An adaptive variable step RK4 high-precision landing point real-time prediction method for rocket capture arm recovery

Abstract

The application discloses a self-adaptive variable step RK4 high-precision landing point real-time prediction method for rocket capture arm recovery, relates to the technical field of rocket recovery trajectory prediction and rocket capture arm dynamic capture control, and discloses the following technical scheme. The method comprises the following steps: synchronously collecting rocket six-degree-of-freedom flight states and recovery working condition parameters; constructing a self-adaptive step adjusting model, dividing a far-field cruising stage and a near-field capture stage according to a falling speed, and dynamically adjusting an RK4 iteration step; performing differential trajectory deduction and landing point fine correction for different stages; constructing a multi-source disturbance convergence criterion, introducing a dynamic error correction coefficient to compensate and calibrate trajectory drift; and outputting real-time landing point prediction results and matching a capture arm motion response period. The application solves the problem that traditional fixed step algorithms cannot simultaneously consider real-time performance and precision, and effectively improves the alignment precision and success rate of dynamic recovery.

Description

Technical Field

[0001] This invention relates to the fields of rocket recovery trajectory prediction and dynamic capture control technology for rocket capture arms, specifically to an adaptive variable step size RK4 high-precision real-time prediction method for rocket capture arm recovery. Background Technology

[0002] Reusable first-stage rocket technology is a key technology for reducing space launch costs and improving the reusability of space equipment. Compared with traditional fixed-point landing and fixed-net interception recovery methods, the dynamic clamping rocket recovery scheme using a capture arm has advantages such as strong adaptability to operating conditions, high recovery positioning accuracy, and high recovery and reuse efficiency. It is an important development direction for intelligent rocket recovery technology at present.

[0003] Existing technologies generally employ the fixed-step RK4 algorithm for iterative prediction of rocket landing trajectories. Most existing methods simplify the translation of the center of mass and use single-dimensional attitude modeling. Applying this type of fixed-step algorithm to the dynamic capture conditions of rocket capture arms exhibits significant applicability limitations. During the high-altitude, high-speed, far-field flight phase of the rocket, fixed small-step iterative simulations are inefficient, with simulation time far exceeding the tolerance requirements of real-time prediction output. During the near-field, low-speed capture phase, fixed large-step iterative simulations suffer from severe accuracy deviations. Due to the neglect of three-axis attitude coupling perturbation information and the mismatch with the real-time dynamic pose of the capture arm, the final calculated landing point and clamping attitude fitting error is excessively large. Furthermore, the existing fixed-step RK4 algorithm is prone to trajectory drift and divergence in complex low-altitude environments, causing the final output parameters to fail to meet the alignment requirements of the capture arm's dynamic response, easily leading to alignment deviations and even recovery failure. Summary of the Invention

[0004] To overcome the aforementioned deficiencies of the prior art, embodiments of the present invention provide an adaptive variable step size RK4 high-precision real-time landing point prediction method for rocket capture arm recovery to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: an adaptive variable step size RK4 high-precision real-time prediction method for rocket capture arm recovery, comprising the following steps: S1, synchronously acquiring rocket six-degree-of-freedom descent flight state parameters and recovery condition parameters; wherein, the rocket six-degree-of-freedom descent flight state parameters include the rocket's real-time three-dimensional descent flight speed, real-time spatial position altitude, rocket body pitch angle, yaw angle, roll angle, three-axis attitude disturbance angular velocity, and attitude disturbance amplitude; the recovery condition parameters include the real-time motion position of the capture arm end, real-time motion rate, and low-altitude atmospheric turbulence intensity; S2, constructing an adaptive step size adjustment model based on the rocket six-degree-of-freedom descent flight state parameters and recovery condition parameters, and dividing the high-speed far-field cruise phase and low-speed phase according to the rocket's real-time three-dimensional descent flight speed. In the near-field capture phase, a large iteration step size of the RK4 algorithm is configured during the high-speed far-field cruise phase, and a small iteration step size is configured during the low-speed near-field capture phase; S3, during the high-speed far-field cruise phase, RK4 trajectory iteration calculation is performed with a large iteration step size to solve for the rocket's predicted landing point, and during the low-speed near-field capture phase, RK4 trajectory iteration calculation is performed with a small iteration step size to correct the landing point coordinates; S4, based on the low-altitude atmospheric turbulence intensity, the three-axis attitude disturbance angular velocity, and the attitude disturbance amplitude, a multi-source disturbance convergence criterion is constructed and a dynamic error correction coefficient is calculated. The dynamic error correction coefficient is used to compensate and calibrate the trajectory drift error generated during the RK4 trajectory iteration calculation process, output the rocket's real-time landing point prediction result, and match the update frequency of the rocket's real-time landing point prediction result with the capture arm motion response cycle.

[0006] In a preferred embodiment, the specific process of synchronously acquiring the rocket's six-degree-of-freedom descent flight state parameters and recovery condition parameters is as follows: The rocket's six-degree-of-freedom descent flight state parameters are acquired through a ground telemetry system; the low-altitude atmospheric turbulence intensity, the real-time position of the capture arm's end effector, and the real-time velocity are acquired through an environmental monitoring module and a capture arm control system; a linear interpolation time alignment method is used to construct a uniform discrete reference time axis according to the capture arm control cycle; the acquired parameters are sorted in ascending order of timestamps; for each reference synchronization moment, two adjacent sets of original sampled data are selected and substituted into the linear interpolation formula to calculate the standardized observation value corresponding to the unified moment, thus completing time-series registration; a first-order exponential low-pass filter is used to suppress noise in the standardized observation values ​​after time-series registration; a fixed threshold is set based on the single-step parameter change to perform outlier removal; and minimum-maximum linear normalization is performed based on the upper and lower limits of the physical parameters.

[0007] In a preferred embodiment, the rocket's real-time three-dimensional descent velocity is used to divide the high-speed far-field cruise phase and the low-speed near-field capture phase. The specific process for configuring a large iteration step size for the RK4 algorithm during the high-speed far-field cruise phase and a small iteration step size during the low-speed near-field capture phase is as follows: A preset threshold for the rocket's three-dimensional descent velocity and a near-field capture altitude threshold are established. When the rocket's real-time three-dimensional descent velocity exceeds the threshold, it is determined to be in the high-speed far-field cruise phase, and a fixed large iteration step size is used to substitute into the RK4 iterative formula to solve the rocket's six-degree-of-freedom dynamic equations iteratively. When the rocket's real-time three-dimensional descent velocity is less than or equal to the threshold and the real-time spatial position altitude is lower than the near-field capture altitude threshold, it is determined to be in the low-speed near-field capture phase, and the small iteration step size is gradually reduced according to the altitude range.

[0008] In a preferred embodiment, the specific process of performing RK4 trajectory iteration calculations to solve for the rocket's estimated landing point during the high-speed far-field cruise phase with a large iteration step size, and performing RK4 trajectory iteration calculations to correct the landing point coordinates during the low-speed near-field capture phase with a small iteration step size, is as follows: After each iteration step size switch, the rocket's six-degree-of-freedom descent flight state parameters at the current moment are used as the initial values ​​for iteration. Combined with the rocket's six-degree-of-freedom dynamic differential equations, RK4 fourth-level sub-iteration operations are performed to update the rocket's three-dimensional spatial position frame by frame. The updated rocket three-dimensional spatial position is combined with the extrapolated fixed-duration trajectory curve, and the end coordinates of the extrapolated fixed-duration trajectory curve are used as the rocket's estimated landing point. The boundary constraint correction of the rocket's estimated landing point is performed based on the reachable range formed by the real-time motion position of the capture arm end.

[0009] In a preferred embodiment, before constructing the multi-source disturbance convergence criterion, the specific process of calculating the two types of disturbance deviations is as follows: combining the instantaneous three-dimensional wind speed output by the wind profiler radar and the intensity of low-altitude atmospheric turbulence, a three-dimensional deviation vector of low-altitude atmospheric turbulence is constructed; the single-axis difference between the measured attitude and the nominal attitude corresponding to the pitch angle, yaw angle, and roll angle of the rocket body is extracted, and substituted into the preset attitude coupling matrix to calculate the three-axis residual attitude coupling offset deviation vector of the rocket body; the nominal attitude is the pre-set time-series attitude curve.

[0010] In a preferred embodiment, the specific process of constructing a multi-source disturbance convergence criterion and calculating dynamic error correction coefficients based on the intensity of low-altitude atmospheric turbulence, the angular velocity of three-axis attitude disturbance, and the amplitude of attitude disturbance is as follows: The multi-source disturbance convergence criterion consists of a six-degree-of-freedom attitude disturbance convergence sub-criterion and an atmospheric turbulence convergence sub-criterion; the six-degree-of-freedom attitude disturbance convergence sub-criterion is constructed based on the L2 norm of the three-axis residual attitude coupling offset deviation vector of the rocket body, and the atmospheric turbulence convergence sub-criterion is constructed based on the L2 norm of the three-dimensional deviation vector of low-altitude atmospheric turbulence; the calculated values ​​of the six-degree-of-freedom attitude disturbance convergence sub-criterion and the atmospheric turbulence convergence sub-criterion are weighted and fused to generate a total convergence index, two levels of disturbance thresholds are set to classify the disturbance strength levels, and a dynamic error correction coefficient vector is generated based on the total convergence index using a piecewise linear mapping method.

[0011] In a preferred embodiment, the specific process of compensating and calibrating the trajectory drift error generated during the RK4 trajectory iterative calculation using dynamic error correction coefficients is as follows: the dynamic error correction coefficient vector is coupled element-wise with the three-dimensional deviation vector of low-altitude atmospheric turbulence and the three-axis residual attitude coupling offset deviation vector of the rocket body; the coupling result is embedded into the RK4 trajectory iterative calculation process and the final state recursion stage, and the three-dimensional position parameters, three-dimensional velocity parameters and three-axis attitude parameters output at each stage of the RK4 trajectory iterative calculation are synchronously compensated and corrected dimension-wise.

[0012] In a preferred embodiment, matching the update frequency of the rocket's real-time landing point prediction results with the motion response cycle of the capture arm further includes the following process: extracting the rocket's real-time landing point prediction results after compensation and calibration, constructing an optimal clamping point cost function with capture arm position constraints and velocity reachability domain constraints; and solving the optimal clamping point cost function using the gradient projection method to obtain the optimal clamping target point for the rocket body section to adapt to the clamping position.

[0013] In a preferred embodiment, after obtaining the optimal clamping target position, the following process is also included: inputting the Cartesian space coordinates of the optimal clamping target position into the inverse kinematics solution model of the capture arm to calculate the target rotation angle and end motion speed command of the left and right capture arms; collecting the motion position and motion speed of the capture arm and converting the actual motion pose of the capture arm.

[0014] In a preferred embodiment, after obtaining the actual motion pose of the capture arm, the following process is also included: in the next frame prediction iteration, the deviation term between the actual motion pose of the capture arm and the optimal clamping target position is extracted and cross-cycle closed-loop correction is performed; the real-time landing point prediction result of the rocket and the optimal clamping target position are refreshed cycle by cycle, and the terminal motion speed command is issued to drive the capture arm to adjust the terminal running trajectory.

[0015] The technical effects and advantages of this invention are as follows:

[0016] (1) An adaptive variable step size RK4 high-precision real-time landing point prediction method for rocket capture arm recovery. Based on synchronously collected full-dimensional flight state and low-altitude operating condition parameters, an adjustment model is constructed. The cruise and capture conditions are divided according to the rocket's descent speed, and the RK4 iteration step size is configured differently. The computational efficiency of trajectory extrapolation is ensured during the far-field cruise phase, and high-precision fitting of the landing trajectory is achieved during the near-field capture phase. This method overcomes the technical limitation of traditional fixed step size algorithms in predicting the entire flight range, where extrapolation efficiency and fitting accuracy cannot be simultaneously achieved.

[0017] (2) An adaptive variable step size RK4 high-precision real-time landing point prediction method for rocket capture arm recovery. By constructing a multi-source perturbation convergence criterion adapted to near-field dynamic capture and calculating the dynamic error correction coefficient, the predicted trajectory drift caused by the coupling between low-altitude atmospheric turbulence and rocket body attitude is offset from the bottom layer of iterative calculation. The landing point prediction update frequency after perturbation compensation can be directly matched with the timing of the capture arm motion response cycle, which greatly improves the convergence stability of the prediction model under complex working conditions and provides reliable data support for dynamic alignment and precise clamping operations.

[0018] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0019] Figure 1 This is a flowchart of an adaptive variable step size RK4 high-precision real-time landing point prediction method for rocket capture arm recovery according to the present invention.

[0020] Figure 2 This is a schematic diagram of the adaptive variable step size working condition switching logic of the present invention.

[0021] Figure 3 This is a diagram illustrating the multi-source disturbance error correction mechanism of the present invention.

[0022] Figure 4 This is a schematic diagram of the rocket capture arm dynamic recovery linkage prediction system of the present invention. Detailed Implementation

[0023] This application provides an adaptive variable step size RK4 high-precision real-time landing point prediction method for rocket capture arm recovery. This method solves the problems of divergence in landing point prediction trajectory caused by environmental disturbances and attitude coupling during rocket dynamic recovery, as well as severe mismatch in capture arm alignment accuracy caused by fixed step size iteration.

[0024] The overall approach of the scheme in this application embodiment is as follows: Simultaneously acquire the rocket's six-degree-of-freedom descent flight state parameters and recovery condition parameters; construct an adaptive step-size adjustment model based on the descent flight state parameters, capture arm motion condition parameters, and low-altitude turbulence parameters; divide the rocket's real-time three-dimensional descent flight speed into two iterative conditions: a high-speed far-field cruise phase and a low-speed near-field capture phase; dynamically match and adjust the iteration step size of the RK4 algorithm; perform differentiated RK4 trajectory iteration calculations for different iterative conditions: in the high-speed far-field cruise phase, a large iteration step size is used to quickly solve for the rocket's estimated landing point, efficiently completing the macroscopic trajectory extrapolation; in... During the low-speed near-field acquisition phase, a small iteration step size is used to refine the landing point coordinates, improving the trajectory fitting accuracy. A multi-source disturbance convergence criterion adapted to the rocket's six-degree-of-freedom near-field dynamic acquisition is constructed. For two core disturbance factors, namely low-altitude atmospheric turbulence interference and rocket body six-degree-of-freedom residual attitude coupling disturbance, a dynamic error correction coefficient is introduced to compensate for and iteratively calibrate the trajectory drift error generated during the RK4 iteration process in real time. The real-time landing point prediction result of the rocket after disturbance calibration is output, so that the prediction update frequency matches the millisecond-level motion response cycle of the acquisition arm, providing real-time data support for the dynamic alignment and precise clamping acquisition of the acquisition arm.

[0025] Example 1; please refer to Figure 1 This invention provides a technical solution: an adaptive variable step size RK4 high-precision real-time landing point prediction method for rocket capture arm recovery, comprising the following steps: S1, synchronously acquiring rocket six-degree-of-freedom descent flight state parameters and recovery condition parameters; wherein, the rocket six-degree-of-freedom descent flight state parameters include the rocket's real-time three-dimensional descent flight speed, real-time spatial position altitude, rocket body pitch angle, yaw angle, roll angle, three-axis attitude disturbance angular velocity, and attitude disturbance amplitude; the recovery condition parameters include the real-time motion position of the capture arm end, real-time motion rate, and low-altitude atmospheric turbulence intensity; S2, constructing an adaptive step size adjustment model based on the rocket six-degree-of-freedom descent flight state parameters and recovery condition parameters, dividing the high-speed far-field cruise phase and the low-speed near-field phase according to the rocket's real-time three-dimensional descent flight speed. In the capture phase, a large iteration step size of the RK4 algorithm is configured during the high-speed far-field cruise phase, and a small iteration step size is configured during the low-speed near-field capture phase; S3, during the high-speed far-field cruise phase, RK4 trajectory iteration calculation is performed with a large iteration step size to solve for the rocket's predicted landing point, and during the low-speed near-field capture phase, RK4 trajectory iteration calculation is performed with a small iteration step size to correct the landing point coordinates; S4, based on the low-altitude atmospheric turbulence intensity, the three-axis attitude disturbance angular velocity, and the attitude disturbance amplitude, a multi-source disturbance convergence criterion is constructed and a dynamic error correction coefficient is calculated. The dynamic error correction coefficient is used to compensate and calibrate the trajectory drift error generated during the RK4 trajectory iteration calculation process, output the rocket's real-time landing point prediction result, and match the update frequency of the rocket's real-time landing point prediction result with the capture arm motion response cycle.

[0026] In this implementation scheme, step S1 is used to construct a unified reference data source before prediction and simulation. This step aligns the multi-source heterogeneous data from both spatial and temporal dimensions. In the spatial dimension, the rocket's six-degree-of-freedom descent flight state parameters (i.e., translational velocity, position and altitude in three-dimensional space, and pitch angle, yaw angle, roll angle, and corresponding disturbance amplitude representing rotation) and recovery condition parameters (capture arm position, velocity, and low-altitude atmospheric turbulence intensity) are collected synchronously. In the temporal dimension, a linear interpolation time alignment method is used to construct a discrete reference time axis based on the capture arm control cycle. The parameters with different acquisition frequencies are converted to the same sampling time through linear interpolation, and a first-order exponential low-pass filter is used to suppress sensor noise and transmission errors. The linear interpolation time alignment method is a mathematical method that uses data from known adjacent time points to proportionally extrapolate the target time point data. Here, it is used to eliminate the timing deviation caused by asynchronous sampling. Six degrees of freedom refer to the translation of an object along three orthogonal axes and its rotation around these three axes in three-dimensional space, used to completely describe the rocket's motion state.

[0027] Step S2 establishes an adaptive time discretization mechanism for predictive calculations. This step abandons the traditional fixed-step-size extrapolation method and establishes an adaptive step-size adjustment model. Using the acquired real-time three-dimensional descent velocity of the rocket as the core criterion, the entire descent process is divided into a high-speed far-field cruise phase and a low-speed near-field capture phase. During the high-speed cruise phase at long distances and high altitudes, the rocket's state changes relatively smoothly, and the system is configured with a large iteration step size for the RK4 algorithm to reduce computational load and accelerate the extrapolation speed. When the rocket approaches the ground and enters the low-speed near-field capture phase, the system gradually reduces the iteration step size, providing more dense time sampling points. The RK4 algorithm refers to the fourth-order Runge-Kutta algorithm, a numerical integration method for solving initial value problems of nonlinear ordinary differential equations with high precision, used here to extrapolate the rocket's trajectory under the dynamic model; the iteration step size refers to the time interval between two adjacent calculations in the numerical computation.

[0028] Step S3 is used to specifically perform the calculation of the rocket's predicted landing point. This step receives the iteration step size issued in step S2 and the initial value state after preprocessing in step S1, and substitutes it into the rocket's six-degree-of-freedom dynamic equations for integration. During the high-speed far-field cruise phase, the rocket's three-dimensional spatial position is updated frame by frame using a large iteration step size, and the macroscopic predicted landing point is extrapolated. During the low-speed near-field capture phase, a small iteration step size is used for high-frequency calculations, and boundary constraints are established in conjunction with the reachable range of the capture arm's motion to refine the coordinates of the predicted landing point. The dynamic equations refer to the mathematical equations describing the relationship between the motion state of an object and the forces acting on it. Here, they are used to calculate the rocket's acceleration, velocity, and position changes based on the force state of the rocket. Boundary constraints are reasonable physical range limits set for the calculation results to prevent the calculation of invalid landing points that exceed the physical limits of the capture arm.

[0029] Step S4 is used to eliminate trajectory calculation errors caused by environmental disturbances and attitude deviations, and outputs the final control parameters. This step uses measured parameters to calculate the three-dimensional deviation vector of low-altitude atmospheric turbulence and the three-axis residual attitude coupling offset deviation vector of the rocket body, and combines the two types of deviation vectors to construct a multi-source disturbance convergence criterion. By calculating the L2 norm of the deviation vector and weighted fusion, a total convergence index is generated, which is then mapped to generate dynamic error correction coefficients. The correction coefficients are embedded into the sub-iteration calculation process of RK4 mentioned above, and the position, velocity, and attitude parameters output at each stage are compensated dimension by dimension. Finally, the real-time landing point prediction result of the rocket after disturbance calibration is output, and the data transmission frequency is matched with the control cycle of the capture arm. The term L2 norm refers to the square root of the sum of the squares of the elements in the vector, which is used here to quantify the overall magnitude of the deviation vector; the dynamic error correction coefficients refer to a set of multiplicative or additive compensation factors calculated in real time according to the real-time deviation magnitude, which are used to offset the mismatch error of the mathematical model within the numerical iteration.

[0030] Specifically, the process of synchronously acquiring the rocket's six-degree-of-freedom descent flight state parameters and recovery condition parameters is as follows: The rocket's six-degree-of-freedom descent flight state parameters are acquired through a ground telemetry system; the low-altitude atmospheric turbulence intensity, the real-time position of the capture arm's end effector, and the real-time velocity are acquired through an environmental monitoring module and the capture arm control system; a linear interpolation time alignment method is used to construct a uniform discrete reference time axis according to the capture arm control cycle; the acquired parameters are sorted in ascending order of timestamps; for each reference synchronization moment, two adjacent sets of original sampled data are selected and substituted into the linear interpolation formula to calculate the standardized observation value corresponding to the unified moment, thus completing time-series registration; a first-order exponential low-pass filter is used to suppress noise in the standardized observation values ​​after time-series registration; a fixed threshold is set based on the single-step parameter change to perform outlier removal; and minimum-maximum linear normalization is performed based on the upper and lower limits of the physical parameters.

[0031] In this implementation scheme, the ground telemetry system receives telemetry data transmitted from the rocket and forwards the relevant six-degree-of-freedom descent flight status parameters to the ground computing server. The environmental monitoring module is a wind profiler radar deployed within the rocket recovery site area, which outputs instantaneous three-dimensional wind speed within the sampling period in real time. , , The wind speed sequence within a preset sliding time window T is taken, and the intensity of low-altitude atmospheric turbulence is solved using the classical formula for calculating turbulence intensity. The solution formula is: In the formula: , , The average wind speed across the three axes within the window. To average the wind speed, the final output is the unified low-altitude atmospheric turbulence intensity parameter for that moment. The ground-based computing server uses its unified system clock as the global time base. Rocket telemetry data, wind profiler radar data, and capture arm motion parameters are each bound to the device hardware timestamps. A linear interpolation time alignment method is used to perform time-series registration on the three types of heterogeneous data sources: First, a uniform discrete reference time axis is constructed based on the capture arm control cycle. Each type of observation parameter is sorted in ascending order by timestamp. For each reference synchronization moment, two adjacent sets of original sampling data are selected and substituted into the linear interpolation formula to calculate the standardized observation value corresponding to that unified moment. The six-degree-of-freedom state parameters, low-altitude turbulence parameters, and capture arm pose parameters with different sampling frequencies are uniformly interpolated to the same discrete sampling moment, eliminating time-series deviations caused by asynchronous sampling and transmission delays from multiple devices, and achieving strict synchronous acquisition of all-dimensional operating parameters. The linear interpolation registration calculation formula is: In the formula: , For adjacent raw sampling times of the sensor, , Corresponding observed values; To establish a globally unified benchmark for synchronization, These are the synchronized observations output after time alignment. A first-order exponential low-pass filter is used to suppress noise in all synchronized observation parameters. The filtering iteration formula is as follows: In the formula, These are the original acquired parameters at time t. These are the filtered parameters. ∈(0,1) represents the preset filtering smoothing coefficient. Simultaneously, a fixed threshold outlier removal rule is set. When the change in a single-step parameter exceeds the reasonable limit of the physical quantity's change, the abnormal sampling point is directly removed, and the previous time-series filtered value is used to complete the result, suppressing gross errors caused by sensor jumps and wireless transmission errors. For each type of physical parameter, a minimum-maximum linear normalization is performed based on the upper and lower allowable limits of the parameter, uniformly mapping all parameter dimensions to the [0,1] interval. All normalized parameters are then input into the subsequent adaptive step size adjustment model and the RK4 iterative solution module, completing the entire preprocessing process in this step.

[0032] Specifically, the rocket's real-time three-dimensional descent velocity is used to divide the high-speed far-field cruise phase into a low-speed near-field capture phase. The process of configuring a large iteration step size for the RK4 algorithm during the high-speed far-field cruise phase and a small iteration step size during the low-speed near-field capture phase is as follows: Preset thresholds for the rocket's three-dimensional descent velocity and near-field capture altitude. When the rocket's real-time three-dimensional descent velocity exceeds the threshold, it is determined to be in the high-speed far-field cruise phase, and a fixed large iteration step size is used to substitute into the RK4 iterative formula to solve the rocket's six-degree-of-freedom dynamic equations iteratively. When the rocket's real-time three-dimensional descent velocity is less than or equal to the threshold and the real-time spatial position altitude is lower than the near-field capture altitude threshold, it is determined to be in the low-speed near-field capture phase, and the small iteration step size is gradually reduced according to the altitude range.

[0033] In this implementation scheme, this step dynamically allocates system computing power based on the physical spatial location of the rocket's descent. The high-speed far-field cruise phase corresponds to the process where the rocket is at a high altitude and falls at extremely high speeds. During this phase, the accumulated error is limited, and the system directly calls upon a pre-set fixed large time span for integral calculation to deduce the macroscopic descent trajectory. The low-speed near-field capture phase corresponds to the process where the rocket approaches the end of the capture arm. The system extracts the current real-time flight altitude and matches it with the corresponding altitude range, progressively reducing the discrete time intervals. This numerical adjustment logic balances the calculation time at high altitudes and the trajectory resolution at low altitudes without complex differential calculations. This scheme presets the rocket's three-dimensional resultant velocity determination threshold at 70 m / s and the near-field capture altitude threshold at 500 m. When the rocket's real-time three-dimensional descent velocity is greater than 70 m / s, a fixed large iteration step size of 0.2 s is used for rapid simulation. When the flight velocity is less than or equal to 70 m / s and the altitude is below 500 m, the step size is gradually reduced according to the altitude range: 0.1 s step size is used in the 200 m to 500 m range, 0.05 s step size is used in the 100 m to 200 m range, and 0.01 s step size is used below 100 m. Specific engineering parameter benchmarks are provided to ensure stable convergence of the simulation. Figure 2 As shown, the system receives real-time three-dimensional descent flight speed and altitude data, inputting it into the adaptive step size adjustment model for logical judgment. The decision branches in the figure clearly illustrate the flow process of the two-level operating conditions. When the high-speed condition is met, the left branch of the flow guide is configured with a large step size; when the low-speed and low-altitude condition is met, the right branch of the flow guide is configured with a small step size, thereby achieving adaptive control of the subsequent RK4 iteration calculation frequency.

[0034] Specifically, the process of calculating the predicted rocket landing point using RK4 trajectory iteration with a large iteration step size during the high-speed far-field cruise phase and correcting the landing point coordinates using RK4 trajectory iteration with a small iteration step size during the low-speed near-field capture phase is as follows: After each iteration step size switch, the rocket's six-degree-of-freedom descent flight state parameters at the current moment are used as the initial values ​​for iteration. Combined with the rocket's six-degree-of-freedom dynamic differential equations, RK4 fourth-level sub-iteration operations are performed to update the rocket's three-dimensional spatial position frame by frame. The updated rocket three-dimensional spatial position is combined with the extrapolation of a fixed-duration trajectory curve, and the coordinates of the end of the extrapolated fixed-duration trajectory curve are used as the predicted rocket landing point. The predicted rocket landing point is then corrected by boundary constraints based on the reachable range formed by the real-time motion position of the capture arm end.

[0035] In this implementation scheme, the differentiated RK4 trajectory iteration calculation for different iterative conditions involves using the current full six-degree-of-freedom state of the rocket as the initial value for each step size switch, and performing standard RK4 iteration calculations frame-by-frame to update the rocket's three-dimensional spatial position. Simultaneously, the boundary constraints of the landing point are corrected by combining the real-time reachability range of the capture arm, progressively refining the discrete-time granularity to achieve high-precision fitting between the rocket's descent trajectory and the landing point coordinates, meeting the centimeter-level high-precision alignment requirements of the capture arm's end effector. The core calculation formula for RK4 trajectory iteration is: In the formula, This is the rocket's six-degree-of-freedom state vector at time n, containing three-dimensional position, three-dimensional translational velocity, three-axis attitude angles, and three-axis attitude angular velocities. This is the rocket's six-degree-of-freedom state vector updated at time n+1 after one RK4 iteration calculation, and the trajectory recursion output for this step, used to update the landing point and flight trajectory. The six-degree-of-freedom dynamic differential equations for the rocket's descent process; This is the real-time iteration step size output after adaptive adjustment in this step; The slope at the start of the interval represents the rate of change of the state at the very beginning of the iteration interval; To estimate the slope 1 at the midpoint of the half-step, use... Extrapolate the intermediate state by half a step, then substitute it into the dynamic differential equation to obtain the rate of change at the midpoint, and make the first correction to the nonlinear trajectory; To estimate the slope 2 at the midpoint of the half-step, we use... Extrapolate by half a step again to obtain the corrected midpoint state, and solve the midpoint slope a second time to further suppress dynamic nonlinearity error; To estimate the slope at the endpoint of the whole step length, use Extrapolate a complete step size to obtain the predicted state at the end of the interval, solve for the rate of change at the end point, and complete the dynamic trend at the end of the interval.

[0036] Specifically, before constructing the convergence criterion for multi-source disturbances, the specific process of calculating the two types of disturbance deviations is as follows: combining the instantaneous three-dimensional wind speed output by the wind profiler radar and the intensity of low-altitude atmospheric turbulence, a three-dimensional deviation vector of low-altitude atmospheric turbulence is constructed; the single-axis difference between the measured attitude and the nominal attitude corresponding to the pitch angle, yaw angle, and roll angle of the rocket body is extracted, and substituted into the preset attitude coupling matrix to calculate the three-axis residual attitude coupling offset deviation vector of the rocket body; the nominal attitude is the pre-set time-series attitude curve.

[0037] In this implementation scheme, the deviation components that cause distortion in the physical model are separated from the atmospheric environment measurements and the dynamic response values ​​of the rocket body. The three-dimensional deviation vector of low-altitude atmospheric turbulence refers to the difference in velocity fluctuations of irregular airflow in three-dimensional space detected by wind profiler radar. The nominal attitude refers to the ideal time-series flight attitude pre-written into the system according to the predetermined trajectory during the ground mission phase. The preset attitude coupling matrix is ​​a linear algebraic matrix used to describe the degree of mutual interference correlation when the spacecraft rotates around different axes. The system directly subtracts the nominal attitude angles from the actual measured yaw, roll, and pitch angles of the rocket, multiplies the resulting one-dimensional difference matrix, and calculates the true attitude offset caused by the combined effects of three-axis motion interference, providing basic data for determining whether the trajectory calculation has converged.

[0038] Specifically, the process of constructing a multi-source disturbance convergence criterion and calculating dynamic error correction coefficients based on the intensity of low-altitude atmospheric turbulence, the angular velocity of three-axis attitude disturbances, and the amplitude of attitude disturbances is as follows: The multi-source disturbance convergence criterion consists of a six-degree-of-freedom attitude disturbance convergence sub-criterion and an atmospheric turbulence convergence sub-criterion; the six-degree-of-freedom attitude disturbance convergence sub-criterion is constructed based on the L2 norm of the three-axis residual attitude coupling offset deviation vector of the rocket body, and the atmospheric turbulence convergence sub-criterion is constructed based on the L2 norm of the three-dimensional deviation vector of low-altitude atmospheric turbulence; the calculated values ​​of the six-degree-of-freedom attitude disturbance convergence sub-criterion and the atmospheric turbulence convergence sub-criterion are weighted and fused to generate a total convergence index, two levels of disturbance thresholds are set to classify the disturbance strength levels, and a dynamic error correction coefficient vector is generated based on the total convergence index using a piecewise linear mapping method.

[0039] In this implementation scheme, the multi-source disturbance convergence criterion is divided into a six-degree-of-freedom attitude disturbance convergence sub-criterion and an atmospheric turbulence convergence sub-criterion. The six-degree-of-freedom attitude disturbance convergence sub-criterion is constructed based on the L2 norm of the three-axis residual attitude coupling offset vector of the rocket body: In the formula, The value of the convergence criterion for the three-axis residual attitude perturbation of the rocket body represents the total coupling offset of the rocket's current actual attitude relative to the theoretical nominal recovery attitude; Using the vector norm 2, the modulus of the three-axis attitude deviation is solved, and the three-dimensional coupling deviation is quantized into a single scalar convergence index. The three-axis residual attitude coupling offset vector of the rocket body is denoted as , and is a three-dimensional column vector. ; , , These represent the residual attitude deviations of the roll, pitch, and yaw angles relative to the theoretical nominal trajectory. The atmospheric turbulence convergence criterion is constructed based on the L2 norm of the low-altitude turbulence deviation vector. In the formula, As a convergent criterion for atmospheric turbulence, the total deviation of triaxial airflow disturbance of atmospheric turbulence in the carrier coordinate system is quantified. Here, is the three-dimensional deviation vector of low-altitude turbulence, and is a three-dimensional column vector. ; represent the three-axis velocity disturbance deviation components introduced by atmospheric turbulence in the forward, lateral, and normal directions along the rocket body axis. The overall convergence index is obtained by weighted fusion after solving for the values ​​of the two sub-criterions separately. In the formula, Weighting coefficients for atmospheric turbulence terms, The weighting coefficients for the attitude disturbance term are both pre-calibrated through simulation experiments. Then, they are segmented and mapped to generate six-dimensional dynamic error correction coefficients, which synchronously correct the initial values ​​of the RK4 iteration trajectory and the iteration convergence threshold in real time, thereby suppressing trajectory drift caused by attitude and atmospheric coupling disturbances.

[0040] Specifically, the process of compensating and calibrating the trajectory drift error generated during the RK4 trajectory iteration calculation using dynamic error correction coefficients is as follows: The dynamic error correction coefficient vector is coupled element-wise with the three-dimensional deviation vector of low-altitude atmospheric turbulence and the three-axis residual attitude coupling offset deviation vector of the rocket body; the coupling result is embedded into the RK4 trajectory iteration calculation process and the final state recursion stage, and dimensional compensation and correction are synchronously performed on the three-dimensional position parameters, three-dimensional velocity parameters, and three-axis attitude parameters output at each stage of the RK4 trajectory iteration calculation. Combined with... Figure 3 As shown, the multi-source disturbance error correction mechanism of this invention constitutes a closed-loop compensation system. Environmental data provided by the wind profiler radar and the measured attitude difference generate two types of deviation vectors, respectively. These two data streams undergo L2 norm calculation and weighted fusion in the convergence criterion module, and the resulting dynamic error correction coefficient vector is fed back and embedded into the core RK4 four-level sub-iteration loop. Through low-level parameter coupling, the system achieves real-time cancellation and calibration of drift errors in each calculation step of trajectory extrapolation.

[0041] In this implementation scheme, macroscopic environmental disturbances are transformed into specific mathematical correction and compensation quantities and applied to the underlying logic of trajectory extrapolation. Element-by-element coupling refers to multiplying the values ​​of each dimension within the generated dynamic error correction coefficient vector into the corresponding spatial coordinate axis dimensions of the low-altitude atmospheric turbulence three-dimensional deviation vector and the rocket body's three-axis residual attitude coupling offset deviation vector, respectively. Embedding the RK4 trajectory iterative calculation process and the final state recursion stage means that the numerical parameters obtained from the aforementioned coupling calculation are simultaneously superimposed in each sub-iteration step of solving the dynamic differential equation and in the final calculation of generating the state vector for the next moment. This process ensures that the three-dimensional position parameters, three-dimensional velocity parameters, and three-axis attitude parameters output at each level directly cancel out model mismatch terms at the computational level.

[0042] Specifically, matching the update frequency of the rocket's real-time landing point prediction results with the motion response cycle of the capture arm also includes the following processes: extracting the rocket's real-time landing point prediction results after compensation and calibration, constructing the optimal clamping point cost function with capture arm position constraints and velocity reachability domain constraints; and solving the optimal clamping point cost function using the gradient projection method to obtain the optimal clamping target point for the rocket body section to adapt to the clamping position.

[0043] In this implementation scheme, the optimal physical gripping position is found by combining the predicted landing point coordinates with the physical motion limits of the mechanical hardware. The optimal gripping point cost function is a mathematical model used to evaluate the relative deviation of a specific gripping position. The system uses the gradient projection method to find the spatial coordinates corresponding to the minimum value of this function. The gradient projection method is a numerical calculation method used to solve nonlinear optimization problems with specific variable range constraints. Based on the calibrated near-field predicted landing point of the rocket, an optimal gripping point cost function with multiple constraints including the position and velocity reachability domain of the capture arm is constructed: In the formula, The value of the comprehensive cost function for the clamping point; Let be the Cartesian three-dimensional coordinate vector of the end effector gripping point of the robotic arm to be optimized. The three-dimensional coordinate vector for predicting the rocket's landing point; The vector 2 norm represents the spatial Euclidean distance deviation between the gripping point and the predicted landing point; To constrain the penalty weighting coefficient; This is a multi-hardware constraint penalty function used to impose penalty constraints on infeasible points that exceed the capture arm joint limits, workspace reachability, and velocity limits. The gradient projection method is used to solve this constrained nonlinear optimization problem, finding the minimum value corresponding to the valence function. As the Cartesian three-dimensional coordinate vector of the optimal clamping point in the rocket body section, the Cartesian spatial coordinates of the optimal clamping point are input into the inverse kinematics solution model of the capture arm: In the formula, The target rotation angle commands for each joint of the capture arm are output by the inverse kinematics; Solve the mapping function for the inverse kinematics of the robotic arm; The actual joint rotation angle of the capture arm in the previous control cycle is used as the initial value for inverse iteration to ensure trajectory smoothness. The target rotation angles of the left and right capture arms and the end-effector velocity commands are calculated. The capture arm control system collects the capture arm's position and velocity in real time, calculates the actual motion pose of the capture arm, and transmits it back to the ground computing server. In the next frame prediction iteration, the deviation term between the actual pose of the capture arm and the optimal clamping point is introduced to complete the cross-cycle closed-loop correction. The predicted landing point and clamping target point of the rocket near-field capture are refreshed cycle by cycle. Motion commands are continuously issued to drive the capture arm to dynamically adjust its end-effector trajectory, eliminating the time lag caused by data transmission and command scheduling, and realizing lag-free dynamic following and precise clamping capture throughout the rocket's approach.

[0044] Specifically, after obtaining the optimal clamping target position, the following process is also included: inputting the Cartesian space coordinates of the optimal clamping target position into the inverse kinematics solution model of the capture arm to solve the target rotation angle and end motion speed command of the left and right capture arms; collecting the motion position and motion speed of the capture arm and converting the actual motion pose of the capture arm.

[0045] In this implementation scheme, the target position coordinates in three-dimensional space are converted into motor motion commands that can be directly executed by the underlying hardware. The Cartesian space coordinates of the optimal gripping point are input into the inverse kinematics solution model of the capture arm, and the inverse kinematics solution model calculation formula is used. The target rotation angle and end-effector velocity commands of the left and right capture arms are calculated. The capture arm control system collects the capture arm's position and velocity in real time, calculates the actual motion posture of the capture arm, and transmits it back to the ground computing server. In the next frame prediction iteration, the deviation term between the actual posture of the capture arm and the optimal clamping point is introduced to complete the cross-cycle closed-loop correction. The predicted landing point and clamping target point of the rocket near-field capture are refreshed cycle by cycle, and motion commands are continuously issued to drive the capture arm to dynamically adjust the end-effector trajectory, eliminating the time lag caused by data transmission and command scheduling, and realizing zero-lag dynamic following and precise clamping capture throughout the rocket's approach.

[0046] Specifically, after obtaining the actual motion pose of the capture arm, the following process is also included: in the next frame prediction iteration, the deviation term between the actual motion pose of the capture arm and the optimal clamping target position is extracted and cross-cycle closed-loop correction is performed; the real-time landing point prediction result of the rocket and the optimal clamping target position are refreshed cycle by cycle, and the terminal motion speed command is issued to drive the capture arm to adjust the terminal running trajectory.

[0047] In this implementation plan, a continuous refresh and error feedback control mechanism is established to achieve lag-free dynamic tracking and capture operations. In the next frame's prediction iteration, the deviation between the actual pose of the capture arm and the optimal clamping point is introduced to complete cross-cycle closed-loop correction. Cross-cycle closed-loop correction refers to comparing the actual physical pose of the capture arm in the current control cycle with the optimal clamping target point in the coordinate system, extracting the spatial coordinate deviation value as a compensation parameter input into the iteration calculation of the next frame. The system iteratively refreshes the predicted landing point and clamping target point of the rocket's near-field capture cycle by cycle, continuously issuing motion commands to drive the capture arm to dynamically adjust its end-effector trajectory, eliminating the timing lag caused by data transmission and command scheduling, and achieving lag-free dynamic tracking and precise clamping capture throughout the rocket's approach. This timing synchronization and cross-cycle closed-loop correction mechanism eliminates the lag and timing mismatch defects of the traditional fixed-step RK4 iteration, avoiding capture arm alignment failure and rocket recovery failure due to prediction deviations. Figure 4 As shown, the linkage prediction system of this invention presents a collaborative physical architecture from the information acquisition end to the computing and control end. The ground computing server, as the core processing hub, receives multi-source state parameters from the environmental detection module and the telemetry system and performs the aforementioned high-frequency RK4 prediction calculation. The optimal gripping point command, which is finally predicted, is sent to the capture arm control system through a low-latency network. At the same time, the actual pose data of the capture arm is fed back to the computing server as a feedback stream, forming a closed-loop prediction control chain across cycles, ensuring hard real-time synchronization between prediction and physical gripping.

[0048] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A high-precision real-time prediction method for the landing point of an adaptive variable-step RK4 rocket capture arm recovery system, characterized in that... Includes the following steps: S1. Synchronously acquire the rocket's six-degree-of-freedom descent flight status parameters and recovery condition parameters; among them, the rocket's six-degree-of-freedom descent flight status parameters include the rocket's real-time three-dimensional descent flight speed, real-time spatial position altitude, rocket body pitch angle, yaw angle, roll angle, three-axis attitude disturbance angular velocity, and attitude disturbance amplitude; the recovery condition parameters include the real-time motion position of the capture arm end, real-time motion speed, and low-altitude atmospheric turbulence intensity; S2. An adaptive step size adjustment model is constructed based on the rocket's six-degree-of-freedom descent flight state parameters and recovery condition parameters. The high-speed far-field cruise phase and the low-speed near-field capture phase are divided according to the rocket's real-time three-dimensional descent flight speed. The large iteration step size of the RK4 algorithm is configured in the high-speed far-field cruise phase, and the small iteration step size of the RK4 algorithm is configured in the low-speed near-field capture phase. S3. During the high-speed far-field cruise phase, RK4 trajectory iterative calculation is performed with a large iteration step size to solve the rocket's estimated landing point. During the low-speed near-field capture phase, RK4 trajectory iterative calculation is performed with a small iteration step size to correct the landing point coordinates. S4. Construct a multi-source disturbance convergence criterion based on the intensity of low-altitude atmospheric turbulence, the angular velocity of the three-axis attitude disturbance, and the amplitude of the attitude disturbance, and calculate the dynamic error correction coefficient. Use the dynamic error correction coefficient to compensate and calibrate the trajectory drift error generated during the RK4 trajectory iteration calculation process, output the real-time landing point prediction result of the rocket, and match the update frequency of the real-time landing point prediction result of the rocket with the motion response cycle of the capture arm.

2. The adaptive variable step size RK4 high-precision real-time prediction method for rocket capture arm recovery according to claim 1, characterized in that: The specific process for simultaneously acquiring the rocket's six-degree-of-freedom descent flight status parameters and recovery condition parameters is as follows: The rocket's six-degree-of-freedom descent flight status parameters are collected by the ground telemetry system, and the low-altitude atmospheric turbulence intensity, real-time movement position of the capture arm end, and real-time movement speed are collected by the environmental detection module and the capture arm control system. The linear interpolation time alignment method is adopted. A uniform discrete reference time axis is constructed according to the control cycle of the capture arm. The collected parameters are sorted in ascending order of timestamp. For each reference synchronization time, two adjacent sets of original sampling data are selected and substituted into the linear interpolation formula to solve the standardized observation value corresponding to the unified time to complete the time registration. First-order exponential low-pass filtering is used to suppress noise in the standardized observations after time-series registration. A fixed threshold is set according to the single-step parameter change to perform outlier removal. Minimum-maximum linear normalization is performed based on the upper and lower limits of physical parameters.

3. The adaptive variable step size RK4 high-precision real-time prediction method for rocket capture arm recovery according to claim 1, characterized in that: The rocket's real-time three-dimensional descent flight speed is used to divide the high-speed far-field cruise phase into a low-speed near-field capture phase. The specific process of configuring the RK4 algorithm with a large iteration step size during the high-speed far-field cruise phase and a small iteration step size during the low-speed near-field capture phase is as follows: Preset the three-dimensional combined velocity determination threshold and the near-field capture altitude threshold for rocket descent; When the rocket's real-time three-dimensional descent flight speed is greater than the threshold for the rocket's three-dimensional descent resultant velocity, it is determined to be in the high-speed far-field cruise phase. A fixed large iteration step size is then used to substitute into the RK4 iteration formula to iteratively solve the rocket's six-degree-of-freedom dynamic equations. When the rocket's real-time three-dimensional descent velocity is less than or equal to the rocket's three-dimensional descent resultant velocity threshold, and the real-time spatial position altitude is lower than the near-field capture altitude threshold, it is determined to be in the low-speed near-field capture stage, and the small iteration step size is reduced step by step according to the altitude range.

4. The adaptive variable step size RK4 high-precision real-time prediction method for rocket capture arm recovery according to claim 1, characterized in that: The specific process of calculating the predicted rocket landing point using RK4 trajectory iteration with a large iteration step size during the high-speed far-field cruise phase and correcting the landing point coordinates using RK4 trajectory iteration with a small iteration step size during the low-speed near-field capture phase is as follows: After each iteration step size switch, the rocket's six-degree-of-freedom descent flight state parameters at the current moment are used as the initial values ​​for iteration. Combined with the rocket's six-degree-of-freedom dynamic differential equations, the RK4 fourth-level sub-iteration operation is performed to update the rocket's three-dimensional spatial position frame by frame. By combining the updated rocket three-dimensional spatial position extrapolated to a fixed-duration trajectory curve, the coordinates of the end of the extrapolated fixed-duration trajectory curve are used as the rocket's predicted landing point. The estimated landing point of the rocket is corrected by boundary constraints based on the reachable range formed by the real-time movement position of the capture arm end.

5. The adaptive variable step size RK4 high-precision real-time prediction method for rocket capture arm recovery according to claim 1, characterized in that: Before constructing the convergence criterion for multi-source disturbances, the specific process of calculating the two types of disturbance biases is as follows: By combining the instantaneous three-dimensional wind speed output by the wind profiler radar with the intensity of low-level atmospheric turbulence, a three-dimensional deviation vector of low-level atmospheric turbulence is constructed. Extract the single-axis differences between the measured attitude and the nominal attitude corresponding to the pitch angle, yaw angle, and roll angle of the rocket body, and substitute them into the preset attitude coupling matrix to calculate the three-axis residual attitude coupling offset deviation vector of the rocket body; the nominal attitude is the pre-set time-series attitude curve.

6. The adaptive variable step size RK4 high-precision real-time prediction method for rocket capture arm recovery according to claim 5, characterized in that: The specific process of constructing a multi-source disturbance convergence criterion and calculating dynamic error correction coefficients based on low-altitude atmospheric turbulence intensity, three-axis attitude disturbance angular velocity, and attitude disturbance amplitude is as follows: The multi-source perturbation convergence criterion consists of a six-degree-of-freedom attitude perturbation convergence criterion and an atmospheric turbulence convergence criterion; The six-DOF attitude perturbation convergence criterion is constructed based on the L2 norm of the three-axis residual attitude coupling offset deviation vector of the rocket body, and the atmospheric turbulence convergence criterion is constructed based on the L2 norm of the three-dimensional deviation vector of low-altitude atmospheric turbulence. The calculated values ​​of the six-degree-of-freedom attitude perturbation convergence criterion and the atmospheric turbulence convergence criterion are weighted and fused to generate a total convergence index. Two levels of perturbation thresholds are set to classify the perturbation strength. Based on the total convergence index, a dynamic error correction coefficient vector is generated using a piecewise linear mapping method.

7. The adaptive variable step size RK4 high-precision real-time prediction method for rocket capture arm recovery according to claim 6, characterized in that: The specific process of compensating and calibrating the trajectory drift error generated during the RK4 trajectory iteration calculation using dynamic error correction coefficients is as follows: The dynamic error correction coefficient vector is coupled element-wise with the three-dimensional deviation vector of low-altitude atmospheric turbulence and the three-axis residual attitude coupling offset deviation vector of the rocket body, respectively. The coupling results are embedded into the RK4 trajectory iterative calculation process and the final state recursion stage, and the three-dimensional position parameters, three-dimensional velocity parameters and three-axis attitude parameters output at each level of the RK4 trajectory iterative calculation are synchronously compensated and corrected dimension by dimension.

8. The adaptive variable step size RK4 high-precision real-time prediction method for rocket capture arm recovery according to claim 1, characterized in that: Matching the update frequency of the rocket's real-time impact prediction results with the motion response cycle of the capture arm, and also... Includes the following processes: Extract the real-time landing point prediction results of the rocket after compensation and calibration, and construct the optimal clamping point cost function with capture arm position constraints and velocity reachability domain constraints; The gradient projection method is used to solve the cost function of the optimal clamping point, and the optimal clamping target point for the adapted clamping position of the rocket body section is obtained.

9. The adaptive variable step size RK4 high-precision real-time prediction method for rocket capture arm recovery according to claim 8, characterized in that: After obtaining the optimal clamping target point, the following process is also included: Input the Cartesian space coordinates of the optimal clamping target point into the inverse kinematics solution model of the capture arm to calculate the target rotation angle and end motion speed command of the left and right capture arms; The capture arm's position and speed are collected, and its actual pose is calculated.

10. The adaptive variable step size RK4 high-precision real-time prediction method for rocket capture arm recovery according to claim 9, characterized in that: After obtaining the actual motion pose of the capture arm, Includes the following processes: In the next frame prediction iteration, the deviation between the actual motion pose of the capture arm and the optimal clamping target position is extracted and cross-cycle closed-loop correction is performed. The system iterates and refreshes the real-time landing point prediction results and the optimal clamping target position of the rocket on a cycle-by-cycle basis, and issues terminal motion speed commands to drive the capture arm to adjust its terminal trajectory.

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