Robot dynamics modeling and parameter identification method considering friction normal force

Abstract

The invention relates to a robot dynamics modeling and parameter identification method considering friction normal force. Comprising the steps of 1, designing a motion track; 2, the friction torque and the contact surface normal force of the robot are extracted; 3, filtering the collected friction torque; 4, establishing a coupling model of the friction force and the contact normal force of the friction surface; 5, identifying parameters of the friction force and contact surface normal force coupling model; 6, designing an excitation track; 7, acquiring the position, speed, acceleration and torque data of the robot, and filtering; 8, a robot dynamic model based on the coulomb viscous friction model is constructed and linearized, and a least square method is adopted for parameter identification; and 9, establishing a robot dynamics model considering the influence of the normal force of the friction contact surface, and carrying out parameter identification. According to the invention, the coupling between the gravity, inertia force and the like of the robot and friction can be solved to a certain extent, and the problem of coupling between the gravity, inertia force and the like of a traditional dynamic model and friction is avoided.

Description

Technical Field

[0001] This invention belongs to the field of robotics technology, specifically a method for robot dynamics modeling and parameter identification that considers frictional normal force. Background Technology

[0002] In the Fourth Industrial Revolution, where artificial intelligence and machine automation are central, robots occupy a crucial strategic position. Robot applications in manufacturing, such as palletizing and sorting, require higher movement speeds to improve production efficiency. High-speed robot control widely employs motion planning and control schemes based on robot dynamics models. Therefore, high-precision robot dynamics models are essential for model-based control. However, traditional robot dynamics models do not consider the influence of the normal force on joint friction contact surfaces, leading to coupling between friction and gravity, inertial forces, etc., in the parameter identification results. This is detrimental to scenarios where model decoupling is required. The selection and establishment of mathematical friction models, as well as the identification of parameters for mathematical friction models and robot dynamics models, are key technologies in robot dynamics modeling and parameter identification. However, current robot dynamics modeling and parameter identification suffer from the following technical problems: traditional dynamics models do not consider the influence of the normal force on friction and lack corresponding parameter identification schemes; traditional friction models such as Strabeck do not consider the influence of the normal force on contact surfaces during modeling, merely establishing the friction model as a function related to gravity. Summary of the Invention

[0003] To address the aforementioned issues, this invention provides a robot dynamics modeling and parameter identification method that considers frictional normal force. This method can, to some extent, resolve the coupling between robot gravity, inertial force, and friction, avoiding the coupling problems of gravity, inertial force, and friction in traditional dynamics models. It is more suitable for scenarios where dynamics models are decoupled.

[0004] The technical solution of this invention is described below in conjunction with the accompanying drawings:

[0005] This invention provides a method for robot dynamics modeling and parameter identification considering frictional normal force, comprising the following steps:

[0006] Step 1: Design a motion trajectory;

[0007] Step 2: Execute the motion trajectory from Step 1 in position control mode, collect the robot's speed and torque data, and extract the robot's friction torque and contact surface normal force.

[0008] Step 3: Filter the collected friction torque;

[0009] Step 4: Establish a coupled model of friction force and normal force at the friction surface;

[0010] Step 5: Identify the parameters of the coupled model of friction force and contact surface normal force using a metaheuristic optimization algorithm;

[0011] Step 6: Design an excitation trajectory;

[0012] Step 7: Execute the motion trajectory from Step 6 in position control mode, collect the robot's position, velocity, acceleration, and torque data, and perform filtering.

[0013] Step 8: Construct and linearize the robot dynamics model based on the Coulomb viscous friction model, and use the least squares method for parameter identification;

[0014] Step 9: Establish a robot dynamics model that considers the influence of the normal force on the frictional contact surface and identify the parameters.

[0015] Furthermore, the specific method for step one is as follows:

[0016] 11) For any joint of the robot To make any one joint perform a single-joint, uniform reciprocating motion; that is, to lock the other joints still and make the joint move at a single speed. Rotating at a constant speed;

[0017] 12) Set the speed range of uniform motion to include two speed ranges: low speed and high speed. The joint motion range should be based on fully stimulating the robot's motion characteristics and should not exceed the robot's joint motion limits, and should be able to move in both clockwise and counterclockwise directions.

[0018] Furthermore, the specific method for step two is as follows:

[0019] 21) The robot's speed is obtained from the differential position of the motor encoder. Torque data is divided into motor output torque and joint friction contact surface normal force. The joint friction contact surface normal force is defined as... The motor output torque is derived from the motor torque output current sampling, and the equivalent output torque of the motor is calculated using the following formula:

[0020]

[0021] In the formula, This is the equivalent output torque of the motor; Sample current for the motor; This represents the torque constant of the servo motor; For single-joint transmission ratio;

[0022] 22) Calculate the robot's frictional torque and the normal force on the joint friction contact surface, which are extracted using the following formulas:

[0023]

[0024]

[0025] In the formula, and These are the joint torques collected during the clockwise and counterclockwise movements of a single joint of the robot, respectively. The extracted frictional torque; The extracted normal force of the friction contact surface; The joint angular velocity of the robot is obtained by differentiating the numerical values ​​of the joint positions; This refers to the joint angle position.

[0026] Furthermore, the specific method for step three is as follows:

[0027] 31) The collected friction torque is filtered using Butterworth filtering.

[0028] Furthermore, the specific method for step four is as follows:

[0029] 41) Establish a coupled model of friction and Coriolis force, as shown below:

[0030]

[0031] In the formula, This is a Coulomb friction phenomenon; It is static friction; This is a viscous phenomenon; For stribeck speed; This refers to the normal force at the friction contact surface. , It is a constant coefficient used to characterize the effect of load torque. It is a symbolic function; Coulomb friction coefficient; Joint angular velocity; The frictional torque is given by the parameter to be identified. , , , , , .

[0032] Furthermore, the specific method for step five is as follows:

[0033] 51) A metaheuristic optimization algorithm is used to identify the parameters of the friction model, and a genetic algorithm is used for parameter identification.

[0034] 52) Set constraints as shown in formula (5):

[0035] (5)

[0036] 53) Set the optimization objective fitness function as follows:

[0037]

[0038] in, For the first The frictional torque value extracted from each joint; This refers to the estimated friction torque calculated by the genetic algorithm in each iteration. To find the minimum value of the function.

[0039] Furthermore, the specific method for step six is ​​as follows:

[0040] The specific method for step six is ​​as follows:

[0041] 61) Design an excitation trajectory with the following expression:

[0042]

[0043] In the formula, For periodicity; This is the modulo operation; The coefficients of the fifth-degree polynomial are represented as follows: , function For the series harmonic order; The fundamental frequency of the trajectory is the same for all joints; , As a coefficient term, it determines the amplitude of the trajectory movement; set , Thus, the fundamental frequency is determined. ; Plan the angular position of the i-th joint to determine the excitation trajectory; For summation index; , , , for : Coefficients of a fifth-degree polynomial;

[0044] 62) A genetic algorithm is used to find parameters based on the following optimization criteria:

[0045]

[0046] In the formula, The condition number of the observation matrix. The observation matrix is ​​the equation of motion of the robot. , , Limitations on the displacement, velocity, and acceleration of the joints; The set of robot end-effector poses corresponding to the excitation trajectory; Cartesian space for robot motion.

[0047] Furthermore, the specific method for step seven is as follows:

[0048] 71) Execute the motion trajectory of step six in position control mode, and collect the robot's position, velocity, acceleration, and torque data; where the robot's position information is obtained from the joint encoder, the velocity and acceleration information is calculated by differentiating the position values, and the torque data is the motor current output.

[0049] 72) Use a Butterworth filter to filter the data.

[0050] Furthermore, the specific method for step eight is as follows:

[0051] 81) Establish a robot dynamics model based on the Coulomb viscous friction model and linearize it as follows:

[0052]

[0053] In the formula, These are the angular displacement, angular velocity, and angular acceleration of each joint of the robot. For the inertial torque of a six-degree-of-freedom robot; Coriolis torque for a six-degree-of-freedom robot; For the gravitational torque of a six-degree-of-freedom robot; The frictional torque is obtained using the Coulomb viscous friction model, which is given by Equation 10.2. The driving torque of the robot joint is obtained by sampling the output torque of the joint motor;

[0054] Coulomb viscous friction is also expressed in linear form, and equation (9) can be rewritten as:

[0055]

[0056]

[0057] In the formula, This is the observation matrix corresponding to the robot's dynamics equations; will use express, This represents the minimum set of inertial parameters for the robot. The information obtained from step five includes position, velocity, acceleration, torque, and... Substitution, that is, solving for the parameters using the least squares method. :

[0058]

[0059] Furthermore, the specific method for step nine is as follows:

[0060] 91) The robot dynamics model considering the normal force of the frictional contact surface is given by equation (12.1), where As given by equation (12.2), The calculation method is given by equation (12.3):

[0061]

[0062]

[0063]

[0064] In the formula, The position, velocity, acceleration, and torque information, calculated by equation (11), are obtained from step seven. Similarly, by substituting the position, velocity, acceleration, torque information, and the friction parameters expressed in step five, the minimum parameter set of the robot dynamics model considering the normal force of the friction contact surface is solved using the following equation. :

[0065]

[0066] The beneficial effects of this invention are as follows:

[0067] 1) In terms of robot friction modeling, this invention addresses the issue that traditional robot dynamics models do not consider the influence of the normal force of the joint friction contact surface on friction, which leads to the coupling between friction and gravity, inertial force, etc. in the parameter identification results of the robot dynamics model. It establishes a friction model that considers the normal force of the friction contact surface, thus solving the coupling problem between the traditional friction model and gravity, inertial force, etc.

[0068] 2) Regarding the identification of robot dynamic model parameters, since the friction model considering the normal force of the friction contact surface and the MCG term in the dynamic model constitute a composite function, the traditional one-step least squares method cannot solve the dynamic model parameters. Therefore, to address this problem, this invention first identifies the model parameters based on the Coulomb viscous friction model, and then substitutes them into the friction model considering the normal force of the friction contact surface to solve the dynamic model parameters by the least squares method. Attached Figure Description

[0069] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0070] Figure 1 This is an overall flowchart of the present invention;

[0071] Figure 2 Image showing the effect of friction parameter identification;

[0072] Figure 3 A schematic diagram of the joint angle positions for collecting the excitation trajectory;

[0073] Figure 4 A schematic diagram of the joint angular velocity for collecting the excitation trajectory;

[0074] Figure 5 A schematic diagram of the joint angular acceleration for the excitation trajectory;

[0075] Figure 6 A schematic diagram of the motor output torque for collecting the excitation trajectory;

[0076] Figure 7 This is a schematic diagram comparing the torques of joint 1;

[0077] Figure 8 This is a schematic diagram comparing the torques at joint 2;

[0078] Figure 9 This is a schematic diagram comparing the torques of the three joints;

[0079] Figure 10 This is a schematic diagram comparing the torques of joint 4.

[0080] Figure 11 This is a schematic diagram comparing the torques of joint 5.

[0081] Figure 12 This is a schematic diagram comparing the torques of joint 6. Detailed Implementation

[0082] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0083] Example 1

[0084] See Figure 1This invention provides a method for robot dynamics modeling and parameter identification considering frictional normal force, comprising the following steps:

[0085] Step 1: Design a motion trajectory, as follows:

[0086] 11) For any joint of the robot To make any one joint perform a single-joint, uniform reciprocating motion; that is, to lock the other joints still and make the joint move at a single speed. Rotating at a constant speed;

[0087] 12) Set the speed range for uniform motion to include two speed ranges: low speed and high speed. The low speed range should have more speed sampling points than the high speed range. The joint motion range should be designed to fully excite the robot's motion characteristics and should not exceed the robot's joint motion limits, allowing for movement in both clockwise and counterclockwise directions.

[0088] The low-speed range is the joint speed of 1-20 degrees per second;

[0089] The high-speed range is defined as a joint speed of 20 degrees per second or higher.

[0090] Step 2: Execute the motion trajectory from Step 1 in position control mode, collect the robot's speed and torque data, and extract the robot's friction torque and contact surface normal force. The specific method is as follows:

[0091] 21) The robot's speed is obtained from the differential position of the motor encoder, and the torque data is divided into motor output torque and joint friction contact surface normal force; among which, the joint friction contact surface normal force is defined as... The motor output torque is derived from the motor torque output current sampling, and the equivalent output torque of the motor is calculated using the following formula:

[0092]

[0093] In the formula, This is the equivalent output torque of the motor; Sample current for the motor; This represents the torque constant of the servo motor; For single-joint transmission ratio;

[0094] 22) Calculate the robot's frictional torque and the normal force on the joint friction contact surface, which are extracted using the following formulas:

[0095]

[0096]

[0097] In the formula, and These are the joint torques collected during the clockwise and counterclockwise movements of a single joint of the robot, respectively. The extracted frictional torque; The extracted normal force of the friction contact surface; The joint angular velocity of the robot is obtained by differentiating the numerical values ​​of the joint positions; This refers to the joint angle position.

[0098] Step 3: Filter the collected friction torque. The specific method is as follows:

[0099] 31) This invention uses Butterworth filtering to filter the collected friction torque.

[0100] Step 4: Establish a coupled model of friction force and normal force at the friction surface. The specific method is as follows:

[0101] 41) Establish a coupled model of friction and Coriolis force, as shown below:

[0102]

[0103] In the formula, This is a Coulomb friction phenomenon; It is static friction; This is a viscous phenomenon; For stribeck speed; This refers to the normal force at the friction contact surface. , It is a constant coefficient used to characterize the effect of load torque. It is a symbolic function; Coulomb friction coefficient; This refers to the joint angle position; The joint friction torque is given; the parameter to be identified is: , , , , , .

[0104] Step 5: Identify the parameters of the coupled model of friction force and contact surface normal force using a metaheuristic optimization algorithm. The specific method is as follows:

[0105] 51) A metaheuristic optimization algorithm is used to identify the parameters of the friction model, and a genetic algorithm is used for parameter identification.

[0106] 52) Set constraints as shown in formula (5):

[0107] (5)

[0108] 53) Set the optimization objective fitness function as follows:

[0109]

[0110] in, For the first The frictional torque value extracted from each joint; This refers to the estimated friction torque calculated by the genetic algorithm in each iteration. To find the minimum value of the function.

[0111] Step 6: Design an excitation trajectory, the specific method is as follows:

[0112] 61) Design an excitation trajectory with the following expression:

[0113]

[0114] In the formula, For periodicity; This is the modulo operation; The coefficients of the fifth-degree polynomial are represented as follows: , function For the series harmonic order; The fundamental frequency of the trajectory is the same for all joints; , As a coefficient term, it determines the amplitude of the trajectory movement; set , Thus, the fundamental frequency is determined. ; Plan the angular position of the i-th joint to determine the excitation trajectory; For summation index; , , , for : represents the coefficients of a fifth-degree polynomial;

[0115] 62) A genetic algorithm is used to find parameters based on the following optimization criteria:

[0116]

[0117] In the formula, The condition number of the observation matrix. The observation matrix is ​​the equation of motion of the robot. , , Limitations on the displacement, velocity, and acceleration of the joints; The set of robot end-effector poses corresponding to the excitation trajectory; Cartesian space for robot motion.

[0118] Step 7: Execute the motion trajectory from Step 6 in position control mode, collect the robot's position, velocity, acceleration, and torque data, and perform filtering. The specific method is as follows:

[0119] 71) Execute the motion trajectory of step six in position control mode, and collect the robot's position, velocity, acceleration, and torque data; where the robot's position information is obtained from the joint encoder, the velocity and acceleration information is calculated by differentiating the position values, and the torque data is the motor current output.

[0120] 72) Use a Butterworth filter to filter the data.

[0121] Step 8: Construct and linearize the robot dynamics model based on the Coulomb viscous friction model, and use the least squares method for parameter identification. The specific method is as follows:

[0122] 81) Establish a robot dynamics model based on the Coulomb viscous friction model and linearize it as follows:

[0123]

[0124] In the formula, These are the angular displacement, angular velocity, and angular acceleration of each joint of the robot. For the inertial torque of a six-degree-of-freedom robot; Coriolis torque for a six-degree-of-freedom robot; For the gravitational torque of a six-degree-of-freedom robot; The frictional torque is obtained using the Coulomb viscous friction model and is given by Equation 10.2. The driving torque of the robot joint is obtained by sampling the output torque of the joint motor;

[0125] Coulomb viscous friction is also expressed in linear form, and equation (9) can be rewritten as:

[0126]

[0127]

[0128] In the formula, This is the observation matrix corresponding to the robot's dynamics equations; will use express, This represents the minimum set of inertial parameters for the robot. The information obtained from step five includes position, velocity, acceleration, torque, and... Substitution, that is, solving for the parameters using the least squares method. :

[0129]

[0130] Step 9: Establish a robot dynamics model that considers the influence of the normal force at the frictional contact surface and identify the parameters. The specific method is as follows:

[0131] 91) The robot dynamics model considering the normal force of the frictional contact surface is given by equation (12.1), where As given by equation (12.2), The calculation method is given by equation (12.3):

[0132]

[0133]

[0134]

[0135] In the formula, The position, velocity, acceleration, and torque information, calculated by equation (11), are obtained from step seven. Similarly, by substituting the position, velocity, acceleration, torque information, and the friction parameters expressed in step five, the minimum parameter set of the robot dynamics model considering the normal force of the friction contact surface is solved using the following equation. :

[0136]

[0137] Example 2

[0138] This embodiment verifies the effectiveness of the friction model parameter identification in Embodiment 1 and the dynamic model parameter identification considering the friction contact surface.

[0139] The robot's single joints acquired position, velocity, and torque information at speeds ranging from -2 rad / s to 2 rad / s, and the parameter identification results are as follows: Figure 2 As shown.

[0140] Figure 2 Experimental results show that the parameter identification method based on genetic algorithm proposed in this invention can effectively identify the friction model of the robot, and the model has a good fitting effect.

[0141] The robot executes an excitation trajectory, such as Figure 3 , Figure 4 , Figure 5 and Figure 6 The image shows the position, velocity, acceleration, and motor output torque information of the excitation trajectory executed by the robot.

[0142] in, Figure 3 In the figure, q1, q2, q3, q4, q5, and q6 are the data collected and filtered after the excitation trajectory angular positions of joints 1 to 6, respectively.

[0143] Figure 4 In the figure, dq1, dq2, dq3, dq4, dq5, and dq6 are the collected and filtered data of the excitation trajectory angular velocities of joints 1 to 6, respectively.

[0144] Figure 5 ddq1, ddq2, ddq3, ddq4, ddq5, and ddq6 are the collected and filtered data of the excitation trajectory angular acceleration of joints 1 to 6, respectively.

[0145] Figure 6 Tau1, Tau2, Tau3, Tau4, Tau5, and Tau6 are the data of motor output torque acquisition and filtering for the excitation trajectory of joints 1 to 6, respectively.

[0146] from Figures 3-6 The data indicates that this is the data obtained after the excitation trajectory was acquired and filtered in step seven, and it is used for parameter identification in steps eight and nine.

[0147] Figures 7-12 This is a comparison chart of the model's predicted values ​​and the motor's output torque.

[0148] Figures 7-12 Experimental results show that the robot dynamics modeling and parameter identification method proposed in this invention, which considers the influence of the normal force of the friction contact surface, can effectively identify the dynamics model parameters of the robot, and the model has a good fitting effect.

[0149] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for robot dynamics modeling and parameter identification considering frictional normal force, characterized in that, Includes the following steps: Step 1: Design a motion trajectory; Step 2: The robot executes the motion trajectory of Step 1 in position control mode. In position control mode, the robot performs motion control according to the given desired position in each control cycle, collects the robot's speed and torque data, and extracts the robot's friction torque and contact surface normal force. Step 3: Filter the collected friction torque; Step 4: Establish a coupled model of friction force and normal force at the friction surface; Step 5: Identify the parameters of the coupled model of friction force and contact surface normal force using a metaheuristic optimization algorithm; Step 6: Design an excitation trajectory; Step 7: Execute the motion trajectory from Step 6 in position control mode, collect the robot's position, velocity, acceleration, and torque data, and perform filtering. Step 8: Construct and linearize the robot dynamics model based on the Coulomb viscous friction model, and use the least squares method for parameter identification; Step 9: Establish a robot dynamics model that considers the influence of the normal force on the frictional contact surface and identify the parameters.

2. The method for robot dynamics modeling and parameter identification considering frictional normal force according to claim 1, characterized in that, The specific method for step one is as follows: 11) For any joint of the robot, make that joint perform a single-joint uniform reciprocating motion; that is, lock the other joints and make the joint rotate at a uniform speed alone. 12) Set the speed range of uniform motion to include two speed ranges: low speed and high speed. The low speed range is set to a joint angular velocity of 1 to 20 degrees per second, and the high speed range is set to a joint angular velocity of 30 to 120 degrees per second. The joint motion range is based on the ability to fully stimulate the robot's motion characteristics and does not exceed the robot's joint motion limits, and the motion is carried out in both clockwise and counterclockwise directions.

3. The method for robot dynamics modeling and parameter identification considering frictional normal force according to claim 1, characterized in that, The specific method for step two is as follows: 21) The robot's speed is obtained from the differential position of the motor encoder. Torque data is divided into motor output torque and joint friction contact surface normal force. The joint friction contact surface normal force is defined as... The motor output torque is derived from the motor torque output current sampling, and the equivalent output torque of the motor is calculated using the following formula: In the formula, This is the equivalent output torque of the motor; Sample current for the motor; This represents the torque constant of the servo motor; For single-joint transmission ratio; 22) Calculate the robot's frictional torque and the normal force on the joint friction contact surface, which are extracted using the following formulas: In the formula, and These are the joint torques collected during the clockwise and counterclockwise movements of a single joint of the robot, respectively. The extracted frictional torque; The extracted normal force of the friction contact surface; The joint angular velocity of the robot is obtained by differentiating the numerical values ​​of the joint positions. This refers to the joint angle position.

4. The method for robot dynamics modeling and parameter identification considering frictional normal force according to claim 1, characterized in that, The specific method for step three is as follows: 31) The collected friction torque is filtered using Butterworth filtering.

5. The method for robot dynamics modeling and parameter identification considering frictional normal force according to claim 1, characterized in that, The specific method for step four is as follows: 41) Establish a coupled model of friction and Coriolis force, as shown below: In the formula, This is a Coulomb friction phenomenon; It is static friction; This is a viscous phenomenon; For Stribeck speed; This refers to the normal force at the friction contact surface. , It is a constant coefficient used to characterize the effect of load torque. It is a symbolic function; Coulomb friction coefficient; Joint angular velocity; The joint friction torque is given; the parameter to be identified is: , , , , , .

6. The method for robot dynamics modeling and parameter identification considering frictional normal force according to claim 1, characterized in that, The specific method for step five is as follows: 51) A metaheuristic optimization algorithm is used to identify the parameters of the friction model, and a genetic algorithm is used for parameter identification. 52) Set constraints as shown in formula (5): （5） 53) Set the optimization objective fitness function as follows: in, For the first The frictional torque value extracted from each joint; This refers to the estimated friction torque calculated by the genetic algorithm in each iteration. To find the minimum value of the function.

7. The method for robot dynamics modeling and parameter identification considering frictional normal force according to claim 1, characterized in that, The specific method for step six is ​​as follows: The specific method for step six is ​​as follows: 61) Design an excitation trajectory with the following expression: In the formula, For periodicity; This is the modulo operation; The coefficients of the fifth-degree polynomial are represented as follows: , function For the series harmonic order; The fundamental frequency of the trajectory is the same for all joints; , As a coefficient term, it determines the amplitude of the trajectory motion; set , Thus, the fundamental frequency is determined. ; Plan the angular position of the i-th joint to determine the excitation trajectory; For summation index; , , , for : represents the coefficients of a fifth-degree polynomial; 62) A genetic algorithm is used to find parameters based on the following optimization criteria: In the formula, The condition number of the observation matrix. The observation matrix is ​​the equation of motion of the robot. , , Limitations on the displacement, velocity, and acceleration of the joints; The set of robot end-effector poses corresponding to the excitation trajectory; Cartesian space for robot motion.

8. The method for robot dynamics modeling and parameter identification considering frictional normal force according to claim 1, characterized in that, The specific method for step seven is as follows: 71) Execute the motion trajectory of step six in position control mode, and collect the robot's position, velocity, acceleration, and torque data; where the robot's position information is obtained from the joint encoder, the velocity and acceleration information is calculated by differentiating the position values, and the torque data is the motor current output. 72) Use a Butterworth filter to filter the data.

9. The method for robot dynamics modeling and parameter identification considering frictional normal force according to claim 1, characterized in that, The specific method for step eight is as follows: 81) Establish a robot dynamics model based on the Coulomb viscous friction model and linearize it as follows: In the formula, These are the angular displacement, angular velocity, and angular acceleration of each joint of the robot. For the inertial torque of a six-degree-of-freedom robot; Coriolis torque for a six-degree-of-freedom robot; For the gravitational torque of a six-degree-of-freedom robot; The frictional torque is obtained using the Coulomb viscous friction model. The driving torque of the robot joint is obtained by sampling the output torque of the joint motor; Coulomb viscous friction is also expressed in linear form, and equation (9) can be rewritten as: In the formula, This is the observation matrix corresponding to the robot's dynamics equations; will use express, This represents the minimum set of inertial parameters for the robot. The information obtained from step five includes position, velocity, acceleration, torque, and... Substitution, that is, solving for the parameters using the least squares method. :

10. The method for robot dynamics modeling and parameter identification considering frictional normal force according to claim 1, characterized in that, The specific method for step nine is as follows: 91) The robot dynamics model considering the normal force of the frictional contact surface is given by equation (12.1), where As given by equation (12.2), The calculation method is given by equation (12.3): In the formula, The position, velocity, acceleration, and torque information, calculated by equation (11), are obtained from step seven. Similarly, by substituting the position, velocity, acceleration, torque information, and the friction parameters expressed in step five, the minimum parameter set of the robot dynamics model considering the normal force of the friction contact surface is solved using the following equation. :

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