A method for ballistic trajectory correction

Abstract

The application discloses a trajectory correction method, which comprises the following steps: presetting the state quantity of the projectile, presetting the action set of the pulse thrust corrector for the correction of the projectile, presetting the correction range of the hit point, and presetting the target point in the correction range; constructing a strategy prediction model by taking the current state of the projectile as the input and taking the action corresponding to the maximum reward value of the next moment in the action set as the output; calculating the reward value and the generation value; updating the reward value by using the generation value, updating the strategy prediction model, and then combining the cross-entropy function to calculate the action executed in the current state and the action executed in the next moment, so as to obtain an optimal strategy prediction model; and inputting the optimal strategy prediction model according to the collected state of the projectile, and outputting the trajectory correction result of the projectile. The application provides an intelligent action sequence decision-making means for the field of flight trajectory correction, and improves the trajectory correction precision.

Description

Technical Field

[0001] This invention belongs to the field of trajectory correction control, and specifically relates to a ballistic trajectory correction method. Background Technology

[0002] Traditional non-continuous pose correction motion sequence prediction methods prioritize algorithm speed while sacrificing correction accuracy.

[0003] One type of algorithm employs mathematical analytical methods for solving the problem, or uses model predictive control and projectile linear theory to determine the action execution logic based on mathematical calculations of the predicted impact point azimuth and distance deviation. Methods involved include uniform design experiment, regression analysis, enumeration, and tabulation-interpolation. These methods offer high computational efficiency, but they rely heavily on prerequisites such as a pre-defined ideal trajectory and prior correction coefficients. These are parameters that are difficult to estimate accurately. Furthermore, as the ignition set (action set) increases, similar methods experience reduced solution efficiency and computational difficulties. In principle, they also heavily depend on the accuracy of the measurement system and the precision of the pre-defined ideal trajectory.

[0004] Another category is ergodic random search algorithms, such as particle swarm optimization, fuzzy control theory, and genetic algorithms. These algorithms can effectively reduce misses, and the optimization of the algorithms themselves also improves the system's anti-interference and robustness. However, they exhibit some common problems, including premature convergence leading to local optima, or being trapped in the oscillating region of local solutions and spending a lot of time without finding a solution, or a rapid increase in solution time and computational cost after adding constraints to the solution. Excessively long convergence periods also significantly reduce their practical effectiveness. Summary of the Invention

[0005] The purpose of this invention is to provide a ballistic trajectory correction method to solve the problems of existing technologies. To achieve the above objective, this invention provides the following technical solution: a ballistic trajectory correction method, comprising the following steps:

[0006] S1. Based on the process of the projectile flying away from the muzzle and starting to fly after receiving the target impact point, the projectile state quantity is preset, the pulse thrust corrector action set for correcting the projectile is preset, the target impact point correction range is preset, and the target point within the correction range is preset.

[0007] S2. Using the current state of the projectile as input and the action corresponding to the maximum reward value in the next moment of the action set as output, construct a policy prediction model.

[0008] S3. Within the correction range of the target hit point, calculate the reward value and cost value of the action to be performed based on the current state obtained by the strategy prediction model.

[0009] S4. Update the reward value using the cost value, update the action to be performed in the current state to the state at the next moment, and update the strategy prediction model. Then, combine the cross-entropy function to calculate the action to be performed in the current state and the action to be performed at the next moment, and determine whether the preset success rate is reached. If so, the strategy prediction model corresponding to the success rate is the optimal strategy prediction model; otherwise, return to step S3.

[0010] S5. Collect the state of the projectile, input the optimal strategy prediction model obtained in step S4, and output the trajectory correction result.

[0011] Furthermore, in the aforementioned step S1, the state variables are s = (x, y, z, v, sinθ) a cosθ a sinψ2,cosψ2, ω ξ , ω η , ω ζ , γ, sinφ2, cos φ2, sinφ a cosφ a ) T Where x, y, z represent the coordinates of the projectile's center of mass, v is the projectile velocity, and the trajectory angle is... Ballistic deflection spring shaft elevation angle Spear shaft direction angle Rotation roll angle ω ξ , ω η , ω ζ These are the rotational speed components in the spring-axis coordinate system. , .

[0012] Furthermore, in the aforementioned step S1, the action set is A, A={a0, a1, a2, …, a N}; where a N This indicates that the correction force is 0.

[0013] Furthermore, in step S1 above, the correction range for the target hit point is obtained as follows:

[0014] S1.1, Based on the time it takes for the projectile to receive the target's point of impact. and the preset cut-off time generate Trajectory points within the interval;

[0015] S1.2, in ~ The trajectory range is For range The target point is randomly generated after the target maneuvers. , but , Where D is The maximum correction range obtained by the projectile when a random action is selected within the interval;

[0016]

[0017] .

[0018] Furthermore, in the aforementioned step S2, the current state of the projectile is used as input, and the action corresponding to the maximum reward value in the next moment of the action set is used as output to construct a policy prediction model; this includes the following sub-steps:

[0019] S2.1, Action Set , ;

[0020] calculate Corresponding phase angle ;

[0021] S2.2, Utilizing kinematic and dynamic model functions Calculate r in the next time step of the action set m (t+k);

[0022] S2.3 Calculate the action corresponding to the maximum reward value in the next moment as follows:

[0023] ;

[0024] Furthermore, in the aforementioned step S4, updating the reward value using the cost value specifically involves:

[0025] The reward value is calculated using the following formula: ;

[0026] The cost value is calculated using the following formula: ,

[0027] The reward value is updated using the substitution value as follows: , For Lagrange operators.

[0028] Compared to existing technologies, the advantages of this invention are as follows: This invention optimizes the solution accuracy and performance of discontinuous attitude correction action sequence prediction methods. By treating the aircraft as an intelligent agent, the trajectory correction control process based on direct force action is transformed into a constrained Markov decision process. A model prediction strategy guides the correction projectile through initial unconstrained training, accelerating the training process. Then, Lagrange multipliers are used to transform the original problem into an unconstrained one, realizing the solution of the constrained Markov decision problem for predicting the triggering timing of a finite number of momentum correction mechanisms using the Lagrange method combined with the policy gradient method. This method enables special aircraft (such as projectiles) to make adaptive decisions on trajectory correction actions in high-dimensional action spaces and under environmental constraints, providing an intelligent action sequence decision-making method for the field of flight trajectory correction and improving trajectory correction accuracy. Attached Figure Description

[0029] Figure 1 This is the network structure diagram of the present invention.

[0030] Figure 2 It is a graph of cross-entropy calculation for actions.

[0031] Figure 3 This is a graph showing the prediction results from the dynamic model.

[0032] Figure 4 This is a comparison diagram of the ballistics of the embodiments.

[0033] Figure 5 This is a graph showing the trend of the corrected ballistic velocity deflection angle in the embodiment. Detailed Implementation

[0034] To better understand the technical content of the present invention, specific embodiments are described below in conjunction with the accompanying drawings.

[0035] In this invention, various aspects of the invention are described with reference to the accompanying drawings, in which numerous illustrative embodiments are shown. Embodiments of the invention are not limited to those depicted in the drawings. It should be understood that the invention is implemented through any of the various concepts and embodiments described above, as well as the concepts and embodiments described in detail below, because the concepts and embodiments disclosed herein are not limited to any particular implementation. Furthermore, some aspects of the invention disclosed may be used alone or in any suitable combination with other aspects of the invention disclosed.

[0036] like Figure 1 As shown, S1, based on the process of the projectile flying away from the muzzle and starting to fly after receiving the target impact point, the projectile state quantity is preset, the action set of the pulse thrust corrector for correcting the projectile is preset, the correction range of the target impact point is preset, and the target point within the correction range is preset.

[0037] The state variables are s = (x, y, z, v, sinθ) a cosθ a sinψ2, cosψ2, ω ξ , ω η , ω ζ , γ,sinφ2, cos φ2, sinφ a cosφ a ) T x, y, z represent the coordinates of the projectile's center of mass, v is the projectile velocity, and the trajectory angle is... Ballistic deflection spring shaft elevation angle Spear shaft direction angle Rotation roll angle ω ξ , ω η , ω ζ These are the rotational speed components in the spring-axis coordinate system. , .

[0038] Let the action set be A, A = {a0, a1, a2, …, a} N}; where a N This indicates that the correction force is 0 N, meaning it is selected to be inactive. The sequence calculation starts from 0, meaning 0# is on the η-axis of the projectile coordinate system. The position α of each corrector within the projectile. i The calculation method is as follows: Where ri represents the total angle rotated by the i-th time, and α i This represents the position of the i-th element in [0, 2π]. This represents the remainder function.

[0039] The mission of anti-aircraft artillery ballistic correction projectiles is to effectively damage or hit the target during the projectile's ascent phase. The projectile is pre-programmed to... Upon receiving information about the target's maneuver, trajectory correction needs to begin. To ensure that the generated target point remains within the projectile's correction range during training, an interception termination time is set. Then, under the launch conditions, the unguided trajectory is calculated and determined. Trajectory points within the interval, and in ~ The trajectory range is For range The target point is randomly generated after the target maneuvers. , but , Where D is The maximum destination range that the projectile can obtain when a random action is selected within the interval.

[0040]

[0041] .

[0042] S2. Using the projectile's current state as input and the action corresponding to the maximum reward value in the next time step as output, construct a policy prediction model. The policy prediction model is established, where the Actor-Crictic network includes three networks: a value function Vr, a policy π, and a cost function Vc. The policy network estimates the probability of each action being selected based on the current state. For the output value, the tf.nn.log_softmax function is used to map the output to the probability interval while ensuring that the output value does not underflow. Actions are sampled using a multinomial distribution. .

[0043] The script for building the policy prediction model is as follows:

[0044] Given: Random policy Randomly initialize the network

[0045] Collect training dataset ={S, A, A uses a random strategy to select...

[0046] Initialize the online training dataset ,

[0047] ForEpoch = 1 ~ max_epoch do

[0048] Using datasets and Training using gradient descent method

[0049] End For

[0050] use Determine the Model Predict Policy (MPP):

[0051] Fort = 0 ~ do

[0052] Get the current state :

[0053] Sampling action sequence ,

[0054] ,

[0055] Calculate action sequence Corresponding phase angle ;

[0056] use Calculate r m (t+k);

[0057]

[0058] Actions to be taken in the current state;

[0059] End For

[0060] S3. Within the correction range of the target hit point, calculate the reward value and cost value of the action to be performed based on the current state obtained by the strategy prediction model.

[0061] The cost function is defined as the immediate cost that a projectile will incur when it performs an action that violates the constraints. In this task, the environmental constraint c indicates that each action cannot exceed a finite number of times it can be performed, with an upper bound of d (d is set to 2, indicating that a single action should not be selected more than 2 times).

[0062] ,

[0063] The correction effect determines the reward value after each action. Based on the target of the ballistic correction, the closer the projectile is to the designated target point after performing a certain action, the higher the reward value should be. The reward function is designed as a dense type (continuous value), utilizing appropriate coefficients. , The relative distance between projectile targets represents the instantaneous reward, as shown in the following formula, where... This is a function for calculating the target vector.

[0064] .

[0065] S4. Update the reward value using the cost value, and update the action to be performed in the current state to the state at the next moment. Update the policy prediction model, and then use the cross-entropy function to calculate the action to be performed in the current state and the action to be performed at the next moment. Determine whether the preset success rate has been reached. If so, the policy prediction model corresponding to the success rate is the optimal policy prediction model. Otherwise, return to step S3.

[0066] The training initial phase is guided by the MPP policy, and the policy network is developed using the Trust Region Policy Optimization (TRPO) method and the Lagrange algorithm. The training script is as follows:

[0067] Known: A reinforcement learning algorithm TRPO

[0068] Reward function:

[0069] Cost function:

[0070] Guidance strategy update epoch count:

[0071] ForEpoch = 1 ~ Total number of steps / Number of steps in each Epoch (do)

[0072] Generate a target , Initialization state

[0073] Fort = 0 ~ Each Epoch contains the number of steps, do.

[0074] IfEpoch

[0075] Generate an optimal action from MPP:

[0076] Else

[0077] from Generate an action

[0078] Obtained from the output of the neural network and

[0079] The agent takes a selective action.

[0080] Calculate immediate return value and cost value ,

[0081] If the penalty reward value does

[0082] Recalculate the reward value after adding the penalty.

[0083] Storage state sequence

[0084] Else

[0085] Storage state sequence [

[0086] If the task is completed or the Episode round ends, do

[0087] If the task is completed but the episode has not ended, do...

[0088] ,

[0089] Else by Network output value acquisition , make

[0090] Depend on Network output value acquisition , make

[0091] Reset Environment

[0092] Update the Lagrange operator:

[0093] Update policy network:

[0094] Update value function network: ,

[0095] in It is the cross-entropy between the output of the policy network and the corresponding selected action. The output value of the policy network is first calculated by taking the softmax value and then the logarithm (log value). During the MPP phase, the former is 1, and the latter is 0 except for the current action probability which is 1. Return is the cumulative reward R, and Cost_retrun is the cumulative cost R. c A represents the reward advantage function, and Ac represents the cost advantage function.

[0096] After training, an optimal policy network model will be obtained. .

[0097] To verify the effectiveness of the trajectory correction algorithm of the present invention, a certain caliber air defense ballistic correction projectile based on pulse thrust was selected. The main implementation parameters in step S1 are shown in Table 1 below:

[0098] Table 1

[0099]

[0100] For all policy networks and value function networks, a multi-layer perceptron network structure is used, with tanh activation function in the hidden layers, four hidden layers, each containing 256 neurons, and a linear activation function in the output layer. Each episode ends when the distance between the projectile and the target point is less than [a certain value]. (That is, ensuring the projectile's correction endpoint CEP is within the distance threshold) or exceeds the maximum number of steps in the episode, but the maximum number of steps in the episode (max timesteps) should be within the effective interception time. This experiment assumes a maximum number of steps of 100 and a simulation step size of 0.002 s. The total number of training rounds is set to 2.50E4, i.e., 2.50E4 / 100 epochs. The MPP phase has 1.3E3 rounds. The policy network is updated every 1024 steps. After each network update, the updated policy network is tested, and the success rate of the projectile completing the mission is calculated. The cross-entropy of the action is calculated as follows. Figure 2 As shown. The predictive effect is as follows Figure 3 As shown in the figure. In a certain example, t_sample=7.88s, the endpoint of the uncontrolled projectile trajectory is [4202.22, 3937.99, -0.76]. The target point with significant lateral deviation is verified to be g= [4200, 3931, -18], g∈G. The simulation yields the corrected endpoint coordinates as [4201.79, 3932.10, -18.42], as shown in Figure 4 below. The trend of its velocity deflection angle is as follows. Figure 5 .

[0101] While the present invention has been described above with reference to preferred embodiments, it is not intended to limit the invention. Those skilled in the art can make various modifications and refinements without departing from the spirit and scope of the invention. Therefore, the scope of protection of the present invention shall be determined by the claims.

Claims

1. A method for correcting ballistic trajectory, characterized in that, Perform the following steps: S1. Based on the process of the projectile flying away from the muzzle and starting to fly after receiving the target impact point, the projectile state quantity is preset, the pulse thrust corrector action set for correcting the projectile is preset, the target impact point correction range is preset, and the target point within the correction range is preset. Wherein, the state variables are s = (x, y, z, v, sinθ) a cosθ a sinψ2, cosψ2, ω ξ , ω η , ω ζ , γ,sinφ2, cos φ2, sinφ a cosφ a ) T Where x, y, z represent the coordinates of the projectile's center of mass, v is the projectile velocity, and the trajectory angle is... Ballistic deflection spring shaft elevation angle Spear shaft direction angle Rotation roll angle ω ξ , ω η , ω ζ These are the rotational speed components in the spring-axis coordinate system. , ; Let the action set be A, A = {a0, a1, a2, …, a} N }; where a N This indicates that the correction force is 0; In step S1, the correction range of the target impact point is obtained according to the following steps: S1.1, Based on the time it takes for the projectile to receive the target's point of impact. and the preset cut-off time generate Trajectory points within the interval; S1.2, in ~ The trajectory range is For range The target point is randomly generated after the target maneuvers. , but , Where D is The maximum correction range obtained by the projectile when a random action is selected within the interval; ； S2. Using the current state of the projectile as input and the action corresponding to the maximum reward value in the next moment of the action set as output, construct a policy prediction model; including the following sub-steps: S2.1, Action Set , ; calculate Corresponding phase angle ; S2.2, Utilizing kinematic and dynamic model functions Calculate r in the next time step of the action set m (t+k); S2.3 Calculate the action corresponding to the maximum reward value in the next moment as follows: ； S3. Within the correction range of the target hit point, calculate the reward value and cost value of the action to be performed based on the current state obtained by the strategy prediction model. S4. Update the reward value using the cost value, update the action to be performed in the current state to the state at the next moment, and update the strategy prediction model. Then, combine the cross-entropy function to calculate the action to be performed in the current state and the action to be performed at the next moment, and determine whether the preset success rate is reached. If so, the strategy prediction model corresponding to the success rate is the optimal strategy prediction model; otherwise, return to step S3. S5. Collect the state of the projectile, input the optimal strategy prediction model obtained in step S4, and output the trajectory correction result.

2. The ballistic trajectory correction method according to claim 1, characterized in that, In step S4, updating the reward value using the cost value specifically involves: The reward value is calculated using the following formula: ; The cost value is calculated using the following formula: , The reward value is updated using the substitution value as follows: , For Lagrange operators.

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