High-precision trajectory planning method based on deep neural network and adaptive moment estimation

Abstract

The application discloses a high-precision trajectory planning method based on a deep neural network and adaptive moment estimation, and belongs to the field of aircraft trajectory optimization.The application is realized in the following way: a deep neural network is used to perform high-precision approximation on an aircraft dynamics model, and online trajectory planning is performed based on adaptive moment estimation; a large number of high-credibility mapping samples of the current state quantity of the aircraft and control instructions-the next moment state of the aircraft are generated through high-precision offline simulation; a plurality of sets of loss functions are designed; the current state quantity of the aircraft and the control instructions-the next moment state of the aircraft are supervised and learned; and a deep neural network is used to accurately describe the dynamics model of the aircraft. The trajectory optimization based on adaptive moment estimation is performed based on the deep neural network, a control sequence U is obtained, the flight trajectory of the aircraft is obtained according to numerical integration, the trade-off between the precision and efficiency of online trajectory planning is realized, and the trajectory optimization of a strong nonlinear system under a complex disturbance environment is realized.

Description

Technical Field

[0001] This invention belongs to the field of aircraft trajectory optimization technology, and particularly relates to a high-precision trajectory planning method based on deep neural networks and adaptive moment estimation. Background Technology

[0002] Due to the constraints of complex dynamics and diverse mission requirements, the trajectory optimization problem is typically described as an optimal control problem encompassing dynamic constraints, process constraints, endpoint constraints, and performance indicators that the aircraft must satisfy. Considering the strong nonlinearity inherent in the aircraft's dynamic model, traditional trajectory optimization methods based on physical models and numerical optimization often suffer from high computational cost, slow solution speed, and susceptibility to local optima, making it extremely challenging to obtain the optimal flight trajectory that meets mission requirements online. Therefore, researching online trajectory optimization methods that combine modern intelligent algorithms is of great significance.

[0003] To quickly and accurately obtain the gradients of the index function and control variables and improve the efficiency of optimization, existing online trajectory optimization methods mostly simplify the dynamic model. For example, they ignore the Earth's rotation and use quadratic polynomials to describe the relationship between aerodynamic lift / drag and the aircraft's Mach number and angle of attack, thereby reducing the difficulty of trajectory optimization. However, this method has a significant drawback: the trajectory planning result is actually infeasible. That is, although the flight trajectory of the aircraft is successfully planned, it does not match the actual physical model of the aircraft. Summary of the Invention

[0004] To address the problem that oversimplification of dynamic models in existing trajectory optimization problems leads to practically infeasible results, this invention aims to provide a high-precision trajectory planning method based on deep neural networks and adaptive moment estimation. This method utilizes deep neural networks to perform high-precision approximation of the aircraft's dynamic model and performs online trajectory planning based on adaptive moment estimation. High-reliability offline simulations generate a large number of highly reliable mapping samples between the aircraft's current state variables and control commands / next-moment states. Multiple loss functions (mean absolute error and root mean square error) are designed. Through supervised learning of these mapping samples, deep neural networks accurately describe the aircraft's dynamic model. The trajectory planning based on adaptive moment estimation using deep neural networks improves the accuracy and efficiency of online trajectory planning for aircraft.

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

[0006] The high-precision trajectory planning method based on deep neural networks and adaptive moment estimation disclosed in this invention includes the following steps:

[0007] Step 1: Create a high-precision aircraft dynamics model dataset based on the mission scope of the aircraft.

[0008] Based on the characteristics of the aircraft's mission scope and actual flight environment, high-precision simulation environments are used to simulate real flight conditions and generate high-quality simulation data.

[0009] Step 1.1: Using a validated flight simulation platform, set different flight states, including cruise, maneuver, climb, and descent. By adjusting the flight control input parameters, generate clear and precise high-precision dynamic simulation data.

[0010] Step 1.2: For each flight state, record the aircraft's position and speed parameters, and accurately record the control input corresponding to each set of data.

[0011] Step 1.3: Label the generated dynamic simulation data sequence, mark the key dynamic parameters of the aircraft position and velocity, as well as the corresponding control inputs, and record the specific values ​​of each state variable in the spatial coordinate system.

[0012] Step 1.4: To generate more comprehensive and richer dynamic data, different combinations of control inputs are designed and executed for specific flight states to ensure that the dataset has sufficient diversity to improve the training effect of the deep neural network in the subsequent step two.

[0013] Step 2: Based on the high-precision aircraft dynamics model dataset built in Step 1, a deep neural network is established through supervised learning of the mapping samples of the current state variables of the aircraft and the control commands to the state of the aircraft at the next moment.

[0014] Step 2.1: Based on a multi-layer fully connected neural network, construct the current state of the spacecraft. and control commands For input, the state of the aircraft at the next moment. This is the output deep neural network. Where x, y, z are the aircraft's position; V is the aircraft's velocity; θ is the aircraft's velocity tilt angle; and ψ is the aircraft's velocity deflection angle.

[0015] Step 2.2: Define the loss function of the deep neural network as a combination of the root mean square error (RMSE) and the mean absolute error (MAE), that is:

[0016]

[0017] in, λ1 and λ2 represent the predicted state of the neural network; λ1 and λ2 are the weight coefficients, respectively; and N is the number of samples participating in a single training iteration.

[0018] Step 3: Configure the parameters required for network training, train the deep neural network until a well-trained deep neural network that meets the preset training requirements is obtained.

[0019] The learning rate, batch size, weight initialization method, weight decay coefficient, optimization method, and number of iterations are set. Based on a high-precision aircraft dynamics model dataset, the network parameters are optimized using the backpropagation algorithm until the training error converges and reaches the required accuracy, resulting in a trained deep neural network NN(φ), where φ represents the parameters of the deep neural network.

[0020] Step 4: Based on the deep neural network trained in Step 3, accurately describe the dynamic model of the aircraft, perform trajectory optimization based on adaptive moment estimation based on the deep neural network, build the trajectory optimal control problem, and improve the accuracy of the aircraft's online trajectory optimization.

[0021] Step 4.1: The constraints that the aircraft must meet during flight include:

[0022]

[0023] In the formula: X is the aircraft state vector; Q s For example, q represents the heat flux of the aircraft; q represents the dynamic pressure; n represents the overload; t0 represents the initial time; t represents the initial time. f At the endpoint, X0, X f These are the initial and final states of the aircraft, α. min α max These are the minimum and maximum angle-of-attack constraints, β. min β max These are the minimum and maximum sideslip angle constraints, k 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;

[0024] Step 4.2: Construct the optimal control model for discretized trajectory optimization as follows:

[0025]

[0026] In the formula, J is the objective function, U is the aircraft control variable, which is also the optimization variable of this optimal problem, Q, R, and K are the weight coefficients of each term in the objective function, and g j Here, Δt is the constraint function; Δt is the discretization step size; N is the number of discrete points.

[0027] Step 4.3: Transform the original optimal control model, converting the inequality constraints into penalty functions, to obtain the transformed optimal control problem:

[0028]

[0029] Step 5: Solve the trajectory optimal control problem constructed in Step 4 based on adaptive moment estimation. Based on the solution of the trajectory optimal control problem, realize high-precision online trajectory planning based on deep neural network to improve the efficiency of online trajectory planning of aircraft.

[0030] Step 5.1: Simplify equation (4) as follows:

[0031]

[0032] For this optimization problem, an adaptive moment estimation method is used for fast solution. The specific update rule is as follows:

[0033]

[0034] in, These are first-order statistical moments; β1 and β2 are the second-order statistical moments; τ is the learning rate; β1 and β2 are the exponential decay rates estimated by the first and second moments; ε is a small constant to prevent division by zero.

[0035] Based on the chain rule, we obtain:

[0036]

[0037] in Determined by the deep neural network, it is a lower diagonal matrix, calculated using the chain rule, as follows:

[0038]

[0039]

[0040]

[0041] Based on equation (6), the control variable U is iterated continuously until U meets the convergence threshold or reaches the maximum number of iterations, and the trajectory optimization problem is solved.

[0042] Step 5: Solve the trajectory optimal control problem constructed in Step 4 based on adaptive moment estimation. Based on the solution of the trajectory optimal control problem, implement high-precision online trajectory planning based on deep neural network to obtain the control sequence U. Obtain the flight trajectory of the aircraft based on numerical integration to improve the efficiency of online trajectory planning of the aircraft.

[0043] Beneficial effects:

[0044] 1. This invention discloses a high-precision trajectory planning method based on deep neural networks and adaptive moment estimation. It uses deep neural networks to perform high-precision approximation of the aircraft dynamics model, solving the problem of trajectory infeasibility caused by model simplification in traditional methods. The deep neural network utilizes a large amount of high-reliability simulation data and, through supervised training with a combined loss function, accurately captures the nonlinear mapping relationship between state variables and control commands. The deep neural network takes the current state and control variables as input and outputs the state at the next moment, ensuring that the optimized trajectory strictly conforms to the dynamics model and guaranteeing the trajectory's practical executability.

[0045] 2. This invention discloses a high-precision trajectory planning method based on deep neural networks and adaptive moment estimation. It introduces adaptive moment estimation to solve the optimal trajectory control problem, overcoming the bottlenecks of traditional numerical optimization methods, such as high computational cost and susceptibility to local optima. Adam efficiently handles high-dimensional non-convex optimization problems caused by deep neural networks by dynamically adjusting the learning rate and gradient moment estimation. Combined with the chain rule, it rapidly calculates the gradient of the objective function with respect to the control variables, enabling iterative updates of the control sequence. This meets the millisecond-level response requirements of online trajectory planning for aircraft, and is particularly suitable for real-time replanning tasks under complex disturbance environments.

[0046] 3. The high-precision trajectory planning method based on deep neural networks and adaptive moment estimation disclosed in this invention constructs a collaborative framework of "offline high-precision training + online rapid optimization": In the offline stage, a deep neural network model is trained using large-scale simulation data; in the online stage, this model is directly invoked to construct the trajectory optimization problem, and Adam is used for efficient solution. Time-consuming high-precision computation is moved to the offline stage, while the online stage only requires lightweight network inference and gradient updates, avoiding the burden of solving complex differential equations online as in traditional methods. Simultaneously, the penalty function mechanism seamlessly integrates process constraints into the optimization objective, further accelerating the solution while ensuring safety, achieving global optimization of multiple performance indicators such as flight time and energy consumption, and improving the optimality and real-time performance of trajectory optimization. Attached Figure Description

[0047] Figure 1 Neural network structure diagram

[0048] Figure 2 Overall architecture diagram of trajectory optimization

[0049] Figure 3 Longitude-Latitude Diagram of Trajectory Planning Results

[0050] Figure 4 Longitude-elevation diagram of trajectory planning results Detailed Implementation

[0051] 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.

[0052] The high-precision trajectory planning method based on deep neural networks and adaptive moment estimation disclosed in this embodiment is implemented in the following steps:

[0053] Step 1: Create a high-precision aircraft dynamics model dataset based on the mission scope of the aircraft.

[0054] Based on the characteristics of the aircraft's mission scope and actual flight environment, high-precision simulation environments are used to simulate real flight conditions and generate high-quality simulation data.

[0055] Step 1.1: Using a validated flight simulation platform, set different flight states, including cruise, maneuver, climb, and descent. By adjusting the flight control input parameters, generate clear and precise high-precision dynamic simulation data.

[0056] Step 1.2: For each flight state, record the aircraft's position and speed parameters, and accurately record the control input corresponding to each set of data.

[0057] Step 1.3: Label the generated dynamic simulation data sequence, mark the key dynamic parameters of the aircraft position and velocity, as well as the corresponding control inputs, and record the specific values ​​of each state variable in the spatial coordinate system.

[0058] Step 1.4: To generate more comprehensive and richer dynamic data, different combinations of control inputs are designed and executed for specific flight states to ensure that the dataset has sufficient diversity to improve the training effect of the deep neural network in the subsequent step two.

[0059] Step 2: Based on the high-precision aircraft dynamics model dataset built in Step 1, a deep neural network is established through supervised learning of the mapping samples of the current state variables of the aircraft and the control commands to the state of the aircraft at the next moment.

[0060] Step 2.1: Based on a multi-layer fully connected neural network, construct the current state of the spacecraft. and control commands For input, the state of the aircraft at the next moment. This is the output deep neural network. Where x, y, z are the aircraft's position; V is the aircraft's velocity; θ is the aircraft's velocity tilt angle; and ψ is the aircraft's velocity deflection angle. The specific deep neural network structure is as follows: Figure 1 The neural network structure diagram is shown.

[0061] Step 2.2: Define the loss function of the deep neural network as a combination of the root mean square error (RMSE) and the mean absolute error (MAE), that is:

[0062]

[0063] in, λ1 and λ2 represent the predicted state of the neural network; λ1 and λ2 are the weight coefficients, respectively; and N is the number of samples participating in a single training iteration.

[0064] Step 3: Configure the parameters required for network training, train the deep neural network until a well-trained deep neural network that meets the preset training requirements is obtained.

[0065] The network training was implemented using the PyTorch deep learning framework on a single RTX 3090. The initial learning rate was set to 0.001, the batch size to 512, the network weights were initialized using Xavier, the weight decay coefficient was set to 0.0001, the Adam optimization algorithm was used, and the number of training iterations was set to 500.

[0066] Based on a high-precision aircraft dynamics model dataset, the network parameters are optimized using the backpropagation algorithm until the training error converges and reaches the required accuracy, resulting in a trained deep neural network NN(φ), where φ represents the parameters of the deep neural network.

[0067] Step 4: Based on the deep neural network trained in Step 3, accurately describe the dynamic model of the aircraft, perform trajectory optimization based on adaptive moment estimation based on the deep neural network, build the trajectory optimal control problem, and improve the accuracy of the aircraft's online trajectory optimization.

[0068] Step 4.1: The constraints that the aircraft must meet during flight include:

[0069]

[0070] In the formula: X0 = [4500m / s 2 ,0°,90°,6416000m,118.7955°,26.5105°], X0=[2500m / s 2 ,0°,90°,6396000m,141.1633°,16.439582°]. α min =-20°, α max =20°, β min =-20°, β max =20°, Q smax =149.4kWh / m 2 ;k Q =9.4369×10 -5 ;q min =70kPa; qmax =400kPa; n max =20

[0071] Step 4.2: Construct the optimal control model for discretized trajectory optimization as follows:

[0072]

[0073]

[0074] Where N = 300, Δt = 2s.

[0075] Step 4.3: Transform the original optimal control model, converting the inequality constraints into penalty functions, to obtain the transformed optimal control problem:

[0076]

[0077] Step 5: Solve the trajectory optimal control problem constructed in Step 4 based on adaptive moment estimation. Based on the solution of the trajectory optimal control problem, realize high-precision online trajectory planning based on deep neural network to improve the efficiency of online trajectory planning of aircraft.

[0078] Step 5.1: Simplify equation (4) as follows:

[0079]

[0080] For this optimization problem, an adaptive moment estimation method is used for fast solution. The specific update rule is as follows:

[0081]

[0082] Among them, τ=0.003; β1=3×10 -4 β2=3×10 -4 ε = 1 × 10 -5 .

[0083] Based on the chain rule, we obtain:

[0084]

[0085] in Determined by the deep neural network, it is a lower diagonal matrix, calculated using the chain rule, as follows:

[0086]

[0087]

[0088]

[0089] Based on equation (6), the control variable U is iterated continuously until U meets the convergence threshold or reaches the maximum number of iterations.

[0090] Step 5: Solve the trajectory optimal control problem constructed in Step 4 based on adaptive moment estimation. Based on the solution to the trajectory optimal control problem, implement high-precision online trajectory planning using a deep neural network to obtain the control sequence U. Obtain the flight trajectory of the aircraft using numerical integration. The results are 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.

[0091] 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 high-precision trajectory planning method based on deep neural networks and adaptive moment estimation, characterized in that: Includes the following steps: Step 1: Based on the mission scope of the aircraft, create a high-precision aircraft dynamics model dataset; Step 2: Based on the high-precision aircraft dynamics model dataset built in Step 1, a deep neural network is established through supervised learning of the mapping samples between the current state variables of the aircraft and the control commands and the state of the aircraft at the next moment. Step 2 is implemented as follows: Step 2.1: Based on a multi-layer fully connected neural network, construct the current state of the spacecraft. and control commands For input, the state of the aircraft at the next moment. The deep neural network is the output; where y and z represent the position of the aircraft; V represents the velocity of the aircraft. The aircraft's speed tilt angle; The deflection angle of the aircraft's speed; Step 2.2: Define the loss function of the deep neural network as a combination of the root mean square error (RMSE) and the mean absolute error (MAE), that is: in, The state predicted by the neural network; The weighting coefficients are respectively; N is the number of samples participating in a single training iteration; Step 3: Configure the parameters required for network training, train the deep neural network until a well-trained deep neural network that meets the preset training requirements is obtained; Step 4: Based on the deep neural network trained in Step 3, accurately describe the dynamic model of the aircraft, perform trajectory optimization based on adaptive moment estimation based on the deep neural network, build the trajectory optimal control problem, and improve the accuracy of the aircraft's online trajectory optimization; Step 4 is implemented as follows: Step 4.1: The constraints that the aircraft must meet during flight include: In the formula: X is the aircraft state vector; q represents the heat flux of the aircraft; q represents the dynamic pressure; n represents the overload. At the starting time, The final moment, , These are the initial state and the final state of the aircraft, respectively. , These are the minimum and maximum angle-of-attack constraints, respectively. , These are the minimum and maximum constraints for the sideslip angle, respectively. The heat flux coefficient is... For maximum heat flux constraint, , These are the minimum and maximum dynamic pressure constraints, respectively. Maximum overload constraint; Step 4.2: Construct the optimal control model for discretized trajectory optimization as follows: In the formula, J is the objective function, U is the aircraft control variable, which is also the optimization variable for this optimal control problem, and Q, R, and K are the weight coefficients of each term in the objective function. For constraint functions; N is the discretization step size; N is the number of discrete points. , ; Step 4.3: Transform the original optimal control model, converting the inequality constraints into penalty functions, to obtain the transformed optimal control problem: Step 5: Solve the trajectory optimal control problem constructed in Step 4 based on adaptive moment estimation. Based on the solution of the trajectory optimal control problem, implement high-precision online trajectory planning based on deep neural network to obtain the control sequence U. Obtain the flight trajectory of the aircraft based on numerical integration to improve the efficiency of online trajectory planning of the aircraft. Step 5 is implemented as follows: Step 5.1: Simplify equation (4) as follows: For this optimal control problem, an adaptive moment estimation method is used for fast solution. The specific update rule is as follows: in, These are first-order statistical moments; These are second-order statistical moments; The learning rate; The exponential decay rate estimated by the second moment when it is the first moment; To prevent division by zero of small constants; Based on the chain rule, we obtain: in Determined by the deep neural network, it is a lower diagonal matrix, calculated using the chain rule, as follows: Based on equation (6), the control variable U is iterated continuously until U meets the convergence threshold or reaches the maximum number of iterations, and the trajectory optimization problem is solved.

2. The high-precision trajectory planning method based on deep neural networks and adaptive moment estimation as described in claim 1, characterized in that: In step 1, Based on the characteristics of the aircraft's mission scope and actual flight environment, high-precision simulation environments are used to simulate real flight conditions and generate high-quality simulation data.

3. The high-precision trajectory planning method based on deep neural networks and adaptive moment estimation as described in claim 2, characterized in that: Step 1 is implemented as follows: Step 1.1: Using a validated flight simulation platform, set different flight states, including cruise, maneuver, climb, and descent. By adjusting the flight control input parameters, generate clear and precise high-precision dynamic simulation data. Step 1.2: For each flight state, record the aircraft's position and speed parameters, and accurately record the control inputs corresponding to each set of data; Step 1.3: Label the generated dynamic simulation data sequence, mark the key dynamic parameters of the aircraft position and velocity, as well as the corresponding control inputs, and record the specific values ​​of each state variable in the spatial coordinate system; Step 1.4: To generate more comprehensive and richer dynamic data, design and execute different combinations of control inputs for specific flight states to ensure that the dataset has sufficient diversity.

4. The high-precision trajectory planning method based on deep neural networks and adaptive moment estimation as described in claim 3, characterized in that: Step 3 is implemented as follows: Set the learning rate, batch size, weight initialization method, weight decay coefficient, optimization method, and number of iterations; based on a high-precision aircraft dynamics model dataset, optimize the network parameters using the backpropagation algorithm until the training error converges and reaches the desired accuracy to obtain a trained deep neural network. ,in These are the parameters of the deep neural network.

5. The high-precision trajectory planning method based on deep neural networks and adaptive moment estimation as described in claim 1, 2, 3, or 4, characterized in that: It also includes step 6: Based on the control sequence U obtained in step 5, the flight trajectory of the aircraft is obtained by numerical integration, which significantly improves the accuracy and real-time performance of trajectory generation, realizes the trade-off between accuracy and efficiency in online trajectory planning, and thus achieves trajectory optimization of strongly nonlinear systems under complex disturbance environments.

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