A high-precision inertial parameter calculation method

Abstract

This invention discloses a high-precision inertial parameter calculation method, belonging to the field of inertial parameter calculation, comprising the following steps: acquiring physical quantity data of a target object under multi-degree-of-freedom motion; preprocessing and normalizing the physical quantity data to obtain a transformed data sequence; establishing an accurate dynamic model based on the structure and motion characteristics of the target object; identifying inertial parameters of the dynamic model through an optimization algorithm to obtain the optimal estimated values ​​of the inertial parameters; substituting the obtained inertial parameters into the dynamic model, verifying accuracy and iteratively optimizing through simulation testing, and finally obtaining high-precision inertial parameters; outputting the final high-precision inertial parameters and applying them to an engineering system. This invention can improve the accuracy and efficiency of inertial parameter calculation and meet the inertial parameter calculation needs of target objects under multi-degree-of-freedom motion in different fields, providing general technical support for system design and optimization in various fields.

Description

Technical Field

[0001] This invention mainly relates to the field of inertial parameter calculation, specifically a high-precision inertial parameter calculation method. Background Technology

[0002] In numerous fields such as aerospace, navigation and guidance, and industrial automation control, accurate inertial parameters play a crucial role in the performance and precision of a system. For example, in the attitude control of aircraft, inaccurate inertial parameters can lead to serious problems such as flight attitude deviation and navigation errors. In the field of industrial automation control, the accuracy of inertial parameters directly affects the motion control precision and stability of automated equipment. If inertial parameters are inaccurate, it may lead to abnormal equipment operation, reduced production efficiency, and decreased product quality.

[0003] Currently, although some technologies related to inertial parameters exist, such as the "Inertial Parameter Synthesis Method, Device, Terminal Equipment, and Storage Medium" disclosed in patent application number 202410376095.0, which mainly focuses on improving the accuracy of inertial parameter synthesis calculation for automotive parts, it lacks completeness and versatility in its methodological process, making it difficult to meet the needs of other fields for calculating the inertial parameters of target objects under multi-degree-of-freedom motion. Patent application number 202411303336.5 discloses "A High-Precision Inertial Measurement Device and its Measurement Method," primarily applied to inertial measurement in the field of camera shooting. It improves inertial measurement accuracy by eliminating time delay errors, but its application scenarios are relatively limited and cannot meet the requirements of complex engineering systems such as aerospace and industrial automation control for inertial parameter calculation.

[0004] In summary, existing inertial parameter correlation techniques have certain limitations and cannot meet the urgent needs of many fields for high-precision inertial parameters. Therefore, developing a new inertial parameter calculation method with wider applicability and higher accuracy has significant practical significance and application value. Summary of the Invention

[0005] The present invention addresses the problem that existing technical solutions are too simplistic and provides a solution that is significantly different from existing technologies. It mainly provides a high-precision inertial parameter calculation method to solve the problem mentioned in the background that existing inertial parameter related technologies cannot meet the urgent needs of many fields for high-precision inertial parameters.

[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows: A high-precision method for calculating inertial parameters includes the following steps: S1. Obtain physical quantity data of the target object under multi-degree-of-freedom motion; S2. The physical quantity data obtained in step S1 is preprocessed and normalized to obtain the transformed data sequence; S3. Establish an accurate dynamic model based on the structure and motion characteristics of the target object; S4. The inertial parameters of the dynamic model in step S3 are identified by an optimization algorithm, and the optimal estimated values ​​of the inertial parameters are obtained. S5. Substitute the inertial parameters obtained in step S4 into the dynamic model, and verify the accuracy and iteratively optimize through simulation tests to finally obtain high-precision inertial parameters. S6. Output the final high-precision inertial parameters and apply them to the corresponding engineering system.

[0007] Furthermore, in step S1, a high-precision sensor is used to collect physical quantity data of the target object.

[0008] Furthermore, the high-precision sensor includes multiple inertial measurement units installed at different key parts of the target object; the selection of key parts is determined based on the structural and motion characteristics of the target object; and the installation direction of the inertial measurement units is precisely calibrated to ensure that there is a predetermined relative angular relationship between their coordinate axes.

[0009] Further, in step S2, the preprocessing includes: using an adaptive threshold filtering algorithm to remove obvious outliers and using smoothing filtering technology to reduce high-frequency noise interference, thereby obtaining purified physical quantity data; wherein, the threshold setting of the adaptive threshold filtering algorithm is dynamically adjusted based on the statistical analysis results of historical data of the target object's motion, and the window size of the smoothing filter is adaptively determined according to the data change rate.

[0010] Further, in step S2, the normalization process includes: (1) Based on the preprocessed and purified physical quantity data, the attitude of the target object is calculated using the quaternion differential equation updated by the rotation matrix. In the calculation process, the Taylor series expansion method is used to approximate the solution of the quaternion differential equation to reduce the computational complexity and improve the computational efficiency. At the same time, an error compensation term is introduced to correct the cumulative error caused by the approximate solution, thereby obtaining a high-precision target object attitude matrix sequence. (2) Based on the obtained attitude matrix sequence, the physical quantity data after preprocessing and purification are transformed to a unified reference coordinate system. During the transformation process, the influence of the slight change in the relative position between each inertial measurement unit caused by the deformation of the target object or local vibration is fully considered. The transformation is carried out by establishing a dynamic transformation model between the local coordinate system and the unified reference coordinate system to obtain an accurate transformation data sequence.

[0011] Furthermore, in step S3, the dynamic model is a multi-degree-of-freedom dynamic equation system built on the basis of the Newton-Euler equations.

[0012] Furthermore, step S3 includes: based on the conversion data sequence obtained in step S2 and the pre-measured and stored detection position information of the target object, calculating the force vector sequence acting on each corresponding part of the target object using Newton's second law; during the calculation process, the calculation of the force vector is verified in real time, and calculation errors are detected and corrected in a timely manner by comparing the change trend of the force vector at adjacent time moments with the kinematic law of the target object.

[0013] Furthermore, in step S4, the global search capability of the particle swarm optimization algorithm is first used to quickly locate the possible optimal solution region in the parameter space. Then, the least squares method is used to perform a precise local search within this region to obtain the optimal estimate of the inertial parameters.

[0014] Furthermore, in step S4, the calculated force vector sequence is substituted into the above dynamic model, and the equation is solved using an optimization algorithm based on gradient descent. During the execution of the optimization algorithm, a dynamic step size adjustment strategy is set to accelerate the convergence speed and prevent getting trapped in local optima, thereby accurately calculating the inertial parameters of the target object.

[0015] Further, in step S5, the simulation test includes: simulating the motion state of the target object under the same motion conditions, calculating the theoretical physical quantity data, comparing it with the actual collected physical quantity data, and calculating the error index; if the error index is greater than the preset accuracy threshold, then backtracking to step S1 to check the accuracy of hardware installation and data acquisition, or adjusting the relevant parameters in the parameter identification algorithm in step S4, and recalculating the inertial parameters until the error index meets the accuracy requirements.

[0016] Furthermore, the above steps included coupled frequency response function measurement and dynamic stiffness identification, specifically including: (1) Measurement of coupled frequency response function Measurement equipment: A high-precision force hammer (excitation end) and a laser vibration meter (response end) are used, which work synchronously with the inertial measurement unit (IMU) in step S1 to ensure that the data timestamps are consistent.

[0017] Measurement method: Apply single-point pulse excitation to the key part of the target object (corresponding to the IMU installation position), collect the excitation force signal (F(ω)) and response acceleration signal (A(ω)), and obtain the coupled frequency response function H(ω)=A(ω)F(ω) in the frequency domain through Fourier transform (ω is the angular frequency, covering the main motion frequency range of the target object [ω1, ω2]).

[0018] Dynamic stiffness identification can be completed by measuring only one set of coupled frequency response functions, eliminating the need for multiple independent tests and reducing operational complexity and equipment dependence.

[0019] (2) Calculation of dynamic stiffness Based on the mechanical relationship between the coupled frequency response function and dynamic stiffness (K(ω)): K(ω)=1H(ω)·Meq(ω), where Meq(ω) is the equivalent mass in the frequency domain (determined by the structural characteristics of the target object).

[0020] Specific calculation: The coupled frequency response function H(ω) is fitted by the least squares method to eliminate measurement noise interference. The dynamic stiffness curve K(ω) in the frequency domain is obtained by substituting it into the preset equivalent mass model.

[0021] Verification mechanism: If the dynamic stiffness curve shows abnormal abrupt changes (such as exceeding the preset physical reasonable range), backtrack to step S1 to check the accuracy of the excitation position or the stability of the sensor installation, and remeasure until the requirements are met.

[0022] (3) Integration with dynamic models The identified dynamic stiffness K(ω) is used as a constraint and embedded into the Newton-Euler dynamic equation system in step S3 to supplement and construct the "inertia parameter-dynamic stiffness" coupling equation: τ=M(θ)θ¨+C(θ,θ˙)θ˙+K(ω)θ, where τ is the torque vector, θ is the attitude angle vector, M is the inertia matrix, and C is the Coriolis / centrifugal force matrix.

[0023] This coupling equation can reduce the degrees of freedom for inertial parameter identification, avoid parameter estimation getting stuck in local optima, and improve the convergence accuracy of subsequent optimization algorithms (such as particle swarm optimization + least squares method).

[0024] Compared with the prior art, the beneficial effects of the present invention are as follows: High-precision calculation results: This invention comprehensively acquires physical quantity data of the target object under multi-degree-of-freedom motion, and establishes an accurate dynamic model using advanced preprocessing and normalization methods. Then, optimization algorithms are applied for inertial parameter identification, accuracy verification under simulation testing, and iterative optimization. The resulting inertial parameters have extremely high accuracy. Compared with existing technologies, this significantly reduces various problems caused by inaccurate inertial parameters. For example, in the aerospace field, it can effectively avoid flight attitude deviations and navigation errors caused by inertial parameter deviations, ensuring flight safety; in the field of industrial automation control, it can ensure high-precision motion control of automated equipment, improving production efficiency and product quality.

[0025] Wide Applicability: The high-precision inertial parameter calculation method proposed in this invention breaks through the limitation of existing technologies in a single application scenario. It can be applied to multiple fields such as aerospace, navigation and guidance, and industrial automation control, meeting the inertial parameter calculation needs of target objects under multi-degree-of-freedom motion in different fields, and providing general technical support for system design and optimization in various fields.

[0026] Superior detection accuracy and reliable data support: This invention employs advanced data acquisition and processing technology, which significantly improves the detection accuracy of physical quantity data during inertial parameter calculation. This advantage lays a solid foundation for precise system control, ensuring that the acquired data is accurate and reliable, greatly enhancing the accuracy of system control based on inertial parameters, and effectively avoiding system malfunctions caused by data deviations.

[0027] Simplified testing process and enhanced system flexibility: This invention simplifies the testing process by requiring only the measurement of a set of coupled frequency response functions to identify dynamic stiffness. This significantly reduces the difficulty of operation, decreases the reliance on complex testing equipment, and makes the entire system more flexible and convenient in practical applications. It can adapt to the testing needs of different scenarios and greatly improves work efficiency.

[0028] Highly efficient computing power and shortened development cycle: This invention, through optimized algorithms and processes, can quickly calculate the required inertial parameters. This not only significantly improves work efficiency but also effectively shortens the product development cycle, enabling related products to be launched to the market faster and enhancing enterprise competitiveness. Simultaneously, by reducing reliance on precision instruments, long-term maintenance costs are reduced, resulting in significantly improved economic benefits.

[0029] A complete and scientific computational process: This invention possesses a complete computational process, forming a closed-loop scientific system from data acquisition and processing to model building, parameter identification, accuracy verification, and iterative optimization. Compared with the shortcomings of existing technologies in terms of the completeness of the methodological process, the computational process of this invention is more rigorous and comprehensive, with each step closely linked, effectively improving the reliability and stability of inertial parameter calculation and providing a solid foundation for subsequent applications in engineering systems.

[0030] Significant economic and social benefits: Because this invention can provide high-precision inertial parameters, its application in various fields can reduce system operational risks and minimize additional costs and losses caused by inaccurate inertial parameters, resulting in significant economic benefits. Simultaneously, in fields such as aerospace, which are crucial to public safety and national strategy, improving system stability and reliability will also bring immeasurable social benefits.

[0031] In summary, this invention has achieved several innovative breakthroughs at the technical level and has demonstrated many significant advantages in practical applications, which is of great significance for improving the accuracy and efficiency of inertial parameter calculation.

[0032] The present invention will be explained in detail below with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0033] Figure 1 The flowchart shows the high-precision inertial parameter calculation method provided by this invention. Detailed Implementation

[0034] To facilitate understanding of the present invention, a more comprehensive description of the present invention will be given below with reference to the accompanying drawings, which illustrate several embodiments of the present invention. However, the present invention can be implemented in different forms and is not limited to the embodiments described in the text. Rather, these embodiments are provided to make the disclosure of the present invention more thorough and complete.

[0035] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly associated with those skilled in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to limit the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0036] Please refer to the attached document carefully. Figure 1 A high-precision method for calculating inertial parameters includes the following steps: Step a, Data Acquisition. High-precision sensors are used to acquire data on the target object's forces, torques, accelerations, angular velocities, and other physical quantities during multi-degree-of-freedom motion. The acquisition frequency is set between 200Hz and 500Hz to ensure data integrity and accuracy, and the sampling time is maintained for at least 120 seconds to obtain sufficient sample data.

[0037] A. Data setting basis: (1) The rationality of the sampling frequency (X=200Hz~Y=500Hz) To satisfy the Nyquist sampling theorem: the typical highest frequency of multi-degree-of-freedom motion of a target object is 50-100Hz (such as the attitude adjustment frequency of a drone or the joint movement frequency of a robotic arm). According to the Nyquist theorem, the sampling frequency must be at least twice the highest frequency of the signal. A minimum sampling frequency of 200Hz ensures complete capture of motion signals within 100Hz, while a maximum frequency of 500Hz covers sudden high-frequency dynamics (such as airflow disturbances or mechanical impacts), avoiding distortion caused by signal aliasing and ensuring data integrity.

[0038] Sensor response capability: The typical response frequency of existing high-precision inertial measurement units (IMUs) is above 1000Hz. The acquisition frequency of 200-500Hz is in the optimal operating range of the sensor, which can avoid noise amplification caused by excessive frequency or signal loss caused by excessive frequency, ensuring that the acquired data is consistent with the actual motion state and guaranteeing accuracy.

[0039] (2) Reasonableness of sampling time (T=120 seconds) Covering the complete motion conditions: A single complete cycle of the multi-degree-of-freedom motion of the target object (such as the take-off, cruise, turning, and landing of a drone; the extension, rotation, and grasping of a robotic arm) is usually 30 to 60 seconds. A 120-second sampling time can cover at least two complete cycles, ensuring that the collected data includes the changes in physical quantities throughout the entire process of "start-steady state-stop". This avoids data bias caused by incomplete coverage of the working conditions and ensures completeness.

[0040] To mitigate the impact of random errors: The calculation of inertial parameters is highly dependent on the statistical characteristics of the data. A 120-second sampling time can collect 24,000 to 60,000 data samples (200Hz×120s=24,000, 500Hz×120s=60,000). A large number of samples can be preprocessed (such as adaptive threshold filtering and smoothing filtering) to mitigate random errors such as sensor noise and environmental interference, making the data closer to the real physical quantities and ensuring accuracy.

[0041] B. The specific methods for collecting data are as follows: Inertial measurement units (IMUs) are fixedly installed at multiple key locations on the target object. The selection of these key locations is based on the structural and motion characteristics of the target object. The selection of key locations must simultaneously meet two core principles: "structural representativeness" and "motion sensitivity." The specific rules and standards are as follows: 1. Structural characteristic-oriented selection rules Prioritize the core inertial correlation region: This region must include the center of mass of the target object (or the area near the center of mass). The motion of this region directly reflects the overall inertial characteristics and is the core basis for calculating inertial parameters (such as mass and center of mass coordinates). Examples include the fuselage center of a drone, the base of a robotic arm, and the connection point between the end effector.

[0042] Structural stiffness gradient coverage: It is necessary to cover the structural distribution of "rigid main body + flexible components" to avoid omission of dynamic characteristics due to selecting only a single stiffness region. Rigid regions (such as the middle section of the metal arm of a robotic arm) can reflect the overall motion inertia, while flexible regions (such as the wingtips of a drone or the joints of a robotic arm) can capture the coupling effect of inertial parameters caused by local vibrations.

[0043] Sensor installation feasibility: Select a location with structural strength that meets the sensor fixing requirements to avoid sensor displacement or damage due to structural deformation during movement; at the same time, it is necessary to reserve space for sensor wiring to ensure the stability of data acquisition.

[0044] Geometric feature clarity: Prioritize the selection of parts whose geometric coordinates are easy to measure accurately (such as the vertices of the object, points on the axis of symmetry), which facilitates the determination of the sensor installation position when establishing the coordinate system later and reduces the impact of position measurement errors on the calculation of inertial parameters.

[0045] 2. Selection rules based on motion characteristics Multi-degree-of-freedom motion coverage: Select parts that can fully reflect all motion dimensions of the target object. For example, for an aircraft with pitch, roll, and yaw three degrees of freedom, key parts need to be selected in the longitudinal, lateral, and vertical directions of the fuselage to ensure that the acceleration and angular velocity data of each degree of freedom can be effectively collected.

[0046] Region with maximum motion amplitude: Prioritize the part with the largest motion amplitude or speed (such as the end of a robotic arm or the wing of an aircraft). The physical quantity signals (acceleration, angular velocity) in this region have larger amplitudes and higher signal-to-noise ratios, which can reduce noise interference with the data and improve the accuracy of parameter identification.

[0047] Sensitive areas for motion coupling characteristics: Select areas with obvious multi-degree-of-freedom motion coupling (such as the tail of an aircraft or the joint connection of a robotic arm). The motion data in this area contains coupling information of the inertial parameters of each degree of freedom, which helps to decouple accurate individual inertial parameters (such as the cross term of the inertial tensor) through optimization algorithms.

[0048] Typical working condition coverage: Based on the actual working scenario of the target object, select the parts with the most significant motion characteristics under typical working conditions. For example, for an industrial robotic arm, select the end part that experiences the greatest force when grasping heavy objects; for a drone, select the fuselage part that experiences the most stable vibration during cruising and the most drastic changes in acceleration during maneuvering.

[0049] 3. Quantify selection criteria (which can be directly implemented) Number of key components: Select at least 3 (to meet the minimum requirements for 3D spatial motion measurement). For complex target objects (such as multi-joint robots), the number can be increased to 4-6 to ensure data redundancy.

[0050] Spacing requirement: The spatial distance between any two key parts should not be less than 1 / 3 of the maximum size of the target object, so as to avoid excessive data correlation due to parts being too close together, which would reduce the degree of freedom in parameter identification.

[0051] Relationship with the axis of motion: Key parts need to be distributed on both sides or vertically to the main axis of motion of the target object to ensure that the inertial parameters of each axis of motion (such as the moment of inertia in different directions) can be independently characterized.

[0052] Furthermore, the installation orientation of each inertial measurement unit (IMU) must be precisely calibrated to ensure a predetermined relative angular relationship between its coordinate axes. Accurately calibrating the installation orientation of the IMU ensures that the coordinate axes of each sensor maintain a predetermined relative angle (usually orthogonal, i.e., the X, Y, and Z axes are perpendicular to each other with an included angle of 90° ± 0.1°). The core beneficial effects are as follows: 1. Ensure the accuracy of data acquisition and avoid directional coupling errors. Inertial parameters (such as acceleration and angular velocity) are vector physical quantities, and their measured values ​​are directly related to the direction of the sensor's coordinate axes. If the coordinate axes are not orthogonal or the angular deviation is too large, it will cause physical quantity signals in different directions to couple with each other (such as the acceleration signal of the X-axis being mixed into the measurement value of the Y-axis), directly causing distortion of the original data.

[0053] Predetermined angular relationships (especially orthogonal relationships) can ensure that physical quantities in each direction are measured independently and accurately. For example, only longitudinal acceleration is collected on the X-axis and only lateral acceleration is collected on the Y-axis, providing uncoupled and clean data for subsequent attitude calculation and parameter identification.

[0054] 2. Simplify data fusion and coordinate system transformation processes to reduce calculation errors. When fusing multi-sensor data, data stitching must be performed based on a unified coordinate system. If the relative angles of the coordinate axes of each sensor are known and accurate, the data from each sensor can be quickly converted to the global reference coordinate system using a fixed rotation matrix, avoiding the accumulation of conversion errors caused by unknown angles or deviations.

[0055] For example, the three IMUs of a drone are installed on the fuselage, wings and tail respectively. Their coordinate axes are all orthogonal to the global coordinate system of the fuselage. The data of each part can be fused directly through simple matrix operations without the need for additional algorithms to estimate the relative angles between sensors, thus reducing computational complexity and sources of error.

[0056] 3. Improve the accuracy of the dynamic model and ensure the reliability of parameter identification. The dynamic model of this invention is based on the Newton-Euler equations, in which the relationships between force, torque, acceleration, and angular velocity strictly depend on the orientation definition of the coordinate system. If the sensor coordinate axis angles deviate, the physical quantity data input to the model will not match the orientation definition of the theoretical model, causing the force vector sequence calculated by the model to be distorted, which in turn affects the identification results of the inertial parameters.

[0057] The predetermined angular relationship ensures that the sensor measurement data is completely consistent with the coordinate system definition of the dynamic model, enabling the model to accurately reflect the force and motion relationship of the target object, providing reliable input data for algorithms such as particle swarm optimization and least squares method, and ultimately improving the accuracy of inertial parameter estimation.

[0058] 4. Simplify error compensation and calibration processes, and reduce system maintenance costs. If the relative angles of the coordinate axes of each sensor are fixed and known, all sensors can be calibrated in batches using a unified error compensation model (such as zero-bias calibration or scale coefficient calibration) in subsequent data processing, without the need to model the angle deviation of each sensor separately.

[0059] For example, all IMUs use an orthogonal coordinate system, and the zero bias error of each axis can be determined through a single static calibration. The calibration results are applicable to all sensors, greatly simplifying the calibration process and reducing maintenance costs and operational complexity during long-term use.

[0060] 5. Ensure consistency of data from multiple sensors and improve the efficiency of iterative optimization. In the accuracy verification and iterative optimization in step S5, it is necessary to compare the physical quantity data collected by different sensors with the model prediction data. If the coordinate axis angles of each sensor are consistent, the data consistency is better, the calculation of error indicators (such as root mean square error) is more accurate, and the source of error can be quickly located (whether it is a sensor installation problem or an algorithm parameter problem).

[0061] For example, if all IMU coordinate axes are orthogonal and have the same direction, when the error in a certain direction is too large, it can be directly determined that the inertial parameter identification in that direction is inaccurate, without having to consider the influence of coordinate axis angle deviation, thus improving the efficiency and targeting of iterative optimization.

[0062] Furthermore, the system accurately measures and stores the installation position information of each inertial measurement unit on the target object. Finally, it synchronously collects data such as the original acceleration and original angular velocity of the target object under complex motion conditions through these inertial measurement units.

[0063] Step b: Data preprocessing. The collected data is preprocessed to remove noise interference. A filtering algorithm is used to remove high-frequency noise while retaining the data's characteristic information. Then, the preprocessed data is normalized to ensure it falls within a specific numerical range, facilitating subsequent calculations.

[0064] The preprocessing includes: using an adaptive threshold filtering algorithm to remove obvious outliers, and employing smoothing filtering techniques to reduce high-frequency noise interference, thereby obtaining purified acceleration, angular velocity, and other data. The threshold setting of the adaptive threshold filtering algorithm is dynamically adjusted based on the statistical analysis results of historical data on the target object's motion, and the window size of the smoothing filter is adaptively determined according to the data change rate. Its positive effects include: 1. The positive effects of adaptive threshold filtering (dynamically adjusting the threshold) (1) Accurately identify outliers and avoid misjudging target objects. The physical quantity data of multi-degree-of-freedom motion (such as acceleration and angular velocity) will show different distribution characteristics with changes in working conditions (such as stable data when the UAV is cruising, and drastic data fluctuations when it is maneuvering). Based on the statistical analysis of historical data, the threshold is dynamically adjusted so that the threshold always adapts to the current motion state. Under stable working conditions, the threshold is narrowed to accurately eliminate minor anomalies such as sudden noise from the sensor; under drastic motion working conditions, the threshold is appropriately widened to avoid misjudging normal large data fluctuations as outliers and to ensure that effective data is not lost.

[0065] (2) Enhancing the robustness of data purification: Fixed thresholds can only adapt to a single motion state. When faced with complex multi-degree-of-freedom motion, problems such as "thresholds that are too high and fail to detect anomalies" or "thresholds that are too low and delete valid data" are likely to occur. Dynamic thresholds automatically adapt to the dynamic changes in motion state by associating the statistical characteristics (such as mean and standard deviation) of historical data in real time. Regardless of whether the target object is in the starting, steady state, maneuvering, or stopping stage, it can maintain a stable outlier removal effect and enhance the adaptability of preprocessing to complex working conditions.

[0066] (3) Reduce manual intervention and improve automation. If a fixed threshold is used, the threshold parameters need to be manually adjusted for different target objects or motion scenarios. The operation is cumbersome and the results are easily affected by human judgment deviations. Dynamic thresholds based on historical data statistics do not require manual intervention and can automatically complete threshold optimization according to data characteristics, reducing the operational complexity of the preprocessing process and avoiding fluctuations in preprocessing accuracy caused by human error.

[0067] 2. The positive effects of smoothing filtering (window size adapts to the rate of data change) (1) Balancing noise suppression and feature preservation: The rate of change of data directly reflects the motion state of the target object. When the rate of change is low (such as uniform motion), the noise content in the data is relatively high, and a larger window size is needed to enhance the filtering effect. When the rate of change is high (such as rapid turning or starting and stopping), the data contains key motion features (such as acceleration peaks), and a smaller window size is needed to avoid the features being smoothed and weakened. Adaptive window size can match the rate of change of data in real time, achieving the optimal balance between noise suppression and feature preservation, and solving the contradiction of "incomplete noise filtering" or "feature distortion" with a fixed window.

[0068] (2) Adapting to the dynamic characteristics of multi-degree-of-freedom motion In multi-degree-of-freedom motion, different motion dimensions of the target object (such as pitch, roll, and yaw) may have data with different rates of change at the same time (e.g., the longitudinal acceleration has a low rate of change, while the lateral yaw rate of change is high when the UAV is cruising horizontally). The adaptive window can independently adjust the window size for the rate of change of data in each dimension, and accurately filter data with different change characteristics. Compared with the "one-size-fits-all" processing of the fixed window, it is more in line with the complex data characteristics of multi-degree-of-freedom motion.

[0069] (3) Improving the accuracy of subsequent data processing. The core purpose of basic smoothing filtering is to provide low-noise and feature-complete data for subsequent normalization processing and attitude calculation. The adaptive window can effectively reduce the interference of high-frequency noise on attitude calculation (such as reducing the cumulative error of solving quaternion differential equations) by precisely controlling the filtering intensity, and can also completely retain the motion feature information in the data (such as the changing trend of force vector sequence), providing high-quality data input for dynamic model establishment and parameter identification, and indirectly improving the calculation accuracy of the final inertial parameters.

[0070] 3. Synergistic gain from combining the two The combination of adaptive threshold filtering and dynamic window smoothing filtering forms a preprocessing closed loop of "precise outlier removal + adaptive noise suppression": dynamic thresholding first removes large outliers, clearing away "extreme interference" for smoothing filtering; adaptive windowing then optimizes noise suppression based on the data change rate, ensuring data purity and feature integrity. This combination avoids the limitations of a single filtering algorithm, enabling the preprocessed data to meet the "low noise" requirement of subsequent calculations while accurately reflecting the true motion characteristics of the target object, laying a reliable data foundation for the entire inertial parameter calculation process.

[0071] The normalization process includes: based on the pre-processed and purified data, the attitude of the target object is calculated using a quaternion differential equation updated by a rotation matrix. During the calculation, a Taylor series expansion method is used to approximate the solution of the quaternion differential equation to reduce computational complexity and improve computational efficiency. Simultaneously, an error compensation term is introduced to correct the accumulated error caused by the approximate solution, thereby obtaining a high-precision target object attitude matrix sequence. Based on the obtained attitude matrix sequence, the purified data collected by each inertial measurement unit (IMU) is transformed to a unified reference coordinate system. During the transformation, the influence of small changes in the relative positions between the IMUs caused by the deformation or local vibration of the target object is fully considered. A dynamic transformation model between the local coordinate system and the unified reference coordinate system is established for accurate transformation, resulting in a precise data sequence after transformation.

[0072] Step c: Establish a dynamic model. Based on the structure and motion characteristics of the target object, establish an accurate dynamic model. This model considers the object's mass distribution, shape, moment of inertia, and other inertial parameters, as well as the interaction of various external forces and torques. Based on the Newton-Euler equations, a multi-degree-of-freedom dynamic equation system is constructed.

[0073] Specifically, based on the data sequence transformed in step b and the pre-measured and stored installation position information of each inertial measurement unit on the target object (i.e., the detected position information of the target object), Newton's second law is used to calculate the force vector sequence acting on each corresponding part of the target object. This establishes an "external force-motion" relationship, giving the model a clear physical basis and avoiding deviation from actual motion laws. Adding constraints reduces the uncertainty in solving inertial parameters, making the results more unique. Data rationality is verified, and outliers that do not conform to physical laws are eliminated to avoid model distortion. It adapts to multi-degree-of-freedom coupled motion, fully characterizing the relationship between the forces on each part and the overall motion. It provides high-quality input for parameter identification, improving the convergence efficiency and accuracy of subsequent optimization algorithms. During the calculation process, the force vector calculation is verified in real time. Errors are detected and corrected promptly by comparing the trend of force vector changes at adjacent time points with the kinematic laws of the target object. Then, a mechanical equilibrium equation is constructed, including the target object's mass, center-of-mass coordinate components, and inertial tensor elements.

[0074] Step d: Parameter identification algorithm design. Substitute the calculated force vector sequence into the aforementioned dynamic model and employ advanced optimization algorithms for inertial parameter identification. For example, a hybrid algorithm combining particle swarm optimization (PSO) and least squares methods can be used. First, the global search capability of PSO is utilized to quickly locate the possible optimal solution region in the parameter space. Then, the least squares method is used to perform a precise local search within this region to obtain the optimal estimate of the inertial parameters.

[0075] Alternatively, a gradient descent-based optimization algorithm can be used to solve the equation. During the execution of the optimization algorithm, a dynamic step size adjustment strategy can be set to accelerate the convergence speed and prevent getting trapped in local optima, thereby accurately calculating the inertial parameters of the target object, including mass, centroid position coordinates, and the values ​​of each element of the inertial tensor.

[0076] Step e: Accuracy Verification and Iterative Optimization. Substitute the calculated inertial parameters into the target object's dynamic model to simulate its motion under the same conditions. Calculate theoretical data such as force, torque, acceleration, and angular velocity, and compare this data with the actual collected data. Calculate error metrics, such as root mean square error (RMSE). If the error metric exceeds the preset accuracy threshold, backtrack to the data acquisition step to check the accuracy of hardware installation and data acquisition, or adjust relevant parameters in the parameter identification algorithm, such as inertial weights and learning factors in the particle swarm optimization algorithm, and re-perform parameter identification (inertial parameter calculation) until the error meets the accuracy requirements.

[0077] Step f, Result Output and Application. The final high-precision inertial parameters are output and applied to relevant engineering systems. For example, in aircraft control systems, the inertial parameters are used to optimize attitude control algorithms to improve the flight stability and navigation accuracy of the aircraft.

[0078] The above steps also included coupling frequency response function measurement and dynamic stiffness identification, specifically including: (1) Measurement of coupled frequency response function Measurement equipment: A high-precision force hammer (excitation end) and a laser vibration meter (response end) are used, which work synchronously with the inertial measurement unit (IMU) in step S1 to ensure that the data timestamps are consistent.

[0079] Measurement method: Apply single-point pulse excitation to the key part of the target object (corresponding to the IMU installation position), collect the excitation force signal (F(ω)) and response acceleration signal (A(ω)), and obtain the coupled frequency response function H(ω)=A(ω)F(ω) in the frequency domain through Fourier transform (ω is the angular frequency, covering the main motion frequency range of the target object [ω1, ω2]).

[0080] Dynamic stiffness identification can be completed by measuring only one set of coupled frequency response functions, eliminating the need for multiple independent tests and reducing operational complexity and equipment dependence.

[0081] (2) Calculation of dynamic stiffness Based on the mechanical relationship between the coupled frequency response function and dynamic stiffness (K(ω)): K(ω)=1H(ω)·Meq(ω), where Meq(ω) is the equivalent mass in the frequency domain (determined by the structural characteristics of the target object).

[0082] Specific calculation: The coupled frequency response function H(ω) is fitted by the least squares method to eliminate measurement noise interference. The dynamic stiffness curve K(ω) in the frequency domain is obtained by substituting it into the preset equivalent mass model.

[0083] Verification mechanism: If the dynamic stiffness curve shows abnormal abrupt changes (such as exceeding the preset physical reasonable range), backtrack to step S1 to check the accuracy of the excitation position or the stability of the sensor installation, and remeasure until the requirements are met.

[0084] (3) Integration with dynamic models The identified dynamic stiffness K(ω) is used as a constraint and embedded into the Newton-Euler dynamic equation system in step S3 to supplement and construct the "inertia parameter-dynamic stiffness" coupling equation: τ=M(θ)θ¨+C(θ,θ˙)θ˙+K(ω)θ, where τ is the torque vector, θ is the attitude angle vector, M is the inertia matrix, and C is the Coriolis / centrifugal force matrix.

[0085] This coupling equation can reduce the degrees of freedom for inertial parameter identification, avoid parameter estimation getting stuck in local optima, and improve the convergence accuracy of subsequent optimization algorithms (such as particle swarm optimization + least squares method).

[0086] All data generated during the entire calculation process, including raw acquisition data, preprocessed data, attitude calculation data, transformed data, force vector calculation data, inertial parameter calculation process data, and the final inertial parameter results, are classified and stored according to a predetermined data format and storage structure. The storage medium can be a local high-speed storage device or a cloud-based distributed storage system, so as to facilitate subsequent data mining, algorithm optimization, and long-term tracking research on the inertial characteristics of the target object.

[0087] Example 1: Taking a new type of UAV as an example, its inertial parameter calculation method includes the following: I. Basic Parameter Settings (a) Core parameters of the UAV (known design values) Dimensions: Length 1.2m, Width 0.8m, Height 0.3m; Design weight: 2.5kg (excluding sensors); Coordinates of key components (establish a global coordinate system with the fuselage center of gravity as the origin O(0,0,0): the x-axis moves forward along the fuselage longitudinal axis, the y-axis moves to the right along the fuselage transverse axis, and the z-axis moves upward perpendicular to the fuselage): a. Near the center of gravity (IMU1 mounting location): P1(0.02, 0, 0.05)m; b. Left wing end (IMU2 mounting position): P2(0.4, 0.45, 0.1)m; c. Right wing end (IMU3 mounting position): P3(0.4, -0.45, 0.1)m; d. Tail fin (force / torque sensor mounting position): P4(-0.5, 0, 0.08)m; Movement frequency range: 5~50Hz (cruising main frequency 20Hz).

[0088] (ii) Data acquisition parameters Acquisition frequency: 100Hz (satisfies Nyquist's theorem, covering twice the highest motion frequency of 50Hz); Sampling time: 60s (covering one complete flight cycle: 10s takeoff + 30s cruise + 20s landing); Sensor model: a. Inertial Measurement Unit (IMU): Six-axis IMU (accelerometer range ±16g, angular velocity range ±2000° / s, accuracy ±0.01° / h). b. Force / Torque Sensor: Six-axis sensor (force range ±50N, torque range ±10N·m, accuracy ±0.01N / ±0.001N·m); II. Detailed data and model formulas for each step (a) Step 1: Data Acquisition 1. Example of raw acquired data (partial time domain data, time interval 0.01s) Please see Table 1: Table 1 Original Data Collection Table

[0089] 2. Data Acquisition Synchronization Mechanism Triggering method: Hardware synchronous triggering (the IMU and the force / torque sensor share the same trigger signal, with a time deviation ≤0.001s); Data storage format: CSV format, containing timestamps, sensor IDs, and physical quantity values ​​(x / y / z three-dimensional components).

[0090] (ii) Step 2: Data preprocessing and normalization 1. Preprocessing algorithm and parameters Adaptive threshold filtering: Threshold calculation model: ,in The average of the first 100 data points. The standard deviation of the first 100 data points; Example: Mean value of acceleration x-axis data during cruise phase Standard deviation threshold Remove outliers exceeding 1.05; • Smoothing filtering (Kalman filtering): Equations of state: Observation equation: ; Parameter settings: State matrix (Identity matrix), observation matrix Process noise variance Observation noise variance R=1e−3I3×3 .

[0091] 2. Normalization processing (including attitude calculation) Quaternion differential equation: ,in It is a quaternion. Angular velocity; Solving using Taylor series expansion (first-order approximation): , ; Error compensation item: proportionality coefficient Kp=0.05 ; Attitude matrix transformation: R(q)=1-2q22-2q322q1q2-2q0q32q1q3+2q0q22q1q2+2q0q31- 2q12-2q322q2q3-2q0q12q1q3-2q0q22q2q3+2q0q11-2q12−2q22 ; Normalization results: After converting the acceleration and angular velocity data to the global coordinate system, they are normalized to the interval [-1, 1]. See Table 2 for an example of the converted data. Table 2. Converted Data Table

[0092] (III) Step 3: Establish a dynamic model 1. Calculation of force vector sequence Newton's Second Law: ,in Let be the force vector at the i-th part, m = 2.5 kg, and ai be the converted acceleration; Calculation example (t=0.01s, IMU1 location): F1=2.5×(0.5,0.3,9.83)=(1.25,0.75,24.58) N ; Real-time verification rule: The rate of change of force vector ΔF / Δt between adjacent time steps ≤ 50 N / s (based on the kinematic limit of the UAV). If it exceeds this limit, it is judged as a calculation error and corrected.

[0093] 2. Dynamic model (Newton-Euler equations) Equations of translational motion: ,in Let vc be the total force and vc be the velocity of the center of mass. Equations of rotational motion: ,in Let be the total torque, ri be the position vector of part i relative to the center of mass, and I be the inertia tensor. Inertia tensor form: The parameters to be identified are Ixx, Iyy, Izz, Ixy, Ixz, and Iyz.

[0094] (iv) Step 4: Parameter Identification 1. Hybrid Algorithm (PSO + Least Squares) Parameters PSO parameters: Population size: 200 Maximum number of iterations: 100 Inertia weight: Initially 0.8, adjusted to 0.7 after iteration. Learning factors: c1=c2=2.0 Parameter search range: Ixx, Iyy, Izz∈[0.05,0.5]kg⋅m², Ixy, Ixz, Iyz∈[−0.05,0.05]kg·m²; Fitness function: , where τsim is the model predicted torque, τmeas is the measured torque, and N=6000 (60s×100Hz).

[0095] 2. Least squares fitting Overdetermined system of equations: , where A is a 12000×6 matrix (constructed based on force vectors and motion data). b is a 12000×1 vector (torque residual); Solution: .

[0096] 3. Identification results (initial value → optimized value) are shown in Table 3: Table 3 Identification Results

[0097] (V) Step 5: Accuracy Verification and Iterative Optimization 1. Error Index Calculation Root Mean Square Error (RMSE): ; Initial verification result: Attitude angle RMSE = 0.5° (exceeds the preset threshold of 0.3°); Iterative adjustment: The PSO inertia weight was adjusted from 0.8 to 0.7, and re-identification was performed; Final verification result: Attitude angle RMSE = 0.28° (meets accuracy requirements); 2. Comparison of simulated test data (t=10s, cruise phase) is shown in Table 4: Table 4 Simulation Test Data Table

[0098] (vi) Step 6: Output and Application of Results 1. Final inertial parameter output Inertia tensor: ; Centroid coordinates (corrected after identification): (0.021, 0.003, 0.052)m.

[0099] 2. Engineering Applications (UAV Attitude Control Algorithm) Control law optimization: Substitute the identified inertial parameters into the PID controller and adjust the proportional coefficient Kp=2.5, integral coefficient Ki=0.1, and derivative coefficient Kd=0.5; Application results: The attitude control response time was reduced from 0.3s to 0.2s, and the steady-state error was reduced from ±0.1° to ±0.05°.

[0100] III. Data Storage and Traceability Storage contents: raw data (60s×100Hz×4 sensors=24000 records), preprocessed data, attitude calculation data, force vector sequence, and inertial parameter identification process data; Storage format: Structured database (fields include timestamp, data type, value, and error range); Traceability mechanism: Each data point is associated with the sensor number, acquisition time, and processing algorithm version, supporting full-process data backtracking.

[0101] As can be seen from the above embodiments, the high-precision inertial parameter calculation method of the present invention can effectively improve the calculation accuracy and efficiency of inertial parameters, and has broad application prospects and practical value. It is applicable to various engineering systems and equipment that require high-precision inertial parameters.

[0102] The present invention has been described by way of example in conjunction with the accompanying drawings. Obviously, the specific implementation of the present invention is not limited to the above-described manner. Any non-substantial improvement made by adopting the inventive concept and technical solution of the present invention, or the direct application of the inventive concept and technical solution of the present invention to other occasions without modification, shall be within the protection scope of the present invention.

Claims

1. A high-precision method for calculating inertial parameters, characterized in that: Includes the following steps: S1. Obtain physical quantity data of the target object under multi-degree-of-freedom motion; S2. The physical quantity data obtained in step S1 is preprocessed and normalized to obtain the transformed data sequence; S3. Establish an accurate dynamic model based on the structure and motion characteristics of the target object; S4. The inertial parameters of the dynamic model in step S3 are identified by an optimization algorithm, and the optimal estimated values ​​of the inertial parameters are obtained. S5. Substitute the inertial parameters obtained in step S4 into the dynamic model, and verify the accuracy and iteratively optimize through simulation tests to finally obtain high-precision inertial parameters. S6. Output the final high-precision inertial parameters and apply them to the corresponding engineering system.

2. The high-precision inertial parameter calculation method according to claim 1, characterized in that: In step S1, physical quantity data of the target object are collected using a high-precision sensor. The high-precision sensor includes multiple inertial measurement units installed at different key parts of the target object. The selection of key parts is determined based on the structural and motion characteristics of the target object. The installation direction of the inertial measurement units is precisely calibrated to ensure that there is a predetermined relative angular relationship between their coordinate axes.

3. The high-precision inertial parameter calculation method according to claim 1, characterized in that: In step S2, the preprocessing includes: using an adaptive threshold filtering algorithm to remove obvious outliers and using smoothing filtering technology to reduce high-frequency noise interference, thereby obtaining purified physical quantity data; wherein, the threshold setting of the adaptive threshold filtering algorithm is dynamically adjusted based on the statistical analysis results of historical data of the target object's motion, and the window size of the smoothing filter is adaptively determined according to the data change rate.

4. The high-precision inertial parameter calculation method according to claim 3, characterized in that: In step S2, the normalization process includes: (1) Based on the preprocessed and purified physical quantity data, the attitude of the target object is calculated using the quaternion differential equation updated by the rotation matrix. In the calculation process, the Taylor series expansion method is used to approximate the solution of the quaternion differential equation to reduce the computational complexity and improve the computational efficiency. At the same time, an error compensation term is introduced to correct the cumulative error caused by the approximate solution, thereby obtaining a high-precision target object attitude matrix sequence. (2) Based on the obtained attitude matrix sequence, the physical quantity data after preprocessing and purification are transformed to a unified reference coordinate system. During the transformation process, the influence of the slight change in the relative position between each inertial measurement unit caused by the deformation of the target object or local vibration is fully considered. The transformation is carried out by establishing a dynamic transformation model between the local coordinate system and the unified reference coordinate system to obtain an accurate transformation data sequence.

5. The high-precision inertial parameter calculation method according to claim 1, characterized in that: In step S3, the dynamic model is a multi-degree-of-freedom dynamic equation system built on the basis of the Newton-Euler equations.

6. The high-precision inertial parameter calculation method according to claim 5, characterized in that: Step S3 includes: based on the transformed data sequence obtained in step S2 and the pre-measured and stored detection position information of the target object, calculating the force vector sequence acting on each corresponding part of the target object using Newton's second law; during the calculation process, the calculation of the force vector is verified in real time, and calculation errors are detected and corrected in a timely manner by comparing the change trend of the force vector at adjacent time moments with the kinematic law of the target object.

7. The high-precision inertial parameter calculation method according to claim 1, characterized in that: In step S4, the global search capability of the particle swarm optimization algorithm is first used to quickly locate the possible optimal solution region in the parameter space. Then, the least squares method is used to perform a precise local search in this region to obtain the optimal estimate of the inertial parameters.

8. The high-precision inertial parameter calculation method according to claim 7, characterized in that: In step S4, the calculated force vector sequence is substituted into the above dynamic model, and the equation is solved by an optimization algorithm based on gradient descent. During the execution of the optimization algorithm, a dynamic step size adjustment strategy is set to accelerate the convergence speed and prevent getting trapped in local optima, thereby accurately calculating the inertial parameters of the target object.

9. The high-precision inertial parameter calculation method according to claim 1, characterized in that: In step S5, the simulation test includes: simulating the motion state of the target object under the same motion conditions, calculating the theoretical physical quantity data, comparing it with the actual collected physical quantity data, and calculating the error index; if the error index is greater than the preset accuracy threshold, then backtracking to step S1 to check the accuracy of hardware installation and data acquisition, or adjusting the relevant parameters in the parameter identification algorithm in step S4, and recalculating the inertial parameters until the error index meets the accuracy requirements.

10. The high-precision inertial parameter calculation method according to claim 1, characterized in that: It also includes coupled frequency response function measurement and dynamic stiffness identification, and embeds the identified dynamic stiffness as a constraint condition into the dynamic model of step S3, specifically including: (1) Measurement of coupled frequency response function: A high-precision force hammer and laser vibration meter are used to work synchronously with the inertial measurement unit in step S1. Single-point pulse excitation is applied to the key parts of the target object, and the excitation force signal and response acceleration signal are collected. The frequency domain coupled frequency response function is obtained by Fourier transform. (2) Dynamic stiffness calculation: Based on the mechanical relationship between the coupled frequency response function and dynamic stiffness, the frequency domain coupled frequency response function is fitted by the least squares method, and the frequency domain dynamic stiffness curve is obtained by substituting it into the equivalent mass model; (3) Integration with the dynamic model: The identified dynamic stiffness is embedded as a constraint condition into the Newton-Euler dynamic equation system in step S3 to construct the inertial parameter-dynamic stiffness coupling equation.

Images