An aircraft online trajectory planning method based on iterative linear quadratic regulator

Abstract

The application discloses an aircraft online trajectory planning method based on an iterative linear quadratic regulator and belongs to the field of aircraft trajectory optimization.The application realizes the following method: a high-fidelity aircraft dynamics model constraint considering the earth rotation and the flattening is constructed to realize the accurate characterization of the aircraft dynamic characteristics; the speed, the speed inclination angle, the speed deflection angle, the geocentric distance, the longitude and the latitude of the aircraft are taken as the state variables, and the attack angle and the sideslip angle are taken as the control variables, so that an optimal control model of the aircraft trajectory planning problem is constructed, and the constraint conditions include the dynamics constraint, the path constraint, the initial and terminal constraints and the control constraint; the iterative linear quadratic regulator is used for solving to obtain the optimal control variable U of the trajectory planning and the optimal trajectory of the aircraft, so that the real-time performance and the accuracy of the trajectory planning are improved; and according to the control sequence U, the flight trajectory of the aircraft is obtained according to numerical integration, so that the accuracy and the efficiency of the online trajectory planning are balanced, and the trajectory optimization of the strong nonlinear system under the complex disturbance environment is realized.

Description

Technical Field

[0001] This invention belongs to the field of aircraft trajectory optimization and relates to an online trajectory planning method for aircraft based on an iterative linear quadratic regulator. Background Technology

[0002] Due to the constraints of complex dynamics and diverse mission requirements, the trajectory planning problem is typically described as an optimal control problem encompassing dynamic constraints, process constraints, endpoint constraints, and performance indices that the aircraft must satisfy. Considering the strong nonlinearity inherent in the aircraft's dynamic model, directly solving this optimal control problem using trajectory optimization methods such as sequential convex optimization often involves iteratively solving multiple sub-optimal control problems, resulting in low efficiency and a high probability of non-convergence. This makes obtaining the optimal flight trajectory that meets mission requirements extremely challenging. Therefore, researching an efficient and highly convergent online trajectory optimization method is of great significance.

[0003] To improve real-time computational performance, existing online trajectory optimization methods often simplify the aircraft dynamics model, such as ignoring higher-order coupling effects of aerodynamic parameters (see X. Liu, Z. Shen, P. Lu. Entry trajectory optimization by second-order cone programming. J. Guid., Control, Dyn., 2016; 39(2):227-241.) and ignoring the curvature of the Earth (see D. Zhao, Z. Song. Reentry trajectory optimization with waypoint and no-fly zone constraints using multiphaseconvex programming. Acta Astronautica, 2017; 137:60–69.). While this simplification strategy reduces the numerical solution complexity of the optimization problem, it leads to significant deviations between the planned trajectory and the actual physical model, manifesting as control commands being feasible in theoretical calculations but causing system instability during actual execution. In recent years, iterative optimization frameworks based on differential dynamic programming have received widespread attention due to their efficiency in nonlinear system control. This method dynamically constructs a locally linearized model and iteratively solves the time-domain difference Riccati equation, enabling simultaneous optimization of the state trajectory and control strategy while preserving the complete nonlinear dynamic characteristics. It also utilizes backpropagation to quickly calculate the gradient of the objective function. Based on this, this invention proposes a trajectory planning algorithm employing an iterative linear quadratic regulator. By embedding a high-fidelity aircraft dynamics model, it achieves accurate characterization of the aircraft's dynamic characteristics. Furthermore, its incremental optimization mechanism balances the real-time performance of online computation with trajectory feasibility, providing a new technical path for trajectory optimization of strongly nonlinear systems under complex disturbance environments. Summary of the Invention

[0004] To address the need for highly reliable online trajectory optimization for aircraft in complex and uncertain scenarios, and to overcome the shortcomings of existing online trajectory optimization methods in terms of convergence and real-time performance, this invention aims to provide an online trajectory planning method for aircraft based on an iterative linear quadratic regulator. By embedding a high-fidelity aircraft dynamics model, it avoids error accumulation caused by conventional linearization, achieving accurate characterization of the aircraft's dynamic characteristics. Relying on the incremental optimization mechanism of the iterative linear quadratic regulator, it balances the real-time performance of online computation with trajectory feasibility. This online trajectory optimization method based on the iterative linear quadratic regulator significantly improves the speed and reliability of trajectory generation while ensuring trajectory optimization accuracy and feasibility, achieving a trade-off between accuracy and efficiency in online trajectory planning, and ultimately realizing trajectory optimization for strongly nonlinear systems under complex disturbance environments.

[0005] To achieve the above objectives, the present invention adopts the following technical solution.

[0006] This invention discloses an online trajectory planning method for aircraft based on an iterative linear quadratic regulator, comprising the following steps:

[0007] Step 1: Construct a high-fidelity aircraft dynamics model constraint that takes into account the Earth's rotation and oblateness to achieve accurate characterization of the aircraft's dynamic characteristics.

[0008] The high-fidelity aircraft dynamics model is constructed as shown in equation (1):

[0009]

[0010] Where V,γ,ψ,r,θ, Let m and represent the aircraft's velocity, velocity tilt angle, velocity deflection angle, geocentric distance, longitude, latitude, and mass, respectively; g is the acceleration due to gravity; X, Y, and Z are the axial, longitudinal, and lateral aerodynamic forces, respectively, and their specific expressions are as follows:

[0011]

[0012] Where S is the reference area of ​​the aircraft; ρ is the atmospheric density:

[0013]

[0014] Where ρ0 is the atmospheric density at 0 altitude; R0 is the Earth's radius; H s This is the atmospheric density correction constant.

[0015] C X C Y and C Z G is the triaxial aerodynamic coefficient; V G γ and G ψ Corrections for the dynamic model of Earth's rotation and oblateness:

[0016]

[0017] Where: ω e g is the Earth's rotational angular velocity. J This is a gravitational perturbation.

[0018] Equation (1) can be simplified as follows:

[0019]

[0020] in, Let U be the state vector of the aircraft, and U = [α, β] be the control variables of the aircraft.

[0021] Step 2: Combining the constraints of the dynamic model established in Step 1, construct the optimal control model for the aircraft trajectory planning problem, using the aircraft's speed, speed tilt angle, speed deflection angle, geocentric distance, longitude, and latitude as state variables, and angle of attack and sideslip angle as control variables. The constraints include dynamic constraints, path constraints, start-end constraints, and control constraints.

[0022] Step 2.1: In addition to the dynamic model constraints established in Step 1, the aircraft also needs to satisfy the following constraints during flight: terminal state constraints, control constraints, and process constraints.

[0023] ①Terminal state constraints:

[0024]

[0025] Where: t0 is the initial time, t f At the endpoint, X0, X f These are the initial state and the final state of the aircraft, respectively.

[0026] ② Control constraints:

[0027]

[0028] Where: α min α max These are the minimum and maximum angle-of-attack constraints, β. min β max These are the minimum and maximum constraints for the sideslip angle, respectively.

[0029] ③ Process constraints:

[0030]

[0031] Q s q represents the heat flux of the aircraft; n represents the dynamic pressure of the aircraft; k represents the overload; q represents the heat flux of the aircraft. Q Q is the heat flux coefficient. smax For maximum heat flux constraint, q min q max These are the minimum and maximum dynamic pressure constraints, respectively, n max This is the maximum overload constraint.

[0032] Let the constraints (6)-(8) be denoted as:

[0033] g(X,U)≤0 (9)

[0034] Step 2.2: Combining the dynamic model constraints from Step 1 with the path constraints, start-end constraints, and control constraints from Step 2.1, the optimal control model for discrete parameterized trajectory optimization is constructed as follows:

[0035]

[0036] In the formula, J is the objective function; the aircraft control variable U = [α, β] is the optimization variable; t k The state and control variables of the aircraft at that moment; The right-hand function of the dynamic equation shown in equation (1) at discrete points The values ​​at the points; Q, R, and K are the weight coefficients of each term in the objective function; After discretizing the constraint function shown in equation (6), at the discrete point t k The corresponding constraints; Δt is the discretization step size; N is the number of discrete points.

[0037] Step 2.3: To facilitate the rapid solution of the iterative linear quadratic regulator in Step 3, the original optimal control model established in Step 2.2 is transformed, converting the inequality constraints into obstacle functions in the objective function, resulting in the transformed optimal control problem:

[0038]

[0039] Where γ is a user-defined weighting coefficient.

[0040] Equation (8) is the optimal control model for the aircraft trajectory planning problem.

[0041] Step 3: Let the iteration step i = 1. For the optimal control model of the aircraft trajectory planning problem constructed in Step 2, use the iterative linear quadratic regulator to solve it, obtain the optimal control variable U for trajectory planning, and obtain the optimal trajectory of the aircraft, thereby improving the real-time performance and accuracy of trajectory planning.

[0042] Step 3.1: Simplify equation (8) as follows:

[0043]

[0044] in, It is the cost at the end; It is every moment t k The cost.

[0045] Step 3.2: Based on the reference control sequence under the current iteration step i Calculating the aircraft reference trajectory using the Euler method's fast forward propagation

[0046]

[0047] Step 3.3: In the initial reference trajectory and At this point, a second-order Taylor expansion is performed on the dynamic model shown in equation (1) to achieve linearization:

[0048]

[0049] Among them, A k B k These are the Jacobian matrices of the dynamic equations with respect to the state and control variables, respectively.

[0050] Step 3.4: In the reference trajectory and The cost function at each time step Perform a first-order expansion, as shown in equation (12):

[0051]

[0052] The local second-order expansion is shown below:

[0053]

[0054] Step 3.5: Calculate the correction amount for the control variables based on the Bellman optimality principle and the maximum principle.

[0055] ① Definition Indicates t k to t N The cumulative cost at any given time t. Based on the Bellman optimality principle, the cost at any given time t is obtained recursively. k The minimum cost V(k):

[0056]

[0057] definition

[0058] ②Based on equation (8), we obtain t N The derivative of V(N-1) at point:

[0059]

[0060] ③ Based on the principle of maximum value, The optimal control can be determined by first-order conditions:

[0061]

[0062] in, At the same time, Performing a Taylor expansion, we get:

[0063]

[0064] Among them, Q XIt is Q k For the current state The first derivative; Q U It is Q k For the current control command The first derivative; Q XX It is Q k For the current state The second derivative; Q UU It is Q k For the current control command The second derivative of .

[0065] Equation (16) is transformed into:

[0066]

[0067] Based on equation (18), we obtain The analytical expression is as follows:

[0068]

[0069] in,

[0070]

[0071] ④ Calculate t k The derivative of the time-value function:

[0072]

[0073] Repeat steps ③-④ to update the control commands at all times based on equation (19), complete a complete control command update process, and obtain the updated control sequence U.

[0074] Step 3.6: i = i + 1, based on the updated control sequence U, execute steps 3.2 to 3.5 again to iteratively update the control commands, directly changing the relative change of the cost function. The value is less than the threshold, or the change in the control sequence is less than the set threshold.

[0075] Step 4: Based on the control sequence U obtained in Step 3, the flight trajectory of the aircraft is obtained by numerical integration, which significantly improves the speed and reliability of trajectory generation, achieves a trade-off between accuracy and efficiency in online trajectory planning, and thus realizes trajectory optimization of strongly nonlinear systems under complex disturbance environments.

[0076] Beneficial effects:

[0077] 1. This invention discloses an online trajectory planning method for aircraft based on an iterative linear quadratic regulator. By embedding a high-fidelity dynamic model that includes Earth's rotation, oblateness effect, and higher-order aerodynamic coupling, it accurately characterizes the dynamic characteristics of the aircraft in the real physical environment. This avoids physical deviations caused by model simplification in traditional methods (such as ignoring curvature or higher-order aerodynamic terms), breaks through the limitations of simplified models in traditional trajectory planning, significantly improves the consistency between the trajectory and the actual physical environment, ensures the theoretical feasibility and actual execution stability of control commands, and solves the core contradiction of theoretically feasible solutions but actual execution instability.

[0078] 2. This invention discloses an online trajectory planning method for aircraft based on an iterative linear quadratic regulator. Relying on the incremental optimization mechanism of iLQR, a locally linearized model is dynamically constructed based on a second-order Taylor expansion in each iteration. The state trajectory and control strategy are simultaneously optimized through the Bellman optimality principle and the minimum principle. Under the premise of preserving the complete nonlinear dynamic characteristics, the method achieves fast calculation of backpropagation gradient and efficient solution of time-domain difference Riccati equation, solving the problems of poor convergence and easy divergence of traditional sequential convex optimization methods. It provides a reliable trajectory optimization method for strongly nonlinear and multi-constraint scenarios.

[0079] 3. This invention discloses an online trajectory planning method for aircraft based on an iterative linear quadratic regulator. This method is capable of handling dynamic constraints, process constraints (heat flux / dynamic pressure / overload), control constraints (angle of attack / sideslip angle boundaries), and terminal state constraints. Through adaptive adjustment of obstacle function weights, it ensures trajectory safety while avoiding excessive contraction of the feasible region. Combining a high-fidelity dynamic model and the iLQR optimization framework, it achieves real-time online trajectory generation under complex disturbance environments, ensuring strict satisfaction of process constraints and high-precision arrival at the terminal conditions. Attached Figure Description

[0080] Figure 1 Overall process diagram

[0081] Figure 2 Longitude-Latitude Diagram of Trajectory Planning Results

[0082] Figure 3 Longitude-elevation diagram of trajectory planning results Detailed Implementation

[0083] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0084] like Figure 1 As shown in the overall flowchart, this embodiment discloses an online trajectory optimization method based on an iterative linear quadratic regulator. The specific implementation steps are as follows:

[0085] Step 1: Construct a high-fidelity aircraft dynamics model constraint that takes into account the Earth's rotation and oblateness to achieve accurate characterization of the aircraft's dynamic characteristics.

[0086] The high-fidelity aircraft dynamics model is constructed as shown in equation (11):

[0087]

[0088] Where V,γ,ψ,r,θ, Let m and represent the aircraft's velocity, velocity tilt angle, velocity deflection angle, geocentric distance, longitude, latitude, and mass, respectively; g is the acceleration due to gravity; X, Y, and Z are the axial, longitudinal, and lateral aerodynamic forces, respectively, and their specific expressions are as follows:

[0089]

[0090] Where S = 0.86m 2 ρ is the reference area of ​​the aircraft; ρ is the atmospheric density.

[0091]

[0092] Where, ρ0 = 1.225 kg / m 3 The atmospheric density at 0 m altitude; R0 = 6371000 m is the Earth's radius; H s =7110 is the atmospheric density correction constant.

[0093] C X C Y and C Z G is the triaxial aerodynamic coefficient; V G γ and G ψ Corrections for the dynamic model of Earth's rotation and oblateness:

[0094]

[0095] Where: ω e g is the Earth's rotational angular velocity. J This is a gravitational perturbation.

[0096] Equation (1) can be simplified as follows:

[0097]

[0098] in, Let U be the state vector of the aircraft, and U = [α, β] be the control variables of the aircraft.

[0099] Step 2: Combining the constraints of the dynamic model established in Step 1, construct the optimal control model for the aircraft trajectory planning problem, using the aircraft's speed, speed tilt angle, speed deflection angle, geocentric distance, longitude, and latitude as state variables, and angle of attack and sideslip angle as control variables. The constraints include dynamic constraints, path constraints, start-end constraints, and control constraints.

[0100] Step 2.1: In addition to the dynamic model constraints established in Step 1, the aircraft also needs to satisfy the following constraints during flight: terminal state constraints, control constraints, and process constraints.

[0101] ①Terminal state constraints:

[0102]

[0103] Where: t0 is the initial time, t f At the endpoint, X0 = [4500m / s², 0°, 90°, 6416000m, 118.7955°, 26.5105°], X0 = [2500m / s², 0°, 90°, 6396000m, 141.1633°, 16.439582°].

[0104] ② Control constraints:

[0105]

[0106] Where: α min =-20°, α max =20°, β min =-20°, β max =20°.

[0107] ③ Process constraints:

[0108]

[0109] Q smax =149.4kWh / m 2 ;k Q =9.4369×10 -5 ;q min =70kPa; q max =400kPa; n max =20.

[0110] Step 2.2: Combining the various constraint functions from Step 2.1, construct the optimal control model for discrete parameterized trajectory optimization as follows:

[0111]

[0112] Where N = 300, Δt = 2s.

[0113] Step 2.3: To facilitate the rapid solution of the iterative linear quadratic regulator in Step 3, the original optimal control model established in Step 2.2 is transformed, converting the inequality constraints into obstacle functions in the objective function, resulting in the transformed optimal control problem:

[0114]

[0115] Where γ = 1 × 10 5 .

[0116] Step 3: Let the iteration step i = 1. For the optimal control model of the aircraft trajectory planning problem constructed in Step 2, use the iterative linear quadratic regulator to solve it, obtain the optimal control variable U for trajectory planning, and obtain the optimal trajectory of the aircraft, thereby improving the real-time performance and accuracy of trajectory planning.

[0117] Step 3.1: Simplify equation (8) as follows:

[0118]

[0119] in, It is the cost at the end; It is every moment t k The cost.

[0120] Step 3.2: Based on the reference control sequence under the current iteration step i Calculating the aircraft reference trajectory using the Euler method's fast forward propagation

[0121]

[0122] Step 3.3: In the initial reference trajectory and At this point, a second-order Taylor expansion is performed on the dynamic model shown in equation (1) to achieve linearization:

[0123]

[0124] Among them, A k B k These are the Jacobian matrices of the dynamic equations with respect to the state and control variables, respectively.

[0125] Step 3.4: In the reference trajectory and The cost function at each time step The first-order expansion is shown below:

[0126]

[0127] The local second-order expansion is shown below:

[0128]

[0129] Step 3.5: Calculate the correction amount for the control variables based on the Bellman optimality principle and the maximum principle.

[0130] ① Definition Indicates t k to t N All accumulated costs at any given moment. According to Bell.

[0131] Mann's optimality principle, which obtains any time t through recursion. k The minimum cost V(k):

[0132]

[0133] At the same time, for ease of explanation in the following text, the definition is...

[0134] ②Based on equation (8), it is easy to obtain t N The derivative of V(N-1) at point:

[0135]

[0136] ③ Based on the principle of maximum value, The optimal control can be determined by first-order conditions:

[0137]

[0138] in At the same time, Performing a Taylor expansion, we get:

[0139]

[0140] Among them, Q X It is Q k For the current state The first derivative; Q U It is Q k For the current control command The first derivative; Q XX It is Q k For the current state The second derivative; Q UU It is Q k For the current control command The second derivative of .

[0141] Therefore, equation (16) can be transformed into:

[0142]

[0143] Based on equation (18), it is easy to obtain The analytical expression is as follows:

[0144]

[0145] in:

[0146]

[0147] ④ Update t k The derivative of the time-value function:

[0148]

[0149] Repeat steps ③-④ to update the control commands at all times based on equation (19) to complete a complete control command update process.

[0150] Step 3.6: i = i + 1, based on the updated control instructions, execute steps 3.2 to 3.5 again, iteratively updating the control instructions until the relative change of the cost function is achieved. The value is less than the threshold, or the change in the control sequence is less than the set threshold.

[0151] Step 4: Based on the control sequence U obtained in Step 3, the flight trajectory of the aircraft is obtained through numerical integration, and the result is as follows. Figure 2 Longitude-latitude diagram of trajectory planning results and Figure 3 The trajectory planning results are illustrated in the longitude-elevation diagram. This significantly improves the speed and reliability of trajectory generation, achieving a balance between accuracy and efficiency in online trajectory planning, and ultimately enabling trajectory optimization for highly nonlinear systems under complex disturbance environments.

[0152] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for online trajectory planning of an aircraft based on an iterative linear quadratic regulator, characterized in that: Includes the following steps: Step 1: Construct a high-fidelity aircraft dynamics model constraint that takes into account the Earth's rotation and oblateness to achieve accurate characterization of the aircraft's dynamic characteristics; Step 2: Combining the constraints of the dynamic model established in Step 1, construct the optimal control model for the aircraft trajectory planning problem, with the aircraft's speed, speed tilt angle, speed deflection angle, geocentric distance, longitude, and latitude as state variables, and angle of attack and sideslip angle as control variables. The constraints include dynamic constraints, path constraints, start-end constraints, and control constraints. Step 3: Let the iteration step i = 1. For the optimal control model of the aircraft trajectory planning problem constructed in Step 2, use the iterative linear quadratic regulator to solve it, obtain the optimal control variable U for trajectory planning, and obtain the optimal trajectory of the aircraft, thereby improving the real-time performance and accuracy of trajectory planning. Step 4: Based on the control sequence U obtained in Step 3, the flight trajectory of the aircraft is obtained by numerical integration, which significantly improves the speed and reliability of trajectory generation, achieves a trade-off between accuracy and efficiency in online trajectory planning, and thus realizes trajectory optimization of strongly nonlinear systems under complex disturbance environments.

2. The online trajectory planning method for an aircraft based on an iterative linear quadratic regulator as described in claim 1, characterized in that: The implementation method for step one is as follows: The high-fidelity aircraft dynamics model is constructed as shown in equation (1): Where V,γ,ψ,r,θ, Let m and represent the aircraft's velocity, velocity tilt angle, velocity deflection angle, geocentric distance, longitude, latitude, and mass, respectively; g is the acceleration due to gravity; X, Y, and Z are the axial, longitudinal, and lateral aerodynamic forces, respectively, and their specific expressions are as follows: Where S is the reference area of ​​the aircraft; ρ is the atmospheric density: Where ρ0 is the atmospheric density at 0 altitude; R0 is the Earth's radius; H s This is the atmospheric density correction constant; C X C Y and C Z G is the triaxial aerodynamic coefficient; V G γ and G ψ Corrections for the dynamic model of Earth's rotation and oblateness: Where: ω e g is the Earth's rotational angular velocity. J For gravitational perturbation; Equation (1) can be simplified as follows: in, Let U be the state vector of the aircraft, and U = [α, β] be the control variables of the aircraft.

3. The online trajectory planning method for an aircraft based on an iterative linear quadratic regulator as described in claim 2, characterized in that: The implementation method for step two is as follows: Step 2.1: In addition to the dynamic model constraints established in Step 1, the constraints that the aircraft needs to satisfy during flight include terminal state constraints, control constraints, and process constraints. Step 2.2: Combining the dynamic model constraints in Step 1 with the path constraints, start-end constraints, and control constraints in Step 2.1, construct the optimal control model for discrete parameterized trajectory optimization; Step 2.3: To facilitate the rapid solution of the iterative linear quadratic regulator in Step 3, the original optimal control model established in Step 2.2 is transformed, and the inequality constraints are transformed into obstacle functions in the objective function, resulting in the transformed optimal control problem, i.e., the optimal control model of the aircraft trajectory planning problem.

4. The online trajectory planning method for an aircraft based on an iterative linear quadratic regulator as described in claim 3, characterized in that: In step 2.1, ①Terminal state constraints: Where: t0 is the initial time, t f At the endpoint, X0, X f These are the initial state and the final state of the aircraft, respectively. ② Control constraints: Where: α min α max These are the minimum and maximum angle-of-attack constraints, β. min β max These are the minimum and maximum constraints for the sideslip angle, respectively. ③ Process constraints: Q s q represents the heat flux of the aircraft; n represents the dynamic pressure of the aircraft; k represents the overload; q represents the heat flux of the aircraft. Q Q is the heat flux coefficient. smax For maximum heat flux constraint, q min q max These are the minimum and maximum dynamic pressure constraints, respectively, n max Maximum overload constraint; Let the constraints (6)-(8) be denoted as: g(X,U)≤0 (9) 5. The online trajectory planning method for an aircraft based on an iterative linear quadratic regulator as described in claim 4, characterized in that: In step 2.2, the optimal control model for discrete parameterized trajectory optimization is constructed as follows: In the formula, J is the objective function; the aircraft control variable U = [α, β] is the optimization variable; t k The state and control variables of the aircraft at that moment; The right-hand function of the dynamic equation shown in equation (1) at discrete points The values ​​at the points; Q, R, and K are the weight coefficients of each term in the objective function; After discretizing the constraint function shown in equation (6), at the discrete point t k The corresponding constraints; Δt is the discretization step size; N is the number of discrete points.

6. The online trajectory planning method for an aircraft based on an iterative linear quadratic regulator as described in claim 5, characterized in that: In step 2.3, The transformed optimal control problem: Where γ is a user-defined weighting coefficient.

7. The online trajectory planning method for an aircraft based on an iterative linear quadratic regulator as described in claim 6, characterized in that: The implementation method for step three is as follows: Step 3.1: Simplify equation (8) as follows: in, It is the cost at the end; It is every moment t k The cost; Step 3.2: Based on the reference control sequence under the current iteration step i Calculating the aircraft reference trajectory using the Euler method's fast forward propagation Step 3.3: In the initial reference trajectory and At this point, a second-order Taylor expansion is performed on the dynamic model shown in equation (1) to achieve linearization: Among them, A k B k These are the Jacobian matrices of the dynamic equations with respect to the state and control variables, respectively. Step 3.4: In the reference trajectory and The cost function at each time step Perform a first-order expansion, as shown in equation (12): The local second-order expansion is shown below: Step 3.5: Calculate the correction amount for the control variables based on the Bellman optimality principle and the maximum principle. Step 3.6: i = i + 1, based on the updated control sequence U, execute steps 3.2 to 3.5 again to iteratively update the control commands, directly changing the relative change of the cost function. The value is less than the threshold, or the change in the control sequence is less than the set threshold.

8. The online trajectory planning method for an aircraft based on an iterative linear quadratic regulator as described in claim 7, characterized in that: Step 3.5 is implemented as follows: ① Definition Indicates t k to t N The cumulative cost at any given time t; based on the Bellman optimality principle, the cost at any given time t is obtained recursively. k The minimum cost V(k): definition ②Based on equation (8), we obtain t N The derivative of V(N-1) at point: ③ Based on the principle of maximum value, The optimal control can be determined by first-order conditions: in, At the same time, Performing a Taylor expansion, we get: Among them, Q X It is Q k For the current state The first derivative; Q U It is Q k For the current control command The first derivative; Q XX It is Q k For the current state The second derivative; Q UU It is Q k For the current control command The second derivative; Equation (16) is transformed into: Based on equation (18), we obtain The analytical expression is as follows: in, ④ Calculate t k The derivative of the time-value function: Repeat steps ③-④ to update the control commands at all times based on equation (19), complete a complete control command update process, and obtain the updated control sequence U.

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