Trajectory planning method for aircraft cluster based on inertial navigation

Abstract

The application relates to a kind of trajectory planning methods of aircraft cluster based on inertial navigation, which comprises: for each aircraft in the aircraft cluster, according to the parameter set of the current discrete step of the aircraft, the trajectory efficiency of the current discrete step of the aircraft is constructed;For each aircraft, according to the trajectory efficiency of the current discrete step of the aircraft, the cost function of the next discrete step of the current discrete step of the aircraft, the discount factor, the cost function of the current discrete step of the aircraft is constructed;According to the cost function of the current discrete step of each aircraft, a total cost function is constructed;With the function value of the total cost function as the target, the discrete three-dimensional acceleration set of each aircraft is solved.

Description

Technical Field

[0001] This application belongs to the field of aircraft navigation technology, and specifically relates to a trajectory planning method for aircraft swarms based on inertial navigation. Background Technology

[0002] With the development of the low-altitude economy, scenarios involving multiple aircraft working together, such as multiple aircraft performing tasks simultaneously, are becoming increasingly common. How to plan the flight paths of multiple aircraft has become a technical problem that needs to be solved. Summary of the Invention

[0003] This application provides a trajectory planning method for aircraft clusters based on inertial navigation, which is used to solve the problem of how to plan the trajectories of multiple aircraft.

[0004] This application provides a trajectory planning method for aircraft swarms based on inertial navigation, the method comprising:

[0005] For each aircraft in the aircraft cluster, the trajectory efficiency of the aircraft at the current distance is constructed based on the parameter set of the aircraft at the current distance. The parameter set of the aircraft at the current distance includes: the time efficiency parameter of the aircraft at the current distance, the obstacle avoidance parameter of the aircraft within the city at the current distance, and the collision avoidance parameter between the aircraft at the current distance.

[0006] For each aircraft, a cost function for the aircraft in the current departure walk is constructed based on the aircraft's trajectory performance in the current departure walk, the cost function of the aircraft in the next departure walk, and the discount factor.

[0007] Construct the total cost function based on the cost function of each aircraft at the current distance walk;

[0008] With the objective of minimizing the function value of the total cost function, the discrete three-dimensional acceleration set of each aircraft is solved, wherein the discrete three-dimensional acceleration set of the aircraft includes: the discrete three-dimensional acceleration of the aircraft in the current departure walk, the discrete three-dimensional acceleration of the aircraft in the last departure walk, and the discrete three-dimensional acceleration of the aircraft in each intermediate departure walk between the current departure walk and the last departure walk.

[0009] In one possible implementation, the trajectory performance of the aircraft at the current distance walk is constructed based on the parameter set of the aircraft at the current distance walk, including:

[0010] Based on the parameter set of the aircraft in the current departure walk and the weight of each parameter in the parameter set of the aircraft in the current departure walk, the trajectory performance of the aircraft in the current departure walk is constructed, where the trajectory performance of the aircraft in the current departure walk is the weighted sum of all parameters in the parameter set of the aircraft in the current departure walk.

[0011] In one possible implementation, the time efficiency parameter for an aircraft at its current distance from the walk is the longest total distance traveled by the aircraft divided by the total distance traveled by the aircraft cluster.

[0012] In one possible implementation, when the distance between the aircraft and any obstacle at the current distance from the walk is greater than the safe distance, the obstacle avoidance parameter of the aircraft at the current distance from the walk is 0; when the distance between the aircraft and at least one obstacle at the current distance from the walk is not greater than the safe distance, the obstacle avoidance parameter of the aircraft at the current distance from the walk is determined based on the shortest distance from the obstacle corresponding to each aircraft at the current distance from the walk, wherein the shortest distance from the obstacle corresponding to the target aircraft at the current distance from the walk is the shortest distance included in the set of distances between each obstacle at the current distance from the walk and the target aircraft, and the target aircraft is any aircraft.

[0013] In one possible implementation, when the distance between the aircraft and at least one obstacle at the current distance from the walk is not greater than a safe distance, the obstacle avoidance parameter of the aircraft at the current distance from the walk is the longest distance in the set of shortest distances from obstacles corresponding to each aircraft at the current distance from the walk, divided by the shortest distance from obstacles corresponding to the aircraft at the current distance from the walk.

[0014] In one possible implementation, when the distance between the currently disembarking aircraft and any other aircraft is greater than a safe distance, the collision avoidance parameter of the aircraft among the currently disembarking aircraft is 0; when the distance between the aircraft and at least one other aircraft among the currently disembarking aircraft is not greater than a safe distance, the collision avoidance parameter of the aircraft among the currently disembarking aircraft is determined based on the shortest distance among the aircraft corresponding to each of the currently disembarking aircraft, wherein the shortest distance among the aircraft corresponding to the target aircraft among the currently disembarking aircraft is the shortest distance included in the set of distances between the target aircraft among the currently disembarking aircraft and each other aircraft.

[0015] In one possible implementation, when the distance between an aircraft and at least one other aircraft currently at the walk distance is not greater than a safe distance, the collision avoidance parameter of an aircraft currently at the walk distance is the longest distance in the set of shortest distances between aircraft corresponding to each of the aircraft currently at the walk distance, divided by the shortest distance between aircraft corresponding to the aircraft currently at the walk distance.

[0016] In one possible implementation, the cost function of the aircraft in the current departure walk is the sum of the product of the cost function of the aircraft in the next departure walk and the discount factor, and the trajectory performance of the aircraft in the current departure walk.

[0017] In one possible implementation, the total cost function is the sum of the cost functions of each aircraft at the current departure walk.

[0018] In one possible implementation, the discrete three-dimensional acceleration set for each aircraft is solved by minimizing the function value of the total cost function, including:

[0019] The snow ablation optimization algorithm is used to solve for the discrete three-dimensional acceleration set of each aircraft by minimizing the function value of the total cost function.

[0020] Beneficial effects:

[0021] This system enables the planning of flight paths for multiple aircraft, i.e., aircraft clusters. When planning the flight paths of an aircraft cluster, it considers multiple aspects of each aircraft's information across multiple departure walks (the current departure walk and the next departure walk), including time efficiency parameters related to cost, obstacle avoidance parameters within the city to ensure aircraft safety, and collision avoidance parameters between aircraft to ensure safety. This comprehensively considers the factors affecting the cost and safety of the aircraft cluster's flight path, enabling the planning of flight paths for aircraft clusters with lower costs and higher safety. It can also address dynamic obstacle avoidance and collaborative planning for multiple aircraft in urban environments, considering constraints such as path, obstacle avoidance, and collision avoidance. With the optimization objective of maximizing task timeliness, a real-time dynamic obstacle avoidance planning model for multi-aircraft clusters is established. The snow ablation optimization algorithm is used to solve the collaborative planning problem, achieving collaborative dynamic planning of low-altitude flight paths under multiple constraints. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of this specification or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the embodiments of this specification. For those skilled in the art, other drawings can be obtained based on these drawings.

[0023] Figure 1 This is a flowchart illustrating the trajectory planning method for an aircraft cluster based on inertial navigation provided in an embodiment of this application. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. It should be noted that, unless otherwise specified, the implementation methods and features in the implementation methods in this disclosure can be combined, separated, interchanged, and / or rearranged. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0025] The terminology used herein is for the purpose of describing particular embodiments and is not intended to be limiting. As used herein, unless the context clearly indicates otherwise, the singular forms “a” and “the” are intended to include the plural forms as well. Furthermore, when the terms “comprising” and / or “including” and variations thereof are used in this specification, it indicates the presence of the stated features, integrals, steps, operations, parts, components, and / or groups thereof, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, parts, components, and / or groups thereof. It should also be noted that, as used herein, the terms “substantially,” “about,” and other similar terms are used as approximate terms rather than as terms of degree, thus explaining the inherent biases in measurements, calculated values, and / or provided values ​​that would be recognized by one of ordinary skill in the art.

[0026] refer to Figure 1 The diagram illustrates a flowchart of the trajectory planning method for an aircraft cluster based on inertial navigation provided in an embodiment of this application.

[0027] The trajectory planning method for aircraft clusters based on inertial navigation provided in this application includes steps S101-S104.

[0028] In step S101, for each aircraft in the aircraft cluster, the trajectory efficiency of the aircraft in the current distance walk is constructed based on the parameter set of the aircraft in the current distance walk. The parameter set of the aircraft in the current distance walk includes: the time efficiency parameter of the aircraft in the current distance walk, the obstacle avoidance parameter of the aircraft in the current distance walk within the city, and the collision avoidance parameter of the aircraft in the current distance walk.

[0029] In step S102, for each aircraft, a cost function for the aircraft in the current departure walk is constructed based on the aircraft's trajectory performance in the current departure walk, the cost function of the aircraft in the next departure walk in the current departure walk, and the discount factor.

[0030] In step S103, a total cost function is constructed based on the cost function of each aircraft at the current distance walk.

[0031] In step S104, with the objective of minimizing the function value of the total cost function, the discrete three-dimensional acceleration set of each aircraft is solved. The discrete three-dimensional acceleration set of the aircraft includes: the discrete three-dimensional acceleration of the aircraft in the current departure walk, the discrete three-dimensional acceleration of the aircraft in the last departure walk, and the discrete three-dimensional acceleration of the aircraft in each intermediate departure walk between the current departure walk and the last departure walk.

[0032] The discrete three-dimensional acceleration of aircraft i at a distance from walk i includes: the acceleration of aircraft i in the x-direction at a distance from walk i, the acceleration of aircraft i in the y-direction at a distance from walk i, and the acceleration of aircraft i in the z-direction at a distance from walk i. The x-direction refers to the direction of the x-axis in the corresponding coordinate system, the y-direction refers to the direction of the y-axis in the corresponding coordinate system, and the z-direction refers to the direction of the z-axis in the corresponding coordinate system. The corresponding coordinate system can be the world coordinate system.

[0033] Where aircraft i can be any aircraft in the aircraft cluster. Distance i can be any distance from the set.

[0034] In the embodiments of this application, "off-walk" can be understood as: a discretized time step. For an aircraft, the aircraft's current off-walk position is given.

[0035] For aircraft i and distance m, the position of aircraft i at distance m can be determined based on the position of aircraft i at the previous distance m (distance m-1) and the discrete three-dimensional acceleration of aircraft i at the previous distance m (distance m-1).

[0036] Among them, the distance m can be any distance except the last distance.

[0037] As an example, the position of aircraft i at distance m can be determined using discrete equations, based on the position of aircraft i at the previous distance m (distance m-1) and the discrete three-dimensional acceleration of aircraft i at the previous distance m (distance m-1). Discrete equations are obtained by discretizing the aircraft's dynamic model.

[0038] As an example, the dynamic model of an aircraft is as follows:

[0039]

[0040] in, V , c , ψ These are, respectively, the aircraft's speed, trajectory inclination angle, and trajectory deviation angle. x , y , zRepresents the position coordinates of an aircraft in three-dimensional space, using subscripts. i Indicates the aircraft number, t Indicates time. a x , a y , a z Indicates that the aircraft is in x , y , z Acceleration in the direction of acceleration is a controlled variable.

[0041] In this embodiment, the difference between the last step away from the current step and the previous step away is a preset number of iteration steps.

[0042] The current distance from the set point is denoted as distance from set point k. Starting from set point k, iterate n steps backward, where n is the number of iterations. The last distance from the set point is denoted as distance from set point k+n.

[0043] In step S104, the discrete three-dimensional accelerations at distance k, distance k+1, and distance k+n are solved.

[0044] In the embodiments of this application, the position of each aircraft in the current departure step in the aircraft cluster is given. After determining the discrete three-dimensional acceleration set of each aircraft, the position of each aircraft in each departure step in the set including the last departure step, the current departure step and each intermediate departure step between the last departure step can be determined according to the position of each aircraft in the current departure step in the aircraft cluster and the discrete three-dimensional acceleration set of each aircraft.

[0045] For aircraft i, the position of aircraft i in each of the sets of intermediate departure steps, including the last departure step, the current departure step, and the last departure step, can be determined based on the position of aircraft i in the current departure step and the discrete three-dimensional acceleration set of aircraft i.

[0046] In this embodiment of the application, after determining the position of each aircraft in each departure step of the departure step set, the trajectory of each aircraft can be determined based on the position of each aircraft in each departure step of the set including the last departure step, the current departure step and each intermediate departure step between the last departure step.

[0047] For aircraft i, the trajectory of aircraft i is determined based on the position of aircraft i in each of the sets of intermediate departure steps, including the last departure step, the current departure step and the last departure step.

[0048] For aircraft i, the starting point of aircraft i's trajectory can be: aircraft i at its current position away from the walk, and the ending point of aircraft i can be: aircraft i at its last position away from the walk.

[0049] Here, aircraft i can be any aircraft in the aircraft cluster.

[0050] For aircraft i, the position of each departure step in the set including the current departure step, the last departure step, and each intermediate departure step can be respectively used as a waypoint on the track of aircraft i. When aircraft i flies along the track, it starts from the first waypoint, i.e., the position of the current departure step, and arrives at each of the other waypoints on the track of aircraft i in sequence.

[0051] In this embodiment of the application, any related technology algorithm that plans a trajectory based on given waypoints can be used to generate the trajectory of aircraft i based on all waypoints of aircraft i.

[0052] As an example, the straight line between every two adjacent waypoints on an aircraft's track is taken as a subtrack of the aircraft, and all the subtracks of the aircraft constitute the aircraft's track.

[0053] In the embodiments of this application, track performance F Considering time efficiency F time Obstacle avoidance in the city F obstacle Collision avoidance between aircraft F crash .

[0054] In one possible implementation, constructing the trajectory performance of aircraft i in the current departure walk, based on the parameter set of aircraft i in the current departure walk, includes: constructing the trajectory performance of aircraft i in the current departure walk based on the parameter set of aircraft i in the current departure walk and the weight of each parameter in the parameter set of aircraft i in the current departure walk, wherein the trajectory performance of aircraft i in the current departure walk is a weighted sum of all parameters in the parameter set of aircraft i in the current departure walk.

[0055] The flight performance F of aircraft i at the current distance from the walk is expressed as:

[0056]

[0057] in, a 1, a 2, a 3 indicates weight. F time This represents the time efficiency parameter of aircraft i at the current distance from the walk. F obstacleThis represents the obstacle avoidance parameters for aircraft i within the current distance of the city where it is currently walking. F crash This represents the collision avoidance parameters for aircraft i at the current distance from other aircraft.

[0058] Here, aircraft i can be any aircraft in the aircraft cluster.

[0059] In this embodiment of the application, time efficiency can be improved. F time Defined as the total distance traveled by the aircraft, and normalized. Time efficiency is related to the aircraft's distance; for example, if an aircraft avoids a building, it will increase the distance traveled, while shortening the distance may result in a collision with the building.

[0060] In one possible implementation, the time efficiency parameter of aircraft i at the current distance from the walk is the longest total distance of aircraft i divided by the total distance of the aircraft cluster.

[0061] The time efficiency parameter of aircraft i at the current departure time is expressed as:

[0062]

[0063] in, F time,i This represents the time efficiency parameter of aircraft i at the current distance from the walk. L i This represents the total distance traveled by aircraft i. This represents the longest total distance traveled in the aircraft cluster.

[0064] The total distance traveled by an aircraft cluster refers to the total distance traveled by each aircraft in the cluster.

[0065] The total distance traveled by aircraft i can represent the total number of kilometers that aircraft i has flown. The total distance traveled by aircraft i can also refer to the distance traveled between the current time step and the last time step.

[0066] In one possible implementation, the time efficiency parameter of aircraft i at distance j can be: the longest total distance of aircraft i divided by the total distance of the aircraft cluster.

[0067] Here, the distance step j can be any distance step in the set that includes each intermediate distance step and the last distance step.

[0068] Here, aircraft i can be any aircraft in the aircraft cluster.

[0069] In one possible implementation, when the distance between aircraft i and any obstacle at the current distance from the walking aircraft is greater than the safe distance, the obstacle avoidance parameter of aircraft i at the current distance from the walking aircraft is 0; when the distance between aircraft i and at least one obstacle at the current distance from the walking aircraft is not greater than the safe distance, the obstacle avoidance parameter of aircraft i at the current distance from the walking aircraft is determined based on the shortest distance from each obstacle corresponding to the walking aircraft at the current distance from the walking aircraft, wherein the shortest distance from the obstacle corresponding to the target aircraft at the current distance from the walking aircraft is the shortest distance included in the set of distances between each obstacle at the current distance from the walking aircraft and the target aircraft, and the target aircraft is any aircraft.

[0070] In one possible implementation, when the distance between aircraft i and at least one obstacle currently in the walk is not greater than a safe distance, the obstacle avoidance parameter of aircraft i in the city currently in the walk is the longest distance included in the set of shortest distances between aircraft i and obstacles currently in the walk, divided by the shortest distance between aircraft i and obstacles currently in the walk.

[0071] When the distance between aircraft i and at least one obstacle in the current distance from the walk is not greater than the safe distance, the obstacle avoidance parameters of aircraft i within the city in the current distance from the walk can be expressed as:

[0072]

[0073] This represents the obstacle avoidance parameters of aircraft i within the city limits when the distance between the aircraft and at least one obstacle at the current distance from the walkway is no greater than the safe distance. This represents the longest distance included in the set of shortest distances from the current distance to the obstacle corresponding to each of the aircraft being walked. This represents the shortest distance from the obstacle corresponding to the current walking aircraft i.

[0074] S i,m Indicates aircraft i To the obstacle m The safe distance between the aircraft and the center of the obstacle is... R safe ,but S i,m < R safe This indicates that the aircraft has been traversed; the traversal time indicates the aircraft. i It intersects with at least one obstacle. min ( S i,m ) indicates aircraft i The minimum distance to all obstacles is fixed. i After that m The index represents the worst-case scenario in the planning. The larger the size, the safer it is. It is to find the minimum ( ) for all aircraft. S i,m The maximum value found after that is a normalization process. F obstacle,j When the minimum value is taken, the aircraft i The furthest from the obstacle.

[0075] If aircraft i No obstacle was crossed. S im > R safe This indicates that the aircraft did not cross the border. i It does not intersect with any obstacles. .

[0076] In one possible implementation, when the distance between aircraft i and any obstacle from walk j is greater than the safe distance, the obstacle avoidance parameter of aircraft i within the city from walk j is 0; when the distance between aircraft i and at least one obstacle from walk j is not greater than the safe distance, the obstacle avoidance parameter of aircraft i within the city from walk j is the longest distance included in the set of shortest distances from each aircraft to walk j divided by the shortest distance from the obstacle corresponding to aircraft i from walk j.

[0077] Here, the distance step j can be any distance step in the set that includes each intermediate distance step and the last distance step.

[0078] Here, aircraft i can be any aircraft in the aircraft cluster.

[0079] In one possible implementation, when the distance between the currently walking aircraft i and any other aircraft is greater than a safe distance, the collision avoidance parameter of aircraft i among the currently walking aircraft is 0; when the distance between aircraft i and at least one other aircraft among the currently walking aircraft is not greater than a safe distance, the collision avoidance parameter of aircraft i among the currently walking aircraft is determined based on the shortest distance among the aircraft corresponding to each aircraft among the currently walking aircraft, wherein the shortest distance among the aircraft corresponding to the currently walking target aircraft is the shortest distance included in the set of distances between the currently walking target aircraft and each other aircraft.

[0080] In one possible implementation, when the current distance from at least one other aircraft walking with aircraft i is not greater than a safe distance, the collision avoidance parameter of aircraft i at the current distance from walking aircraft is the longest distance included in the set of shortest distances between aircraft corresponding to each walking aircraft at the current distance, divided by the shortest distance between aircraft corresponding to walking aircraft i at the current distance.

[0081] It should be noted that "other aircraft" is relative to a specific aircraft. For aircraft i, "other aircraft" refers to all aircraft in the aircraft cluster other than aircraft i.

[0082] When the current distance from at least one other aircraft to aircraft i is not greater than the safe distance, the collision avoidance parameters of aircraft i among the aircraft currently in the walk can be expressed as:

[0083]

[0084] This represents the collision avoidance parameters for aircraft i when the current distance from at least one other aircraft in the walk is no greater than the safe distance. This represents the longest distance included in the set of shortest distances between the current and the corresponding aircraft for each aircraft. This represents the shortest distance between the current aircraft and the aircraft corresponding to the walking aircraft i.

[0085] min ( B i,j ) indicates aircraft i The minimum distance to all other aircraft is fixed. i After that j The index represents the worst-case scenario in the planning. The larger the size, the safer it is. It is to find the minimum ( ) for all aircraft. B i,j The maximum value found after that is a normalization process. F crash, j The aircraft travels the farthest when the minimum value is reached.

[0086] If the distance between aircraft i and other aircraft is greater than the safety threshold, then .

[0087] In one possible implementation, when the distance between aircraft i and any other aircraft at distance j is greater than the safe distance, the collision avoidance parameter of aircraft i at distance j is 0; when the distance between aircraft i and at least one other aircraft at distance j is not greater than the safe distance, the collision avoidance parameter of aircraft i at distance j is the longest distance included in the set of shortest distances between aircraft corresponding to each aircraft at distance j divided by the shortest distance between aircraft i corresponding to aircraft at distance j.

[0088] Here, the distance step j can be any distance step in the set that includes each intermediate distance step and the last distance step.

[0089] Here, aircraft i can be any aircraft in the aircraft cluster.

[0090] In one possible implementation, the cost function of the aircraft in the current departure walk is the sum of the product of the cost function of the aircraft in the next departure walk and the discount factor, and the trajectory performance of the aircraft in the current departure walk.

[0091] In this embodiment of the application, the process of constructing the cost function of aircraft i at distance j is the same as the process of constructing the cost function of aircraft i at the current distance j.

[0092] Here, the distance step j can be any distance step in the set that includes each intermediate distance step and the last distance step.

[0093] Here, aircraft i can be any aircraft in the aircraft cluster.

[0094] In one possible implementation, the cost function of aircraft i in off-walk j is the sum of the product of the cost function of aircraft i in the (j+1)th off-walk and the discount factor, and the track performance of aircraft i in off-walk j.

[0095] Here, the distance step j can be any distance step in the set that includes each intermediate distance step and the last distance step.

[0096] It should be noted that the last departure step is departure step k+N, and the next departure step is departure step k+N+1. The cost function of aircraft i in departure step k+N+1 is 0.

[0097] The cost function of aircraft i at the current distance walk can be expressed as:

[0098]

[0099] in, J ( x i ( k ) represents the cost function of aircraft i at the current distance from the walk. This indicates the flight path performance of aircraft i at its current distance from the walk. This indicates the current position of aircraft i, which is also its distance from the walk distance k. This represents the discrete three-dimensional acceleration of aircraft i at the current distance step, i.e., distance step k. l Indicates the discount factor, 0 < l <1, J ( x i ( k +1)) represents the cost function of aircraft i in the next departure step, i.e., departure step k+1, after the current departure step.

[0100] After expanding the cost function of aircraft i for the next departure walk, the cost function of aircraft i for the current departure walk can be expressed as:

[0101]

[0102] In one possible implementation, the total cost function is the sum of the cost functions of each aircraft at the current distance walk.

[0103] Total cost function J Represented as:

[0104]

[0105] F Indicates track effectiveness, l It is a discount factor and 0 < l <1, where n is the number of iterations.

[0106] The above equation shows that the cost function at a distance k from the walk consists of two parts: ① based on the current state x ( k ) and control a ( k ) indicators F ② The future index function estimated recursively F ( k +1), F ( k +2)... discount summation.

[0107] In this embodiment of the application, the optimization variable is denoted as u, and u can be expressed as:

[0108]

[0109] In this embodiment of the application, in step S104, any algorithm that optimizes multiple variables under given optimization objectives and constraints, such as particle swarm optimization or gray wolf algorithm, can be used to minimize the total cost function value and solve for the discrete three-dimensional acceleration set of each aircraft.

[0110] In one possible implementation, solving for the discrete three-dimensional acceleration set of each aircraft with the objective of minimizing the function value of the total cost function includes: using a snow ablation optimization algorithm to solve for the discrete three-dimensional acceleration set of each aircraft with the objective of minimizing the function value of the total cost function.

[0111] The following describes the process of using the snow ablation optimization algorithm to solve for the discrete three-dimensional acceleration set of each aircraft, with the objective of minimizing the total cost function:

[0112] The snow ablation optimization algorithm targets a population corresponding to an aircraft cluster. Each individual in the population represents a different aircraft within the cluster, and the individual's vector includes the discrete three-dimensional acceleration values, which may represent the aircraft's acceleration. The number of aircraft in the cluster is M, the number of dispersion steps is N, and the three-dimensional acceleration set includes accelerations in three directions. Therefore, the population size D = 3MN, and the population Z can be represented as...

[0113]

[0114] The population is randomly divided into an exploratory population and a development population, with both populations of the same size. Some snow may evaporate into water vapor after melting, thus entering the exploration process.

[0115] During the exploration phase, when individual snow or water turns into water vapor, the population will exhibit irregular movements and disperse. This irregular movement can be regarded as Brownian motion, corresponding to the global exploration phase.

[0116] At this point, the position update formula for individuals i=1, 2, …, K is:

[0117]

[0118] Where T is the generation number of the population. I ( T Let be a D-dimensional Brownian motion vector, which follows a normal distribution with a mean of 0 and a variance of 1. This indicates element-wise multiplication. z avg ( T () represents the average position of the population. G ( T ) represents the optimal solution in the current generation. z ( T ) is the first T Individuals in the next iteration i , r 1 is a random number between [0, 1]. E ( T ) refers to individuals randomly selected from elite individuals.

[0119]

[0120] During the development phase, when individual snowflakes melt into water, the search entity is guided to explore the vicinity of the current optimal solution locally, mathematically represented as:

[0121]

[0122] in, R This represents the snow melting rate. At this point, the individual... i=1, 2…, K The position update formula is:

[0123]

[0124] in, r 2 is a random number between [0, 1].

[0125] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0126] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented in hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0127] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of this application. It should be understood that the above description is only a specific embodiment of this application and is not intended to limit the scope of protection of this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A trajectory planning method for aircraft swarms based on inertial navigation, characterized in that: The method includes: For each aircraft in the aircraft cluster, the trajectory efficiency of the aircraft at the current distance is constructed based on the parameter set of the aircraft at the current distance. The parameter set of the aircraft at the current distance includes: the time efficiency parameter of the aircraft at the current distance, the obstacle avoidance parameter of the aircraft within the city at the current distance, and the collision avoidance parameter between the aircraft at the current distance. For each aircraft, a cost function for the aircraft in the current departure walk is constructed based on the aircraft's trajectory performance in the current departure walk, the cost function of the aircraft in the next departure walk, and the discount factor. Construct the total cost function based on the cost function of each aircraft at the current distance walk; With the objective of minimizing the function value of the total cost function, the discrete three-dimensional acceleration set of each aircraft is solved, wherein the discrete three-dimensional acceleration set of the aircraft includes: the discrete three-dimensional acceleration of the aircraft in the current departure walk, the discrete three-dimensional acceleration of the aircraft in the last departure walk, and the discrete three-dimensional acceleration of the aircraft in each intermediate departure walk between the current departure walk and the last departure walk.

2. The method according to claim 1, characterized in that: Based on the parameter set of the aircraft at the current distance, the trajectory performance of the aircraft at the current distance is constructed, including: Based on the parameter set of the aircraft in the current departure walk and the weight of each parameter in the parameter set of the aircraft in the current departure walk, the trajectory performance of the aircraft in the current departure walk is constructed, where the trajectory performance of the aircraft in the current departure walk is the weighted sum of all parameters in the parameter set of the aircraft in the current departure walk.

3. The method according to claim 1, characterized in that: The time efficiency parameter for an aircraft at its current distance from the walk is the longest total distance among the total distances of the aircraft and the total distances of the aircraft cluster.

4. The method according to claim 1, characterized in that: When the distance between the aircraft and any obstacle at the current distance from the walking aircraft is greater than the safe distance, the obstacle avoidance parameter of the aircraft at the current distance from the walking aircraft is 0. When the distance between the aircraft and at least one obstacle at the current distance from the walking aircraft is not greater than the safe distance, the obstacle avoidance parameter of the aircraft at the current distance from the walking aircraft is determined based on the shortest distance from the obstacle corresponding to each aircraft at the current distance from the walking aircraft. The shortest distance from the obstacle corresponding to the target aircraft at the current distance from the walking aircraft is the shortest distance in the set of distances between each obstacle at the current distance from the walking aircraft and the target aircraft. The target aircraft is any aircraft.

5. The method according to claim 4, characterized in that: When the distance between the aircraft and at least one obstacle at the current distance from the walk is not greater than the safe distance, the obstacle avoidance parameter of the aircraft at the current distance from the walk is the longest distance in the set of shortest distances from obstacles corresponding to each aircraft at the current distance from the walk, divided by the shortest distance from obstacles corresponding to the aircraft at the current distance from the walk.

6. The method according to claim 1, characterized in that: When the distance between the aircraft currently at the walk and any other aircraft is greater than the safe distance, the collision avoidance parameter of the aircraft among the aircraft currently at the walk is 0; when the distance between the aircraft and at least one other aircraft currently at the walk is not greater than the safe distance, the collision avoidance parameter of the aircraft among the aircraft currently at the walk is determined based on the shortest distance among the aircraft corresponding to each of the aircraft currently at the walk, wherein the shortest distance among the aircraft corresponding to the target aircraft currently at the walk is the shortest distance included in the set of distances between the target aircraft currently at the walk and each other aircraft.

7. The method according to claim 6, characterized in that: When the distance between an aircraft and at least one other aircraft at the current distance from the walk is not greater than the safe distance, the collision avoidance parameter of the aircraft at the current distance from the walk is the longest distance in the set of shortest distances between aircraft corresponding to each of the aircraft at the current distance from the walk, divided by the shortest distance between aircraft corresponding to the aircraft at the current distance from the walk.

8. The method according to claim 1, characterized in that: The cost function of an aircraft in the current departure walk is the sum of the product of the cost function of the aircraft in the next departure walk and the discount factor, and the trajectory performance of the aircraft in the current departure walk.

9. The method according to claim 1, characterized in that: The total cost function is the sum of the cost functions of each aircraft at the current distance from the walk.

10. The method according to any one of claims 1-9, characterized in that: With the objective of minimizing the total cost function, the discrete three-dimensional acceleration set for each aircraft is obtained by solving for: The snow ablation optimization algorithm is used to solve for the discrete three-dimensional acceleration set of each aircraft by minimizing the function value of the total cost function.

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