Aircraft closed-loop robust trajectory optimization method, equipment and medium

Abstract

The invention belongs to the technical field of aircraft task capability evaluation, and particularly relates to an aircraft closed-loop robust trajectory optimization method and device and a medium, which can form closed-loop robust trajectory optimization, remarkably improve the robustness of a flight trajectory and ensure high precision and strong robustness of guidance. The method is based on uncertainty propagation, and comprises steering engine, lifting surface and engine fault and random parameter uncertainty representation modeling, aircraft capability boundary prediction, convex optimization online trajectory planning and online capability prediction of graph point cloud deep learning task capability mapping.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft mission capability evaluation, and particularly relates to a closed-loop robust trajectory optimization method, device and medium for an aircraft. Background Art

[0002] Trajectory optimization is an important part of aircraft design. Existing trajectory planning methods are all studied based on deterministic environmental parameters and dynamic models. During the flight process, the standard trajectory is stably tracked through a tracking control loop, so as to ensure that the actual trajectory of the aircraft has a certain robustness against uncertain disturbances. The shortcoming of this method is that the ability of the aircraft to resist various uncertain disturbances is completely realized by the tracking control loop, which increases the design difficulty and pressure of the tracking control loop. Especially for long-range guided rockets, their dynamics are highly nonlinear. In addition to conventional constraints such as the impact point and impact angle during flight, there may also be constraints such as impact velocity, overload, dynamic pressure, and interception threat avoidance. The feasible region of the flight trajectory is severely compressed, and it is particularly affected by the uncertainties of initial conditions, model aerodynamics and environmental parameters. At the same time, due to cost limitations, etc., the ability of long-range rockets to correct deviations without power is weak. Therefore, it is necessary to consider the influence of uncertain factors in the trajectory planning stage, study the closed-loop control method of robust trajectory planning, and improve the robustness of trajectory tracking guidance. Summary of the Invention

[0003] In view of this, the present invention provides a closed-loop robust trajectory optimization method, device and medium for an aircraft, which can form a closed-loop robust trajectory optimization, significantly improve the robustness of the flight trajectory, and ensure high precision and strong robustness of guidance.

[0004] To achieve the above object, the technical solution of the present invention is as follows:

[0005] A closed-loop robust trajectory optimization method for an aircraft, comprising:

[0006] Step 1: According to specific mission requirements, establish constraints and index functions, and construct an optimal control model for the trajectory optimization of a guided rocket including refined dynamics;

[0007] Step 2: Based on the optimal control model constructed in Step 1, use the convex optimization method to quickly obtain a reference trajectory that satisfies all constraints;

[0008] Step 3: Segment the reference trajectory according to time, range or other quantities at a certain interval. There are two corresponding nodes on each segment, and an optimal control model for robust trajectory tracking on this time domain with respect to these discrete nodes is specified within the specified time domain range;

[0009] Step 4: Update the relevant parameters in the optimal control model for robust trajectory tracking, propagate the dynamic uncertainties in the time domain, and obtain the uncertainties of the state variables at each discrete node.

[0010] Step 5: Solve the robust trajectory tracking problem in the time domain.

[0011] Step 6: Apply the control quantity obtained in the first interval above to the aircraft. If the termination condition is not met, update the current state of the aircraft as the initial state for the next-stage optimization, roll the time domain forward by one interval, and return to Step 4.

[0012] Among them, in Step 2, it is completed on the ground before launch, and the processor is used to generate the optimal reference trajectory; for the specific trajectory, the optimal control model is optimized, and the convex optimization method is used for convex clipping. While maintaining its non-linear characteristics, the convexification of the optimal control model is completed to make the convex optimization solution converge.

[0013] Among them, in Step 1, the optimal control model for aircraft trajectory planning is:

[0014]

[0015] In the formula: is the refined dynamic model of the guided rocket; x is the state variable; u is the control variable; g j (x, u, a, t) ≤ 0 is the process constraint; x i (t 0 ) = x i0 is the initial condition; x i (t f ) = x if is the terminal constraint.

[0016] Among them, in Step 3, the influence of uncertainties is introduced into the optimal control model for trajectory tracking under certainty to form a robust trajectory tracking problem.

[0017] Among them, in Step 4, based on the linearized dynamic model in Step 3 The covariance analysis method is used to propagate the dynamic uncertainties, and the means and standard deviations (μ|, σ|) of the trajectory state variables, process constraints g, terminal states, etc. are obtained.

[0018] Among them, in Step 4, the error caused by linearization is eliminated by the closed-loop feedback strategy of model predictive control.

[0019] Among them, in Step 3, the optimal control model for trajectory tracking under certainty:

[0020]

[0021] Among them, (X(m) - X r (m)) 2 and (U(m) - U r (m)) 2 respectively represent the deviations of the state variables (such as speed, position, speed angle, etc.) for trajectory tracking and the control two deviations.

[0022] Among them, small deviation linearization is used for linearization processing to form the dynamic linear equality constraints within the time domain range [k, k + p] Among them, A and B are respectively the first-order partial derivatives of the right function f(x, u, a, t) of the differential equation with respect to the state variable x and the control variable u at the current reference trajectory;

[0023] Form the robust trajectory tracking problem:

[0024]

[0025] Among them, μ| and σ| respectively represent the mean and standard deviation of the corresponding quantity under the action of uncertainty.

[0026] The present invention also provides an electronic device, which includes a processor and a memory for storing executable instructions that can be executed by the processor; the processor is configured to read the executable instructions from the memory and execute the instructions to implement the method of the present invention.

[0027] The present invention also provides a computer-readable storage medium, where the storage medium stores a computer program, and the computer program is used to execute the method of the present invention.

[0028] Beneficial effects:

[0029] 1. The method of the present invention is based on uncertainty propagation and includes servo and lifting surface and engine fault and random parameter uncertainty characterization modeling, aircraft ability boundary prediction, convex optimization online trajectory planning, and online ability prediction of graph point cloud deep learning task capabilities. Specifically, the present invention aims at the requirements of high-precision and strong robustness for aircraft trajectory optimization and guidance, and proposes a closed-loop robust trajectory optimization method based on uncertainty propagation and stochastic model predictive control theory. By constructing a model predictive control architecture including uncertainty, optimal control instructions are generated in the rolling time domain framework, making the flight trajectory insensitive to the influence of uncertainty. At the same time, using the natural feedback control form of model predictive control, a closed-loop robust trajectory optimization is formed, significantly improving the robustness of the flight trajectory and ensuring high-precision and strong robustness of guidance.

[0030] 2. In the method of the present invention, in view of the requirements of aircraft trajectory optimization, high-precision guidance, and strong robustness, a trajectory optimization method based on the idea of optimal control is established. Uncertainty is injected into the dynamic equation of the guided rocket. Under the framework of Receding Horizon Control (RHC), a robust ballistic optimization stochastic optimal control model containing uncertainty is constructed. A fast dynamic uncertainty propagation method based on covariance analysis is proposed, and a closed-loop robust ballistic real-time optimization method based on convex optimization is established, forming a complete closed-loop robust trajectory optimization method based on the theory of efficient uncertainty propagation and stochastic model predictive control.

[0031] 3. The method of the present invention realizes convex optimization fast reference trajectory optimization considering the refined dynamics of the aircraft under complex multi-constraints and fast uncertainty propagation of the trajectory tracking deviation.

[0032] 4. In the method of the present invention, trajectory tracking based on stochastic model predictive control and real-time solution of closed-loop robust trajectory convex optimization are carried out.

[0033] 5. Compared with the traditional method of open-loop trajectory planning + ballistic tracking guidance, the guidance method of the present invention based on online trajectory optimization + model predictive control directly considers the influence of uncertainty in trajectory planning, and by virtue of the natural feedback closed-loop control characteristics of stochastic model predictive control, the advantages of fast calculation of convex optimization and covariance analysis, a closed-loop robust trajectory optimization architecture is formed, achieving the robustness of the flight trajectory in the sense of closed-loop, and improving the guidance accuracy and anti-interference ability.

[0034] 6. The method and technology proposed by the present invention can provide effective theoretical guidance and technical support for the trajectory optimization and guidance of aircraft under the influence of uncertainty. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is the flow chart of the closed-loop robust trajectory optimization method for the aircraft of the present invention.

[0036] Figure 2 is the schematic structural diagram of the electronic device provided by the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0037] The present invention provides a closed-loop robust trajectory optimization method for an aircraft, and its specific implementation process Figure 1 . The closed-loop robust trajectory optimization method for the aircraft of the present invention considers uncertainty and specifically includes the following operating steps:

[0038] Step 1: According to specific task requirements, establish constraints and index functions, and construct an optimal control model for the trajectory optimization of a guided rocket containing refined dynamics. The optimal control model for aircraft trajectory planning can be described as follows:

[0039]

[0040] In the formula: is the refined dynamic model of the guided rocket; x is the state variable, usually including state variables such as velocity, position, and velocity angle; u is the control variable, usually the flight angle of attack and sideslip angle; g j (x, u, a, t) ≤ 0 are process constraints, such as overload constraints and threat avoidance constraints; x i (t 0 ) = x i0 is the initial condition; x i (t f ) = x if is the terminal constraint.

[0041] Step 2: Based on the optimal control model constructed in Step 1, use the convex optimization method to quickly obtain a reference trajectory that satisfies all constraints. This process is completed on the ground before launch, and a high-performance processor can be used to generate the optimal reference trajectory as quickly as possible [X r , U r .

[0042] Here, the optimal control model for trajectory optimization can be targeted, and the convex optimization method can be used to perform convex clipping on it. While trying to maintain its non-linear characteristics, the convexification of the optimal control model is completed, so that the convex optimization solution can converge quickly and reliably, ensuring the accuracy and speed of trajectory generation.

[0043] Step 3: Segment the above reference trajectory according to time, range, or other quantities at a certain interval. There are two corresponding nodes for each segment. Specify the time domain range [k, k + p], and construct the optimal control model for robust trajectory tracking regarding these discrete nodes in this time domain.

[0044] First, establish the optimal control model for trajectory tracking under certainty:

[0045]

[0046] Among them, (X(m) - X r (m)) 2 and (U(m) - U r (m)) 2 respectively represent the deviations of the state variables (such as velocity, position, and velocity angle) and control variables for trajectory tracking.

[0047] In practice, due to the influence of uncertainties, directly solving the optimal control command generated by Equation (2) may cause the flight trajectory to deviate seriously from the expected trajectory, violate the constraints, and lead to the failure of the mission. Based on Equation (2), the influence of uncertainties is introduced. It is assumed that the uncertainties act on the dynamic system in the form of parameter a, and its probability distribution model is given. Taking the uncertainty of the aerodynamic coefficient as an example, the calculation under the influence of uncertainties is as follows:

[0048]

[0049] where N D , N L and N C are normal distribution random variables with a mean of 0 and a given variance. C DN , C LN and C CN represent the nominal values of the drag, lift, and side force coefficients respectively; N D , N L and N C are included in the uncertainty parameter vector a. For the remaining uncertainties, such as the initial state observation deviation and mass deviation, the uncertainty parameters can be introduced with reference to Equation (3).

[0050] Since the interval of the rolling time domain is small at this time, the flight time is short, and the flight distance is not long, some conditions in the dynamic model can be simplified. For example, the earth curvature, gravitational acceleration, dynamic pressure, etc. can all be regarded as constants. At the same time, the model is not highly nonlinear within a single interval, and small deviation linearization is used for linearization processing to form the dynamic linear equality constraint within the time domain range [k, k + p]

[0051]

[0052] where A and B are the first-order partial derivatives of the right function f(x, u, a, t) of the differential equation in Equation (1) with respect to the state quantity x and the control quantity u at the current reference trajectory.

[0053] The following robust trajectory tracking problem is formed:

[0054]

[0055] where μ| and σ| represent the mean and standard deviation of the corresponding quantity under the influence of uncertainties respectively; the safety issues caused by the fluctuations brought by uncertainties are considered in the path constraints.

[0056] Step 4: Let k = 1, update the relevant parameters in Equation (5), and perform the propagation of dynamic uncertainties in the time domain range [k, k + p] to obtain the uncertainties of the state quantities at each discrete node, that is: the mean and variance (μ|, σ|).

[0057] Based on the linearized kinetic model in Step 3 Using the covariance analysis method for kinetic uncertainty propagation, the means and standard deviations (μ|, σ|) of the trajectory state variables, process constraints g, terminal states, etc. are obtained. Only one numerical integration in this time domain range is required to complete the uncertainty propagation, and the accuracy similar to that of Monte Carlo simulation can be obtained, avoiding multiple large-scale calls to forward numerical integration, significantly improving the computational efficiency, and providing the necessary conditions for the implementation and solution of robust trajectory tracking. Moreover, the error caused by the linearization here can be eliminated by the closed-loop feedback strategy of model predictive control.

[0058] Step 5: Solve the robust trajectory tracking problem in the time domain range [k, k + p], that is, Equation (5), so that the generated trajectory can track the reference trajectory as robustly and stably as possible in the probabilistic sense, the influence of uncertainty is as small as possible, and the feasibility and rationality of the flight trajectory are ensured. Since the scale of the optimization problem is small and the uncertainty propagation is very fast, the rapidity of the solution here can be ensured.

[0059] Step 6: Apply the control quantity obtained in the above first interval to the aircraft. If the termination condition is not satisfied, update the current state of the aircraft as the initial state x for the next stage of optimization ik0 , let k = k + 1, roll the time domain forward by one interval, and return to Step 4.

[0060] The embodiment of the present application also provides an electronic device, Figure 2The structure of the electronic device provided by the embodiments of the present invention is shown. For example, the electronic device 20 may include a processor 21, a memory 22, and a transmission device 23. The processor 21 is used to execute the aircraft closed-loop robust trajectory optimization method mentioned in the above embodiments. The processor and the memory may be connected through a bus or other means. Taking the connection through the bus as an example. The transmission device can be connected to the processor and the memory in a wired or wireless manner. The memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs, non-transitory computer-executable programs, and modules, such as the program instructions and modules corresponding to the aircraft closed-loop robust trajectory optimization method in the embodiments of the present application. The processor executes various functional applications and data processing of the processor by running the non-transitory software programs, instructions, and modules stored in the memory, that is, the aircraft closed-loop robust trajectory optimization method in the above method embodiments is implemented. The memory may include a program storage area and a data storage area. Among them, the program storage area may store an operating system and application programs required for at least one function; the data storage area may store data created by the processor and the like. In addition, the memory may include a high-speed random access memory, and may also include a non-transitory memory, such as at least one magnetic disk storage device, a flash memory device, or other non-transitory solid-state storage devices. In some embodiments, the memory may optionally include a memory remotely provided relative to the processor, and these remote memories may be connected to the processor through a network. Examples of the above network include but are not limited to the Internet, an enterprise intranet, a local area network, a mobile communication network, and combinations thereof. The one or more modules are stored in the memory and, when executed by the processor, execute the aircraft closed-loop robust trajectory optimization method in the embodiments.

[0061] As another aspect, the present application also provides a computer-readable storage medium. The computer-readable storage medium may be the computer-readable storage medium included in the device in the above embodiments; or it may exist separately and not be assembled into the device. The computer-readable storage medium may be a tangible storage medium, such as a random access memory (RAM), a memory, a read-only memory (ROM), an electrically programmable ROM, an electrically erasable programmable ROM, a register, a floppy disk, a hard disk, a removable storage disk, a CD-ROM, or any other form of storage medium known in the art. The computer-readable storage medium stores one or more programs, and the one or more programs are used by one or more processors to execute the aircraft closed-loop robust trajectory optimization method described in the present application.

[0062] The above are the preferred embodiments of the present invention and are not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A closed-loop robust trajectory optimization method for an aircraft, characterized in that: include: Step 1: According to the specific mission requirements, constraints and indicator functions are established to construct the optimal control model for guided rocket trajectory optimization including refined dynamics; Step 2: Based on the optimal control model constructed in step 1, a convex optimization method is used to quickly obtain a reference trajectory that satisfies all constraints; Step 3: Divide the reference trajectory into segments according to time, range or other quantities at certain intervals, with each segment corresponding to two nodes, and construct an optimal control model for robust trajectory tracking of these discrete nodes in the time domain within a specified time domain range; Step 4: Update the relevant parameters in the optimal control model of robust trajectory tracking, propagate dynamic uncertainty in the time domain, and obtain the uncertainty of the state quantity at each discrete node; Step 5: Solve the robust trajectory tracking problem in the time domain; Step 6: Apply the control quantity obtained in the first interval to the aircraft. If the termination condition is not met, update the current state of the aircraft as the initial state for the next stage of optimization, scroll forward one interval in the time domain, and return to step 4.

2. The method according to claim 1, characterized in that In the step 2, it is completed on the ground before launching, and the optimal reference trajectory is generated by using a processor; the optimal control model is optimized for the specific trajectory, and the convex optimization method is used to convexify and trim it, and the convexification of the optimal control model is completed while maintaining its nonlinear characteristics, so that the convex optimization solution converges.

3. The method according to claim 2, characterized in that In step 1, the optimal control model for aircraft trajectory planning is: Where: is the refined dynamics model of the guided rocket; x is the state variable; u is the control variable; g j (x,u,a,t)≤0 is a process constraint; x i (t0) = x i0 is the initial condition; x i (t f )=x if is a terminal constraint.

4. The method according to claim 3, characterized in that In the step three, the influence of uncertainty is introduced into the optimal control model of trajectory tracking under determinism to form a robust trajectory tracking problem.

5. The method according to any one of claims 1 to 3, characterized in that: In step 4, based on the linearized kinetic model in step 3, The covariance analysis method is used to propagate dynamic uncertainty, and the mean and standard deviation (μ| , σ|).

6. The method according to claim 5, characterized in that In step 4, the error caused by linearization is eliminated through a closed-loop feedback strategy of model predictive control.

7. The method according to any one of claims 1 to 3, characterized in that: In step 3, the optimal control model for trajectory tracking under determinism is: Among them, (X( m ) - X r ( m )) 2 and(U( m ) - U r ( m )) 2 They respectively represent the state quantity (such as speed, position, velocity angle, etc.) deviation of trajectory tracking and the two control deviations.

8. The method according to any one of claims 1 to 3, characterized in that: Small deviation linearization is used for linearization to form dynamic linear equality constraints in the time domain range [k, k+p] Among them, A and B are the right-hand functions of the differential equation f( x,u,a, t ) The first-order partial derivatives of the state variable x and the control variable u at the current reference trajectory; Form the robust trajectory tracking problem: Among them, μ| , σ|represents the mean and standard deviation of the corresponding quantity under the action of uncertainty.

9. An electronic device, characterized in that: The electronic device includes a processor and a memory for storing executable instructions of the processor; the processor is used to read the executable instructions from the memory and execute the instructions to implement the aircraft closed-loop robust trajectory optimization method described in any one of claims 1-8 above.

10. A computer-readable storage medium, characterized in that: The storage medium stores a computer program, and the computer program is used to execute the aircraft closed-loop robust trajectory optimization method described in any one of claims 1-8.

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