A method and apparatus for measuring human arm impedance

Abstract

This invention discloses a method and device for measuring the impedance of a human arm. The method includes: Step 1, designing a dual-arm humanoid robot and constructing a dynamic model, with the robot collecting operational data on the interaction between the human arm and the robot's arms; Step 2, preprocessing the operational data by denoising, numerical differentiation, data synchronization, and mean calculation; Step 3, using the preprocessed data, establishing a human impedance model through linear regression, calculating impedance parameters based on mass, damping, and stiffness under different arm angles and interaction forces, and minimizing the loss function to optimize the model parameters; Step 4, fitting and plotting a three-dimensional surface using B-spline surface equations based on the calculated impedance parameters to demonstrate the impedance characteristics under different arm angles and interaction forces. This invention enables comprehensive analysis of the impedance characteristics of the human arm during anthropomorphic operations, contributing to applications in fields such as robot-human collaborative work and biomechanical research.

Description

Technical Field

[0001] This invention relates to the field of impedance simulation measurement technology, and in particular to a method and device for measuring the impedance of a human arm. Background Technology

[0002] Currently, methods for measuring the impedance of the human arm mainly rely on a single sensor or a simple mechanical device, which suffers from low measurement accuracy and complex operation. Existing technologies struggle to apply specific perturbation forces to the human arm in a real-world operating environment to elicit and measure its impedance characteristics, particularly the nonlinear impedance characteristics under different arm angles and interaction forces. Summary of the Invention

[0003] To address the aforementioned technical problems in the existing technology, this invention proposes a method and device for measuring the impedance of a human arm, thereby improving measurement accuracy and ease of operation, and enabling the fitting of impedance parameters under different arm angles and interaction forces to measure the impedance characteristics of the human arm under different arm angles and interaction forces. The specific technical solution is as follows:

[0004] A method for measuring impedance of a human arm, comprising:

[0005] Step 1: Design a dual-arm humanoid robot and build its dynamic model. The robot collects operational data on the interaction between the tested human arm and the robot's two arms, and labels and classifies the data under different arm angles and interaction forces of the tested human arm.

[0006] Step two involves preprocessing the data by denoising, numerical differentiation, data synchronization, and mean calculation.

[0007] Step 3: Using preprocessed data, establish a human body impedance model through linear regression, calculate impedance parameters based on mass, damping, and stiffness under different arm angles and interaction forces, and minimize the loss function to optimize the model parameters.

[0008] Step four: Based on the calculated impedance parameters, fit and plot a three-dimensional surface using the B-spline surface equation to show the impedance characteristics under different arm angles and interaction forces.

[0009] Furthermore, the denoising uses bandpass filtering technology; the numerical differentiation derives velocity and acceleration from displacement data through numerical difference calculation to obtain complete motion information; the data synchronization uses timestamp or signal synchronization technology to calibrate and align multi-sensor data to ensure that all sensor data are synchronized so that each time point corresponds to a data sample; the data mean calculation averages the operational data collected multiple times for the same arm angle and interaction force to obtain a unique operational data sequence.

[0010] Furthermore, the specific expression for establishing the human body impedance model is as follows:

[0011]

[0012] Where: t∈(t0,t e ), t0 is the starting time of applying the perturbation to the human arm, t e The time for disturbance cancellation. dx(t) and dF(t) are preprocessed data;

[0013] dx(t) = x(t) - x(t0), dF(t) = F(t) - F(t0), where x(t) and F(t) are the temporal sequences of arm position and force;

[0014] These are impedance parameters, representing mass, damping, and stiffness, respectively. Indicates the arm angle, f ext Indicates interactive force;

[0015] By using linear regression, formula (1) can be rearranged into a matrix format:

[0016] Y = XΘ + E,

[0017] in:

[0018] Y = dF(t);

[0019]

[0020] Furthermore, the loss function expression of the human body impedance model is as follows:

[0021] The arm angle for each group is calculated by minimizing the loss function. and interaction force f ext The corresponding impedance parameters.

[0022] Furthermore, step four specifically involves: based on the obtained impedance parameters, using the B-spline surface equation, solving and collecting the results for each arm angle. and interaction force f ext The corresponding mass, damping, and stiffness data are used to form a three-dimensional data point set, resulting in a result derived from the arm angle. Interaction force f ext The surface formed by the impedance parameters describes different arm angles. and interaction force f ext Impedance characteristics.

[0023] A human arm impedance measuring device, comprising:

[0024] A two-armed humanoid robot, comprising: a two-degree-of-freedom waist section for adjusting posture;

[0025] Two seven-degree-of-freedom robotic arms, one on the left and one on the right, are used to interact with the human arm.

[0026] A two-degree-of-freedom head with a vision system is used to detect the arm angle of a human arm in real time.

[0027] Seat and securing straps: Used to secure the test personnel; the test personnel sit on a seat with a backrest, and the human torso is secured by the securing straps. The seat is connected to the robot base, so that there is no relative movement between the human torso and the two-armed humanoid robot during the measurement process.

[0028] Wrist fixation device: Connected to the end of a seven-DOF robotic arm, used to connect and fix the human arm;

[0029] Six-dimensional force sensors at the end of the arm: These are installed at the ends of two seven-degree-of-freedom robotic arms and connected to the tester's arm via a wrist fixation device to obtain the force between the human arm and the robotic arm.

[0030] Controller: Installed inside the body of the dual-armed humanoid robot, it collects sensor data via the EtherCAT high-speed bus and is used to control the movement of the dual-armed humanoid robot, process the collected data, and calculate the impedance of the human arm.

[0031] Furthermore, the controller specifically includes:

[0032] The data acquisition module is used to collect and store the force, position, and arm angle data at each time point during the operation.

[0033] The data preprocessing module is used to perform noise reduction, numerical differentiation, data synchronization, and mean calculation on the collected data.

[0034] The impedance analysis and modeling module is used to establish a linear regression model based on mass, damping, and stiffness, and to calculate impedance parameters under different arm angles and interaction forces.

[0035] The surface fitting module is used to perform three-dimensional surface fitting based on impedance parameter data using B-spline surface equations, displaying the characteristic surface of the human arm's arm angle and interaction force with impedance parameters.

[0036] This invention provides a high-precision and easy-to-operate human arm impedance measurement device and method, which can provide an assessment of human impedance characteristics under the influence of arm angle and interaction force, and realize a comprehensive analysis of human arm impedance characteristics during anthropomorphic operation. This is helpful for applications in fields such as collaborative work between robots and humans and biomechanical research. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the human arm impedance measuring device of the present invention;

[0038] The components are: 1-Dual-arm humanoid robot; 2-Vision system; 3-Test personnel; 4-Seat; 5-Securation strap; 6-Wrist fixation device; 7-End-effector six-dimensional force sensor.

[0039] Figure 2 This is a coordinate system diagram of the dual-armed humanoid robot described in this invention. Detailed Implementation

[0040] To make the objectives, technical solutions, and technical effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0041] like Figure 1 As shown, the present invention discloses a human arm impedance measuring device, comprising:

[0042] Dual-arm humanoid robot 1: Used to measure the position of human arms, specifically including the following components:

[0043] The two-degree-of-freedom waist section enables the robot to flexibly adjust its posture;

[0044] A two-DOF head incorporating an advanced vision system 2 for real-time detection of the arm angle of a human arm;

[0045] Two high-precision seven-degree-of-freedom robotic arms on the left and right accurately collect the operation position and hand movements.

[0046] Seat 4 and fixing strap 5: used to fix the test personnel 3 and prevent relative movement of the human body; specifically, the test personnel sit on the seat 4 with a backrest, and the human body torso is fixed by the fixing strap 5. The seat 4 is connected to the robot base to ensure that there is no relative movement between the human body torso and the two-armed humanoid robot 1 during the experiment.

[0047] Wrist fixation device 6: used to connect and fix the human arm to prevent relative displacement between the tested human arm and the end six-dimensional force sensor 7 and the robot arm.

[0048] The six-dimensional force sensor 7 is installed at the end of the robotic arm of the dual-arm humanoid robot 1 and connected to the arm of the tester 3. It is used to measure the force between the human arm and the two arms of the humanoid robot.

[0049] Controller: Installed inside the body of the dual-armed humanoid robot, it collects sensor data via the EtherCAT high-speed bus and is used to control the movement of the dual-armed humanoid robot, process the collected data, and calculate the impedance of the human arm.

[0050] Specifically, the controller includes: a data acquisition module, used to collect and store the force, position, and arm angle data at each time point during the operation;

[0051] The data preprocessing module is used to perform noise reduction, numerical differentiation, data synchronization, and mean calculation on the collected data.

[0052] The impedance analysis and modeling module is used to establish a linear regression model based on mass, damping, and stiffness, and to calculate impedance parameters under different arm angles and interaction forces.

[0053] The surface fitting module is used to perform three-dimensional surface fitting based on impedance parameter data using B-spline surface equations, displaying the characteristic surface of the human arm's arm angle and interaction force with impedance parameters.

[0054] This invention also proposes a method for measuring the impedance of a human arm, specifically as follows:

[0055] Constructing the dynamic model of the two-armed humanoid robot:

[0056] like Figure 2 As shown, the dual-armed humanoid robot 1 is divided into three parts: left arm, right arm, and waist. B represents the base coordinate system of the left and right arms and the output coordinate system of the waist; O represents the base coordinate system of the waist. r B is the coordinate system of the right arm's first joint; l Let E be the coordinate system of the left arm's first joint; r Output coordinate system for the right arm; E r Output the coordinate system for the left arm;

[0057] Using the modified DH parameter method, all joints are rotational joints, and the dynamics of each part are obtained according to Newton-Euler method:

[0058] z0: [0 0 1] T ;

[0059] n: Number of joints;

[0060] g: Gravitational acceleration vector described by the waist base coordinate system O;

[0061] The angular velocity at joint i in the link coordinate system; for the robotic arm when i = 0, it is the angular velocity at base coordinate system B, which is generated by the waist movement; for the waist when i = 0, it is the angular velocity at base coordinate system O and... For the waist, when i = n + 1, it is the angular velocity at point B in the output coordinate system of the waist;

[0062] The angular acceleration at point i in the link coordinate system is the same as the angular acceleration at point B in the base coordinate system when i = 0 for the robotic arm; this angular acceleration is generated by the waist movement. For the waist when i = 0, it is the same as the angular acceleration at point O in the base coordinate system. For the waist, when i = n + 1, it is the angular acceleration at point B in the output coordinate system of the waist;

[0063] The linear velocity at point i in the link coordinate system; for the robotic arm when i = 0, it is the linear velocity at point B in the base coordinate system, which is generated by the waist movement; for the waist when i = 0, it is the linear velocity at point O in the base coordinate system and... For the waist, when i = n + 1, it is the linear velocity at coordinate B in the output coordinate system of the waist;

[0064] The linear acceleration at point i in the link coordinate system; for the robotic arm when i = 0, it is the linear acceleration at point B in the base coordinate system, which is generated by the waist movement; for the waist when i = 0, it is the linear acceleration at point O in the base coordinate system and For the waist, when i = n + 1, it is the linear acceleration at point B in the output coordinate system of the waist;

[0065] The linear acceleration described by the center-of-mass coordinate system in the link coordinate system i;

[0066] The rotation matrix of coordinate system i-1 relative to i;

[0067] Position description in coordinate system i-1 under coordinate system i description;

[0068] The position of the center of mass is described by coordinate system i. The origin of the center of mass coordinate system ic is located at the center of mass of the link, and the orientation of each coordinate axis is the same as that of the link coordinate system i.

[0069] m i Link i is the mass of the link in coordinate system ci;

[0070] The inertia tensor of link i relative to the centroid coordinate system ci;

[0071] J i Moment of inertia of joint i;

[0072] f i i : Force acting on coordinate system i; for the robotic arm, when i=0, it is the force acting on the base coordinate system B, and when i=n+1, it is the external force acting on the end coordinate system n+1; for the waist, when i=0, it is the force acting on the base coordinate system O, and when i=m+1, it is the sum of the robotic arm forces acting on coordinate system m+1, i.e., coordinate system B.

[0073] The torque acting on coordinate system i; for the robotic arm, when i=0, it is the torque acting on the base coordinate system B, and when i=n+1, it is the external torque acting on the end coordinate system n+1; for the waist, when i=0, it is the torque acting on the base coordinate system O, and when i=m+1, it is the sum of the robotic arm torques acting on coordinate system m+1.

[0074] Joint friction torque;

[0075] f ext External forces and torques;

[0076] τ i Joint torque;

[0077] q i : Joint i position;

[0078] Joint i velocity;

[0079] Joint i acceleration;

[0080] Use the subscripts l, r, and w to distinguish between the left arm, right arm, and waist.

[0081] Dynamics of each part:

[0082] Extrapolation of velocity and acceleration: i = 1, 2, ..., n k ;

[0083]

[0084] Force and torque internal extrapolation: i = n k ,n k -1,…,2,1,k=l,r,w;

[0085]

[0086] The state equation is expressed as:

[0087]

[0088] in:

[0089]

[0090] J k It is a Jacobian matrix.

[0091] The left arm, right arm, and waist act together on coordinate system B. From the recursive equations for force and torque mentioned above, it can be seen that the sum of the forces and torques acting on the left and right arms at coordinate system B is the external force acting on the waist, i.e.:

[0092]

[0093] From the recursive equations for velocity and acceleration described above, we can see that the velocity and acceleration at coordinate system B in the waist output position serve as the recursive inputs for the velocity and acceleration of the left and right arms, i.e.:

[0094]

[0095] The inward displacement of the waist force / torque can be divided into two parts:

[0096]

[0097] Obviously there are:

[0098]

[0099] in:

[0100] The dynamic equations are derived recursively by combining them with the robotic arm:

[0101]

[0102]

[0103] in:

[0104]

[0105] They are transformed into:

[0106]

[0107] Adding them together yields the whole-body dynamics model:

[0108]

[0109] Among them: Among them: The acceleration, velocity, and position of the humanoid arms' joints are respectively: For the joint torque of the two arms in a humanoid shape;

[0110] The inertia matrix;

[0111] The matrix represents the Coriolis force and centripetal force.

[0112] It is the gravity vector; It is a Jacobian matrix; The interaction force between the human body and the two-armed humanoid figure; Friction at the joints of a humanoid robot.

[0113] Zero-force drag function implemented:

[0114] The dual-armed humanoid robot operates in torque mode and uses the aforementioned dynamic model to calculate the driving force, propelling the robot to move freely. The external force f in the dynamic model... ext Measured by the end-effector six-dimensional force sensor 7.

[0115] Apply external disturbance force:

[0116] Based on the task requirements, design the arm angle... and interaction force f ext External disturbance function This perturbation has a short duration and is randomly applied multiple times during the operation to stimulate the impedance characteristics of the human arm. Due to the short perturbation time, the arm angle during the perturbation period... and interaction force f ext It is approximately a constant value.

[0117] Data acquisition and processing, specifically including:

[0118] Preset experimental parameters: for arm angle and interaction force f ext Group settings, arm angle The angles are set to 0, 10, 20, ..., 90 degrees, and the interaction force is f. ext The values ​​are set to 0, 10, 20, ..., 90 Newtons.

[0119] Two phases of experiments were conducted: one with no interference and one with interference. The tasks were identical in both phases, and the data acquisition covered different arm angles. and interaction force f ext The details are as follows:

[0120] Phase 1: The human arm drags the humanoid robot arm to complete the task in accordance with the normal dual-arm operation process without disturbance. During the operation, the six-dimensional force sensor 7 at the end of the arm collects the operating force, the dual arms of the humanoid dual-arm robot measure the operation position, and the head vision system 2 of the humanoid dual-arm robot measures the arm angle of the human arm.

[0121] Phase Two: Following the normal dual-arm operation process, as the human arm drags the humanoid robot arm to complete the task, according to the external force disturbance function... An external force is applied to interfere with the operation. During the operation, the six-dimensional force sensor 7 at the end of the robot collects the operating force, the two arms of the humanoid dual-arm robot measure the operating position, and the head vision system 2 of the humanoid dual-arm robot measures the arm angle of the human arm.

[0122] Training period: The first stage is repeated multiple times to allow operators to become familiar with the operating procedures and adapt to the measurement structure. The data used is used to analyze the level of operator proficiency and the consistency of operations.

[0123] Interference data acquisition period: After multiple disturbance-free operations with good operational consistency, multiple second-stage data acquisitions are performed, and the arm angle is measured by the vision system. Following the principle of proximity, the force sensor measures the interaction force f as a value among 0, 10, 20, ..., 90 degrees. ext Following the principle of proximity, the value is approximated to one of 0, 10, 20, ..., 90 N, ultimately yielding different arm angles. and interaction force f ext The time sequence of position x(t) and force F(t) under the given conditions.

[0124] Preprocessing of data collected under multiple interference conditions includes:

[0125] Noise reduction: Bandpass filtering technology is used to filter and reduce high-frequency noise and low-frequency operating noise in the signal, while retaining the effective intermediate frequency signal;

[0126] Numerical differentiation: Velocity and acceleration are derived from displacement data through numerical difference calculations to obtain complete motion information;

[0127] Data synchronization: Use timestamp or signal synchronization technology to calibrate and align multi-sensor data to ensure that all sensor data are synchronized so that each point in time corresponds to a data sample;

[0128] Data mean calculation: for the same arm angle and interaction force f ext The average of multiple collected sequence data is taken to obtain a unique operational data sequence, thereby obtaining accurate motion information.

[0129] A human body impedance model is established, with the following expression:

[0130]

[0131] Where: t∈(t0,t e ), t0 is the initial time of applying the disturbance, t e The time for disturbance removal;

[0132] dx(t)=x(t)-x(t0), dF(t)=F(t)-F(t0);

[0133] All are about q, F is a unit diagonal matrix function, representing mass, damping, and stiffness, respectively.

[0134] Fitting human body impedance parameters:

[0135] A linear regression model is established, and the impedance parameters are obtained through data fitting. Preprocessed and simplified data is used. dx(t) and dF(t) are used to construct a linear regression equation, which is then rearranged into a matrix format:

[0136] Y = XΘ + E,

[0137] in:

[0138] Y = dF(t);

[0139]

[0140] Define the model's loss function:

[0141]

[0142] Minimize the loss function to calculate the arm angle for each group. and interaction force f ext Corresponding impedance parameters

[0143]

[0144] Fitting the surface of human body impedance parameters:

[0145] Using B-spline surface equations By solving for the fitting control points of mass, damping, and stiffness respectively, the three-dimensional surface fitting equation is obtained, resulting in the equation derived from the arm angle. Interaction force f ext The surface formed by the impedance parameters describes different arm angles. and interaction force f ext Impedance characteristics.

[0146] Based on the above-mentioned method principle, the experimental process of measuring human arm impedance using the device of the present invention includes six steps: experimental preparation, equipment debugging, data acquisition, data preprocessing, impedance model establishment, and human body impedance parameter surface fitting.

[0147] The experimental preparation steps include:

[0148] Preparation of test subject 3: Select healthy test subjects without upper limb diseases to ensure data accuracy; test subjects need to wear light clothing to avoid affecting the operation; test subjects are fixed in a chair with a backrest and anchor straps to ensure their torso stability and prevent relative movement.

[0149] Equipment installation and debugging: Install the end effector six-dimensional force sensor 7 at the end of the robotic arm of the dual-arm humanoid robot 1 and calibrate it to ensure measurement accuracy.

[0150] Experimental environment setup: Ensure that the laboratory environment has moderate temperature and humidity, and maintain sufficient light to reduce external interference; check the stability of the experimental table and surrounding equipment to ensure that the operation will not be affected by external factors.

[0151] The equipment commissioning process includes:

[0152] Initialization of dual-arm humanoid robot 1: Initialize dual-arm humanoid robot 1, including two seven-degree-of-freedom robotic arms, a two-degree-of-freedom waist and head, and place it in the initial state; communicate with the robot through the control panel or computer to set dynamic parameters and calibrate sensors.

[0153] Zero-force mode debugging: Ensure that the dual-arm robot operates in zero-force mode, so that the person being tested can easily drag the robot arm and follow its movement; perform multiple operation tests to ensure that the zero-force control function of the end effector six-dimensional force sensor is normal, and record preliminary data to verify the accuracy of the system.

[0154] Safety Inspection: Inspect the firmness of all mechanical connections and fixing devices to ensure they do not loosen or fall off during the entire experiment; set up safety boundaries and an emergency stop button so that the experiment can be stopped in time in case of an accident to ensure personnel safety.

[0155] The data acquisition process includes:

[0156] The first phase of data acquisition during non-disruptive operation: The subject drags the dual-arm humanoid robot 1 to complete the normal operation task according to the predetermined task operation procedure; the force at each time point during the operation is collected using the end effector six-dimensional force sensor 7, while the dual-arm humanoid robot 1 measures the operation position and the head vision system 2 measures the arm angle of the operator's arm; the operation is repeated multiple times, and different arm angles are recorded. and interaction force f ext Operational data under specific conditions should be collected to ensure sufficient data samples.

[0157] The second phase of data acquisition under disturbance conditions: setting the external force disturbance function. During operation, the robot applies random transient external force disturbances to simulate unexpected situations in actual operation; the person being tested continues to follow the predetermined task operation procedure and drags the dual-arm robot to complete the task; under the influence of disturbance, the sensor and measuring equipment still collect data on force, position and arm angle to ensure the integrity of data sampling under disturbance conditions.

[0158] Data labeling and classification: All collected data are classified according to different arm angles. and interaction force f ext Labeling and categorizing data is essential for subsequent processing and analysis, ensuring the accuracy and completeness of data records and providing a foundation for further data processing.

[0159] The data preprocessing steps include:

[0160] Denoising processing is performed on each data trajectory to improve the accuracy and reliability of the data.

[0161] Numerical differentiation ensures the smoothness and continuity of data during the numerical differentiation process, avoiding the impact of abrupt changes on subsequent modeling.

[0162] Data synchronization ensures that data from multiple sensors are fully synchronized on the timeline, avoiding data inconsistencies caused by time errors.

[0163] The mean calculation involves calculating the mean of multiple operation data under the same experimental conditions to obtain a unique sequence of operation data. This ensures that the mean calculation process is rigorous and reasonable, eliminating random errors and noise.

[0164] The impedance model establishment process includes:

[0165] Linear regression model construction: Based on the preprocessed data, the impedance model equation is constructed using the linear regression method. The equation is expressed in matrix form for easy calculation and processing.

[0166] Define a loss function and minimize it using gradient descent or other optimization algorithms to obtain the arm angle for each group. and interaction force f ext The corresponding impedance parameters.

[0167] Parameter optimization: Based on the collected data, the model parameters are gradually adjusted and optimized through an iterative optimization process to ensure the accuracy and robustness of the model; methods such as cross-validation are used to verify the stability and generalization ability of the model parameters.

[0168] The surface fitting step for human body impedance parameters includes:

[0169] Based on the obtained impedance parameters, the B-spline surface equation is used to collect data for each arm angle. and interaction force fext The corresponding mass, damping, and stiffness data form a three-dimensional data point set.

[0170] Surface Plotting and Verification: Visualize the fitted surface using 3D plotting tools or programming languages, showcasing the mechanical properties of the surface under different conditions. Verify the fitted surface, checking its prediction accuracy at unknown data points to ensure the accuracy of the fitted model.

[0171] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any way. Although the implementation process of the present invention has been described in detail above, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for measuring the impedance of a human arm, characterized in that, include: Step 1: Design a two-armed humanoid robot and build its dynamic model, designing the arm angles... and interactivity External disturbance function , opposite arm angle and interaction Grouping is performed; during the process of a human arm dragging a humanoid robot arm to complete a task, the external force disturbance function is used. An external interference force is applied, and during the operation, the operational force is collected using a six-dimensional force sensor at the end of the robot. The operation position is measured using the two arms of the humanoid dual-arm robot, and the arm angle of the humanoid arm is measured using the head vision system of the humanoid dual-arm robot. The robot collects the operation data of the interaction between the human arm and the robot's two arms. The operation is repeated multiple times, and different arm angles are recorded. and interaction Operational data under specific conditions, and labeled and categorized data under different arm angles and interaction forces of the tested human arm; Step two involves preprocessing the data by denoising, numerical differentiation, data synchronization, and mean calculation. Step 3: Using preprocessed data, establish a human body impedance model through linear regression, calculate impedance parameters based on mass, damping, and stiffness under different arm angles and interaction forces, and minimize the loss function to optimize the model parameters. Step four: Based on the calculated impedance parameters, fit and plot a three-dimensional surface using the B-spline surface equation to show the impedance characteristics under different arm angles and interaction forces.

2. The method for measuring the impedance of a human arm according to claim 1, characterized in that, The denoising uses bandpass filtering; the numerical differentiation derives velocity and acceleration from displacement data through numerical difference calculation to obtain complete motion information; the data synchronization uses timestamp or signal synchronization technology to calibrate and align multi-sensor data to ensure that all sensor data are synchronized so that each time point corresponds to a data sample; the data mean calculation averages the operational data collected multiple times for the same arm angle and interaction force to obtain a unique operational data sequence.

3. The method for measuring the impedance of a human arm according to claim 1, characterized in that, The specific expression for establishing the human body impedance model is as follows: ， （1） in: , The starting moment for applying the perturbation to the human arm. The time for disturbance cancellation. , , and For preprocessing data; , , and It is a temporal sequence of arm position and force; , , These are impedance parameters, representing mass, damping, and stiffness, respectively; By using linear regression, formula (1) can be rearranged into a matrix format: ， in: ； ； 。 4. The method for measuring the impedance of a human arm according to claim 3, characterized in that, The arm angle for each group is calculated by minimizing the loss function. and interaction The corresponding impedance parameters.

5. The method for measuring the impedance of a human arm according to claim 4, characterized in that, Step four specifically involves: based on the obtained impedance parameters, using the B-spline surface equation, solving and collecting the results for each arm angle. and interaction The corresponding mass, damping, and stiffness data are used to form a three-dimensional data point set, resulting in a result derived from the arm angle. Interaction The surface formed by the impedance parameters describes different arm angles. and interaction Impedance characteristics.

6. An apparatus employing the human arm impedance measurement method according to any one of claims 1 to 5, characterized in that, include: A two-armed humanoid robot, comprising: a two-degree-of-freedom waist section for adjusting posture; Two seven-degree-of-freedom robotic arms, one on the left and one on the right, are used to interact with the human arm. A two-degree-of-freedom head with a vision system is used to detect the arm angle of a human arm in real time. Seat and securing straps: Used to secure the test personnel; the test personnel sit on a seat with a backrest, and the human torso is secured by the securing straps. The seat is connected to the robot base, so that there is no relative movement between the human torso and the two-armed humanoid robot during the measurement process. Wrist fixation device: Connected to the end of a seven-DOF robotic arm, used to connect and fix the human arm; Six-dimensional force sensors at the end of the arm: These are installed at the ends of two seven-degree-of-freedom robotic arms and connected to the arm of the tester via a wrist fixation device. They are used to obtain the force between the human arm and the robotic arm. Controller: Installed inside the body of the dual-armed humanoid robot, it collects sensor data via the EtherCAT high-speed bus and is used to control the movement of the dual-armed humanoid robot, process the collected data, and calculate the impedance of the human arm.

7. The apparatus according to claim 6, characterized in that, The controller specifically includes: The data acquisition module is used to collect and store the force, position, and arm angle data at each time point during the operation. The data preprocessing module is used to perform noise reduction, numerical differentiation, data synchronization, and mean calculation on the collected data. The impedance analysis and modeling module is used to establish a linear regression model based on mass, damping, and stiffness, and to calculate impedance parameters under different arm angles and interaction forces. The surface fitting module is used to perform three-dimensional surface fitting based on impedance parameter data using B-spline surface equations, displaying the characteristic surface of the human arm's arm angle and interaction force with impedance parameters.

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