Dynamic projection method for multi-constraint aircraft trajectories

Abstract

This invention relates to a dynamic projection method for multi-constraint aircraft tracks, belonging to the field of aircraft track planning. It addresses the problem of existing methods failing to consider the impact of the Earth's non-uniform shape on track planning, leading to significant projection distortion from non-uniform surface surfaces to the track planning plane. This invention establishes an optimization problem based on the area deformation of the projection plane around the aircraft's current latitude and longitude. Then, it employs an exponential distribution optimization algorithm based on chaotic random sequences to dynamically solve the optimization problem and obtain the optimal projection baseline. Based on the solved projection baseline, a projection model from the non-uniform surface surface to the track planning plane is established. The projection scheme can be dynamically adjusted according to the aircraft's actual position, minimizing projection distortion from the non-uniform surface surface to the track planning plane. This method can be applied to the dynamic projection of aircraft tracks.

Description

Technical Field

[0001] This invention belongs to the field of aircraft trajectory planning, and specifically relates to a dynamic projection method for multi-constraint aircraft trajectories. Background Technology

[0002] Aircraft designed for long-distance unmanned transportation or environmental monitoring possess advantages such as high speed, long range, wide coverage, versatility, and modularity. These aircraft feature powered propulsion systems and high lift-to-drag ratios, enabling them to fly hundreds of kilometers under high-speed airborne deployment conditions. In long-distance, high-speed flight, conventional planar coordinate systems cannot be used; the impact of the Earth's non-uniform shape on trajectory planning must be considered, including projection distortion from non-uniform surface curvature to the trajectory planning plane. However, existing methods primarily operate within conventional planar coordinate systems or preset projection planes, failing to consider the Earth's non-uniform shape or curvature under long-distance flight conditions, and neglecting dynamic adjustments to projection baselines or projection schemes. This results in significant projection distortion from non-uniform surface curvature to the trajectory planning plane and insufficient adaptability to varying flight airspace and latitude / longitude ranges.

[0003] In summary, existing methods do not consider the impact of the Earth's non-uniform shape on trajectory planning, resulting in significant projection distortion from the non-uniform surface to the trajectory planning plane. Therefore, it is essential 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 this invention is to address the problem that existing methods do not consider the impact of the Earth's non-uniform shape on trajectory planning, resulting in large projection distortion from the non-uniform surface to the trajectory planning plane. This invention proposes a dynamic projection method for aircraft with multiple constraints by dynamically adjusting the projection baseline.

[0005] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a dynamic projection method for multi-constraint flight paths of aircraft, the method specifically including the following steps:

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

[0007] The area distortion of the projection plane around the aircraft's current latitude and longitude is:

[0008]

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

[0010] Step 2: Solve the optimization problem established in Step 1 using an improved exponential distribution optimization algorithm, and perform dynamic projection of the trajectory based on the solution results.

[0011] Furthermore, the trajectory model of the aircraft is as follows:

[0012]

[0013] Where V represents the aircraft's speed, γ represents the aircraft's ballistic tilt angle, ψ represents the aircraft's heading angle, h represents the aircraft's altitude, R is the Earth's radius, and a ψ For steering acceleration, G ψ Let ψ' represent the gravitational perturbation acceleration caused by the Earth's non-uniform shape, non-uniform mass distribution, and rotation, where ψ′ is the derivative of ψ. yes The derivative of θ, where θ represents the aircraft's current longitude, and θ′ is the derivative of θ.

[0014] Furthermore, the process of establishing the optimization problem is as follows:

[0015] Calculate area deformation with respect to the projected baseline derivative

[0016]

[0017] The optimization problem is then established as follows:

[0018]

[0019] Where u represents the variable to be optimized.

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

[0021] Step 2: Initialize the population size to N and the population size to x. 1 :

[0022]

[0023] in, and These are the projected baselines of the 1st, 2nd, ..., Nth individuals in the initial population;

[0024] Step 22: Initialize the number of iterations l = 1;

[0025] Steps 2 and 3: Determine if the iteration number l is less than or equal to l max / 2,lmax It is the maximum number of iterations;

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

[0027] Otherwise, proceed to step two five;

[0028] Step 2.4: Calculate the fitness function value for each individual in the generation 1 population. After sorting the fitness function values ​​of each individual in the generation 1 population from smallest to largest, denote the top three individuals in the generation 1 population as follows: and

[0029] Then according to and Calculate the guided solution According to x l , and memoryless matrix y l The candidate population z for the l-th iteration is obtained. l And based on the candidate population z l The updated population x l+1 and the updated memoryless matrix y l+1 ;

[0030] Let l = l + 1 again, and return to steps two and three;

[0031] Step 2.5: Calculate the fitness function value for each individual in the generation 1 population. After sorting the fitness function values ​​of each individual in the generation 1 population from smallest to largest, denote the two individuals with the highest fitness function values ​​in the generation 1 population as follows: and

[0032] Then according to and x l The candidate population z for the l-th iteration is obtained l And based on the candidate population z l The updated population x l+1 Then proceed to step two six;

[0033] Step 26: Determine if the current iteration number is less than 1. max ;

[0034] If the current iteration number is less than l max Then let l = l + 1, and return to execute steps two and three;

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

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

[0037]

[0038] in, It is a guiding solution.

[0039] Furthermore, in step two or four, according to x l , and memoryless matrix y l The candidate population z for the l-th iteration is obtained l The specific process is as follows:

[0040]

[0041] Among them, y l It is the memoryless matrix of the l-th iteration;

[0042]

[0043] in, Let r1 be the variance, r2 be a random number between [-1, 1], and r3 be a random number between [0, 1].

[0044]

[0045] Among them, z l It is the candidate matrix for the l-th iteration.

[0046] Furthermore, the variance for:

[0047]

[0048] Furthermore, the step of basing the data on the candidate population z l The updated population x l+1 Specifically:

[0049]

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

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

[0052]

[0053] Based on the candidate population z l To update the memoryless matrix y l+1 :

[0054]

[0055] Furthermore, in step two five, according to and x l The candidate population z for the l-th iteration is obtained l And based on the candidate population z l The updated population x l+1 The specific process is as follows:

[0056]

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

[0058] Then the population x is updated by comparing the fitness function. l+1 :

[0059]

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

[0061]

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

[0063]

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

[0065] The beneficial effects of this invention are:

[0066] This invention addresses the trajectory planning problem under long-range flight conditions for aircraft. It proposes an exponential distribution optimization algorithm based on chaotic random sequences to dynamically solve for the optimal projection baseline. Then, based on the solved projection baseline, a projection model from the non-uniform surface to the trajectory planning plane is established. The projection scheme can be dynamically modified according to the actual position of the aircraft to minimize the projection distortion from the non-uniform surface to the trajectory planning plane. Attached Figure Description

[0067] Figure 1 It is an improved planar dynamic projection scheme for trajectory planning;

[0068] Figure 2 This is a flowchart of the improved exponential distribution optimization algorithm. Detailed Implementation

[0069] Specific Implementation Method 1: The dynamic projection method for multi-constraint flight paths of aircraft described in this implementation method specifically includes the following steps:

[0070] Step 1: Based on the projection plane around the aircraft's current latitude and longitude (in this invention, "around the current latitude and longitude" refers to a longitude of θ and a latitude span of θ), The optimization problem is established based on the area deformation generated within the region.

[0071] The area distortion of the projection plane around the aircraft's current latitude and longitude is:

[0072]

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

[0074] Step 2: Solve the optimization problem established in Step 1 using an improved exponential distribution optimization algorithm, and perform dynamic projection of the trajectory based on the solution results.

[0075] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the aircraft's trajectory model is as follows:

[0076]

[0077] Where V represents the aircraft's speed, γ represents the aircraft's ballistic tilt angle, ψ represents the aircraft's heading angle, h represents the aircraft's altitude, R is the Earth's radius, and a ψ For steering acceleration, G ψ Let ψ' represent the gravitational perturbation acceleration caused by the Earth's non-uniform shape, non-uniform mass distribution, and rotation, where ψ′ is the derivative of ψ. yes The derivative of θ, where θ represents the aircraft's current longitude, and θ′ is the derivative of θ.

[0078] The other steps and parameters are the same as in Specific Implementation Method 1.

[0079] Based on the aircraft's trajectory model, it can be seen that for the lateral motion of an aircraft, latitude and longitude, ballistic tilt angle, heading angle, and gravitational perturbation depth are coupled. Compared to studying the laws of lateral motion directly on the Earth's curved surface, designing the lateral trajectory in a plane is simpler. Therefore, it is necessary to study a projection scheme that transforms the three-dimensional motion problem into a two-dimensional plane representation. The commonly used Mercator projection method is adopted here. The Mercator projection can realize the transformation from a curved surface to a plane, and the coordinates in the projection plane can be expressed as:

[0080]

[0081] in, Represents the projection baseline, where x and y are the horizontal and vertical coordinates in the projection plane, when At that time, the origin of the coordinates in the projection plane is at zero longitude and zero latitude.

[0082] like Figure 1 As shown, the conventional Mercator projection method considers a 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 in this case, the projection cylinder is tangent to the Earth. The projection baseline is denoted by latitude. It means that when At that time, the projection plane will produce an area deformation S around the aircraft's current latitude and longitude. d Based on the area deformation S d Establish an optimization problem.

[0083] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that the process of establishing the optimization problem is as follows:

[0084] Calculate area deformation with respect to the projected baseline derivative

[0085]

[0086] To minimize projection distortion, it is necessary to make Therefore, it is necessary to consider the latitude of the aircraft. and the latitudinal span of aircraft detection or attack To continuously modify the baseline

[0087] The optimization problem is then established as follows:

[0088]

[0089] Where u represents the variable to be optimized.

[0090] Other steps and parameters are the same as in specific implementation method one or two.

[0091] The multiple constraints in this invention refer to constraints. and

[0092] Specific implementation method four: Combination Figure 2 This embodiment is described below. The difference between this embodiment and one of the specific embodiments one to three is that the specific process of step two is as follows:

[0093] Step 2: Initialize the population size to N and the population size to x. 1 :

[0094]

[0095] in, and These are the projected baselines of the 1st, 2nd, ..., Nth individuals in the initial population;

[0096] Step 22: Initialize the number of iterations l = 1;

[0097] Steps 2 and 3: Determine if the iteration number l is less than or equal to l max / 2,l max It is the maximum number of iterations;

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

[0099] Otherwise, proceed to step two five;

[0100] Step 2.4: Calculate the fitness function value for each individual in the 1st generation population (i.e., calculate...). After sorting the fitness function values ​​of each individual in the l-th generation population from smallest to largest, the top three individuals in terms of fitness function value are denoted as follows: and

[0101] Then according to and Calculate the guided solution According to x l , and memoryless matrix y l The candidate population z for the l-th iteration is obtained l And based on the candidate population z l The updated population x l+1 and the updated memoryless matrix y l+1 ;

[0102] Let l = l + 1 again, and return to steps two and three;

[0103] Step 2.5: Calculate the fitness function value for each individual in the generation 1 population. After sorting the fitness function values ​​of each individual in the generation 1 population from smallest to largest, denote the two individuals with the highest fitness function values ​​in the generation 1 population as follows: and

[0104] Then according to and x l The candidate population z for the l-th iteration is obtained l And based on the candidate population z l The updated population x l+1 Then proceed to step two six;

[0105] Step 26: Determine if the current iteration number is less than 1. max ;

[0106] If the current iteration number is less than l max Then let l = l + 1, and return to execute steps two and three;

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

[0108] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0109] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the method described is based on... and Calculate the guided solution Specifically:

[0110]

[0111] in, It is a guiding solution.

[0112] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0113] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that, in step two or four, according to x... l , and memoryless matrix y l The candidate population z for the l-th iteration is obtained l The specific process is as follows:

[0114]

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

[0116]

[0117] in, Let r1 be the variance, r2 be a random number between [-1, 1], and r3 be a random number between [0, 1].

[0118]

[0119] Among them, z l It is the candidate matrix for the l-th iteration.

[0120] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0121] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that the variance... for:

[0122]

[0123] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0124] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One to Seven in that the step of selecting candidate population z... l The updated population x l+1 Specifically:

[0125]

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

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

[0128]

[0129] Based on the candidate population z l To update the memoryless matrix y l+1 :

[0130]

[0131] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0132] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One to Eight in that, in step two-five, according to... and x l The candidate population z for the l-th iteration is obtained l And based on the candidate population z l The updated population x l +1 The specific process is as follows:

[0133]

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

[0135] Then the population x is updated by comparing the fitness function. l+1 :

[0136]

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

[0138]

[0139] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0140] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One to Nine in that the chaotic sequence generated based on random numbers is specifically as follows:

[0141]

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

[0143] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0144] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A dynamic projection method for multi-constraint flight paths of aircraft, characterized in that, The method specifically includes the following steps: Step 1: Establish an optimization problem based on the area deformation of the projected plane around the aircraft's current latitude and longitude; The area distortion of the projection plane around the aircraft's current latitude and longitude is: in, This represents the area difference between the projected area and the actual area; This indicates the lower limit of the latitude of the area surrounding the aircraft's current latitude and longitude. This indicates the upper limit of latitude of the area surrounding the aircraft's current latitude and longitude. Indicates the projected baseline. Indicates the aircraft's current latitude; The process of establishing the optimization problem is as follows: Calculate area deformation with respect to the projected baseline derivative : The optimization problem is then established as follows: in, Indicates the variable to be optimized; Step 2: Solve the optimization problem established in Step 1 using an improved exponential distribution optimization algorithm, and perform dynamic projection of the trajectory based on the solution results; The specific process of step two is as follows: Step 2: Initialize the population size to N, and initialize the population as follows: : in, , and These are the projected baselines of the 1st, 2nd, ..., Nth individuals in the initial population; Step 22: Initialize the number of iterations ; Steps 2 and 3: Determine the number of iterations Is it less than or equal to? , It is the maximum number of iterations; If the number of iterations Less than or equal to Then proceed to steps two and four; Otherwise, proceed to step two five; Steps 2 and 4: Calculate the first... The fitness function value of each individual in the population for the th generation. After sorting the fitness function values ​​of each individual in the population from smallest to largest, the [number]th [generation] [individual] [is then] [the next generation]. Individuals whose fitness function values ​​rank in the top three of the population are denoted as _____. , and ; Then according to , and Calculate the guided solution ,according to , and memoryless matrix Get the first The candidate population for the next iteration And based on the candidate population The population that has been updated and the updated memoryless matrix ; Again Return to steps two and three; Step 25: Calculate the number of... The fitness function value of each individual in the population for the th generation. After sorting the fitness function values ​​of each individual in the population from smallest to largest, the [number]th [generation] [individual] [is then] [the next generation]. The individuals whose fitness function values ​​rank in the top two of the population are denoted as _____. and ; Then according to , and Get the first The candidate population for the next iteration And based on the candidate population The population that has been updated Then proceed to step two six; Step 26: Determine if the current iteration number is less than [a certain number]. ; If the current iteration number is less than Then let Return to steps two and three; If the current iteration number equals Then calculate the population after the last iteration update. The fitness function value of each individual is calculated, and the individual with the smallest fitness function value is taken as the final solution.

2. The dynamic projection method for multi-constraint flight paths of aircraft according to claim 1, characterized in that, The trajectory model of the aircraft is as follows: in, Indicates the speed of the aircraft. Indicates the trajectory inclination angle of an aircraft. Indicates the heading angle of the aircraft. This indicates the aircraft's altitude, where R is the Earth's radius. For steering acceleration, This represents the gravitational perturbation acceleration caused by the Earth's non-uniform shape, non-uniform mass distribution, and rotation. yes The derivative of yes The derivative of Indicates the aircraft's current longitude. yes The derivative of .

3. The dynamic projection method for multi-constraint flight paths of aircraft according to claim 2, characterized in that, According to , and Calculate the guided solution Specifically: in, It is a guiding solution.

4. The dynamic projection method for multi-constraint flight paths of aircraft according to claim 3, characterized in that, In step two or four, according to , and memoryless matrix Get the first The candidate population for the next iteration The specific process is as follows: in, It is the first The memoryless matrix of the next iteration; in, For variance, A random number between [-1, 1] A random number between [0, 1]; in, It is the first The candidate matrix for the next iteration.

5. The dynamic projection method for multi-constraint flight paths of aircraft according to claim 4, characterized in that, The variance for: 。 6. The dynamic projection method for multi-constraint flight paths of aircraft according to claim 5, characterized in that, The above is based on the candidate population The population that has been updated Specifically: in, It is based on The calculated fitness function value, It is based on The calculated fitness function value; Then the updated population for: Based on the candidate population To update the memoryless matrix : 。 7. The dynamic projection method for multi-constraint flight paths of aircraft according to claim 6, characterized in that, In step two five, according to , and Get the first The candidate population for the next iteration And based on the candidate population The population that has been updated The specific process is as follows: Where b1, b2,…, b N It is a chaotic sequence generated based on random numbers; The population is then updated by comparing the fitness function. : in, It is based on The calculated fitness function value, It is based on The calculated fitness function value; 。 8. The dynamic projection method for multi-constraint flight paths of aircraft according to claim 7, characterized in that, The chaotic sequence generated based on random numbers is specifically: in, and It is a random number between [0, 1].

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