A robot friction torque identification method based on an improved LuGre model

Abstract

The application discloses a robot friction torque identification method based on an improved LuGre model, and the method establishes a multi-factor dynamic robot joint friction model by improving the LuGre friction model, and divides the parameters of the model according to categories; the composition of the robot joint torque and the characteristics of each part are analyzed, the friction torque is indirectly observed from measurable quantities; then, excitation experiments of stable motion states and viscous motion states are respectively designed to identify the static parameters and dynamic parameters in the model; finally, the functional relationship between the robot joint friction torque and the load and temperature is analyzed, the parameters related to the load and temperature in the model are identified, and the robot joint friction model is obtained. The application is an important, effective and low-cost means for improving the control precision of a robot.

Description

Technical Field

[0001] This invention belongs to the field of robot modeling and control technology, and in particular relates to a method for identifying robot friction torque based on an improved LuGre model. Background Technology

[0002] With advancements in robot design and manufacturing, robots are increasingly being widely applied in fields such as precision industrial manufacturing and medical surgery. These fields place high demands on the operational precision of robots, requiring high levels of control accuracy and reliability. Robot control precision is affected by external disturbances and uncertainties, with friction between the internal mechanical structures of robot joints being a significant source of interference. Accurately modeling the frictional torque of robot joints is a crucial means of improving robot control performance.

[0003] In the process of realizing this invention, the inventors discovered that existing robot joint friction modeling techniques have at least the following problems: robot joint friction models usually cannot characterize dynamic characteristics such as hysteresis; they only consider the influence of speed on robot joint friction, but lack consideration of other factors; and the identification of numerous methods is relatively complex. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this application provides a robot friction torque identification method based on an improved LuGre model, solving problems such as neglecting factors other than speed and failing to represent dynamic characteristics. This method introduces multiple factors and improves the LuGre friction model to model the robot joint friction torque. The parameters in the model can be divided into three categories: static parameters, dynamic parameters, and other parameters. By controlling the factors and simplifying the model, experimental excitation of robot joints is designed in groups, collecting data on robot joint friction torque, joint speed, load, and temperature to identify the parameters to be identified in the model.

[0005] To achieve the above objectives, this invention provides a method for identifying robot friction torque based on an improved LuGre model, comprising the following steps:

[0006] S1. Improve the LuGre friction model to establish a robot joint friction model, describe the relationship between robot joint friction torque and joint speed, temperature and load, and divide the model parameters into three categories: static parameters, dynamic parameters and other parameters.

[0007] S2. Analyze the components and characteristics of the robot joint torque, and indirectly collect the friction torque by measuring the joint angle, velocity and joint motor current;

[0008] S3. Design excitation curves for both steady motion and viscous motion states, and identify the static and dynamic parameters in the model.

[0009] S4. When the robot is moving at a constant speed, analyze the functional relationship between the joint friction torque and the load, and between the joint friction torque and the temperature; identify the parameters related to the load and temperature in the model, i.e., other parameters; and finally obtain the robot joint friction model.

[0010] Furthermore, the mathematical expression for establishing the robot joint friction state equation model in S1 is as follows:

[0011]

[0012] Where z is the average deformation of the contact surface bristles in the LuGre model, v is the robot joint rotation speed, and τ f σ is the frictional torque; σ0 is the bristle stiffness coefficient, σ1 is the bristle damping coefficient, and α is the frictional torque. * For Stribeck exponent; α0(τ) L ) represents the Coulomb friction torque, α1(τ) L ) represents the static friction torque, v s (τ L ( ) represents Stribeck's speed, and the three are described as having a load τ L It is a function of the independent variable; α2(T) is the viscous friction coefficient, which is described as a parameter with temperature T as the independent variable;

[0013] Let α0(0) = α 0，0 α1(0)=α 1，0 v s (0)=v s，0 α2(T0)=α 2，0 T0 indicates room temperature.

[0014] Furthermore, the frictional torque τ of the robot joint f The size is related to the speed, temperature and load factors of the robot joint.

[0015] Furthermore, the relationship between the robot joint friction torque and joint velocity, temperature, and load in S1 is specifically defined in the friction model as follows:

[0016] (3.1) When the load on the robot joint is zero and the temperature of the lubricating oil inside the joint is room temperature, i.e., τ L =0, when T=T0, α0(0)=α 0，0， α1(0)=α 1，0 v s (0)=v s，0 α2(T0)=α 2，0 All parameters are simplified to constants, and the friction torque and joint velocity of the robot joint are approximately uniquely related; the parameters of the friction model are simplified into two categories: static parameters and dynamic parameters.

[0017] (3.2) When the robot joint speed is constant and the temperature is normal, the joint friction torque and the load are approximately uniquely related, α0(τ L ), α1(τ L ), v s (τ L All of them are based on τ L The four functions are functions with respect to the independent variable; when the robot joint speed is constant and unloaded, the joint friction torque and temperature are approximately uniquely related, and α2(T) is a function with respect to T;

[0018] α0(τ L ), α1(τ L ), v s (τ L The parameters to be identified in α1 and α2(T) are called other parameters.

[0019] Furthermore, the parameters of the friction model are simplified into two categories: static parameters and dynamic parameters, specifically:

[0020] (4.1) If the robot joints are in a stable motion state, the magnitude and direction of the frictional force remain relatively stable. Approximately 0, the friction model characterizes static friction properties, and the static parameters include α. 0，0 α 1，0 α 2，0 v s，0 and α * ;

[0021] (4.2) Identifiable parameters σ0 and σ1 can be classified as dynamic parameters; when the robot joint is in a viscous state, the relative motion between the contact parts stops, and the robot joint angle is used to replace the mane deformation, the system exhibits hysteresis characteristics and dynamic friction characteristics.

[0022] Furthermore, in step S2, the frictional torque is indirectly collected by measuring the joint angle, velocity, and joint motor current. Specifically, the robot's dynamic equation is first expressed as:

[0023]

[0024] Where M(q) is the robot mass matrix, and q is the robot joint angle. That is, the angular velocity vector v, which represents the v of each joint. Let G(q) be the Coriolis force and centrifugal force, G(q) be the gravitational torque, K be the current-to-torque conversion matrix, I be the joint motor current, and τ be the torque. m The torque of the joint motor is obtained from the motor current I through the transformation matrix K, τ. ext Other external torques on the joint;

[0025] If, without any additional external torque, we only consider one joint of the robot and fix the other joints, the dynamic model of the robot joint can be expressed as:

[0026]

[0027] Where J is the inertia coefficient of a single joint, and q is the joint angle. For joint angular acceleration; I, q and velocity v can be measured directly, τ f It can be indirectly observed as follows:

[0028]

[0029] Furthermore, the method for identifying the static parameters in the model in step S3 specifically involves designing the excitation experiment required to identify the static parameters: designing a constant speed experiment to satisfy a stable motion state, causing the robot to move at a constant speed with multiple different speed values. Under constant speed conditions, the robot joints are in a stable motion state; when there are no other external torque disturbances, the dynamic equations of the robot joints can be simplified to:

[0030] G(q)+τ f (v)=KI=τ m ;

[0031] Under steady motion conditions If the approximation is 0, the model can be simplified to:

[0032] σ0z=g(v)sign(v);

[0033]

[0034] Where sign(v) is the sign function, its value is 1 when v > 0, 0 when v = 0, and -1 when v < 0. Therefore, under steady motion, the direction of the frictional torque is the same as the direction of the angular velocity. When the velocities are the same in magnitude but opposite in direction, the frictional torque is also the same in magnitude but opposite in direction, i.e., τ. f (v)=τ f (-v);

[0035] Then, when the robot joint angles are the same but the velocities are opposite, τ f (v) This can be used to observe:

[0036]

[0037]

[0038]

[0039]

[0040] in, and These represent the measured values ​​of the motor torque when the joint moves in the positive and negative directions at a velocity v, respectively.

[0041] Therefore, frictional torque can be indirectly obtained from the current or torque of the robot joint motor;

[0042] When the constant speed and the theoretical frictional torque value correspond one-to-one, the speed and frictional torque serve as the input and output measurement data for the simplified model, respectively. The static parameter α... 0，0 α 1，0 α 2，0 v s，0 α * It was identified by a nonlinear model.

[0043] Furthermore, the method for identifying the dynamic parameters in the model in step S3 specifically involves designing an excitation curve that satisfies the viscous motion state: designing a sine curve with a velocity in the range of 0-0.25 rad / s and an angular velocity in the range of 0-0.5 rad as the angle curve, limiting the robot joint angular velocity to the range of 0-0.25 rad / s, and the expression for the friction torque of its friction model is:

[0044]

[0045] Where dσ is the deviation between the model and the actual value, and its velocity and frictional torque τ f To simplify the input and output measurement data of the model, the dynamic parameters σ0 and σ1 are obtained by linear regression.

[0046] The robot joint viscous state characteristic is described above. In this state, the joint performs sinusoidal reciprocating motion within the zero-gravity torque angle range of 0-0.5 rad. If there are no other external torque interferences, the robot's dynamic equations are simplified to:

[0047] τ f =τ m .

[0048] Furthermore, the analysis of the functional relationship between joint friction torque and load in S4 is specifically as follows: In the rotary joint of the robot, the load torque τ L It affects the normal force, which in turn affects the Coulomb friction torque; in the model, it affects static friction and Stribeck velocity, α0(τ L ), α1(τ L ), v s (τ L All are described as load τ LThe function, and satisfying α0(0)=α 0，0 α1(0)=α 1，0 v s (0)=v s，0 At constant speed and normal temperature, the friction torque and load are approximately uniquely related, and the friction model simplifies to:

[0049]

[0050] Among them, v c τ represents a constant velocity. L The load torque value is given; by changing the load torque, load torque data and indirectly obtained friction torque data are collected, and the function α0(τ) can be identified through model identification. L ), α1(τ L ), v s (τ L ).

[0051] Furthermore, in S4, the functional relationship between joint friction torque and temperature is analyzed. Specifically, the mechanical components of the robot joint are lubricated with lubricating oil or grease. The viscosity and ultimate shear stress of the lubricant are related to temperature changes. Viscosity has an exponential dependence on temperature, while the ultimate shear stress decreases nonlinearly with increasing temperature. Therefore, the viscosity parameter α2 is expressed as a function α2(T) related to temperature T, and satisfies α2(T0)=α 2，0 When the speed is constant and the load is zero, the frictional torque and temperature are approximately uniquely related, and the friction model simplifies to:

[0052]

[0053] Among them, v c The set constant speed is T0, which is the room temperature. The temperature of the lubricating grease will increase as the robot joint continues to run and will cool down after the movement stops. Temperature data is collected and friction torque data is obtained indirectly. α2(T) can be obtained by fitting the data and the model.

[0054] The present invention has the following beneficial effects:

[0055] As shown in the above embodiments, this application proposes an effective method for identifying robot joint friction models. The model can characterize the dynamic friction characteristics and the influence of multiple factors other than speed on the friction torque. Specifically, the model parameters are categorized, and simplified friction torque observation methods and friction models are set for each scenario. Excitation experiments and data acquisition schemes are designed, and a model identification scheme is adopted based on the model characteristics. This invention is an important, effective, and low-cost means to improve robot control accuracy.

[0056] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0057] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0058] Figure 1 This is a flowchart illustrating the process of establishing a robot joint friction model and identifying model parameters in this embodiment. Detailed Implementation

[0059] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application.

[0060] The following sections provide a detailed description in conjunction with the accompanying drawings and specific embodiments.

[0061] This invention improves the LuGre friction model, establishes a dynamic robot joint friction model that considers multiple factors, and identifies the model parameters. Specifically, it includes the following steps:

[0062] Figure 1 This is a flowchart illustrating a method for establishing and identifying robot joint friction models, as shown in one embodiment of the present invention. Figure 1 As shown, the method specifically includes the following steps:

[0063] S1: Establish a multi-factor dynamic robot joint friction model and classify the parameters.

[0064] The robot joint friction model established in this embodiment is as follows:

[0065]

[0066] Where z is the average deformation of the contact surface bristles in the LuGre model, v is the robot joint rotation speed, and τ f σ is the frictional torque; σ0 is the bristle stiffness coefficient, σ1 is the bristle damping coefficient, and α is the frictional torque. * For the Stribeck exponent; α0(τ) L ) represents the Coulomb friction torque, α1(τ) L ) represents the static friction torque, v s (τ L The three are described as having a load τ, where τ is the Stribeck velocity. Lα is a function of the independent variable; α2(T) is the viscous friction coefficient, described as a parameter with temperature T as the independent variable. Where, let α0(0) = α 0，0 α1(0)=α 1，0 v s (0)=v s，0 α2(T0)=α 2，0 T0 indicates room temperature.

[0067] In this embodiment, α0(τ) is set L )=α 0，0 +α 0，1 |τ L |,α1(τ L )=α 1，0 +α 1，1 |τ L |,v s (τ L ) = v s，0 , Where α 0，1 α 1，1 α 2，1 α 2，2 The parameters to be identified are as follows:

[0068] Load torque τ L By altering the normal force, the Coulomb friction torque and static friction are affected; the greater the normal force, the greater the friction, and this effect is approximately linear. Load may also have a smaller impact on Stribeck's speed. The physical properties of the lubricant within the joint, such as viscosity and ultimate shear stress, change with temperature. Viscosity has an approximately exponential dependence on temperature, while the ultimate shear stress decreases non-linearly with increasing temperature.

[0069] Furthermore, in this embodiment, the model parameters to be identified are divided into three categories based on whether they reflect dynamic friction characteristics and whether they are related to speed. Static parameters include α. 0，0 α 1，0 α 2，0 v s，0 α * The dynamic parameters include σ0 and σ1, and other parameters include α. 0，1 α 1，1 α 2，1 α 2，2 .

[0070] S2: Analyze the components and characteristics of the robot joint torque, and indirectly observe the friction torque through measurable quantities.

[0071] In this embodiment, the robot's dynamic equations are expressed as follows:

[0072]

[0073] Where M(q) is the robot mass matrix, and q is the robot joint angle. That is, the angular velocity vector v, which represents the v of each joint. Let G(q) be the Coriolis force and centrifugal force, G(q) be the gravitational torque, K be the current-to-torque conversion matrix, I be the joint motor current, and τ be the torque. m The torque of the joint motor is obtained from the motor current I through the transformation matrix K, τ. ext For external torques of other joints.

[0074] In this embodiment, to minimize the influence of external forces on the robot, all other joints are locked when dealing with a single robot joint, thereby significantly reducing the coupling between the robot joints and links. In this case, the following dynamic equations can be established for a single joint:

[0075]

[0076] Where J is the inertia coefficient of a single joint, and q is the joint angle. This refers to the joint angular acceleration. I, q, and velocity v can be directly measured, τ f Indirect observation can be achieved through the following formula:

[0077]

[0078] S3: Design excitation curves for both stable and viscous motion states, and identify the static and dynamic parameters in the model.

[0079] In this embodiment, an excitation experiment is designed to identify static parameters: by changing the constant speed value, more than 30 sets of uniform speed experiments are designed non-uniformly within the maximum and minimum speed range, so that the constant speed value distribution in the low-speed segment is denser, so as to comprehensively reflect the characteristics of the low-speed segment and the high-speed segment. In each set, the joint is made to reciprocate in both positive and negative speed directions at a constant speed value within ±180 degrees.

[0080] Under this stimulus experiment design, The method for observing frictional torque is simplified as follows:

[0081] in, and These represent the speeds of the joints. That is, the measured values ​​of the motor torque when the speed v moves in the positive and negative directions.

[0082] In this embodiment, under the constant-speed motion condition of the excitation experiment, the joint is in a stable motion state. Approximately zero, the friction model can be simplified to:

[0083] σ0z=g(v)sign(v);

[0084]

[0085] Where sign(v) is the sign function, its value is 1 when v > 0, 0 when v = 0, and -1 when v < 0. Therefore, under steady motion, the direction of the frictional torque is the same as the direction of the angular velocity. When the velocities are the same in magnitude but opposite in direction, the frictional torque is also the same in magnitude but opposite in direction, i.e., τ. f (v)=τ f (-v);

[0086] Then, when the robot joint angles are the same but the velocities are opposite, τ f (v) This can be used to observe:

[0087]

[0088]

[0089]

[0090]

[0091] in, and These represent the measured values ​​of the motor torque when the joint moves in the positive and negative directions at a velocity v, respectively.

[0092] Therefore, frictional torque can be indirectly obtained from the current or torque of the robot joint motor;

[0093] When the constant speed and the theoretical frictional torque value correspond one-to-one, the speed and frictional torque serve as the input and output measurement data for the simplified model, respectively. The static parameter α... 0，0 α 1，0 α 2，0 v s，0 α * It was identified by a nonlinear model.

[0094] Furthermore, in this embodiment, the constant speed magnitude and the horizontal linear fitting value of the friction torque correspond one-to-one. At this point, the speed value and the friction torque value serve as the input and output measurement data for the simplified model, respectively, with the static parameter α... 0，0 α 1，0 α 2，0 v s，0 α * It was identified by the particle swarm optimization method.

[0095] In this embodiment, an excitation experiment is designed to identify dynamic parameters: sinusoidal curves with velocities in the range of 0-0.25 rad / s and angular velocities in the range of 0-0.5 rad are designed as angle curves. The robot joint angular velocities are limited to the range of 0-0.25 rad / s to maximize the performance of viscous characteristics in the dynamic friction model. The reference angle curve is designed as follows:

[0096] q = 0.1sin(0.2πt)rad, where t is in seconds.

[0097] The aforementioned robot joint viscous state characteristics, in which the joint undergoes sinusoidal reciprocating motion within a zero-gravity torque angle range of 0-0.5 rad, without other external torque interference, the friction torque observation method is simplified as follows:

[0098] τ f =τ m ;

[0099] In this embodiment, the friction model under this experimental design can be simplified as follows:

[0100]

[0101] Where dσ is the deviation between the model and the actual value.

[0102] Furthermore, in this embodiment, the speed and frictional torque τ f To simplify the input and output measurement data of the model, the dynamic parameters σ0 and σ1 are identified using the least squares linear regression method.

[0103] S4: Analyze the functional relationship between joint friction torque and load and temperature, and identify the parameters in the model that are related to load and temperature, i.e., other parameters.

[0104] The frictional torque in a robot joint is not only highly correlated with the joint rotation speed, but also significantly affected by factors such as temperature and load. Based on the principle of controlled variables, the robot is controlled to move at a constant speed, and the functional relationship between joint frictional torque and load and temperature is analyzed.

[0105] In a specific embodiment, under the conditions of constant speed and normal temperature, the frictional torque and the load are approximately uniquely related, and the friction model is simplified to:

[0106]

[0107] Among them, v c τ represents a constant velocity. L This represents the load torque value. In this embodiment, based on the specific expression of the function in S1, the friction model can be further expressed as:

[0108]

[0109] In this experimental design, the robot's joint axes are parallel to the direction of gravity to eliminate the influence of gravity. Friction data is then collected using the following formula:

[0110] τ f =τ m ·

[0111] Furthermore, by altering the load torque and repeating the uniform motion, load torque data and corresponding friction torque data are collected, and α is obtained using a nonlinear least squares method. 0，1 α 1，1 The identification results.

[0112] In a specific embodiment, the robot joints are made to move at a constant speed under no-load conditions, and the frictional torque and temperature are approximately uniquely related.

[0113] Based on the specific expression of the function in S1, the friction model simplifies to:

[0114]

[0115]

[0116] Among them, v c The set constant speed is T0, and the room temperature is T0.

[0117] In this experimental design, the robot's joint axes are parallel to the direction of gravity to eliminate the influence of gravity. Friction data is then collected using the following formula:

[0118] τ f =τ m ;

[0119] Furthermore, by continuously moving or stopping the robot joint for an extended period, the temperature inside the joint can be increased or decreased. Temperature data is collected, and friction torque data is indirectly obtained. The data is then used to perform nonlinear fitting on the model to identify α in α2(T). 2，1 α 2，2 Waiting for parameter identification.

[0120] Thus, the identification results of all parameters to be identified in the model described in S1 are obtained, resulting in a dynamic robot joint friction model considering multiple factors. Furthermore, the effectiveness of the model and parameter set is verified through experimental data collected from other reference motion trajectories.

[0121] It should be understood that the above description is only one embodiment of the present invention, and the present invention is not limited to the structure described above and shown in the accompanying drawings. Several improvements and modifications can be made without departing from the principle of the present invention. The scope of the present invention is limited only by the appended claims.

[0122] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein.

[0123] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope.

Claims

1. A method for identifying robot friction torque based on an improved LuGre model, characterized in that, include: S1. Improve the LuGre friction model to establish a robot joint friction model, describing the relationship between robot joint friction torque and joint speed, temperature, and load. The model parameters are divided into three categories: static parameters, dynamic parameters, and other parameters. Specifically, the relationship between robot joint friction torque and joint speed, temperature, and load in the friction model is as follows: (3.1) When the load on the robot joint is zero and the temperature of the lubricating oil inside the joint is room temperature, i.e. hour, All parameters are simplified to constants, and the friction torque and joint velocity of the robot joint are approximately uniquely related; the parameters of the friction model are simplified into two categories: static parameters and dynamic parameters. (3.2) When the speed of the robot joint is constant and the temperature is at room temperature, the joint friction torque and the load are approximately uniquely related. All are based on The function of the independent variable; when the robot joint speed is constant and unloaded, the joint friction torque and temperature are approximately uniquely related. For The four functions are functions whose independent variables are functions; and The parameters to be identified in the data are called other parameters; S2. Analyze the components and characteristics of the robot joint torque, and indirectly collect the friction torque by measuring the joint angle, velocity and joint motor current; S3. Design excitation curves for both steady motion and viscous motion states, and identify the static and dynamic parameters in the model. S4. When the robot is moving at a constant speed, analyze the functional relationship between the joint friction torque and the load, and between the joint friction torque and the temperature; identify the parameters related to the load and temperature in the model, i.e., other parameters; and finally obtain the robot joint friction model.

2. The robot friction torque identification method based on the improved LuGre model according to claim 1, characterized in that, The mathematical expression for establishing the robot joint friction state equation model in S1 is as follows: ； in, This represents the average deformation of the contact surface hairs in the LuGre model. For the robot joint rotation speed, This is the frictional torque; This is the bristle stiffness coefficient. This is the bristle damping coefficient. Stribeck index; For Coulomb friction torque, For static friction torque, For Stribeck speed, the three are described as being under load. A function of the independent variable; The viscous friction coefficient is described by temperature. The parameter is the independent variable; Among them, let Indicates room temperature.

3. The robot friction torque identification method based on the improved LuGre model according to claim 2, characterized in that, The aforementioned robot joint friction torque The size is related to the speed, temperature and load factors of the robot joint.

4. The robot friction torque identification method based on the improved LuGre model according to claim 3, characterized in that, The parameters of the friction model are simplified into two categories: static parameters and dynamic parameters, specifically: (4.1) If the robot joints are in a stable motion state, the magnitude and direction of the frictional force remain relatively stable. Approximately 0, the friction model characterizes static friction properties, and the static parameters include... ; (4.2) Identifiable parameters These can be categorized as dynamic parameters. When the robot joints are in a viscous state, the relative motion between the contact parts stops. If the robot joint angle is used to replace the bristle deformation, the system exhibits hysteresis characteristics and dynamic friction characteristics.

5. The robot friction torque identification method based on the improved LuGre model according to claim 1, characterized in that, In step S2, the frictional torque is indirectly acquired by measuring the joint angle, speed, and joint motor current. First, the robot's dynamic equations are expressed as: ； in For the robot mass matrix, For robot joint angles, That is, the angular velocity vector That is, to represent each joint. , Coriolis force and centrifugal force, For gravitational torque, This is the conversion matrix from current to torque. This refers to the joint motor current. The torque of the joint motor is determined by the motor current. After transformation matrix get, Other external torques on the joint; If, without any additional external torque, we only consider one joint of the robot and fix the other joints, the dynamic model of the robot joint can be expressed as: ； in The inertia coefficient of a single joint. For joint angle, Joint angular acceleration; and speed It can be measured directly. It can be indirectly observed as follows: 。 6. The robot friction torque identification method based on the improved LuGre model according to claim 4, characterized in that, The method for identifying the static parameters in the model in step S3 specifically involves designing the excitation experiment required for identifying the static parameters: designing a constant speed experiment to satisfy a stable motion state, causing the robot to move at a constant speed with multiple different speed values. Under constant speed conditions, the robot joints are in a stable motion state; when there are no other external torque disturbances, the dynamic equations of the robot joints can be simplified to: ； Under steady motion conditions If the approximation is 0, the model can be simplified to: ； ； in, For a sign function, when The function value is 1 when The function value is 0 when The function value is -1; therefore, under steady motion, the direction of the frictional torque is the same as the direction of the angular velocity. When the velocities are the same in magnitude but opposite in direction, the frictional torque is also the same in magnitude but opposite in direction. ; Then, when the robot joint angles are the same but the velocities are opposite, This can be used for observation: ； ； ； ； in, and These represent the speeds of the joints. Motor torque measurements during forward and reverse motion; Therefore, frictional torque can be indirectly obtained from the current or torque of the robot joint motor. When the constant speed and the theoretical friction torque value correspond one-to-one, the speed and friction torque serve as the input and output measurement data for the simplified model, respectively. The static parameters... It was identified by a nonlinear model.

7. The robot friction torque identification method based on the improved LuGre model according to claim 1, characterized in that, The method for identifying the dynamic parameters in the model in step S3 is as follows: An excitation curve satisfying the viscous motion state is designed: a sine curve with a velocity in the range of 0-0.25 rad / s and an angular velocity in the range of 0-0.5 rad is designed as the angle curve. The robot joint angular velocity is limited to the range of 0-0.25 rad / s. The friction torque expression of its friction model is: ； in, The speed of the deviation between the model and reality and frictional torque To simplify the input and output measurement data of the model, dynamic parameters Obtained by linear regression method; The described robot joint viscous state characteristics, in which the joint is at a zero-gravity torque angle of... If the robot performs sinusoidal reciprocating motion within the range of 0-0.5 rad and there are no other external torques interfering, the robot's dynamic equations simplify to: 。 8. The robot friction torque identification method based on the improved LuGre model according to claim 1, characterized in that, The S4 section analyzes the functional relationship between joint friction torque and load, specifically: in the robot's rotary joint, the load torque... It affects the normal force, which in turn affects the Coulomb friction torque; it also affects static friction and Stribeck velocity in the model. All are described as load A function that satisfies At constant speed and normal temperature, the frictional torque and load are approximately uniquely related, and the friction model simplifies to: ； in, Indicates constant speed. The load torque value is given; by changing the load torque, load torque data and indirectly obtained friction torque data are collected, and the function can be identified through model identification. .

9. The robot friction torque identification method based on the improved LuGre model according to claim 1, characterized in that, The S4 section analyzes the functional relationship between joint friction torque and temperature. Specifically, the mechanical components of the robot joint are lubricated with lubricating oil or grease. The viscosity of the lubricant and the physical properties of the ultimate shear stress are related to temperature changes. The viscosity is exponentially dependent on temperature, while the ultimate shear stress decreases nonlinearly with increasing temperature. Therefore, viscosity parameters Represented as temperature Related functions And satisfy When the speed is constant and the load is zero, the frictional torque and temperature are approximately uniquely related, and the friction model simplifies to: ； in, For the set constant speed, The temperature is set to room temperature; the temperature of the lubricating grease increases as the robot joint continues to operate and cools down after movement stops. Temperature data is collected, and friction torque data is indirectly obtained. By fitting the data with the model, the following can be derived: .

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