Aircraft trajectory design method, computer program product and readable storage medium

Abstract

This invention relates to aircraft trajectory design methods, computer program products, and readable storage media. Based on measurement data of the aircraft's risk level in risk zones, and considering parameters such as its own dynamics model, aerodynamic performance, and engine capabilities, suitable waypoints are selected. By introducing a switching function, the objective function is dynamically adjusted according to whether the aircraft is located in a risk zone. This allows the aircraft to plan its trajectory based on fuel optimization in low-risk zones, while balancing fuel and time optimization in high-risk zones, ultimately achieving a Pareto optimal solution for both aircraft safety and range capability. A sequential convex optimization method is used to achieve rapid trajectory planning. This method enhances the aircraft's adaptability to risk zones, improves aircraft safety, increases the probability of achieving flight mission objectives, and improves overall aircraft performance.

Description

Technical Field

[0001] This invention relates to a method for designing the trajectory of an aircraft, applicable to the field of aircraft trajectory design. Background Technology

[0002] The trajectory planning scenario commonly encountered by aircraft during flight can be viewed as an optimal control problem of maximizing range while minimizing fuel consumption, with the goal of ensuring fuel efficiency. However, when an aircraft traverses a risky area, it often needs to use a specific trajectory for risk avoidance and rapid passage through the risk zone. Therefore, the objective needs to change to ensuring aircraft safety, and the trajectory must meet certain route constraints. Traditional trajectory planning methods typically involve setting a nominal trajectory to avoid risky areas or using extreme overload to avoid risks. However, both of these methods have significant drawbacks. The nominal trajectory method results in a relatively fixed trajectory, which has limited effectiveness in risk avoidance. Once the risk exceeds the capability range set by the nominal trajectory, it becomes impossible to avoid the risk, potentially leading to a significant increase in aircraft safety risks, making it unsuitable for complex and variable risky environments. The extreme overload avoidance method, on the other hand, leads to significant energy loss, resulting in a substantial reduction in flight range or a significant decrease in aircraft speed. Once the aircraft speed decreases, it cannot guarantee rapid passage through the risky area, also increasing aircraft safety risks. Summary of the Invention

[0003] The technical problem addressed in this application is to overcome the shortcomings of existing technologies and provide a trajectory design method for aircraft. This method is a dynamic programming approach for aircraft trajectories based on sequential convex optimization, which can improve the adaptability and safety of aircraft in high-risk areas and solve the problems of poor versatility of nominal trajectories and severe energy loss under extreme overload. It has advantages such as strong versatility, clear methodology, strong operability, and strong adaptability.

[0004] The technical solution provided in this application is as follows:

[0005] A method for designing the trajectory of an aircraft, comprising:

[0006] S1: Considering the airspace environment structure and multi-objective problem, determine the trajectory planning problem;

[0007] S2: The trajectory planning problem, which considers the airspace environment structure and multi-objective problem, is abstracted into a multi-objective continuous optimal control problem. Waypoints are introduced, and the multi-objective continuous optimal control problem is then transformed into a multi-objective mixed integer optimal control problem.

[0008] S3: Design the initial reference trajectory based on the initial and terminal states of the aircraft;

[0009] S4: The second-order Gauss-Lobatta direct collocation method is used to transform the multi-objective mixed-integer optimal control problem into a multi-objective mixed-integer nonlinear programming problem.

[0010] S5: Linearize the multi-objective mixed-integer nonlinear programming problem to obtain a multi-objective mixed-integer linear programming problem; abstract the risk level of the risk area into the airspace environment structure, make waypoint decisions based on the airspace environment structure, and select prior preference strategies based on waypoints and airspace environment structure to transform the multi-objective mixed-integer linear programming problem into a single-objective mixed-integer linear programming problem;

[0011] S6: Solve the single-objective integer linear programming problem using the branch and bound method to obtain the optimal trajectory near the reference trajectory;

[0012] S7: Obtain the state quantity solution error based on the state quantity difference between the initial reference trajectory and the optimal trajectory; if the state quantity solution error exceeds the error tolerance, set the current optimal trajectory as the reference trajectory.

[0013] S8: Repeat steps S6-S7, iterating until the state variables meet the error tolerance, and output the optimal reference trajectory as the initial reference trajectory for 4D trajectory planning.

[0014] S9: The waypoint decision set in the initial reference trajectory of 4D trajectory planning is used as the path constraint for trajectory planning, transforming the mixed integer optimal control problem into an optimal control problem without integer variables;

[0015] S10: The optimal control problem without integer variables is transformed into a nonlinear programming problem by using the second-order Gauss-Lobatta direct collocation method.

[0016] S11: For nonlinear programming problems, a first-order Taylor expansion is used to linearize the problem near the reference trajectory, transforming it into a linear programming problem.

[0017] S12: Solve the simplified linear programming problem to obtain the optimal control quantity and the optimal state quantity under the dynamic model;

[0018] S13: If the error between the optimal state variable and the initial reference trajectory of 4D trajectory planning exceeds the error tolerance, then the current optimal control variable and the optimal state variable will be output as the new initial reference trajectory of 4D trajectory planning.

[0019] S14: Repeat steps S12-S13, iterate until the state variables meet the error tolerance, output the initial reference trajectory for 4D trajectory planning as the planned trajectory, and use the planned trajectory as the reference trajectory for subsequent real-time trajectory planning.

[0020] S15: Determine the risk zone change based on the aircraft's position, and confirm whether to update the airspace environment structure based on the risk zone change. If the airspace structure and waypoint decisions have not changed, there is no need to update the trajectory. If the airspace environment structure is updated, update the prior preference strategy based on the new airspace environment structure to guide waypoint decisions, that is, go to step S2 and iterate to solve the trajectory again. In this way, the planned trajectory is continuously updated in real time until the aircraft reaches the target point.

[0021] The model for the multi-objective mixed-integer optimal control problem in S2 is as follows:

[0022]

[0023] Where x is the state variable of the aircraft, which is a function of time t; u is the control variable of the aircraft, which is a function of time t; z is the waypoint decision set, which is a vector composed of 0 / 1 variables, representing the choice of waypoints; J is the loss function of trajectory planning, which is composed of two indicators: fuel consumption Φ[·] and time consumption L[·]. The dynamic model of the aircraft is denoted by g(x(t),u(t))≤0, which represents the set of path constraints, initial constraints, and terminal constraints; s(x(t),u(t),z)≤0 represents the set of constraints related to the binary decision variable z; t f The terminal time is w1, which is the weight of the fuel consumption Φ[·] index; w2 is the weight of the time consumption L[·] index.

[0024] The waypoint decision set z is: z = {z ij ∈{0,1}i∈V,j∈s}

[0025] Among them, z ij This indicates that there are s waypoints to choose from at time i; V represents the discrete time set of the entire flight segment, and s is the total number of waypoints; z ij =0 means that the waypoint is not selected as a route constraint; ij When = 1, it means that the waypoint is selected as the way constraint.

[0026] The transition from initial state s0 to terminal state s N There is only one path, and for each time step, only one node is selected as the path point. Therefore, the waypoint decision set also satisfies the following constraints:

[0027]

[0028] Each waypoint constraint can be written in the following form:

[0029]

[0030] Where, θ(λ) i(t) represents latitude, λ i (t) represents longitude; θ ij waypoint s ij Latitude.

[0031] The

[0032] In S5, the multi-objective mixed-integer linear programming problem is expressed as:

[0033]

[0034] Among them, w k For the weights of multi-objective indicators; Δm k For fuel consumption; The time consumption function for high-risk areas; x(λ) k ) represents the state variable; u(λ) k ) represents the control variable; z represents the waypoint decision set.

[0035] To address the safety concerns of aircraft navigating high-risk areas, this invention proposes a dynamic strategy trajectory planning method based on sequential convex optimization. This method utilizes measurement data of the aircraft's risk level within the risk zone and selects appropriate waypoints based on parameters such as its own dynamics model, aerodynamic performance, and engine capabilities. By introducing a switching function, the objective function is dynamically adjusted according to whether the aircraft is located in the risk zone. This allows the aircraft to plan its trajectory based on fuel optimization in low-risk areas, while balancing fuel and time optimization in high-risk areas, ultimately achieving a Pareto optimal solution for both aircraft safety and range capability. Rapid trajectory planning is achieved through sequential convex optimization. This method enhances the aircraft's adaptability to risk zones, improves aircraft safety, increases the probability of achieving flight mission objectives, and improves overall aircraft performance.

[0036] In summary, this application includes at least the following beneficial technical effects:

[0037] The flight trajectory planning method proposed in this invention can enhance the adaptability of aircraft in high-risk areas, improve aircraft safety, and enhance the overall performance of aircraft. Attached Figure Description

[0038] Figure 1 The design process of a multi-objective iterative mixed integer convex optimization algorithm is described. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments disclosed in the present invention will be described in further detail below with reference to the accompanying drawings.

[0040] This application discloses a method for designing the trajectory of an aircraft, such as... Figure 1 As shown, including:

[0041] 1. A multi-objective mixed-integer trajectory design method based on prior preference expression strategy:

[0042] The trajectory planning problem considers the airspace environment structure and multi-objective problem. Specifically, it involves: allocating risk zone information to each waypoint to abstract the risk zone into an airspace environment structure; and designing a multi-objective loss function that considers aircraft fuel optimization and time optimization, since fuel optimization and time optimization are taken into account, thus making it a multi-objective problem.

[0043] 2. A method for mixed-integer trajectory planning based on sequential convex optimization (see...) Figure 1 The steps are as follows:

[0044] (1) The trajectory planning problem that considers multiple objectives is abstracted into a multi-objective continuous optimal control problem. Since the airspace environment structure introduces waypoints, the multi-objective continuous optimal control problem is transformed into a multi-objective mixed integer optimal control problem.

[0045] Design an initial reference trajectory based on the initial and terminal states of the aircraft;

[0046] (2) The second-order Gauss-Lobatta direct collocation method is used to transform the multi-objective mixed-integer optimal control problem into a multi-objective mixed-integer nonlinear programming problem;

[0047] (3) In order to improve the accuracy and efficiency of numerical optimization, the above multi-objective mixed integer nonlinear programming problem is linearized to obtain a multi-objective mixed integer linear programming problem; the risk level of the risk area is abstracted into the airspace environment structure, waypoint decision is made according to the airspace environment structure, and prior preference strategy is selected according to waypoint and airspace environment structure, thus transforming the multi-objective mixed integer linear programming problem into a single-objective mixed integer linear programming problem.

[0048] (4) The branch and bound method is used to solve the single-objective integer linear programming problem to obtain the optimal trajectory near the reference trajectory;

[0049] (5) Obtain the state quantity solution error based on the state quantity difference between the initial reference trajectory and the optimal trajectory; if the state quantity solution error exceeds the error tolerance, set the current optimal trajectory as the reference trajectory.

[0050] (6) Repeat steps 4-5 and iterate until the state variables meet the error tolerance. Output the optimal reference trajectory as the initial reference trajectory for 4D trajectory planning.

[0051] 3. An online trajectory planning method based on spatial domain structure, see... Figure 1 ;

[0052] (1) The waypoint decision set in the initial reference trajectory of 4D trajectory planning is used as the path constraint for trajectory planning, and the mixed integer optimal control problem is transformed into an optimal control problem without integer variables.

[0053] (2) The second-order Gauss-Lobatta direct collocation method is used to transform the optimal control problem without integer variables into a nonlinear programming problem;

[0054] (3) For nonlinear programming problems, a first-order Taylor expansion is used to linearize the problem near the reference trajectory, transforming it into a linear programming problem.

[0055] (4) Solve the simplified linear programming problem to obtain the optimal control quantity and the optimal state quantity under the dynamic model.

[0056] (5) If the error between the optimal state quantity and the initial reference trajectory of 4D trajectory planning exceeds the error tolerance, the current optimal control quantity and the optimal state quantity will be output as the new initial reference trajectory of 4D trajectory planning.

[0057] (6) Repeat steps 4-5 and iterate until the state variables meet the error tolerance. Output the initial reference trajectory for 4D trajectory planning as the planned trajectory and use the planned trajectory as the reference trajectory for subsequent trajectory planning. That is, since the trajectory planning is a real-time online updated trajectory planning, the trajectory planning result at the current moment will be used as the initial reference for the trajectory planning at the next moment.

[0058] (7) Determine whether to update the airspace environment structure based on changes in the risk zone. If the airspace structure and waypoint decisions have not changed, there is no need to update the trajectory. If the airspace environment structure is updated, update the prior preference strategy according to the new airspace environment structure to guide waypoint decisions, i.e., go to step 2(1) and iterate to solve the trajectory again. In this way, continuously update the planned trajectory in real time until the aircraft reaches the target point.

[0059] 1. Modeling of Multi-Objective Mixed Integer Optimal Control Problem

[0060] The introduction of multiple objectives into the loss function extends the optimal control problem into a multi-objective problem. Furthermore, the waypoint decision-making process is incorporated into the trajectory planning problem in the higher-level planning. The introduction of decision variables transforms the problem into a multi-objective mixed-integer optimal control problem. Mathematically, the multi-objective mixed-integer optimal control model can be written in the following form:

[0061]

[0062] In the formula: x is the state variable of the aircraft, which is a function of time t; u is the control variable of the aircraft, which is a function of time t; z is the waypoint decision set, which is a vector composed of 0 / 1 variables, representing the choice of waypoints; J is the loss function of trajectory planning, which is composed of two indicators: fuel consumption Φ[·] and time consumption L[·]. The dynamic model of the aircraft is denoted by g(x(t),u(t))≤0, which represents the set of path constraints, initial constraints, and terminal constraints; s(x(t),u(t),z)≤0 represents the set of constraints related to the decision variable z; t f The terminal time is w1, which is the weight of the fuel consumption Φ[·] index; w2 is the weight of the time consumption L[·] index.

[0063] 2. Make waypoint decisions based on the risk level of the risk area.

[0064] For the waypoint selection problem, each waypoint s ij Since there are only two states, namely choosing and not choosing, we can introduce a waypoint decision set z, which is a set of binary decision variables:

[0065] z={z ij ∈{0,1}i∈V,j∈s} (2)

[0066] Among them, z ij This indicates that there are s waypoints to choose from at time i; V represents the discrete time set of the entire flight segment.

[0067] In the formula z ij =0 means that the waypoint is not selected as a route constraint; ij When = 1, it means that the waypoint is selected as the route constraint. The trajectory planning problem, from node s0 (initial state) to s... N (Terminal State) There is only one path. For the waypoint set at each time step, only one node is selected as the path point. Therefore, the waypoint decision set also satisfies the following constraints:

[0068]

[0069] The upper-level decision constraints actually reflect the constraints on the latitude and longitude of the intermediate trajectory. Therefore, the corresponding waypoint constraints can be written in the following form:

[0070]

[0071] Where, θ(λ) i (t) represents latitude, λ i (t) represents longitude; θ ij waypoint s ij Latitude.

[0072] Based on the risk level of each risk zone, different waypoint decisions are made, and trajectory planning is implemented under different risk conditions through waypoint decision planning. By guiding waypoint decisions with risk levels, the mixed-integer optimal control problem is transformed into an optimal control problem without integer variables.

[0073]

[0074] x(t) includes θ(λ) i (t) and λ i (t).

[0075] 3. Solving the multi-objective optimal control problem (multi-objective mixed integer optimal control problem)

[0076] To transform the optimal control problem into a linear programming problem that is easier to solve and to further improve the accuracy of updating the reference trajectory, the second-order Gauss-Lobatta direct collocation method is first used to discretize the multi-objective mixed integer optimal control problem.

[0077] For the latent variable longitude [λ0, λ] f The entire trajectory on the [ ] is discretized into K segments with a spacing dλ. According to the direct collocation method, it can be transformed into a nonlinear programming problem.

[0078] This problem remains difficult to solve directly due to the high nonlinearity in performance indicators and dynamic constraints. Therefore, we consider making the nonlinear part linear and convex, thus transforming the problem into a multi-objective mixed integer linear programming problem.

[0079] The process of linearizing the above multi-objective mixed-integer nonlinear programming problem includes:

[0080] Design a discretized reference trajectory, where:

[0081]

[0082] in, Represents the state variables at time 1-k; This represents the control quantity at time 1-k.

[0083] The nonlinear performance index p(x) k ,u k ) and the dynamic equation f(x) k ,u k The function is expanded into a linear function by generalized first-order Taylor expansion near the reference trajectory:

[0084]

[0085] In the formula, the Peano remainder R nThe true trajectory approaches 0 when it closely approximates the reference trajectory. Matrices A, B, C, and D are the Jacobian matrices of functions AP and f with respect to state variables x and control variables u, respectively.

[0086]

[0087] Through the above linearization, the nonlinear part of the multi-objective mixed-integer nonlinear programming problem is linearly expanded, and the multi-objective mixed-integer nonlinear programming problem is transformed into the following multi-objective mixed-integer linear programming problem.

[0088]

[0089] This multi-objective mixed-integer linear programming problem can be directly solved after being transformed into a single-objective mixed-integer linear programming problem through a prior preference strategy. However, the solution result is not relevant to the reference trajectory. The accuracy is quite sensitive. When the error between the reference trajectory and the planning result is large, the linearization subproblem may lead to no solution or unboundedness. Even if there is a solution, the control quantity may produce high-frequency oscillations. The design of a more accurate reference trajectory requires the planning result for guidance. Therefore, we can consider updating the reference trajectory through an iterative method to gradually approach the optimal trajectory, and solve the problems of no solution and control quantity oscillation when the error is large by introducing a neighbor term and a control quantity penalty term.

[0090] This invention employs a dual-loop programming algorithm to solve multi-objective mixed-integer linear programming problems. The inner loop solves the multi-objective linear programming problem, while the outer loop updates the reference trajectory and waypoint decisions until the error between the solution and the reference trajectory is less than the tolerance, at which point the optimal trajectory is obtained.

[0091] The iterative mixed-integer convex optimization steps are as follows:

[0092] 0. Initialization

[0093] Input reference trajectory Ref, error tolerance ε, maximum number of iterations i max Selecting prior preference strategy 1. Iteration

[0094] Convexing the vicinity of the reference trajectory Ref yields a mixed-integer linear programming subproblem.

[0095] Inner loop: Solving subproblems using branch and bound method

[0096] Output: Optimal trajectory Taj * ={x * ,u *}

[0097] 2. Update

[0098] if||x * -x ref||≥εand i≤i max

[0099] i = i + 1

[0100] Ref=Taj *

[0101] Return to step 2 and continue iterating.

[0102] else

[0103] Proceed to step 33. Output

[0104] Output optimal trajectory Taj * ={x * ,u * ,z} / Exceeded the maximum number of iterations.

[0105] This embodiment also discloses a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of the above-described trajectory design method for an aircraft.

[0106] This embodiment also discloses a computer-readable storage medium storing a computer program / instructions thereon, which, when executed by a processor, implements the steps of the above-described trajectory design method for an aircraft.

[0107] The contents not described in detail in this application specification are common knowledge to those skilled in the art.

[0108] The present application has been described in detail above with reference to specific embodiments and exemplary examples; however, these descriptions should not be construed as limiting the present application. Those skilled in the art will understand that various equivalent substitutions, modifications, or improvements can be made to the technical solutions and implementation methods of the present application without departing from the spirit and scope of the present application, and all such modifications and improvements fall within the scope of the present application. The scope of protection of the present application is determined by the appended claims.

Claims

1. A method for designing the trajectory of an aircraft, characterized in that, include: S1: Considering the airspace environment structure and multi-objective problem, determine the trajectory planning problem; S2: The trajectory planning problem, which considers the airspace environment structure and multi-objective problem, is abstracted into a multi-objective continuous optimal control problem. Waypoints are introduced, and the multi-objective continuous optimal control problem is then transformed into a multi-objective mixed integer optimal control problem. S3: Design the initial reference trajectory based on the initial and terminal states of the aircraft; S4: The second-order Gauss-Lobatta direct collocation method is used to transform the multi-objective mixed-integer optimal control problem into a multi-objective mixed-integer nonlinear programming problem. S5: Linearize the multi-objective mixed-integer nonlinear programming problem to obtain a multi-objective mixed-integer linear programming problem; abstract the risk level of the risk area into the airspace environment structure, make waypoint decisions based on the airspace environment structure, and select prior preference strategies based on waypoints and airspace environment structure to transform the multi-objective mixed-integer linear programming problem into a single-objective mixed-integer linear programming problem; S6: Solve the single-objective integer linear programming problem using the branch and bound method to obtain the optimal trajectory near the reference trajectory; S7: Obtain the state quantity solution error based on the state quantity difference between the initial reference trajectory and the optimal trajectory; if the state quantity solution error exceeds the error tolerance, set the current optimal trajectory as the reference trajectory. S8: Repeat steps S6-S7, iterating until the state variables meet the error tolerance, and output the optimal reference trajectory as the initial reference trajectory for 4D trajectory planning. S9: The waypoint decision set in the initial reference trajectory of 4D trajectory planning is used as the path constraint for trajectory planning, transforming the mixed integer optimal control problem into an optimal control problem without integer variables; S10: The optimal control problem without integer variables is transformed into a nonlinear programming problem by using the second-order Gauss-Lobatta direct collocation method. S11: For nonlinear programming problems, a first-order Taylor expansion is used to linearize the problem near the reference trajectory, transforming it into a linear programming problem. S12: Solve the simplified linear programming problem to obtain the optimal control quantity and the optimal state quantity under the dynamic model; S13: If the error between the optimal state variable and the initial reference trajectory of 4D trajectory planning exceeds the error tolerance, then the current optimal control variable and the optimal state variable will be output as the new initial reference trajectory of 4D trajectory planning. S14: Repeat steps S12-S13, iterate until the state variables meet the error tolerance, output the initial reference trajectory for 4D trajectory planning as the planned trajectory, and use the planned trajectory as the reference trajectory for subsequent real-time trajectory planning. S15: Determine the risk zone change based on the aircraft's position, and confirm whether to update the airspace environment structure based on the risk zone change. If the airspace structure and waypoint decisions have not changed, there is no need to update the trajectory. If the airspace environment structure is updated, update the prior preference strategy based on the new airspace environment structure to guide waypoint decisions, that is, go to step S2 and iterate to solve the trajectory again. In this way, the planned trajectory is continuously updated in real time until the aircraft reaches the target point.

2. The trajectory design method for an aircraft according to claim 1, characterized in that, The model for the multi-objective mixed-integer optimal control problem in S2 is as follows: g(x(t),u(t))≤0 s(x(t),u(t),z)≤0 Where x is the state variable of the aircraft, which is a function of time t; u is the control variable of the aircraft, which is a function of time t; z is the waypoint decision set, which is a vector composed of 0 / 1 variables, representing the choice of waypoints; J is the loss function of trajectory planning, which is composed of two indicators: fuel consumption Φ[·] and time consumption L[·]. The dynamic model of the aircraft is denoted by g(x(t),u(t))≤0, which represents the set of path constraints, initial constraints, and terminal constraints; s(x(t),u(t),z)≤0 represents the set of constraints related to the binary decision variable z; t f The terminal time is w1, which is the weight of the fuel consumption Φ[·] index; w2 is the weight of the time consumption L[·] index.

3. The trajectory design method for an aircraft according to claim 1, characterized in that, The waypoint decision set z is: z={z ij ∈{0,1}i∈V,j∈s} Among them, z ij This indicates that there are s waypoints to choose from at time i; V represents the discrete time set of the entire flight segment, and s is the total number of waypoints; z ij =0 means that the waypoint is not selected as a route constraint; ij When = 1, it means that the waypoint is selected as the way constraint.

4. The trajectory design method for an aircraft according to claim 3, characterized in that: The transition from initial state s0 to terminal state s N There is only one path, and for each time step of the waypoint set, only one node is selected as the path point. Therefore, the waypoint decision set also satisfies the following constraints: Each waypoint constraint can be written in the following form: Where, θ(λ) i (t) represents latitude, λ i (t) represents longitude; θ ij waypoint s ij Latitude.

5. The trajectory design method for an aircraft according to claim 4, characterized in that, The 6. The trajectory design method for an aircraft according to claim 1, characterized in that, In S5, the multi-objective mixed-integer linear programming problem is expressed as: -(x(λ k )-x(λ k-1 ))=0 g(x(λ k ),u(λ k ))≤0 s(x(λ k ),u(λ k ),z)≤0 k = 1, 2, ... K Among them, w k For the weights of multi-objective indicators; Δm k For fuel consumption; The time consumption function for high-risk areas; x(λ) k ) represents the state variable; u(λ) k ) represents the control variable; z represents the waypoint decision set.

7. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the trajectory design method for an aircraft as described in any one of claims 1-6.

8. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the trajectory design method for an aircraft as described in any one of claims 1-6.

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