness function value of each individual in the equation is calculated, and the individual corresponding to the minimum fitness function value is taken as the final solution.

5. The method for dynamic projection of aircraft multi-constrained tracks according to claim 4, characterized in that: The basis and Calculate the bootstrap solution Specifically: in, It is a guided solution.

6. The method for dynamic projection of aircraft multi-constrained tracks according to claim 5, characterized in that: In the step 24, according to x l , and the memoryless matrix y l Get the candidate population z of the lth iteration l , the specific process is: Among them, y l is the memoryless matrix of the lth iteration; in, is the variance, r1 is a random number between [-1,1], and r2 is a random number between [0,1]; Among them, z l is the candidate matrix for the lth iteration.

7. The method for dynamic projection of aircraft multi-constrained tracks according to claim 6, characterized in that: The variance for:

8. The method for dynamic projection of aircraft multi-constrained tracks according to claim 7, characterized in that: According to the alternative population z l Get the updated population x l+1 , specifically: in, is based on The calculated fitness function value, is based on The calculated fitness function value; Then the updated population x l+1 for: According to the alternative population z l To update the memoryless matrix y l+1 :

9. The method for dynamic projection of aircraft multi-constrained tracks according to claim 8, characterized in that: In the step 25, according to and x l Get the candidate population z of the lth iteration l , and according to the alternative population z l Get the updated population x l+1 ; The specific process is: The subscript "mean" indicates the mean value, b1, b2, ..., b N It is a chaotic sequence generated based on random numbers; Then update the population x by comparing the fitness function l+1 : in, is based on The calculated fitness function value, is based on The calculated fitness function value; 10. The method for dynamic projection of aircraft multi-constrained tracks according to claim 9, characterized in that: The chaotic sequence generated based on random numbers is specifically: Where a and b1 are random numbers between [0,1].

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