Robot parameter identification method and system based on temperature load extended friction model

Abstract

The application discloses a robot parameter identification method and system based on a temperature load extended friction model, and relates to the technical field of robot dynamics modeling and control. The method comprises the following steps: optimizing a friction separation path through designing a strict constraint excitation trajectory, collecting experimental data under different temperature load conditions through robot joint friction characteristic testing based on the friction separation path; constructing a Stribeck friction model, performing temperature and load polynomial processing on key parameters, and obtaining a Stribeck effect extended friction model based on temperature, load and speed; and adopting a hierarchical identification scheme of temperature first and then load, and using the Stribeck effect extended friction model of temperature, load and speed to identify robot joint friction parameters from the experimental data. The application realizes accurate identification of robot joint friction characteristics and parameters under variable temperature and variable load combined conditions.

Description

Technical Field

[0001] This invention relates to the field of robot dynamics modeling and control technology, and in particular to a method and system for identifying robot parameters based on a temperature load extended friction model. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] In robot joint structures containing reducers, friction effects exhibit strong nonlinearity due to operating conditions. Temperature variations and load fluctuations are key factors contributing to the complex and variable friction characteristics, and are also the core challenges preventing existing friction models from accurately adapting to actual operating conditions and meeting engineering application requirements. In summary, current joint friction models based on the Stribeck effect struggle to effectively decouple the multiple factors influencing friction characteristics and establish reasonable physical constraints, resulting in low accuracy in model parameter identification. Furthermore, existing friction separation methods suffer from lengthy experimental cycles during data acquisition, failing to obtain friction force data at multiple speeds within a short timeframe. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for robot parameter identification based on a temperature-load-based extended friction model. This overcomes problems such as long friction separation experiment cycles, ineffective decoupling of temperature and load effects by the friction model, redundant model structure, and unreliable identification due to parameter fitting ignoring physical meaning. This invention aims to achieve accurate identification of robot joint friction characteristics and parameters under combined temperature and load conditions through an integrated and targeted model building and experimental testing solution. This provides reliable support for robot dynamics modeling, high-precision torque control, and dynamics simulation, meeting the engineering application needs of high-precision robot operation scenarios.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solution: The first aspect of this invention provides a method for identifying robot parameters based on a temperature-load-based extended friction model, comprising the following steps: By designing a strictly constrained excitation trajectory to optimize the friction separation path, and based on the friction separation path, experimental data under different temperature load conditions are collected through robot joint friction characteristic testing. A Stribeck friction model was constructed, and the key parameters were polynomialized for temperature and load to obtain an extended friction model based on the Stribeck effect of temperature, load, and velocity. A layered identification scheme, prioritizing temperature over load, was adopted. The Stribeck effect of temperature, load, and velocity was used to extend the friction model and identify the joint friction parameters of the robot based on the experimental data.

[0006] Furthermore, a strictly constrained excitation trajectory refers to designing a set of symmetrical variable-speed motions in both directions on a single joint of the robot as an excitation trajectory. This requires imposing constraints on the robot's position, speed, and acceleration in both directions, ensuring that the robot's end effector is in the same position in both directions, but with opposite speeds and the same acceleration.

[0007] Furthermore, the strictly constrained excitation trajectory covers extremely low speed, high speed, and smooth reversing conditions.

[0008] Furthermore, the specific steps for optimizing the friction separation path by designing a strictly constrained excitation trajectory are as follows: A rigid body dynamics model of the robot is constructed based on Newton's and Euler's formulas. Strictly constrained excitation trajectories are executed based on rigid body dynamics models.

[0009] Furthermore, the specific steps for collecting experimental data under different temperature load conditions through robot joint friction characteristic testing are as follows: Experimental preparation for testing the frictional characteristics of robot joints; Wide-temperature-range evolution friction tests were conducted under no-load conditions; Multi-gradient load friction tests were conducted over a wide temperature range.

[0010] Furthermore, the specific steps for preparing for the experiment to test the frictional characteristics of the robot joints are as follows: A temperature sensor is fixedly installed at the target joint of the robot; In the initial state, the robot end effector is kept unloaded, and a strictly constrained excitation trajectory is executed based on the robot's joint motion characteristics; Check the normal operation status of the robot's motion control system, data acquisition system, and temperature sensing system.

[0011] Furthermore, the specific steps for conducting wide-temperature-range evolution friction tests under no-load conditions are as follows: In the initial stage of the experiment, the robot end effector was kept unloaded, and the experiment was switched to constant load temperature mode. Control the robot to continuously perform reciprocating motion and collect real-time temperature data; Pre-set discrete acquisition nodes for joint temperature based on the joint's wide temperature range evolution range; Whenever the joint temperature rises to the discrete acquisition node of the joint temperature, the robot's reciprocating heating motion is immediately interrupted, a strictly constrained excitation trajectory is executed, and the velocity, position, and torque data of the joint under the current thermal state are collected. After the data collection is completed, the reciprocating heating motion is immediately resumed.

[0012] Furthermore, the specific steps for conducting multi-gradient load friction tests over a wide temperature range are as follows: Keep the robot joints at room temperature to ensure stable initial joint temperature; According to the preset gradient, no load and different standard loads are applied to the robot end in sequence to complete the collection of friction data under constant temperature for all gradient loads. Each time the load is changed, the robot joints are controlled to execute a strictly constrained excitation trajectory, and the current speed, position, and torque data of the joints are collected; The joint temperature is fixed as the discrete acquisition node for joint temperature until the joint temperature reaches a thermal equilibrium point where it no longer increases, covering the wide temperature range of joint evolution, and friction data of all temperature nodes are acquired under different standard loads.

[0013] Furthermore, a layered identification scheme, prioritizing temperature over load, was adopted. The specific steps for identifying robot joint friction parameters using the Stribeck effect of temperature, load, and velocity to extend the friction model were as follows: Based on the Stribeck friction model, the first round of parameter identification was completed under no-load and multi-temperature node conditions according to the speed-temperature correlation characteristics, and physical constraints were applied to the friction parameters at each temperature. Then, fixing the identified speed and temperature parameters, we introduced experimental data of multi-gradient external loads over a wide temperature range, performed a quadratic fitting solution on the load-related parameters in the Stribeck friction model, and applied strict physical constraints to the combined friction parameters under each load to obtain the parameter identification results.

[0014] A second aspect of the present invention provides a robot parameter identification system based on a temperature-loaded extended friction model, comprising: The data acquisition module is used to optimize the friction separation path by designing a strictly constrained excitation trajectory, and to collect experimental data under different temperature load conditions based on the friction separation path by testing the friction characteristics of the robot joint. The model building module is used to build the Stribeck friction model, and to perform temperature and load polynomial processing on key parameters to obtain an extended friction model based on the Stribeck effect of temperature, load and speed. The parameter identification module is used to identify robot joint friction parameters by adopting a hierarchical identification scheme of temperature first and then load, and using the Stribeck effect of temperature, load and speed to extend the friction model.

[0015] The above one or more technical solutions have the following beneficial effects: This invention provides a method and system for robot parameter identification based on an extended friction model under temperature load. It achieves complex working condition adaptation, high-precision identification and standardization of experimental procedures for friction modeling, providing reliable model support and experimental assurance for high-precision control of robot joints.

[0016] To address the problems of lengthy experimental cycles, difficulty in quickly acquiring multi-velocity friction force data, and low parameter identification efficiency in traditional friction characteristic testing and parameter identification processes, the present invention achieves rapid acquisition of multi-velocity friction data, shortens the experimental cycle, improves parameter identification efficiency, and provides efficient data support for accurate model parameter identification. Existing methods often employ alternating uniform motion trajectories as experimental paths, resulting in lengthy experimental cycles and difficulty in acquiring multi-velocity friction force data in a short time, significantly reducing parameter identification efficiency and failing to quickly provide comprehensive multi-velocity friction data support for model construction.

[0017] This invention abandons the traditional uniform motion trajectory of alternating forward and reverse motion, and designs a strictly constrained excitation trajectory that includes low speed, high speed and smooth reversal. It does not require lengthy uniform alternation operation, and can capture friction force data at different speeds in a short time, breaking the efficiency limitations of traditional trajectories.

[0018] The trajectory design of this invention is well-suited to the requirements of friction characteristic testing, enabling rapid coverage of multiple speed ranges, significantly shortening the experimental cycle, and ensuring that the collected multi-speed friction force data is comprehensive and complete, effectively improving the efficiency of parameter identification.

[0019] Through the above design, this invention upgrades the traditional inefficient uniform alternating experimental trajectory to a highly efficient strictly constrained excitation trajectory, fundamentally solving the problems of long experimental cycles and low data acquisition efficiency in traditional experiments, and laying a solid foundation for rapid and accurate identification of model parameters.

[0020] To address the issues of poor adaptability to working conditions, incomplete decoupling of temperature and load, and structural redundancy in existing robot joint friction models, this invention achieves accurate modeling under the coupling of multiple factors such as temperature, load, and speed, completes accurate decoupling of temperature and load, simplifies the model structure, and improves the practicality and identification accuracy of the model in engineering.

[0021] Existing methods, such as the traditional Stribeck friction model, only consider the influence of joint motion velocity on friction, or only consider the effect of a single factor, temperature or load. Even some models that consider the influence of temperature and load suffer from design flaws in the coupling terms of these two effects, making it difficult to achieve effective decoupling. Furthermore, the model structure is lengthy and redundant, increasing the complexity of parameter identification, reducing engineering practicality, and failing to adapt to complex working conditions. This invention, through model extension and structural optimization, uses the classic Stribeck model as a basic framework without changing its original physical structure. It constructs the core friction parameters as polynomial functions of temperature and load, achieving accurate decoupling of the influence of temperature and load on friction. This solves the problem of low identification accuracy caused by design flaws in the coupling terms, allowing the model to independently reflect the individual effects of temperature and load on friction.

[0022] This invention abandons the traditional model design that simply merges temperature and load terms, and reasonably simplifies the model structure. While retaining the physical meaning of the model and ensuring modeling accuracy, it reduces the complexity of parameter identification, significantly improves the engineering practicality of the model, and enables it to flexibly adapt to different working conditions.

[0023] This invention achieves a dual improvement in modeling accuracy and engineering practicality through the collaborative design of model expansion and structural optimization, ensuring that the model can accurately adapt to actual complex working conditions.

[0024] To address the problem that neglecting the physical meaning constraints of parameters in the parameter identification and fitting process can easily lead to unreasonable parameters and a decrease in the stability of the control system, this invention achieves a balance between parameter fitting and physical meaning, ensuring the effectiveness of parameter identification and improving the stability and reliability of the robot control system.

[0025] In existing methods, conventional fitting methods often only pursue the minimization of mathematical fitting errors when dealing with complex nonlinear friction models, but ignore the physical constraints corresponding to the model parameters. This can easily lead to the identification of friction parameters with negative values, unreasonable extrema, and other situations that do not conform to actual physical laws. Applying such models to robot control systems will significantly reduce system stability.

[0026] This invention employs a constrained fitting design to balance minimizing mathematical fitting errors with the physical constraints of model parameters during the parameter identification fitting stage. It clarifies the reasonable range of parameter values ​​and prevents unreasonable extreme values ​​and other parameters that do not conform to physical laws, thus ensuring the physical validity of the identification results.

[0027] Based on physically valid and accurate identification parameters, the model can accurately reflect the actual friction characteristics of robot joints. When applied to robot control systems, it can effectively improve the friction compensation accuracy and control stability of the system, and completely avoid serious problems such as control instability caused by unreasonable parameters.

[0028] This invention solves the problem of traditional fitting methods ignoring physical meaning by using fitting design with physical constraints, ensuring the reliability of parameter identification results, providing a reliable guarantee for robot dynamics modeling, high-precision torque control and dynamics simulation, and further improving the stability and operational accuracy of robot control systems.

[0029] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 This is a flowchart of the robot parameter identification method based on the temperature load extended friction model in Embodiment 1 of the present invention; Figure 2 This is the design diagram of the strictly constrained excitation trajectory in Embodiment 1 of the present invention; Figure 3 This is a three-dimensional relationship diagram of robot joint velocity-temperature-friction torque under no-load wide temperature range in Embodiment 1 of the present invention; Figure 4 This is a three-dimensional relationship diagram of robot joint velocity, load torque, and friction torque under constant temperature and variable load in Embodiment 1 of the present invention. Figure 5 This is a fitting effect diagram of the extended friction model based on the Stribeck effect under a certain working condition of temperature-load for different joints in Embodiment 1 of the present invention. Detailed Implementation

[0032] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0033] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof. The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0034] Example 1: Embodiment 1 of the present invention provides a method for robot parameter identification based on a temperature-load extended friction model, such as... Figure 1 As shown, it includes the following steps: S1; The friction separation path is optimized by designing a strictly constrained excitation trajectory. Based on the friction separation path, experimental data under different temperature load conditions are collected by testing the friction characteristics of the robot joint.

[0035] In one specific implementation, this embodiment designs a strictly constrained excitation trajectory and optimizes the friction separation path to achieve rapid and accurate acquisition of friction force data at multiple speeds, shortening the experimental cycle. This embodiment also designs a dedicated experimental scheme adapted to temperature-load dependent operating conditions to conduct friction characteristic tests and collect experimental data under different temperature and load conditions. Specifically, it includes the following steps: S1.1: Design a strictly constrained excitation trajectory.

[0036] Specifically, such as Figure 2 As shown, a strictly constrained excitation trajectory refers to designing a set of symmetrical variable-speed motions in both forward and reverse directions as the excitation trajectory on a single joint of the robot. This requires imposing constraints on the robot's position, velocity, and acceleration in both directions, ensuring that the robot's end effector maintains the same position in both directions while having opposite velocities and the same acceleration. In this embodiment, the strictly constrained excitation trajectory covers extremely low-speed, high-speed, and smooth reversal conditions.

[0037] More specifically, the symmetrical variable-speed motion in this embodiment is essentially a piecewise parabolic spline trajectory. Within a single cycle, the robot undergoes a complete process of constant acceleration start, acceleration step reversal to achieve smooth direction change and zero velocity crossing, and finally constant deceleration to stop. This continuous reciprocating motion design can continuously sweep through extremely low-speed, high-speed, and smooth-direction change conditions in a very short time, thereby efficiently and comprehensively capturing joint static friction breakthroughs and viscous slip characteristics, laying a solid foundation for the rapid acquisition of friction data at multiple speeds.

[0038] To achieve the above process, this embodiment preprocesses the trajectory points input to the robot for movement. This constraint is mainly implemented through time-reversal symmetric logic, specifically as follows: Figure 2As shown, a trajectory is executed in two cycles. After the first cycle is completed, the trajectory is reversed and flipped to obtain a symmetrical second cycle. Therefore, it can be strictly guaranteed that the robot has opposite speeds and the same acceleration when passing through the same absolute position in both directions.

[0039] The advantage of traditional uniform motion is that the acceleration is zero, which eliminates the inertial torque term and makes calculation easier. However, the drawback of variable speed motion is that it introduces strong dynamic coupling, resulting in the acquisition of inertial torque and Coriolis torque that are difficult to eliminate. To overcome this drawback, this embodiment directly utilizes the aforementioned strict constraint condition to subtract the forward driving torque and the reverse driving torque at the same position and take the average. Because under this constraint, gravity is the same, inertial force is the same, and Coriolis force cancels each other out due to opposite velocities. Thus, while enjoying the efficiency of variable speed motion, it perfectly achieves the effective separation of pure friction torque.

[0040] S1.2: Optimize the friction separation path by designing a strictly constrained excitation trajectory.

[0041] S1.2.1: Construct a rigid body dynamics model of the robot based on Newton's and Euler's formulas.

[0042] Specifically, for an open-chain robot with n degrees of freedom, the rigid body dynamics model can be represented by the Newton-Euler equations as follows: .

[0043] in, For joint driving torque, For joint friction torque and inertial torque term Only related to joint angular acceleration Related to; Coriolis force torque and centrifugal torque With joint angular velocity Related to gravitational torque Only related to joint position related.

[0044] S1.2.2: Execute strictly constrained excitation trajectories based on rigid body dynamics models.

[0045] After applying the previously imposed strict constraint excitation trajectory, at the same position, the joint torque in the dynamic models corresponding to the positive and negative velocities can be expressed as: .

[0046] in, For positive joint movement, For the driving torque of the reverse motion joint, For positive motion, Coriolis force and torque and centrifugal force, For the reverse motion, there are the Coriolis force torque and centrifugal torque; for the forward motion, there is the gravitational torque. , is the gravitational torque during reverse motion. , For positive joint friction torque, The frictional torque of the joint in the opposite motion is used. All the above experiments were performed under the condition of symmetrical variable speed motion in the forward and reverse directions as the excitation trajectory designed in this embodiment.

[0047] Furthermore, if the frictional force is generally symmetrical around the origin, then the frictional torque of a single joint... Represented as: .

[0048] The calculation of single-joint friction torque is used in the friction separation and signal processing stage to extract pure friction data from the mixed driving torque, thereby providing an accurate data basis for subsequent steps (such as S3) for friction parameter estimation and model identification.

[0049] Under a strictly constrained trajectory, when the robot moves to the same position in both directions, its acceleration is the same but its velocities are opposite. According to the rigid body dynamics model, the inertial torque, gravitational torque, and velocity-related Coriolis force and centrifugal torque are all equal in magnitude at this point, and will cancel each other out during alternating forward and reverse motion. Combining this with the assumption that friction is generally symmetrical around the origin, subtracting the forward joint driving torque from the reverse joint driving torque and taking the average value perfectly eliminates complex dynamic coupling interference, allowing for a simple and efficient extraction of the pure friction torque.

[0050] If the load is considered as part of the end, then in uniform alternating forward and reverse motion, the inertial force and Coriolis force corresponding to the load will cancel each other out in opposite directions at the same position, ultimately achieving effective separation of frictional torque.

[0051] S1.3: Based on the friction separation path, experimental data under different temperature load conditions are collected through the test of robot joint friction characteristics.

[0052] This embodiment is used to design a dedicated experimental scheme to adapt to temperature-load dependent operating conditions, conduct tests on the frictional characteristics of robot joints, collect experimental data under different temperature and load conditions, and achieve precise decoupling of the nonlinear effects of temperature and load on robot joint friction. This provides reliable data support for building a high-precision temperature-load dependent friction model. Specifically, it includes the following steps: S1.3.1: Experimental preparation for testing the frictional characteristics of robot joints.

[0053] S1.3.1.1: Install a temperature sensor at the target joint of the robot.

[0054] Specifically, high-precision temperature sensors are fixedly installed at the target joints of the robot to ensure that the sensors are in close contact with the joint surface, so as to collect joint temperature data in real time and ensure the accuracy and real-time performance of temperature detection.

[0055] S1.3.1.2: In the initial state, keep the robot end effector unloaded and execute a strictly constrained excitation trajectory based on the robot's joint motion characteristics. Specifically, in the initial state, the robot end effector is kept unloaded. Based on the robot joint motion characteristics, a strictly constrained excitation trajectory is used, that is, when the robot end effector is in the same position in the forward and reverse directions, the speed is opposite and the acceleration is the same. This strictly constrained excitation trajectory needs to cover extremely low speed, high speed and smooth reversal conditions. In addition, for the different mechanical limits and rated speeds of different robot joints, trajectory parameters such as position stroke, peak speed and step acceleration are set in a customized manner. This can comprehensively capture the characteristics of joint static friction breakthrough and viscous slip, laying the foundation for the comprehensive collection of subsequent friction data.

[0056] S1.3.1.3 Check the normal operation status of the robot motion control system, data acquisition system and temperature sensing system to ensure that the robot joint movement is precise and controllable, data acquisition is without loss or interference, and temperature detection error meets the experimental requirements.

[0057] S1.3.2: Conduct wide-temperature-range evolution friction tests under no-load conditions.

[0058] S1.3.2.1: In the initial stage of the experiment, keep the robot end unloaded and switch to the constant load temperature experiment mode.

[0059] Specifically, in the initial stage of the experiment, the robot's end effector was kept unloaded, and the experiment was switched to a constant-load temperature mode. This mode strictly followed the controlled variable method, forcibly fixing the load variable throughout the experiment (i.e., keeping the robot's end effector unloaded), and treating temperature as the only dynamic independent variable for independent examination, thereby eliminating the interference of load fluctuations on frictional characteristics.

[0060] S1.3.2.2: Control the robot to continuously perform reciprocating motion and collect real-time temperature data.

[0061] Specifically, the robot is controlled to continuously perform high-intensity, wide-range reciprocating motions, forcing joint friction to generate heat. At the same time, high-precision temperature sensors monitor joint temperature changes in real time to ensure real-time acquisition and recording of temperature data.

[0062] S1.3.2.3: Preset discrete acquisition nodes for joint temperature based on the joint's wide temperature range evolution.

[0063] Specifically, discrete joint temperature acquisition nodes are preset. In this embodiment, the discrete joint temperature acquisition nodes include 20℃, 25℃, 30℃, 35℃, 40℃, and 45℃, until the joint temperature reaches a thermal equilibrium point where it no longer increases, covering the wide temperature range of joint evolution.

[0064] S1.3.2.4: Whenever the joint temperature rises to the discrete temperature acquisition node, the robot's reciprocating heating motion is immediately interrupted, a strictly constrained excitation trajectory is executed, and the joint's velocity, position, and torque data under the current thermal state are collected. After data collection, the reciprocating heating motion is immediately resumed to ensure the timeliness and accuracy of temperature node data acquisition and to avoid temperature fluctuations affecting data validity. The three-dimensional relationship between robot joint velocity, temperature, and friction torque under no-load wide temperature range is shown in the figure below. Figure 3 As shown.

[0065] S1.3.3: Perform multi-gradient load friction tests over a wide temperature range.

[0066] S1.3.3.1: Control the robot joints to be in a cold state at room temperature to ensure that the initial joint temperature is stable.

[0067] Specifically, after completing the wide-temperature-range evolution friction experiment under no-load conditions, the robot joints were kept at room temperature to ensure that the initial joint temperature was stable, eliminating the influence of residual temperature from previous experiments on the results of this experiment. The single-variable principle of the controlled variable method was strictly followed, with the temperature variable fixed and only the load variable changed.

[0068] S1.3.3.2: Apply no load and different standard loads to the robot end effector in sequence according to the preset gradient, and complete the collection of friction data of all gradient loads under constant temperature.

[0069] Specifically, according to the preset gradient, no load and different standard loads are applied to the robot end effector in sequence. The standard loads are 10%, 30%, 50%, 70%, and 90% of the robot's rated load. Friction data are collected under constant temperature for all gradient loads. After each load switch, it is necessary to ensure that the initial joint temperature is consistent to avoid residual temperature affecting the experimental results during the load switch process.

[0070] S1.3.3.3: Each time the load is changed, the robot joints are controlled to execute a strictly constrained excitation trajectory, and the current speed, position, and torque data of the joints are collected to ensure the integrity and synchronization of the data collection.

[0071] S1.3.3.4 Fix the joint temperature as the discrete acquisition node for joint temperature until the joint temperature reaches the thermal equilibrium point where it no longer increases, covering the wide temperature range evolution of the joint, and collect friction data of all temperature nodes under different standard loads.

[0072] Specifically, the friction data includes a comprehensive dataset from two experimental phases: wide-temperature-range evolution friction tests under no-load conditions and multi-gradient load friction tests under wide-temperature-range conditions. In addition to robot joint velocities, angles, and output torques, the collected data necessarily includes temperature data (such as discrete nodes from 20℃ to 45℃) and external load gradient values ​​set by the system (such as 10% to 90% of the rated load). These together constitute a complete physical record describing the friction performance under multiple operating conditions.

[0073] In this embodiment, the fixed joint temperature is a preset discrete node, including 20℃, 25℃, 30℃, 35℃, 40℃, and 45℃, until the joint temperature reaches a thermal equilibrium point where it no longer increases, covering the wide temperature range of the joint. Steps S1.3.3.2 and S1.3.3.3 are repeated to complete the collection of friction data for all temperature nodes under different standard loads. The three-dimensional relationship between robot joint velocity, load torque, and friction torque under constant temperature and variable load is shown in the figure below. Figure 4 As shown.

[0074] S2: Construct the Stribeck friction model, and perform temperature and load polynomial processing on the key parameters to obtain the extended friction model of the Stribeck effect based on temperature, load and speed.

[0075] In one specific implementation, this embodiment utilizes collected friction data under a wide temperature-load condition framework. Based on the Stribeck friction model, it transforms the traditional fixed-parameter Stribeck model into an extended friction model adaptable to complex operating conditions by performing temperature-load polynomial processing on key model parameters. This effectively decouples the effects of temperature and load, simplifies the model structure, and accurately describes the friction characteristics under different temperature and load conditions. This provides reliable theoretical and model support for subsequent robot joint friction compensation, high-precision dynamic modeling, and high-performance servo control algorithm design.

[0076] In this embodiment, the key parameter refers to the core indicative coefficient within the mathematical formula constructed based on Stribeck's physical laws, which is used to determine the shape of the friction torque curve.

[0077] This embodiment does not disrupt the physical framework of the classic Stribeck model. Instead, it upgrades the fixed "key parameters" in the original model into polynomial functions with temperature and load as independent variables. This approach allows temperature and load to act directly on specific physical characteristics such as Coulomb forces or viscous forces as independent additive terms, effectively avoiding the disordered strong coupling between the two at the underlying formula level and achieving "precise decoupling" of influencing factors. At the same time, compared to directly and rigidly multiplying and dividing temperature and load terms arbitrarily or constructing complex black-box neural networks, low-order polynomials ensure the model's continuity, differentiability, and scalability in the global domain, significantly reducing the mathematical dimension of nonlinear optimization, thereby simplifying the model structure and improving its engineering practicality.

[0078] The specific implementation process is as follows: S2.1: Determine the basic Stribeck friction model structure.

[0079] The mathematical expression based on the Stribeck friction model is as follows: .

[0080] in, The current temperature of the robot's joints is an external environmental condition variable introduced in the extended model. This is the predicted total frictional torque output from the extended friction model based on the Stribeck effect under temperature load. The external load torque borne by the robot joints is an external force condition variable introduced in the extended model. This is used to refer holistically to the currently constructed extended friction model terms based on a specific robot and the Stribeck effect. This is a sign function that outputs 1 or -1 based on the sign of the input joint angular velocity (i.e., forward or reverse rotation). Its physical meaning is to ensure that the calculated frictional torque direction is always strictly opposite to the actual joint movement direction. This usually refers to the velocity-enhancing effect produced by viscous friction. The function describes the speed reduction effect.

[0081] In the traditional Stribeck model, the five key parameters of friction are: Coulomb friction parameters... Static friction parameters viscosity coefficient Stribeck speed With viscosity index The model cannot reflect the effects of temperature and load changes on frictional characteristics, resulting in decreased accuracy under cross-temperature range and variable load conditions.

[0082] S2.2: Perform polynomial expansion of key parameters for temperature and load.

[0083] Specifically, without changing the functional form of the Stribeck model, the five key parameters mentioned above are constructed as temperature T and load torque. The polynomial function is used to implement the parameterized extension of the model, and its expression is as follows:

[0084] in, This represents five key friction parameters under ambient temperature and robot-unloaded conditions. This represents the temperature-load dependent Coulomb friction parameters. This represents the temperature-load dependent static friction parameter. This represents the temperature-load dependent viscosity coefficient. This represents the temperature-load dependent Stribeck velocity. The viscosity index represents the temperature-load dependence. These represent the Coulomb friction parameters, static friction parameters, viscosity coefficient, Stribeck velocity, and viscosity index at room temperature and no load, respectively.

[0085] The index variable represents the order of the temperature polynomial (incrementing from 1). The index variable represents the order of the load polynomial (incrementing from 1). The unified designation represents the highest order of the polynomial fit of the corresponding friction parameters with respect to temperature T. . A unified representation of the corresponding friction parameters with respect to the load variable. The highest order of the polynomial fit. A unified representation of the first degree of each corresponding parameter with respect to the temperature variable T Polynomial weighting coefficients. A unified representation of each corresponding parameter with respect to the load variable The Polynomial weighting coefficients.

[0086] The above equation yields an extended friction model based on the Stribeck effect of temperature, load, and velocity. The order of the polynomial related to temperature and load is appropriately selected according to the relationship between robot joint temperature and friction torque, and the relationship between load torque and friction torque. This varies depending on the robot. In the practical application of the Rokae NB4 robot, a second-order polynomial is used to fit the parameter variation with temperature, while a first-order polynomial is used for load. This strategy makes the model continuous, differentiable, and scalable, facilitating identification and implementation.

[0087] S3: A layered identification scheme of temperature first and then load is adopted. The Stribeck effect of temperature, load and speed is used to extend the friction model to identify the joint friction parameters of the robot based on the experimental data.

[0088] In one specific implementation, this embodiment employs a hierarchical identification scheme prioritizing temperature over load. Based on the Stribeck friction model, the first round of parameter identification is completed under no-load and multi-temperature node conditions, based on the velocity-temperature correlation characteristics. Then, the identified velocity-temperature parameters are fixed, and experimental data from multi-gradient external loads over a wide temperature range are introduced. A secondary fitting solution is then performed on the load-related parameters in the model, ultimately yielding an extended friction model based on the temperature-load-velocity Stribeck effect. This provides a reliable parameter foundation and model support for subsequent robot joint friction compensation, high-precision dynamic modeling, and high-performance servo control algorithm design.

[0089] It is important to note that in the first round of solving in this embodiment, due to the completely unloaded condition, all load-related polynomial terms in the complete model automatically degenerate to zero. The solver faces a simplified velocity-temperature degenerate model, which is used to uniformly and jointly fit and solve for 16 parameters. In the second round of solving, the model reverts to the complete form that includes load characteristics. However, for dimensionality reduction and decoupling, the 16 parameters obtained in the first round are directly fixed as known constants, so that the solver only needs to perform the final fitting and solution for the remaining 5 load-related parameter vectors.

[0090] The specific process is as follows: S3.1: Based on the Stribeck friction model, the first round of parameter identification is completed under no-load and multi-temperature node conditions according to the speed-temperature correlation characteristics, and physical constraints are applied to the friction parameters at each temperature.

[0091] Specifically, the entire experiment was conducted without any external load on the robot's end effector to completely eliminate the interference of load variables on the identification results. Based on the full range of velocity-temperature-friction torque experimental data collected in the early stages, the Matlab interior point method optimization algorithm was used to perform data fitting and friction parameter identification, resulting in friction parameter terms in the model that are only related to motion velocity and joint temperature.

[0092] In this embodiment, temperature is introduced as an externally measurable operating condition variable into the friction model parameter mapping. Under physical feasibility constraints and boundary constraints, an overall cost function is constructed, and a unique parameter vector is obtained through constrained nonlinear optimization. To achieve wide-temperature joint fitting, the global parameter vector to be identified is first defined as follows: .

[0093] in, Defined as the weighting coefficients to be identified in the temperature-dependent friction polynomial, these coefficients are used to quantify the dynamic influence of joint temperature on the basic Stribeck friction characteristics. The number is fixed at 16 because the traditional Stribeck model includes five core physical parameters (Coulomb friction parameter, static friction parameter, Stribeck characteristic velocity, viscosity coefficient, and viscosity exponent). In this embodiment, these five parameters are all expanded using second-order polynomials with respect to temperature; that is, each parameter is expanded and includes three coefficients: a constant term, a first-order term, and a second-order term, resulting in 5 × 3 = 15 coefficients. Then, a final independent constant term—characterizing the decay rate of the Stribeck curve—is added separately. This last term, set as temperature-independent in the first round, represents the exponent. This strictly constitutes a 16-dimensional global parameter vector, which facilitates the unified joint data fitting under multiple temperature conditions using the Matlab interior-point nonlinear optimization algorithm in the backend.

[0094] Establish a set of friction parameters according to temperature-related parameterization: .

[0095] in, Coulomb friction parameters representing temperature dependence Viscosity coefficient representing temperature dependence Stribeck velocity parameters representing temperature dependence Viscosity index, which indicates temperature dependence Static friction parameters that are temperature dependent Parameters characterizing the Stribeck transition characteristics.

[0096] For temperature sets The following experimental data, let the first... The temperature of the first The observed values ​​of joint velocity and frictional torque at each sampling point are as follows: and The model output is denoted as: .

[0097] in, This refers to the predicted value output by the model, specifically the predicted friction torque under no-load conditions based on the velocity-temperature dependent model. For a temperature-dependent Stribeck-based friction model: .

[0098] Therefore, the residual is defined as the difference between the observed value and the predicted value: .

[0099] in, The residuals under no-load conditions are based on the velocity-temperature dependent model. These are the observed frictional torque values ​​under no-load conditions based on a velocity-temperature dependent model.

[0100] To achieve a uniform fit across multiple temperature ranges, an overall cost function is constructed to jointly measure the residuals between all temperatures and sampling points. Considering the potential for outliers or local anomalies in the experimental data, to enhance the robustness of the identification results and ensure the smooth differentiability of the objective function in the global domain to adapt to the optimization algorithm, a smoothing absolute error criterion is adopted instead of the traditional absolute error criterion. Therefore, the global objective function is defined as follows: .

[0101] in, For the first Weighting coefficients for each temperature data point The set smoothing factor is used to eliminate the non-differentiability defect of the absolute error at zero. When the number of sampling points and the noise level are approximately consistent at each temperature, equal weighting can be used. If this formula degenerates into the direct summation of the smoothed absolute errors of all temperature data, it is equivalent to the total error obtained by summing and accumulating the results by temperature. This indicates the preset total number of discrete temperature acquisition nodes for joints (or the total number of temperature conditions participating in joint identification). This represents the total number of sampling points in a single temperature node dataset. Since the core friction parameters of the Stribeck effect extended friction model all have clear physical meanings, their numerical rationality directly determines the physical feasibility of the model and the reliability of the identification results. To avoid non-physical parameters causing model failure during the identification process, and to ensure that the model can accurately characterize the robot joint friction characteristics across all preset temperature nodes and the wide temperature range of the joint evolution, strict physical constraints must be imposed on the friction parameters at each temperature. This not only clarifies the upper and lower bounds of each parameter but also satisfies the core magnitude relationships between the parameters, as follows: .

[0102] Among them, the temperature-dependent Coulomb friction parameters , must meet Temperature-dependent static friction parameters , must meet Furthermore, there is a core size relationship between the parameters—this applies to all preset temperatures. This is the core constraint that conforms to the fundamental physical law that static friction is greater than sliding friction, and it is also the key parameter correlation that distinguishes it from single-parameter upper and lower bound constraints; temperature-dependent Stribeck characteristic velocity parameters. , must meet Stribeck Index Characterizing the decay rate of the Stribeck curve, it must satisfy the following conditions: Temperature-dependent coefficient of viscous friction , must meet Temperature-dependent viscosity index , must meet Furthermore, there are no other mandatory size relationships among the parameters; each parameter only needs to satisfy its own physical constraints and the aforementioned core size relationships. All of the above constraints are embedded in the global optimization process through nonlinear constraint functions to perform real-time verification of friction parameters within a wide temperature range. This fundamentally ensures the physical feasibility of the extended friction model, the reliability of the identification results, and the adaptability to wide temperature range operating conditions.

[0103] S3.2: Fix the identified speed and temperature parameters, introduce experimental data of multi-gradient external loads under a wide temperature range, perform a second-order fitting solution for the load-related parameters in the Stribeck friction model, and apply strict physical constraints to the combined friction parameters under each load to obtain the parameter identification results.

[0104] Specifically, based on the speed-temperature related friction parameters already obtained in S3.1, the values ​​of these parameters are fixed; load-related parameters are introduced into the friction model; based on the friction data collected from all temperature nodes under different standard loads in the early stage, the Matlab interior point method optimization algorithm is used again for secondary fitting and friction parameter identification, and finally the extended friction parameters of the three variables of speed, temperature and load are calculated.

[0105] To obtain unified and interpretable friction model parameters under different temperatures and load conditions, based on the completed temperature parameter identification, load-related terms are further introduced, and a multi-condition joint parameter estimation method is used to globally identify the load parameters. Specifically, temperature-related friction parameters are first... Treating the load parameters as known constants, a global cost function covering all load conditions is constructed based on different load conditions. Then, a constrained nonlinear optimization problem is solved under physical feasibility and boundary constraints to obtain a unique load parameter vector. .

[0106] To characterize the effect of load on friction parameters, a vector of load parameters to be identified is introduced: .

[0107] in, This represents the coefficient of influence of load on Coulomb friction parameters. This represents the coefficient indicating the influence of load on static friction parameters. This represents the coefficient indicating the influence of load on Stribeck's characteristic velocity. This represents the coefficient indicating the influence of load on the viscosity coefficient. This represents the coefficient that indicates the influence of load on the viscosity index.

[0108] Each friction parameter is calculated by adding the load term to the temperature term: .

[0109] in, Represents temperature-load dependent Coulomb friction parameters. The viscosity coefficient representing temperature-load dependence. Stribeck velocity parameters representing temperature-load dependence The viscosity index, representing temperature-load dependence, This represents the temperature-load dependent static friction parameter. Parameters characterizing the Stribeck transition characteristics.

[0110] For the One experimental condition, assuming the temperature of this condition is... The load sequence is Speed ​​measurement is The observed frictional torque is Define load strength: .

[0111] The model output (predicted friction torque) is denoted as: .

[0112] in, This refers to the predicted value output by the model, specifically the predicted friction torque based on the speed-temperature-load dependent extended model under multiple operating conditions. For a temperature-load dependent Stribeck-based friction model: .

[0113] Therefore, the residual is defined as: .

[0114] in, For the residuals of the speed-temperature-load dependent extended model under multiple operating conditions, These are observations based on a speed-temperature-load dependent extended model under multiple operating conditions.

[0115] To ensure that the identified load parameters are applicable to all operating conditions, a global cost function covering all operating condition data is constructed. Considering the possibility of local outliers in different datasets, an absolute error criterion is adopted to enhance robustness, and a global objective function is established: .

[0116] in, This represents the total number of experimental conditions involved in the quadratic fitting (i.e., the total number of composite condition datasets involved in the fitting). For the first Number of sampling points for each working condition These are the weighting coefficients. The set smoothing factor is used to eliminate the non-differentiability defect of the absolute error at zero. When the number of sampling points for each operating condition is approximately consistent with the noise level, equal weighting can be adopted. Then the formula degenerates into the direct summation of the smoothed absolute errors of all temperature data, which is equivalent to the total error obtained by summing and accumulating the results by temperature.

[0117] Since the core friction parameters of the Stribeck effect extended friction model all have clear physical meanings, their numerical rationality directly determines the physical feasibility of the model and the reliability of the identification results. To avoid model failure due to non-physical parameters during the identification process, and to ensure that the model can accurately characterize the robot joint friction characteristics under all preset load conditions, full load gradients, and corresponding temperature combinations, strict physical constraints need to be applied to the combined friction parameters under each load. Combining the correlation between the fixed temperature parameters and the load parameters to be identified, the specific constraint scheme is as follows: The core friction parameters of the extended friction model are composed of a superposition of temperature-fixed parameters and load-related parameters, wherein the temperature-fixed parameters are 16 parameters obtained through global optimization. The load-related parameters to be identified are 5 global optimization parameters. The correlation formulas between each combination of friction parameters and temperature and load are as follows: .

[0118] In this embodiment, the constraint is set as: temperature-load dependent Coulomb friction parameters. , must meet Temperature-load dependent static friction parameters , must meet It has support for all preset temperatures. Temperature-load dependent Stribeck characteristic velocity , must meet Stribeck Index Characterizing the decay rate of the Stribeck curve, it must satisfy the following conditions: Temperature-load dependent coefficient of viscous friction , must meet Temperature-load dependent viscosity index , must meet Furthermore, there are no other mandatory magnitude relationships among the parameters; each only needs to satisfy its own physical constraints and the aforementioned core magnitude relationships. The fitting effect diagram of the extended friction model based on the Stribeck effect under a certain temperature-load condition is shown in the figure below. Figure 5 As shown.

[0119] It should be noted that, compared with the existing technology which only applies static upper and lower bound restrictions to fixed parameters, the special feature of this embodiment is that the constraint conditions are upgraded from static coefficient constraints to dynamic state constraints. That is, the constraint is not directly applied to a single polynomial coefficient to be identified, but to the friction parameters of the complete target body after dynamic evolution by temperature and load torque, ensuring that the system can dynamically verify physical feasibility in real time under any complex working conditions.

[0120] In particular, the following is set in this embodiment It strictly adheres to the fundamental physical law that static friction is greater than sliding friction, effectively avoiding solutions that fail physically due to the pursuit of minimizing mathematical errors in conventional fitting. Furthermore, the physical lower bounds of each combined friction parameter are strictly set at a micropositive number. The design takes into account the tendency of polynomials to diverge in the extrapolation region and avoids the singularity of zeros. This design can be combined with the gradient search direction of the fmincon interior point solver to prevent the Jacobian matrix from becoming singular and the algorithm from crashing due to parameters unexpectedly slipping into negative or zero values ​​when iterating over massive amounts of data.

[0121] Example 2: Embodiment 2 of the present invention provides a robot parameter identification system based on a temperature load extended friction model, comprising: The data acquisition module is used to optimize the friction separation path by designing a strictly constrained excitation trajectory, and to collect experimental data under different temperature load conditions based on the friction separation path by testing the friction characteristics of the robot joint. The model building module is used to build the Stribeck friction model, and to perform temperature and load polynomial processing on key parameters to obtain an extended friction model based on the Stribeck effect of temperature, load and speed. The parameter identification module is used to identify robot joint friction parameters by adopting a hierarchical identification scheme of temperature first and then load, and using the Stribeck effect of temperature, load and speed to extend the friction model.

[0122] The steps and methods involved in the above embodiment two correspond to those in embodiment one. For specific implementation details, please refer to the relevant description section of embodiment one.

[0123] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0124] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. A computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the flow or function according to the embodiments of this application is generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in or transmitted through a computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired or wireless means. The computer-readable storage medium can be any available medium that a computer can access or a data processing device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium, an optical medium, or a semiconductor medium, etc.

[0125] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for robot parameter identification based on a temperature-load-extended friction model, characterized in that, Includes the following steps: By designing a strictly constrained excitation trajectory to optimize the friction separation path, and based on the friction separation path, experimental data under different temperature load conditions are collected through robot joint friction characteristic testing. A Stribeck friction model was constructed, and the key parameters were polynomialized for temperature and load to obtain an extended friction model based on the Stribeck effect of temperature, load, and velocity. A layered identification scheme, prioritizing temperature over load, was adopted. The Stribeck effect of temperature, load, and velocity was used to extend the friction model and identify the joint friction parameters of the robot based on the experimental data.

2. The robot parameter identification method based on the temperature load extended friction model as described in claim 1, characterized in that, Strictly constrained excitation trajectories refer to designing a set of symmetrical variable-speed motions in both directions on a single joint of a robot as excitation trajectories. This requires imposing constraints on the robot's position, speed, and acceleration in both directions, ensuring that the robot's end effector is in the same position in both directions, but with opposite speeds and the same acceleration.

3. The robot parameter identification method based on the temperature load extended friction model as described in claim 1, characterized in that, The strictly constrained excitation trajectory covers extremely low speed, high speed and smooth reversing conditions.

4. The robot parameter identification method based on the temperature load extended friction model as described in claim 1, characterized in that, The specific steps for optimizing the friction separation path by designing a strictly constrained excitation trajectory are as follows: A rigid body dynamics model of the robot is constructed based on Newton's and Euler's formulas. Strictly constrained excitation trajectories are executed based on rigid body dynamics models.

5. The robot parameter identification method based on the temperature load extended friction model as described in claim 1, characterized in that, The specific steps for collecting experimental data under different temperature load conditions through robot joint friction characteristic testing are as follows: Experimental preparation for testing the frictional characteristics of robot joints; Wide-temperature-range evolution friction tests were conducted under no-load conditions; Multi-gradient load friction tests were conducted over a wide temperature range.

6. The robot parameter identification method based on the temperature load extended friction model as described in claim 5, characterized in that, The specific steps for preparing for the experiment to test the frictional characteristics of robot joints are as follows: A temperature sensor is fixedly installed at the target joint of the robot; In the initial state, the robot end effector is kept unloaded, and a strictly constrained excitation trajectory is executed based on the robot's joint motion characteristics; Check the normal operation status of the robot's motion control system, data acquisition system, and temperature sensing system.

7. The robot parameter identification method based on the temperature load extended friction model as described in claim 5, characterized in that, The specific steps for conducting wide-temperature-range evolution friction tests under no-load conditions are as follows: In the initial stage of the experiment, the robot end effector was kept unloaded, and the experiment was switched to constant load temperature mode. Control the robot to continuously perform reciprocating motion and collect real-time temperature data; Pre-set discrete acquisition nodes for joint temperature based on the joint's wide temperature range evolution range; Whenever the joint temperature rises to the discrete acquisition node of the joint temperature, the robot's reciprocating heating motion is immediately interrupted, a strictly constrained excitation trajectory is executed, and the velocity, position, and torque data of the joint under the current thermal state are collected. After the data collection is completed, the reciprocating heating motion is immediately resumed.

8. The robot parameter identification method based on the temperature load extended friction model as described in claim 5, characterized in that, The specific steps for conducting multi-gradient load friction tests over a wide temperature range are as follows: Keep the robot joints at room temperature to ensure stable initial joint temperature; According to the preset gradient, no load and different standard loads are applied to the robot end in sequence to complete the collection of friction data under constant temperature for all gradient loads. Each time the load is changed, the robot joints are controlled to execute a strictly constrained excitation trajectory, and the current speed, position, and torque data of the joints are collected; The joint temperature is fixed as the discrete acquisition node for joint temperature until the joint temperature reaches a thermal equilibrium point where it no longer increases, covering the wide temperature range of joint evolution, and friction data of all temperature nodes are acquired under different standard loads.

9. The robot parameter identification method based on the temperature load extended friction model as described in claim 1, characterized in that, The specific steps for identifying robot joint friction parameters using a layered identification scheme that prioritizes temperature over load, and leverages the Stribeck effect of temperature, load, and velocity to extend the friction model, are as follows: Based on the Stribeck friction model, the first round of parameter identification was completed under no-load and multi-temperature node conditions according to the speed-temperature correlation characteristics, and physical constraints were applied to the friction parameters at each temperature. Then, fixing the identified speed and temperature parameters, we introduced experimental data of multi-gradient external loads over a wide temperature range, performed a quadratic fitting solution on the load-related parameters in the Stribeck friction model, and applied strict physical constraints to the combined friction parameters under each load to obtain the parameter identification results.

10. A robot parameter identification system based on a temperature-load-extended friction model, characterized in that it includes: The data acquisition module is used to optimize the friction separation path by designing a strictly constrained excitation trajectory, and to collect experimental data under different temperature load conditions based on the friction separation path by testing the friction characteristics of the robot joint. The model building module is used to build the Stribeck friction model, and to perform temperature and load polynomial processing on key parameters to obtain an extended friction model based on the Stribeck effect of temperature, load and speed. The parameter identification module is used to identify robot joint friction parameters by adopting a hierarchical identification scheme of temperature first and then load, and using the Stribeck effect of temperature, load and speed to extend the friction model.

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