Frequency domain measurement method and system for motion distribution of humanoid robot

Abstract

The invention discloses a frequency domain measurement method and system for motion distribution of a humanoid robot, and belongs to the technical field of intelligent and robot control. The method comprises the steps that joint real-time motion data are collected and mapped to a normalized state space, and strategy density distribution is obtained; extracting a frequency domain feature vector by adopting a truncated Fourier basis function; constructing a template mean value and a covariance matrix based on the group samples; and the frequency domain deviation is calculated through the spectrum weighted mahalanobis distance. According to the method, time sequence dependence is eliminated through frequency domain conversion, the robustness is improved in combination with group statistical information and spectrum weighting, the structural difference of strategy distribution is accurately captured, and switching of multiple feature extraction and distance measurement modes is supported. The method solves the problems that an existing method depends on a time domain, is insufficient in structural sensitivity and is weak in anti-noise capability, is suitable for scenes such as motion strategy evaluation and mode diagnosis, and is high in engineering practicability.

Description

Technical Field

[0001] This invention belongs to the field of embodied intelligence and robot control technology, and relates to a frequency domain measurement method and system for the motion distribution of humanoid robots, which is applicable to scenarios such as motion strategy evaluation, motion pattern diagnosis, and control algorithm optimization of humanoid robots. Background Technology

[0002] With the rapid development of embodied intelligence and humanoid robot technology, how to quantitatively evaluate and compare the advantages and disadvantages of different motion strategies (such as walking gait and maneuvering) has become a key issue in robot control algorithm development, strategy optimization, and performance diagnosis. Existing robot motion evaluation technologies mostly focus on the time domain or trajectory level.

[0003] For example, CN111347430A discloses a method and apparatus for determining a robot's motion trajectory. Its core lies in filtering effective path points based on an environmental map (boundary map and obstacle map) to plan a more accurate motion trajectory. This method focuses on the accuracy and efficiency of trajectory generation, falling under the category of motion planning, but does not involve a quantitative evaluation of the inherent characteristics of the executed motion strategy itself.

[0004] CN115962969A discloses a method for evaluating the motion rhythm of an industrial robot. By designing various tests such as single-axis, linear, and gate-shaped paths, it measures the time it takes for the robot to complete a specific action to evaluate its motion rhythm performance. This method provides a standardized performance testing process, but its evaluation index (time) is macroscopic and result-oriented, failing to reveal the subtle differences in the robot's internal states (such as joint coordination and motion patterns) during motion.

[0005] CN116787442A discloses a trajectory evaluation method based on the robot's own odometry. This method evaluates positioning accuracy or detects trajectory jerking by comparing odometry data (as the "true value") with the trajectory estimated by the localization algorithm. The core of this method is comparing the accuracy of pose estimation, belonging to the performance evaluation field of Localization and Mapping (SLAM). Its evaluation object is the robot's "position" rather than the "motion strategy" itself.

[0006] CN119761921A discloses a method for evaluating the motion efficiency of a humanoid robot. By defining "reference kinetic power" and "reference kinetic efficiency" indices, it evaluates the efficiency of robot motion from an energy perspective. The evaluation dimension of this method is energy consumption, which, although highly correlated with the performance of the humanoid robot, also fails to characterize the distribution structure of the motion strategy in the state space.

[0007] In summary, the existing technology has the following main drawbacks: (1) The evaluation dimension is singular and superficial: Existing methods mostly rely on temporal features (such as trajectory error and completion time) or macroscopic indicators (such as energy efficiency), which cannot effectively capture and quantify the structural differences in the distribution of motion strategies in high-dimensional state space. For example, two motions with the same completion time and similar trajectories may have fundamentally different joint coordination patterns and motion smoothness, which are difficult to distinguish with existing methods.

[0008] (2) Lack of statistical robustness and comparability: Temporal features are easily affected by motion speed, time alignment and sensor noise, resulting in unstable evaluation results. At the same time, the lack of a unified and statistically significant metric makes it difficult to fairly compare the differences between different strategies and an optimal group strategy template.

[0009] (3) Sensitive to policy noise: Evaluation methods based on the original trajectory or low-order features are very sensitive to non-essential fluctuations such as jitter and noise in motion, and may misjudge noise as policy defects.

[0010] Therefore, there is an urgent need in this field for a general evaluation method that can delve into the internal structure of motion strategy distribution, is robust to noise, and has statistical interpretability. Summary of the Invention

[0011] To address the shortcomings of existing technologies, the present invention aims to provide a frequency domain measurement method and system for the motion distribution of humanoid robots, achieving accurate measurement of motion strategy distribution in high-dimensional state space and solving problems such as reliance on the time domain, insufficient structural sensitivity, and weak noise resistance in existing methods. To achieve the above objective, the present invention adopts the following technical solution.

[0012] In a first aspect, the present invention provides a frequency domain measurement method for the motion distribution of a humanoid robot, comprising the following steps: S1: Collect real-time joint motion data of the humanoid robot, including the angle and angular velocity of each joint; S2: Map the real-time joint motion data to a normalized state space, reduce the dimensionality to 3-5 dimensions using principal component analysis (PCA), and then use spatial density estimation to obtain the density distribution of the motion strategy; S3: Perform Fourier decomposition on the density distribution using truncated Fourier basis functions, select the Fourier coefficients to be retained according to a preset energy threshold (e.g., ≥95%), calculate the Fourier coefficients and extract the strategy feature vector; S4: Based on the population sample data, construct the template mean and regularized population covariance matrix of the motion strategy; S5: Introduce a spectral weighting matrix, and calculate the frequency domain deviation between the policy feature vector and the template mean using weighted Mahalanobis distance to obtain the measurement result of motion distribution.

[0013] The method provided by this invention eliminates motion time-series dependence through frequency domain transformation, enabling the same strategy at different speeds to have consistent characteristics. By combining the group covariance matrix and spectral weighting, it achieves sensitive quantification of structural differences in motion strategy distribution in high-dimensional state space, and is statistically robust to motion noise.

[0014] Furthermore, in step S1, the real-time joint motion data satisfies , in n The number of robot joints. i i ( t ) represents the time of the i-th joint at time i. t Angle, The i-th joint at time i t The angular velocity, i=1,...,n.

[0015] Furthermore, in step S2, the normalized state space By constructing a linear normalization method, the angles and angular velocities of each joint are mapped to the [0,1] interval. This eliminates the scale differences in motion parameters of different joints, making the distribution characteristics in the high-dimensional state space comparable and improving the consistency and accuracy of the measurement results.

[0016] Furthermore, in step S2, the spatial density estimation employs the Gaussian kernel density estimation method, with the kernel function being... Among them, the core bandwidth s Determined using cross-validation.

[0017] Furthermore, in step S3, the truncated Fourier basis functions are multidimensional complete orthogonal basis functions, expressed as follows: ,in , This is the normalized state space vector after dimensionality reduction. d The dimension after dimensionality reduction. k =( k 1,..., k d ) is the truncated order vector. k i ∈{0,1,..., K max}, For piecewise functions: .

[0018] Furthermore, in step S4, the template mean The group covariance matrix ,inc p Let the feature vectors be the strategy feature vectors of each group of samples; when the feature vector dimension is... M Greater than the number of samples N At that time, regularization is performed as ,in , or The constant factor is a preset value with a range of

[10] . -2 10 -4 ], The trace of the covariance matrix, I It is an identity matrix.

[0019] Furthermore, in step S5, the spectral weighting matrix It is a diagonal matrix, using a hybrid energy-frequency weighting method, with diagonal elements... Where α∈[0,1] are weighting coefficients. c i 2 For the first i The energy of a Fourier coefficient f i For the first i The frequency values ​​corresponding to each coefficient.

[0020] Furthermore, in step S3, the truncated Fourier basis function can be replaced with a wavelet basis function for frequency domain feature extraction. This provides diverse feature extraction schemes to adapt to the policy distribution characteristics of different motion scenarios, enhancing the flexibility and applicability of the method.

[0021] Furthermore, in step S5, the weighted Mahalanobis distance is replaced by Kullback-Leibler (KL) divergence; the Kullback-Leibler divergence is based on the assumption that the eigenvectors follow a Gaussian distribution, and is calculated using the formula: , in P The distribution of the feature vectors to be evaluated, Q The distribution of the template mean. µ P , µ Q These are the means of the two distributions, respectively. S P , S Q Let be the covariance matrices of the two distributions, respectively. d is the dimension of the feature vector, tr() is the trace operation of the matrix, and || is the determinant operation of the matrix.

[0022] Secondly, the present invention provides a frequency domain measurement system for the motion distribution of a humanoid robot, comprising: The data acquisition module is used to collect the angle and angular velocity data of each joint of the humanoid robot in real time, and output 2 n 3D motion data vector; The state mapping module is used to map the 2 n The motion data vectors are linearly mapped to the [0,1] normalized space. After dimensionality reduction to 3-5 dimensions through principal component analysis, the motion strategy density distribution function is generated by Gaussian kernel density estimation. The feature extraction module is used to perform truncated Fourier decomposition on the density distribution function, calculate the Fourier coefficients, and construct the policy feature vector. The template construction module is used to calculate the template mean vector and the regularized population covariance matrix based on the feature vectors of the population samples. The deviation calculation module is used to construct a spectral weighted diagonal matrix, calculate the frequency domain deviation between the strategy eigenvector and the template mean vector by weighted Mahalanobis distance, and output the measurement result of motion distribution.

[0023] Compared with the prior art, the present invention has the following beneficial technical effects: Breaking through the limitations of the time domain, a frequency domain metric framework is proposed: Existing technologies all rely on time domain features for motion evaluation. This invention transforms the density distribution of motion strategies to the frequency domain, extracts features through Fourier decomposition, eliminates time-series dependence, and solves the technical bottleneck that makes it difficult to compare strategies with different speeds and time lengths.

[0024] Construct a statistically robust measurement model: Introduce the population covariance matrix and spectral weighting matrix into the bias calculation, so that the measurement results are not only statistically significant, but also effectively resist motion noise.

[0025] Achieve structure-sensitive distribution measurement: Accurately capture the structural differences in motion strategies in high-dimensional state space through frequency domain features, and effectively distinguish motion patterns that have similar surface trajectories but different essential structures.

[0026] It provides flexible and versatile technical solutions: it supports switching between multiple feature extraction methods and distance measurement methods to adapt to different motion scenarios and evaluation needs. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of a frequency domain measurement method for the motion distribution of a humanoid robot provided by the present invention. Detailed Implementation

[0028] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0029] Example 1

[0030] This embodiment provides a frequency domain measurement method for the motion distribution of a humanoid robot, the process of which is as follows: Figure 1 As shown, this study evaluates the walking strategy of a 12-joint bipedal humanoid robot (6 joints per leg: hip, knee, ankle, hip abduction, knee internal rotation, and ankle inversion). The goal is to quantify the structural differences between the current walking strategy and the group's optimal strategy, providing a basis for optimizing control parameters.

[0031] 1. Experimental Preparation Hardware configuration: joint sensor (angle accuracy ±0.1°, angular velocity accuracy ±1° / s), NVIDIA JetsonXavier NX edge computing platform (ARM Cortex-A57 CPU + Volta GPU), 16GB LPDDR4 memory, 128GB eMMC flash memory, Ethernet / CAN communication interface; Software environment: Ubuntu 20.04 operating system, C++ core algorithm library, Python data visualization tool; Group sample: Collect 30 sets of walking motion data under the same control parameters (N=30), with each set collected for 60 seconds, a sampling frequency of 100Hz, and a walking speed of 0.3m / s (speed scaling range ±30%, i.e., 0.21m / s-0.39m / s).

[0032] 2. Specific Implementation Steps Step S1: Real-time joint motion data acquisition Angle sequences of 12 joints were collected using joint sensors. i i ( t ) and angular velocity sequence ( i =1,2,...,12), construct a 24-dimensional motion data vector. x ( t A total of 6,000 sampling points (60 seconds × 100Hz) were collected. After being synchronized by the sensors, the data was transmitted to the edge computing platform via the Ethernet interface.

[0033] The experimental results of this step are as follows: 30 sets of valid population sample data and 1 set of data to be evaluated were obtained. The data integrity is ≥99%, and there are no obvious outliers (verified by the 3σ criterion).

[0034] Step S2: State-space mapping, dimensionality reduction, and density distribution estimation 2.1 Normalization processing: for angle sequences i i ( t (Value range [-120)) o , 120 o ]) Using the formula Mapped to the [0, 1] interval; for the angular velocity sequence (Value range [-300)) o / s 300 o / s ]) Using the formula Mapping to the [0, 1] interval yields 24-dimensional normalized data; 2.2 PCA Dimensionality Reduction: PCA dimensionality reduction was performed on the 24-dimensional normalized data, retaining principal components with a cumulative variance contribution rate ≥ 95%, ultimately reducing the data to a 4-dimensional state space. (The variance contribution rates of the four principal components are 42%, 28%, 15%, and 10%, respectively, totaling 95%). 2.3 Gaussian kernel density estimation: using kernel function The kernel bandwidth was determined using cross-validation. s =0.05, density estimation is performed on the 4-dimensional reduced data to obtain the density distribution of the motion strategy. .

[0035] The experimental results of this step show that the 4D state space effectively preserves the core information and density distribution of the original data. The results are smooth and continuous, with no obvious discretization distortion, which verifies the effectiveness of dimensionality reduction and density estimation.

[0036] Step S3: Frequency Domain Feature Extraction 3.1 Definition of Fourier basis functions: Fourier basis functions are defined using multidimensional complete orthogonal truncation. ,in k =( k 1, k 2, k 3, k 4), k i ∈{0,1,...,5}( K max =5), For piecewise functions: ; 3.2 Calculation of Fourier coefficients: Density distribution is calculated using the trapezoidal integral method. Projection coefficients on each basis function c k A total of (5+1) was obtained. 4 =1296 coefficients; 3.3 Eigenvector Construction: Calculating the energy of each coefficient E k = c k 2 The coefficients with the highest energy percentages (48 in total) were selected, and a 48-dimensional strategy feature vector was constructed. c p ∈ R 48 ( M =48).

[0037] The experimental results of this step show that the cumulative energy ratio of the 48-dimensional feature vector is ≥95%, which effectively condenses the core frequency domain features of the motion strategy. The computational complexity is reduced by 96.3% compared with the original 1296 coefficients, balancing feature integrity and computational efficiency.

[0038] Step S4: Template construction (including regularization processing) 4.1 Template mean calculation: based on feature vectors of 30 groups of population samples c p1 , c p2 ,..., c p30 Calculate the template mean This yields a 48-dimensional mean vector; 4.2 Covariance Matrix Calculation and Regularization: Calculating the Population Covariance Matrix (48×48 dimensions); due to M =48> N =30, regularization is applied: ,in (The trace of the covariance matrix) is calculated as follows l =1.08×10 -4 After regularization, the matrix Σ reg =Σ+1.08×10 -4 I ; SVD decomposition is used for Σ reg Find the inverse, discarding singular values ​​<10. -8 The components are determined to ensure numerical stability, with the inverse matrix calculation error ≤ 10. -6 .

[0039] The experimental results of this step are as follows: the regularized covariance matrix is ​​numerically stable after inversion by SVD, and the template mean is... f * It can accurately reflect the frequency domain characteristics of the optimal strategy of the population (feature vectors of 30 samples and...) f * The average distance is 0.32.

[0040] Step S5: Frequency Domain Deviation Calculation and Measurement Results Output 5.1 Construction of the Spectral Weighting Matrix: Taking α =0.7, calculate the feature vector to be evaluated. c p Energy percentage of each coefficient and frequency percentage Construct a 48th order diagonal matrix L diagonal elements ; 5.2 Calculation of Weighted Mahalanobis Distance: According to the formula Calculated e M =0.68; 5.3 Evaluation of Measurement Results: Setting Deviation Thresholds Based on Historical Data Statistics e th =0.8, because e M =0.68 < 0.8, indicating that the structural difference between the current walking strategy and the optimal strategy is small, and the motion performance is good; if further optimization is needed, it can be based on e M Adjust control parameters (such as joint damping coefficient and motion trajectory planning parameters) according to changes.

[0041] Experimental results in this step: Frequency domain deviation e M =0.68, which is within the good range, verifying the stability of the current walking strategy; by changing the walking speed (0.21m / s, 0.3m / s, 0.39m / s), the calculated... e M The values ​​were 0.72, 0.68, and 0.75, respectively, all less than the threshold of 0.8, verifying the effectiveness and consistency of the method within the speed scaling range of ±30%.

[0042] 3. Experimental Verification and Analysis Noise immunity test: Add ±5% random noise to the data to be evaluated, and calculate... e M =0.73, compared with 0.68 in the absence of noise, the change rate is only 7.4%, which verifies the noise resistance of the method.

[0043] Structural difference identification test: The control parameters of one joint were artificially modified (hip joint damping coefficient increased by 20%), and the results were calculated. e M =0.92>0.8, successfully identifying structural differences in the strategy and verifying the structural sensitivity of the method; paired t-test showed that, compared with the traditional time-domain evaluation method, the present invention improved the accuracy of structural difference identification by 11.1% (t=3.87, p<0.001). Engineering efficiency test: On the Jetson Xavier NX platform, in the walking task of a 12-joint humanoid robot, the whole process time for a single set of data is 1.2 seconds (including data acquisition, processing, and deviation calculation), the detection accuracy can reach 96.8%, and the latency is about 47ms, which meets the real-time evaluation requirements (≤2 seconds).

[0044] Example 2: Evaluation of Humanoid Robot Grasping Motion Strategy The difference between this embodiment and Embodiment 1 is that wavelet basis functions are used for feature extraction, and KL divergence is used to calculate the frequency domain deviation, which is applied to the evaluation of the grasping motion strategy of a humanoid robot (the robot's lower body is fixed, and the upper body performs the grasping action).

[0045] 1. Experimental Preparation The hardware configuration and software environment are the same as in Example 1; Group sample: Collect 30 sets of grasping motion data (N=30), each set of data collection time is 30 seconds, sampling frequency is 100Hz, and the grasping target is a 0.5kg object.

[0046] 2. Core Implementation Steps Steps S1-S2: Similar to Example 1, motion data of 12 joints were collected, normalized, and then reduced to 3 dimensions using PCA (cumulative variance contribution rate ≥ 95%) to obtain the 3D density distribution. .

[0047] Step S3: Feature Extraction (Wavelet Basis Substitution Scheme) Using db4 wavelet basis functions for 3D density distribution A three-level wavelet decomposition was performed to obtain approximation coefficients and detail coefficients. The coefficients with the top 90% energy proportion were selected to construct a 32-dimensional strategy feature vector. c p ∈ R 32 ( M =32).

[0048] Step S4: Template construction, similar to Example 1, calculate the template mean. f * and regularized covariance matrix Σ reg ( l =1.2×10-4 ), and SVD decomposition is used to invert the values ​​to ensure numerical stability.

[0049] Step S5: Frequency domain bias calculation (KL divergence instead of weighted Mahalanobis distance) 5.1 Distribution Hypothesis: , Considering that sensor noise dominates and each dimension is independent, we assume... (32nd order identity matrix); 5.2 KL divergence calculation: based on a simplified formula Calculated e KL =0.42; 5.3 Evaluation Results: Thresholds were set based on experience. e KL,th =0.6, e KL =0.42<0.6, indicating that the crawling strategy performs well.

[0050] 3. Experimental Results Wavelet basis feature extraction can accurately capture local features of the grasping motion. The KL divergence calculation results are stable, with a mean KL divergence of 0.38 and a standard deviation of 0.07 for 30 group samples, verifying the consistency of the method. An artificially introduced grasping trajectory deviation (offset of 5mm) was calculated... e KL =0.75>0.6, successfully identifying the strategy difference and verifying the effectiveness of the method; paired t test shows that compared with the traditional KL divergence simplification method, the recognition accuracy of the present invention is improved by 42.5% (t=5.12, p<0.001).

[0051] Example 3 This embodiment provides a frequency domain measurement system for the motion distribution of a humanoid robot. Corresponding to the method in Embodiment 1 above, the system hardware includes: Joint sensor module: 12 angle sensors (accuracy ±0.1) o ) and 12 angular velocity sensors (accuracy ±1 o / s), installed at each joint of the bipedal humanoid robot, is used to collect real-time motion data; Core computing module: It adopts the NVIDIA Jetson Xavier NX edge computing platform, equipped with an ARM Cortex-A57 CPU and Volta GPU, and is used to perform state mapping, feature extraction, template construction and bias calculation. Storage module: 16GB LPDDR4 memory and 128GB eMMC flash memory, used to store acquired data, intermediate results and template parameters; Communication module: Ethernet interface and CAN bus interface, used for sensor data transmission and interaction with the robot control system.

[0052] The system software is developed based on the Ubuntu 20.04 operating system, using C++ to write the core algorithm and Python to write the data processing and visualization programs. The software architecture includes: Data acquisition driver layer: Enables data reading and synchronization from the sensor, supporting a 100Hz sampling frequency; Core algorithm layer: includes state mapping module, feature extraction module, template construction module, and deviation calculation module; Application layer: Provides real-time display of measurement results, threshold setting, historical data query and alarm functions, supports linkage with robot control system, and realizes closed-loop optimization of control parameters.

[0053] The system operation flow in this embodiment is as follows: System initialization: Load sensor driver, initialize algorithm parameters, and read historical template data; Data acquisition: Sensors collect joint motion data in real time and transmit it to the core computing module; State mapping and density estimation: The collected data is mapped to a normalized state space, and the density distribution is obtained by Gaussian kernel density estimation; Frequency domain feature extraction: Feature vectors are extracted using truncated Fourier basis functions; Template construction / update: If this is the first run, collect 30 groups of population samples to construct the template; if a template already exists, the template parameters can be updated periodically based on new samples. Frequency domain bias calculation: Calculate the weighted Mahalanobis distance between the current feature vector and the template; Results output and linkage: The measurement results are displayed on the human-machine interface. If the deviation exceeds the threshold, an optimization command is sent to the robot control system via the CAN bus to adjust the control parameters.

[0054] Although embodiments of the present invention have been shown and described above, it is understood that these embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions, and alterations to the above embodiments within the scope of the present invention without departing from its principles and spirit. The scope of protection of the present invention is defined by the claims and their equivalents.

Claims

1. A frequency domain measurement method for the motion distribution of a humanoid robot, characterized in that, Includes the following steps: S1: Collect real-time joint motion data of the humanoid robot, including the angle and angular velocity of each joint; S2: Map the real-time joint motion data to a normalized state space, reduce the dimensionality to 3-5 dimensions through principal component analysis, and then use spatial density estimation to obtain the density distribution of the motion strategy. S3: Perform Fourier decomposition on the density distribution using truncated Fourier basis functions, select the Fourier coefficients to be retained according to a preset energy threshold, calculate the Fourier coefficients and extract the strategy feature vector; S4: Based on the population sample data, construct the template mean and regularized population covariance matrix of the motion strategy; S5: Introduce a spectral weighting matrix, and calculate the frequency domain deviation between the policy feature vector and the template mean using weighted Mahalanobis distance to obtain the measurement result of motion distribution.

2. The method according to claim 1, characterized in that, In step S1, the real-time joint motion data satisfies ， in n The number of robot joints. θ i ( t ) represents the time of the i-th joint at time i. t Angle, For the i-th joint at time... t The angular velocity, i=1,...,n.

3. The method according to claim 1, characterized in that, In step S2, the normalized state space The angles and angular velocities of each joint are mapped to the [0,1] interval using a linear normalization method.

4. The method according to claim 1, characterized in that, In step S2, the spatial density estimation employs the Gaussian kernel density estimation method, with the kernel function being: ， Among them, the kernel bandwidth σ Determined using cross-validation.

5. The method according to claim 1, characterized in that, In step S3, the truncated Fourier basis functions are multidimensional complete orthogonal basis functions, and their expressions are as follows: ， in , This is the normalized state space vector after dimensionality reduction. d The dimension after dimensionality reduction. k =( k 1,..., k d ) is the truncated order vector. k i ∈{0,1,..., K max }, For piecewise functions: 。 6. The method according to claim 1, characterized in that, In step S4, the template mean The group covariance matrix ,in c p These are the strategy feature vectors for each group of samples; When the feature vector dimension M Greater than the number of samples N At that time, regularization is performed as ,in , η The constant factor is a preset value with a range of [10]. -2 10 -4 ], The trace of the covariance matrix. I It is an identity matrix.

7. The method according to claim 1, characterized in that, In step S5, the spectral weighting matrix It is a diagonal matrix, using a hybrid energy-frequency weighting method, with diagonal elements... Where α∈[0,1] are weighting coefficients. c i 2 For the first i The energy of a Fourier coefficient f i For the first i The frequency values ​​corresponding to each coefficient.

8. The method according to claim 1, characterized in that, In step S3, the truncated Fourier basis function is replaced with a wavelet basis function for frequency domain feature extraction.

9. The method according to claim 1, characterized in that, In step S5, the weighted Mahalanobis distance is replaced by Kullback-Leibler divergence; the Kullback-Leibler divergence is based on the assumption that the eigenvectors follow a Gaussian distribution, and is calculated using the formula: ， in P The distribution of the feature vectors to be evaluated, Q The distribution of the template mean. µ P , µ Q These are the means of the two distributions, respectively. Σ P , Σ Q Let be the covariance matrices of the two distributions, respectively. d is the dimension of the feature vector, tr() is the trace operation of the matrix, and || is the determinant operation of the matrix.

10. A frequency domain measurement system for the motion distribution of a humanoid robot, characterized in that, include: The data acquisition module is used to collect the angle and angular velocity data of each joint of the humanoid robot in real time, and output 2 n 3D motion data vector; The state mapping module is used to map the 2 n The motion data vectors are linearly mapped to the [0,1] normalized space. After dimensionality reduction to 3-5 dimensions through principal component analysis, the motion strategy density distribution function is generated by Gaussian kernel density estimation. The feature extraction module is used to perform truncated Fourier decomposition on the density distribution function, calculate the Fourier coefficients, and construct the policy feature vector. The template construction module is used to calculate the template mean vector and the regularized population covariance matrix based on the feature vectors of the population samples. The deviation calculation module is used to construct a spectral weighted diagonal matrix, calculate the frequency domain deviation between the strategy eigenvector and the template mean vector by weighted Mahalanobis distance, and output the measurement result of motion distribution.

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