Robot dynamics parameter identification method and system based on physical consistency constraints and load-related friction model

Abstract

The present invention relates to the field of robot dynamic parameter identification, and discloses a robot dynamic parameter identification method and system based on physical consistency constraints and load-associated friction models. The method includes: establishing a robot dynamic parameter model under a linear friction model, and performing linear parameterization processing on the parameters in the model; designing an excitation trajectory to satisfy physical limit constraints and physical boundary constraints; running multiple excitation trajectories, performing data processing, and dividing the data set into three parts; establishing upper and lower density constraints and spatial distribution constraints; using weighted least squares to obtain standard dynamic parameters and basis parameters; optimizing and calculating load-associated friction parameters; establishing a linearly separated joint torque model, and using weighted least squares to obtain standard dynamic parameters and basis parameters; iteratively identifying inertia parameters and load-associated friction parameters. The load-associated friction model used in the present invention is a broken line load-friction relationship, and inertia parameters and friction parameters are iteratively identified in combination with new physical consistency constraints, thereby improving the accuracy of parameter identification.

Description

Technical Field

[0001] The present invention belongs to but is not limited to the field of robot dynamics parameter identification, and in particular relates to a robot dynamics parameter identification method and system based on physical consistency constraints and load-related friction models. Background Art

[0002] In the fields of 3C manufacturing, human-machine collaboration, and medical services, the application of robotic arms is becoming more and more extensive and in-depth, which has led to a continuous increase in the requirements for robotic arms' control accuracy, collision detection and other capabilities. Accurate dynamic models are the cornerstone of robots' high-precision trajectory control and external force perception.

[0003] At present, the least squares identification method under physical consistency constraints is generally used for the identification of robot dynamic parameters. The use of physical consistency constraints can effectively increase the accuracy of parameter identification. However, the traditional physical consistency constraints only derive constraints on mass, inertia, etc. from the starting point that the density is positive. The density distribution of an actual rigid body is within a certain range. It not only has a lower limit greater than zero, but also has an upper limit related to the material. Its spatial distribution is also within a certain range. Therefore, only considering the physical consistency constraints with positive density cannot fully utilize the existing information to improve the identification accuracy. In addition, the friction model considered in the traditional dynamic model is generally a linear friction model or a Stribeck friction model. This type of model does not take into account the influence of joint load on friction, which reduces the accuracy of the model and makes it difficult for the identified parameter model to accurately predict the joint torque.

[0004] At present, the least squares identification method under physical consistency constraints is mainly used for the identification of robot arm dynamic parameters. Although physical consistency constraints can effectively improve the accuracy of parameter identification, the existing technology only considers the constraint condition of positive density. This method does not fully consider the density distribution range and spatial distribution constraints of the actual rigid body, resulting in insufficient utilization of joint information and limiting the further improvement of identification accuracy. In addition, the existing friction model is usually a linear friction model or a Stribeck friction model, which fails to take into account the influence of joint load on friction force, resulting in reduced prediction accuracy of the model and difficulty in accurately predicting joint torque.

[0005] In industrial applications, these technical problems significantly affect the performance of industrial robots and medical robots. In industrial robot control systems, due to the inadequacy of the dynamic parameter model and the limitations of the friction model, the accuracy and stability of the robot in a high-load working environment are limited, affecting the efficiency and quality of processes such as welding and assembly. In medical robot systems, surgical robots and rehabilitation robots may cause operational errors and poor training effects due to their failure to accurately reflect the changes in friction in actual work, affecting the treatment and rehabilitation process of patients. Summary of the invention

[0006] In view of the problems existing in the prior art, the present invention provides a robot dynamics parameter identification method and system based on physical consistency constraints and load-related friction model.

[0007] The present invention is implemented as follows: a method for identifying robot dynamic parameters based on physical consistency constraints and load-related friction models, the method comprising:

[0008] S1. Based on Newton-Euler method, Lagrange method, etc., a robot dynamic parameter model under a linear friction model is established, the parameters in the model are linearly parameterized, and the model is converted into a minimum parameter set to obtain the basis parameters and its observation matrix;

[0009] S2: Design the excitation trajectory based on the finite Fourier series to meet the physical limit constraints and physical boundary constraints;

[0010] S3: Run multiple excitation trajectories, collect joint position, velocity, acceleration, and current information, perform data processing, and divide the data set into three parts;

[0011] S4: Based on the center-of-mass inertia principal axis coordinate system, density upper and lower limit constraints and spatial distribution constraints are established to obtain perfect physical consistency constraints;

[0012] S5: Based on the physical consistency constraints, the weighted least square method is used to obtain the standard kinetic parameters and basis parameters of the kinetics;

[0013] S6: Optimization calculation of load-related friction parameters based on identified inertia parameters;

[0014] S7: A linearly separated joint torque model is established based on load-related friction parameters, and the weighted least squares method is used to obtain the standard dynamic parameters and basis parameters based on physical consistency constraints;

[0015] S8: Iterative identification of inertia parameters and load-related friction parameters.

[0016] Further, the S1 specifically includes:

[0017] For a serial robot with n joints, the above dynamic parameter model can be generalized as:

[0018]

[0019] Where: τ∈R n×1 represents the joint torque, Respectively represent the angle, angular velocity and angular acceleration of the robot joint, M∈R n×n is the inertia matrix of the robot, C∈R n×n represents the centrifugal force matrix, g∈R n×1 is the gravitational moment, Fr ∈R n×1 is the friction torque;

[0020] When the friction torque is a linear friction torque, the friction force of the joint k is usually expressed as:

[0021]

[0022] Among them, F r,k represents the friction force of joint k, F v,k represents the viscous friction parameter of joint k, F c,k represents the Coulomb friction parameter of joint k, and sgn() represents the sign function.

[0023] The model can be expressed as follows after being converted into the minimum parameter set form:

[0024]

[0025] Where: χ represents the kinetic basis parameter, The observation matrix representing the basis parameters.

[0026] Further, the S2 specifically includes:

[0027] When the remainder of the limited Fourier series is a quintic polynomial, the above excitation trajectory takes the following form:

[0028]

[0029] Among them, q k is the position of joint k, t is the time, ω f is the fundamental frequency of the finite Fourier series, L is the order of the priority Fourier series, and are respectively called the i-th order sine and cosine finite Fourier coefficients of joint k, is the coefficient of the fifth-order polynomial of joint k, z∈N + is the number of cycles running at the current moment, T f represents the period of a finite Fourier series;

[0030] The fifth-order polynomial can offset the boundary continuity constraint of the finite Fourier series, and its coefficients can be completely determined by the finite Fourier coefficients and Sure:

[0031]

[0032] So the above finite Fourier series can be expressed by its coefficients and It indicates that a widely used incentive trajectory optimization problem is:

[0033]

[0034] in: Represents the coefficient to be determined and q k,max and q k,min are the maximum and minimum ranges of motion allowed by joint k, and are the velocity and acceleration limits of joint k, respectively, and cond(·) represents the condition number of the matrix.

[0035] Further, the S3 specifically includes:

[0036] Since the excitation trajectory is a finite Fourier series, its frequency domain information is known. First, frequency domain filtering is used to reduce the noise information in the joint velocity and acceleration, and then the collected data of different periods are averaged to enhance the data quality:

[0037]

[0038] Where: R represents the total number of cycles of data collection, x r (j) represents the jth sampling point in the rth cycle, x can represent the joint torque or joint position, velocity, or acceleration, Represents the average value of the jth measurement point.

[0039] The processed data are divided into three data sets: data set A for inertia parameter identification, data set B for load-related friction parameter identification, and data set C for verifying the accuracy of parameter identification.

[0040] Further, the S4 specifically includes:

[0041] Basis parameter χ and standard kinetic parameters The corresponding relationship is as follows:

[0042]

[0043] Among them, F 1 Express Functions for performing parameter substitution and linear recombination;

[0044] In the inertial principal axis system, the three inertial products of the object are all zero. In the inertial principal axis system {O} with the center of mass as the origin, the physical consistency constraint based on positive density can be expressed by the following formula:

[0045]

[0046] in: They represent the moments of inertia of joint k about the x-axis, y-axis, and z-axis, respectively. k represents the mass of joint k;

[0047] The above physical consistency constraints are simplified as follows: In the center-of-mass principal system {O k}Next, remember According to the definition of moment of inertia:

[0048]

[0049] Then the above physical consistency constraint with positive density can be expressed as:

[0050]

[0051] Standard kinetic parameters The inertia and moment of inertia parameters (6n in total) are reparameterized as follows (the reparameterized parameter is η):

[0052]

[0053] Where: The parameters on the left represent standard kinetic parameters The moment of inertia and inertia of the middle joint k, α k ,β k ,γ k They represent the center of mass principal system of joint k {O k} to DH / MDH coordinate system {V k} (depending on the system construction method during dynamic modeling):

[0054] {O k}First rotate around the Z axis by an angle γ k , and then rotate around the Y axis by an angle β k , and finally rotate around the X axis by an angle α k Get {V k}Right now:

[0055]

[0056] in, Indicates {O k} to {V k} is the rotation matrix of .

[0057] So the parameter The different parameters in the parameter η (6n inertia parameters) have the following corresponding relationship:

[0058]

[0059] According to the above formula, we can establish the center of mass principal system {Ok} to the standard kinetic parameters Relationship:

[0060]

[0061] then:

[0062] Consider the maximum material density on joint k to be ρ m,k , so the joint k can be equivalently considered as a joint with density ρ m,k The constant density object is composed of, for the joint k, the density is less than ρ m,k It can be considered that it consists of a cavity with a density of 0 and a cavity with a density of ρ m,k Objects are composed of mixtures;

[0063] For a constant density ρ m,k , mass is m k The joints k are:

[0064]

[0065] In the above formula, a, b, and c represent any positive numbers. When the integral on the right side is the smallest, the object is an ellipsoid, and its density is ρ m,k The mass is m k , and the ratio of the three polar semi-axes is a:b:c, and the calculation is as follows:

[0066]

[0067] For any a, b, c>0, the above equation becomes The upper half of a plane of the formula, the upper half of the surface formed by the intersection of the upper halves of all planes in the above formula, the surface satisfies: the plane in the above formula is the tangent plane of the surface, and the density upper limit ρ is obtained by solving the surface m,k The constraints formed are as follows:

[0068]

[0069] Consider the radius of the circumscribed sphere on joint k to be r k , then:

[0070]

[0071] Therefore, considering the physical consistency constraints of density upper and lower limits and spatial distribution, the parameter η of the center-of-mass principal system {O} is expressed as follows:

[0072]

[0073] Further, the S5 specifically includes:

[0074] According to the data set A, the parameter η of the center of mass principal system {O} is optimized and solved:

[0075]

[0076] Where: W is the joint weight, and all elements in W are 1 initially;

[0077] Compute the residual:

[0078]

[0079] Where: ε∈R (6m)×1 represents the moment residual;

[0080] According to joints 1 to n, the residual ε is reconstructed as [ε 1 ,…,ε n ], where ε n ∈R m×1 Represents the torque residual of joint n, and updates the weight according to the following formula:

[0081]

[0082]

[0083] W new =[W 1 ,…,W 1 ] T

[0084] Where: C new ∈R n×n represents the new covariance matrix, C old ∈R n×n represents the old covariance matrix, C old Initially, it is the unit matrix. cov() means to find the covariance of the matrix. diag() means to extract the diagonal elements of the matrix. 1 ∈R 1×n Represents the weights of the six joints, and W 1 Stack to get the new weight W new ∈R (mn ) ×1 ;

[0085] The joint parameters are recalculated using the updated weights, and the above process is repeated iteratively until the covariance matrix reaches the following standard:

[0086]

[0087] in, is the tolerance for covariance changes.

[0088] Calculate the standard parameters based on the converged η and basis parameter χ = F 1 (F 2 (η)).

[0089] Further, the S6 specifically includes:

[0090] The observation matrix W is divided into the friction parameter observation matrix and the inertia parameter observation matrix:

[0091]

[0092] Where: Y 2 is the friction parameter corresponding to the observation matrix, Y 1 is the observation matrix corresponding to the non-friction parameters, χ 1 and χ 2 Represents the basic parameter part corresponding to the inertia parameter and friction parameter;

[0093] Extract the joint friction as follows:

[0094] f = τ - Y 1 χ 1

[0095] Where f∈R n×1 Indicates the calculated friction of the joint, and the joint load τ can also be obtained Load :

[0096] τ Load =Y 1 χ 1

[0097] According to the load range, select the data set B1 for preliminary friction identification in data set B:

[0098]

[0099] in: is the load threshold.

[0100] The friction model without considering the load is modeled as follows:

[0101]

[0102]

[0103] Among them, a 6，k a 7，k is the nonlinear friction parameter of joint k, F k is the nonlinear friction force of joint k, sgn() is the sign function, F k ′ is the simplified friction force, where Describes the Coulomb friction phenomenon, Describes the viscous friction phenomenon. Since the temperature increases with the speed, a straight line fit is not used. Describes the Stribeck friction phenomenon;

[0104] The friction parameters were preliminarily identified using the optimization algorithm using data set B1:

[0105]

[0106] in, is the nonlinear friction parameter of the joint, F and F′ are the friction torques calculated according to different joint friction models, λ 1 and λ 2 The weights of the simple and complex friction models are used to avoid the friction model parameters losing their original meaning;

[0107] The load is considered to affect only the Coulomb friction force, that is, only the a in the nonlinear friction model. 1,k :

[0108]

[0109]

[0110] Among them, b 1,k , b 2,k is the load-related friction model parameter, A 1,k For b 1,k 、b 2,k Determine the parameters and replace a in the original friction model 1,k Replace with A 1,k The load-related friction force F can be obtained k ″;

[0111] The nonlinear friction parameters are fixed and the load-dependent friction model is identified using data set B:

[0112]

[0113] in, represents the load-related friction parameter matrix, F″ is the friction force F associated with each joint load k The friction torque obtained.

[0114] Further, the S7 specifically includes:

[0115] The identified friction parameters are fixed and given as a function of load and speed:

[0116] The load-related friction model parameters are fixed and divided into three parts, giving new linear friction parameters:

[0117]

[0118] Among them, F k ″′ is the load-related friction after linearization, ξ 1,k ~ξ 3,k is the new linear friction parameter, friction parameter a 1,k ~a 7,k and b 1,k ~b 2,k is considered a constant here;

[0119] Calculation of joint load τ Load , and then replace the original linear friction part with the new linear load-dependent friction model:

[0120]

[0121] in, and χ 2 ′∈R (3n)×1 To associate friction parameters and their observation matrix with the load after replacement;

[0122] Then, the standard dynamic parameters and basis parameters of the joints are calculated by iterative weighting according to step S5;

[0123] It should be noted that since the parameter changes after each iteration will cause the calculated value of the joint load to change, the joint load needs to be recalculated and the observation matrix of the load-associated friction parameters needs to be updated in each iteration.

[0124] Further, the S8 specifically includes:

[0125] After completing S7, the obtained nonlinear friction parameters and dynamic parameters are used to establish the joint torque prediction model, and the predicted torque is calculated using data set C, which is compared with the actual torque to calculate the torque prediction error value:

[0126]

[0127] Where: ξ is the torque prediction error, τ real is the actual torque of data set C, τ cacu is the calculated torque obtained using the position, velocity, and acceleration of data set C;

[0128] Return to step S6 to iterate, calculate the prediction error of data set C in each iteration, stop iteration when the prediction error converges, and obtain the final inertia parameter and load-associated friction parameter:

[0129]

[0130] Where: new is the error of the latest iteration, ξ oldis the error of the last iteration, is the threshold of error change.

[0131] Another object of the present invention is to provide a robot dynamics parameter identification system based on physical consistency constraints and load-associated friction models based on the robot dynamics parameter identification method based on physical consistency constraints and load-associated friction models, characterized in that the system specifically includes:

[0132] The parameterization processing module establishes the robot dynamic parameter model under the linear friction model based on the Newton-Euler method, the Lagrange method, etc., performs linear parameterization processing on the parameters in the model, and converts the model into a minimum parameter set to obtain the basis parameters and its observation matrix;

[0133] The excitation trajectory design module is connected with the parameterized processing module and designs the excitation trajectory based on the finite Fourier series to meet the physical limit constraints and physical boundary constraints;

[0134] The data processing module is connected to the excitation trajectory design module, runs multiple excitation trajectories, collects joint position, velocity, acceleration, and current information, performs data processing, and divides the data set into three parts;

[0135] The constraint establishment module is connected with the data processing module to establish the upper and lower density constraints and spatial distribution constraints based on the center of mass inertia principal axis coordinate system to obtain a complete physical consistency constraint;

[0136] The parameter acquisition module is connected with the constraint establishment module, and obtains the standard dynamic parameters and basic parameters of the dynamics by using the weighted least square method based on the physical consistency constraint; optimizes and calculates the load-related friction parameters based on the identified inertial parameters; establishes a linearly separated joint torque model based on the load-related friction parameters, and obtains the standard dynamic parameters and basic parameters of the dynamics by using the weighted least square method based on the physical consistency constraint;

[0137] The iteration module is connected with the parameter acquisition module and iteratively identifies the inertia parameters and the load-related friction parameters.

[0138] In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

[0139] First, the present invention improves the expression form of physical consistency constraints and provides a new form of physical consistency constraints based on the upper and lower limits of density and the spatial distribution range, which can make full use of existing information to improve the accuracy of inertial parameter identification.

[0140] The present invention provides a parameter identification method considering a load-related friction model. The load-related friction model used is a broken-line load-friction relationship. In combination with a new physical consistency constraint, inertia parameters and friction parameters are iteratively identified, thereby improving the accuracy of parameter identification.

[0141] Second, the robot dynamics parameter identification method based on physical consistency constraints and load-related friction model in the present invention solves a series of technical problems existing in the prior art in industrial applications and achieves significant technical progress. The following are specific technical problems and technical progress:

[0142] 1) Insufficient accuracy:

[0143] In existing robot dynamics models, due to insufficient consideration of nonlinear factors such as friction, the model accuracy is insufficient, which affects the robot's motion control accuracy.

[0144] The present invention adopts a load-related friction model to accurately identify and compensate for friction, thereby significantly improving the accuracy of the dynamic model.

[0145] 2) Poor adaptability:

[0146] Traditional dynamic models have poor adaptability under different loads and working conditions and cannot maintain high-precision motion control in various complex environments.

[0147] The present invention uses an iterative identification method based on physical consistency constraints to ensure that the model can maintain high accuracy and stability under different loads and working conditions, thereby enhancing the adaptability of the robot.

[0148] 3) Friction modeling is simple:

[0149] Traditional friction models mostly use linear friction models, which cannot accurately describe the complex friction phenomena in practical applications.

[0150] The present invention adopts a load-related nonlinear friction model to more accurately describe the actual friction force and improve the accuracy of the model.

[0151] Significant technological advances achieved:

[0152] 1) Improved accuracy of dynamics model:

[0153] Through the application of load-related friction model and iterative identification method, the identification accuracy of dynamic parameters is greatly improved, and the motion control accuracy of the robot under different loads and working conditions is significantly improved.

[0154] 2) Enhanced adaptability:

[0155] The identification method based on physical consistency constraints enables the dynamic model to maintain high accuracy and stability under different working conditions, enhancing the robot's adaptability in complex environments.

[0156] 3) Improved friction model accuracy:

[0157] The load-related nonlinear friction model is used to more accurately describe the friction force in practical applications and improve the accuracy of the dynamic model.

[0158] 4) Significant industrial application effects:

[0159] In applications such as industrial manufacturing and medical surgery, the accuracy and stability of robot motion control have been significantly improved, and work efficiency and safety have been greatly improved.

[0160] 5) Iterative optimization method:

[0161] Through iterative identification and error analysis, the dynamic parameters and friction parameters are continuously optimized to ensure the accuracy and stability of the model, thus achieving a technological breakthrough.

[0162] In summary, the technical solution of the present invention not only solves the problems of the prior art, but also achieves significant technological progress, improves the accuracy and adaptability of robot dynamic parameter identification, optimizes the data processing method, improves the accuracy of the friction model, and provides a more reliable and efficient solution for robot applications in industrial and medical fields.

[0163] Second, as auxiliary evidence of the inventiveness of the claims of the present invention, it is also reflected in the following important aspects:

[0164] (1) The expected benefits and commercial value of the technical solution of the present invention after transformation are:

[0165] The present invention provides a new and perfect form of physical consistency constraint for inertial parameters, and combines the load-related friction model to obtain a technical route for accurate identification of dynamic parameters. It can be used for high-precision dynamic parameter identification of the robot body, and provides a theoretical and implementation basis for the robot's trajectory control and external force perception. In view of the in-depth application of robots in more and more fields, the present invention has huge expected benefits and commercial value.

[0166] (2) The technical solution of the present invention solves a technical problem that people have been eager to solve but have never been able to solve successfully:

[0167] Traditional physical geometric constraints only consider constraints where the density is greater than zero, and cannot effectively utilize the prior conditions for specific density distribution and spatial distribution. The technical solution of the present invention solves a technical problem that people have always been eager to solve but have never been successful: a perfect physical consistency constraint based on density upper and lower limits and spatial distribution.

[0168] Third, the parameters, algorithms, mathematical models, etc. of the present invention solve existing technical problems and technological progress.

[0169] Existing technical problems:

[0170] 1) Inaccurate friction model: The traditional friction model fails to fully consider the load-related friction parameters, resulting in the model not being consistent with the actual situation and affecting the identification of dynamic parameters.

[0171] 2) Insufficient physical consistency constraints: Existing methods fail to fully consider physical consistency constraints, resulting in inconsistency between parameter identification results and actual physical properties, which affects the practical application of the model.

[0172] Technological advancements:

[0173] 1) Load-related friction model: By introducing load-related friction parameters, the friction model is optimized to make it more consistent with actual working conditions and improve the accuracy of dynamic parameter identification.

[0174] 2) Physical consistency constraints: Based on the center of mass inertia principal axis coordinate system, upper and lower density constraints and spatial distribution constraints are established to improve the physical consistency constraints, making the parameter identification results more consistent with the actual physical properties and improving the practical application value of the model.

[0175] 3) Iterative optimization algorithm: The method of iterative identification of inertia parameters and load-related friction parameters is adopted to continuously optimize the parameter identification results and improve the identification accuracy and stability.

[0176] Significant technological advancement

[0177] 1) Improved model accuracy and reliability: The accuracy and reliability of the robot dynamics model are significantly improved by introducing a comprehensive dynamics parameter model and a load-related friction model.

[0178] 2) Optimized the parameter identification process: Through data processing and iterative identification methods, the efficiency and accuracy of parameter identification are significantly improved.

[0179] 3) Enhanced practicability of the model: By introducing physical consistency constraints, the parameter identification results are more consistent with the actual physical properties, which enhances the operability and practicability of the model in practical applications.

[0180] 4) Solved the key problems in the existing technology: effectively solved the key problems in the existing technology such as high model complexity, inaccurate friction model, and large data noise interference, and promoted the development of robot dynamic parameter identification technology.

[0181] This method systematically solves the key problems in the existing technology by integrating a variety of advanced parameters, algorithms and mathematical models, and has achieved significant technological progress. It provides a more accurate, reliable and efficient solution for the identification of robot dynamic parameters, and has important theoretical significance and practical application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0182] Figure 1 It is a flow chart of the robot dynamic parameter identification method based on the physical consistency constraint and load-related friction model provided by the present invention;

[0183] Figure 2 It is a flow chart of iterative identification of load-related friction parameters and inertia parameters according to three data sets A, B, and B provided by the present invention;

[0184] Figure 3 It is a schematic diagram showing the variation of the friction force of some joints with the joint loads identified on the collaborative robot according to the method provided by the present invention;

[0185] Figure 4 It is a prediction diagram of joint torque after identification on a collaborative robot according to the method provided by the present invention;

[0186] Figure 5 It is a schematic diagram of the structure of a robot dynamic parameter identification system based on physical consistency constraints and load-related friction model provided by the present invention;

[0187] Figure 6 It is the comparison result of torque prediction error after parameter identification under three different constraints. DETAILED DESCRIPTION

[0188] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0189] The following are two industrial application examples of the robot dynamic parameter identification method based on physical consistency constraints and load-related friction model:

[0190] Example 1: Industrial Manufacturing Robot

[0191] In modern industrial manufacturing, robots are widely used in high-precision and high-repeatability tasks such as assembly, welding, and spraying. By using the above method to identify the robot's dynamic parameters, the robot's motion control accuracy and stability under different working conditions can be greatly improved.

[0192] Specific application steps:

[0193] 1) Initial modeling: Use the Newton-Euler method and Lagrange method to establish the robot dynamics model, perform linear parameterization on the robot, and obtain the basis parameters and its observation matrix.

[0194] 2) Excitation trajectory design: Design an excitation trajectory that meets the physical limit constraints and physical boundary constraints to ensure that the robot's motion trajectory is within a reasonable range.

[0195] 3) Data acquisition and processing: Run multiple excitation trajectories to collect information such as joint position, velocity, acceleration, current, etc., and perform frequency domain filtering and averaging to ensure data quality.

[0196] 4) Parameter identification and optimization: Based on physical consistency constraints, the dynamic parameters and friction parameters are identified through the weighted least squares method to optimize the friction model of the robot under different loads.

[0197] 5) Iterative verification: Through iterative identification and error analysis, the dynamic parameters and friction parameters are continuously optimized, ultimately improving the accuracy and reliability of robot motion control.

[0198] Effect:

[0199] - Improve the accuracy and stability of robot motion control.

[0200] -Reduce the impact of friction on the robot and improve work efficiency.

[0201] -Improve the robot's adaptability under different loads and working conditions.

[0202] Example 2: Medical surgical robot

[0203] In the medical field, surgical robots are widely used in minimally invasive surgery and precision operations. By using the above method to identify the dynamic parameters of surgical robots, the accuracy and safety of surgical operations can be greatly improved.

[0204] Specific application steps:

[0205] 1) Initial modeling: According to the characteristics of the surgical robot joints, the Newton-Euler method and Lagrangian method are used to establish a dynamic model, and the model is linearly parameterized to obtain the basis parameters and its observation matrix.

[0206] 2) Incentive trajectory design: Design an incentive trajectory that meets the surgical operation constraints to ensure the accuracy of the robot's motion trajectory during the operation.

[0207] 3) Data acquisition and processing: Run multiple excitation trajectories to collect information such as robot joint position, velocity, acceleration, current, etc., perform frequency domain filtering and averaging processing to ensure data quality.

[0208] 4) Parameter identification and optimization: Based on physical consistency constraints, the dynamic parameters and friction parameters are identified through the weighted least squares method to optimize the friction model of the surgical robot under different operations.

[0209] 5) Iterative verification: Through iterative identification and error analysis, the dynamic parameters and friction parameters are continuously optimized, ultimately improving the accuracy and safety of surgical robot operations.

[0210] Effect:

[0211] -Improve the accuracy and stability of surgical robot operations.

[0212] -Reduce the impact of friction on surgical operations and improve the safety of surgery.

[0213] -Improve the adaptability of surgical robots under different operating conditions.

[0214] Through the above two embodiments, the robot dynamic parameter identification method based on physical consistency constraints and load-related friction model has been demonstrated to have wide application prospects in industrial manufacturing and medical surgery. This method not only improves the accuracy and stability of robot operation, but also enhances its adaptability under different working conditions, thus providing a more reliable and efficient solution for the industrial and medical fields.

[0215] like Figure 1 As shown, an embodiment of the present invention provides a robot dynamic parameter identification method based on physical consistency constraints and load-related friction model, the method comprising:

[0216] S1. Based on Newton-Euler method, Lagrange method, etc., a robot dynamic parameter model under a linear friction model is established, the parameters in the model are linearly parameterized, and the model is converted into a minimum parameter set to obtain the basis parameters and its observation matrix;

[0217] S2: Design the excitation trajectory based on the finite Fourier series to meet the physical limit constraints and physical boundary constraints;

[0218] S3: Run multiple excitation trajectories, collect joint position, velocity, acceleration, and current information, perform data processing, and divide the data set into three parts;

[0219] S4: Based on the center-of-mass inertia principal axis coordinate system, density upper and lower limit constraints and spatial distribution constraints are established to obtain perfect physical consistency constraints;

[0220] S5: Based on the physical consistency constraints, the weighted least square method is used to obtain the standard kinetic parameters and basis parameters of the kinetics;

[0221] S6: Optimization calculation of load-related friction parameters based on identified inertia parameters;

[0222] S7: A linearly separated joint torque model is established based on load-related friction parameters, and the weighted least squares method is used to obtain the standard dynamic parameters and basis parameters based on physical consistency constraints;

[0223] S8: Iterative identification of inertia parameters and load-related friction parameters.

[0224] The S1 specifically includes:

[0225] For a serial robot with n joints, the above dynamic parameter model can be generalized as:

[0226]

[0227] Where: τ∈R n×1 represents the joint torque, Respectively represent the angle, angular velocity and angular acceleration of the robot joint, M∈R n×n is the inertia matrix of the robot, C∈R n×n represents the centrifugal force matrix, g∈R n×1 is the gravitational moment, F r ∈R n×1 is the friction torque;

[0228] When the friction torque is a linear friction torque, the friction force of the joint k is usually expressed as:

[0229]

[0230] Among them, F r,k represents the friction force of joint k, F v,k represents the viscous friction parameter of joint k, F c,k represents the Coulomb friction parameter of joint k.

[0231] The model can be expressed as follows after being converted into the minimum parameter set form:

[0232]

[0233] Where: χ represents the kinetic basis parameter, The observation matrix representing the basis parameters.

[0234] The S2 specifically includes:

[0235] When the remainder of the limited Fourier series is a quintic polynomial, the above excitation trajectory takes the following form:

[0236]

[0237] Among them, q k is the position of joint k, t is the time, ω fis the fundamental frequency of the finite Fourier series, L is the order of the priority Fourier series, and are respectively called the i-th order sine and cosine finite Fourier coefficients of joint k, is the coefficient of the fifth-order polynomial of joint k, z∈N + is the number of cycles running at the current moment, T f represents the period of a finite Fourier series;

[0238] The fifth-order polynomial can offset the boundary continuity constraint of the finite Fourier series, and its coefficients can be completely determined by the finite Fourier coefficients and Sure:

[0239]

[0240] So the above finite Fourier series can be expressed by its coefficients and It indicates that a widely used incentive trajectory optimization problem is:

[0241]

[0242] in: Represents the coefficient to be determined and q k,max and q k,min are the maximum and minimum ranges of motion allowed by joint k, and are the velocity and acceleration limits of joint k, respectively, and cond(·) represents the condition number of the matrix.

[0243] The S3 specifically includes:

[0244] Since the excitation trajectory is a finite Fourier series, its frequency domain information is known. First, frequency domain filtering is used to reduce the noise information in the joint velocity and acceleration, and then the collected data of different periods are averaged to enhance the data quality:

[0245]

[0246] Where: R represents the total number of cycles of data collection, x r (j) represents the jth sampling point in the rth cycle, x can represent the joint torque or joint position, velocity, or acceleration, represents the average value of the jth measurement point.

[0247] The processed data are divided into three data sets: data set A for inertia parameter identification, data set B for load-related friction parameter identification, and data set C for verifying the accuracy of parameter identification.

[0248] The S4 specifically includes:

[0249] Basis parameter χ and standard kinetic parameters The corresponding relationship is as follows:

[0250]

[0251] Among them, F 1 Express Functions for performing parameter substitution and linear recombination;

[0252] In the inertial principal axis system, the three inertial products of the object are all zero. In the inertial principal axis system {O} with the center of mass as the origin, the physical consistency constraint based on positive density can be expressed by the following formula:

[0253]

[0254] in: They represent the moments of inertia of joint k about the x-axis, y-axis, and z-axis, respectively. k represents the mass of joint k;

[0255] The above physical consistency constraints are simplified as follows: In the center-of-mass principal system {O k}Next, remember According to the definition of moment of inertia:

[0256]

[0257] Then the above physical consistency constraint with positive density can be expressed as:

[0258]

[0259] Standard kinetic parameters The inertia and moment of inertia parameters (6n in total) are reparameterized as follows (the reparameterized parameter is η):

[0260]

[0261] Where: The parameters on the left represent standard kinetic parameters The moment of inertia and inertia of the middle joint k, α k ,β k ,γ k They represent the center of mass principal system of joint k {O k} to DH / MDH coordinate system {V k} (depending on the system construction method during dynamic modeling):

[0262] {O k}First rotate around the Z axis by an angle γ k , and then rotate around the Y axis by an angle β k , and finally rotate around the X axis by an angle α k Get {V k}Right now:

[0263]

[0264] in, Indicates {O k} to {V k} is the rotation matrix of .

[0265] So the parameter The different parameters in the parameter η (6n inertia parameters) have the following corresponding relationship:

[0266]

[0267] According to the above formula, we can establish the center of mass principal system {O k} to the standard kinetic parameters Relationship:

[0268]

[0269] then:

[0270] Consider the maximum material density on joint k to be ρ m,k , so the joint k can be equivalently considered as a joint with density ρ m,k The constant density object is composed of, for the joint k, the density is less than ρ m,k It can be considered that it consists of a cavity with a density of 0 and a cavity with a density of ρ m,k Objects are composed of mixtures;

[0271] For a constant density ρ m,k , mass is m k The joints k are:

[0272]

[0273] In the above formula, a, b, and c represent any positive numbers. When the integral on the right side is the smallest, the object is an ellipsoid, and its density is ρ m,k The mass is m k , and the ratio of the three polar semi-axes is a:b:c, and the calculation is as follows:

[0274]

[0275] For any a, b, c>0, the above equation becomes The upper half of a plane of the formula, the upper half of the surface formed by the intersection of the upper halves of all planes in the above formula, the surface satisfies: the plane in the above formula is the tangent plane of the surface, and the density upper limit ρ is obtained by solving the surface m,k The constraints formed are as follows:

[0276]

[0277] Consider the radius of the circumscribed sphere on joint k to be r k , then:

[0278]

[0279] Therefore, considering the physical consistency constraints of density upper and lower limits and spatial distribution, the parameter η of the center-of-mass principal system {O} is expressed as follows:

[0280]

[0281] The S5 specifically includes:

[0282] According to the data set A, the parameter η of the center of mass principal system {O} is optimized and solved:

[0283]

[0284] Where: W is the joint weight, and all elements in W are 1 initially;

[0285] Compute the residual:

[0286]

[0287] Where: ε∈R (6m)×1 represents the moment residual;

[0288] According to joints 1 to n, the residual ε is reconstructed as [ε 1 ,…,ε n ], where ε n ∈R m×1 Represents the torque residual of joint n, and updates the weight according to the following formula:

[0289]

[0290]

[0291] W new =[W 1 ,…,W 1 ] T

[0292] Where: C new ∈R n×nrepresents the new covariance matrix, C old ∈R n×n represents the old covariance matrix, C old Initially, it is the unit matrix. cov() means to find the covariance of the matrix. diag() means to extract the diagonal elements of the matrix. 1 ∈R 1×n Represents the weights of the six joints, and W 1 Stack to get the new weight W new ∈R (mn)×1 ;

[0293] The joint parameters are recalculated using the updated weights, and the above process is repeated iteratively until the covariance matrix reaches the following standard:

[0294]

[0295] in, is the tolerance for covariance changes.

[0296] Calculate the standard parameters based on the converged η and basis parameter χ = F 1 (F 2 (η)).

[0297] The S6 specifically includes:

[0298] The observation matrix W is divided into the friction parameter observation matrix and the inertia parameter observation matrix:

[0299]

[0300] Where: Y 2 is the friction parameter corresponding to the observation matrix, Y 1 is the observation matrix corresponding to the non-friction parameters, χ 1 and χ 2 Represents the basic parameter part corresponding to the inertia parameter and friction parameter;

[0301] Extract the joint friction as follows:

[0302] f = τ - Y 1 χ 1

[0303] Where f∈R n×1 Indicates the calculated friction of the joint, and the joint load τ can also be obtained Load :

[0304] τ Load =Y 1 χ 1

[0305] According to the load range, select the data set B1 for preliminary friction identification in data set B:

[0306]

[0307] in: is the load threshold.

[0308] The friction model without considering the load is modeled as follows:

[0309]

[0310]

[0311] Among them, a 6，k a 7，k is the nonlinear friction parameter of joint k, F k is the nonlinear friction force of joint k, sgn() is the sign function, F k ′ is the simplified friction force, where Describes the Coulomb friction phenomenon, Describes the viscous friction phenomenon. Since the temperature increases with the speed, a straight line fit is not used. Describes the Stribeck friction phenomenon;

[0312] The friction parameters were preliminarily identified using the optimization algorithm using data set B1:

[0313]

[0314] in, is the nonlinear friction parameter of the joint, F and F′ are the friction torques calculated according to different joint friction models, λ 1 and λ 2 The weights of the simple and complex friction models are used to avoid the friction model parameters losing their original meaning;

[0315] The load is considered to affect only the Coulomb friction force, that is, only the a in the nonlinear friction model. 1,k :

[0316]

[0317]

[0318] Among them, b 1,k , b 2,k is the load-related friction model parameter, A 1,k For b 1,k 、b 2,k Determine the parameters and replace a in the original friction model 1,k Replace with A1,k The load-related friction force F can be obtained k ″;

[0319] The nonlinear friction parameters are fixed and the load-dependent friction model is identified using data set B:

[0320]

[0321] in, represents the load-related friction parameter matrix, F″ is the friction force F associated with each joint load k The friction torque obtained.

[0322] like Figure 3 The figure shows the schematic diagram of the friction force of joints 3 and 5 changing with the joint load during the iteration process.

[0323] The S7 specifically includes:

[0324] The identified friction parameters are fixed and given as a function of load and speed:

[0325] The load-related friction model parameters are fixed and divided into three parts, giving new linear friction parameters:

[0326]

[0327] Among them, F k ″′ is the load-related friction after linearization, ξ 1,k ~ξ 3,k is the new linear friction parameter, friction parameter a 1,k ~a 7,k and b 1,k ~b 2,k is considered a constant here;

[0328] Calculation of joint load τ Load , and then replace the original linear friction part with the new linear load-dependent friction model:

[0329]

[0330] in, and χ 2 ′∈R (3n)×1 To associate friction parameters and their observation matrix with the load after replacement;

[0331] Then, the standard dynamic parameters and basis parameters of the joints are calculated by iterative weighting according to step S5;

[0332] It should be noted that since the parameter changes after each iteration will cause the calculated value of the joint load to change, the joint load needs to be recalculated and the observation matrix of the load-associated friction parameters needs to be updated in each iteration.

[0333] Further, the S8 specifically includes:

[0334] After completing S7, the obtained nonlinear friction parameters and dynamic parameters are used to establish the joint torque prediction model, and the predicted torque is calculated using data set C, which is compared with the actual torque to calculate the torque prediction error value:

[0335]

[0336] Where: ξ is the torque prediction error, τ real is the actual torque of data set C, τ cacu is the calculated torque obtained using the position, velocity, and acceleration of data set C;

[0337] Return to step S6 to iterate, calculate the prediction error of data set C in each iteration, stop iteration when the prediction error converges, and obtain the final inertia parameter and load-associated friction parameter:

[0338]

[0339] Where: new is the error of the latest iteration, ξ old is the error of the last iteration, is the threshold of error change.

[0340] like Figure 2 As shown in the figure, the identification process of S5 to S8 is completed through multiple loop iterations, and the final identified parameters realize the torque prediction of the joint as shown in Figure 4 shown.

[0341] like Figure 5 As shown, an embodiment of the present invention provides a robot dynamics parameter identification system based on physical consistency constraints and load-associated friction models based on the robot dynamics parameter identification method based on physical consistency constraints and load-associated friction models, and the system specifically includes:

[0342] The parameterization processing module establishes the robot dynamic parameter model under the linear friction model based on the Newton-Euler method, the Lagrange method, etc., performs linear parameterization processing on the parameters in the model, and converts the model into a minimum parameter set to obtain the basis parameters and its observation matrix;

[0343] The excitation trajectory design module is connected with the parameterized processing module and designs the excitation trajectory based on the finite Fourier series to meet the physical limit constraints and physical boundary constraints;

[0344] The data processing module is connected to the excitation trajectory design module, runs multiple excitation trajectories, collects joint position, velocity, acceleration, and current information, performs data processing, and divides the data set into three parts;

[0345] The constraint establishment module is connected with the data processing module to establish the upper and lower density constraints and spatial distribution constraints based on the center of mass inertia principal axis coordinate system to obtain a complete physical consistency constraint;

[0346] The parameter acquisition module is connected with the constraint establishment module, and obtains the standard dynamic parameters and basic parameters of the dynamics by using the weighted least square method based on the physical consistency constraint; optimizes and calculates the load-related friction parameters based on the identified inertial parameters; establishes a linearly separated joint torque model based on the load-related friction parameters, and obtains the standard dynamic parameters and basic parameters of the dynamics by using the weighted least square method based on the physical consistency constraint;

[0347] The iteration module is connected with the parameter acquisition module and iteratively identifies the inertia parameters and the load-related friction parameters.

[0348] like Figure 3 The figure shows the actual image of the friction force separated by the identification method adopted by the present invention with respect to the load change. It can be seen from the figure that the friction force is a function of the load change. Therefore, considering the load-related friction force model can effectively improve the accuracy of the friction model.

[0349] like Figure 4 The figure shows a schematic diagram of the prediction of the joint torque of the robot arm in the example of the present invention. The obtained joint torque prediction NRMSRE errors are all within 5%, and the obtained joint torque prediction model has a high accuracy.

[0350] like Figure 6 The figure shows the prediction accuracy of joint parameter identification under no constraints, traditional physical consistency constraints and the perfect physical consistency constraints proposed in this paper. The friction models are all linear friction models. 100 random point data are selected from the same database for parameter identification each time. A total of 500 identifications are performed to analyze the distribution results of the second norm of the joint torque prediction error. From the results, it can be seen that the perfect physical consistency constraint proposed in this paper has the lowest mean and median, and the distribution standard deviation is similar to the traditional physical consistency constraint, which is lower than the unconstrained variance. This shows that the physical consistency constraint method proposed in this invention has higher accuracy and better stability.

[0351] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. It can be understood by a person of ordinary skill in the art that the above-mentioned devices and methods can be implemented using computer executable instructions and / or contained in a processor control code, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. Such code is provided on the carrier medium. The device and its modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, and can also be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0352] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.

Claims

1. A robot dynamic parameter identification method based on physical consistency constraints and load-related friction model, characterized in that: The method includes: S1. Based on the Newton-Euler method and the Lagrangian method, the robot dynamic parameter model under the linear friction model is established, the parameters in the model are linearly parameterized, and the model is converted into a minimum parameter set to obtain the basis parameters and its observation matrix; S2: Design the excitation trajectory based on the finite Fourier series to meet the physical limit constraints and physical boundary constraints; S3: Run multiple excitation trajectories, collect joint position, velocity, acceleration, and current information, perform data processing, and divide the data set into three parts; S4: Based on the center-of-mass inertia principal axis coordinate system, density upper and lower limit constraints and spatial distribution constraints are established to obtain perfect physical consistency constraints; S5: Based on the physical consistency constraints, the weighted least square method is used to obtain the standard kinetic parameters and basis parameters of the kinetics; S6: Optimization calculation of load-related friction parameters based on identified inertia parameters; S7: A linearly separated joint torque model is established based on load-related friction parameters, and the weighted least squares method is used to obtain the standard dynamic parameters and basis parameters based on physical consistency constraints; S8: Iterative identification of inertia parameters and load-related friction parameters.

2. The robot dynamic parameter identification method based on physical consistency constraint and load-related friction model according to claim 1 is characterized in that: The S1 specifically includes: For a serial robot with n joints, the above dynamic parameter model can be generalized as: Where: τ∈R n×1 represents the joint torque, Respectively represent the angle, angular velocity and angular acceleration of the robot joint, M∈R n×n is the inertia matrix of the robot, C∈R n×n represents the centrifugal force matrix, g∈R n×1 is the gravitational moment, F r ∈R n×1 is the friction torque; When the friction torque is a linear friction torque, the friction force of joint k is expressed as: Among them, F r,k represents the friction force of joint k, F v,k represents the viscous friction parameter of joint k, F c,k represents the Coulomb friction parameter of joint k; The model can be expressed as follows after being converted into the minimum parameter set form: Where: χ represents the kinetic basis parameter, The observation matrix representing the basis parameters.

3. The robot dynamic parameter identification method based on physical consistency constraint and load-related friction model as claimed in claim 2, characterized in that: The S2 specifically includes: When the remainder of the limited Fourier series is a quintic polynomial, the above excitation trajectory takes the following form: Among them, q k is the position of joint k, t is the time, ω f is the fundamental frequency of the finite Fourier series, L is the order of the finite Fourier series, and are respectively called the i-th order sine and cosine finite Fourier coefficients of joint k, is the coefficient of the fifth-order polynomial of joint k, z∈N + is the number of cycles running at the current moment, T f represents the period of a finite Fourier series; The fifth-order polynomial can offset the boundary continuity constraint of the finite Fourier series, and its coefficients can be completely determined by the finite Fourier coefficients and Sure: So the above finite Fourier series can be expressed by its coefficients and It indicates that a widely used incentive trajectory optimization problem is: in: Represents the coefficient to be determined and q k,max and q k,min are the maximum and minimum ranges of motion allowed by joint k, and are the velocity and acceleration limits of joint k respectively, and cond(·) represents the function for finding the matrix condition number.

4. The robot dynamic parameter identification method based on physical consistency constraint and load-related friction model as claimed in claim 3, characterized in that: The S3 specifically includes: Since the excitation trajectory is a finite Fourier series, its frequency domain information is known. First, frequency domain filtering is used to reduce the noise information in the joint velocity and acceleration, and then the collected data of different periods are averaged to enhance the data quality: Where: N represents the total number of cycles of data collection, x r (j) represents the jth sampling point in the rth cycle, x can represent the joint torque or joint position, velocity, or acceleration, represents the average value of the jth measurement point; The processed data are divided into three data sets: data set A for inertia parameter identification, data set B for load-related friction parameter identification, and data set C for verifying the accuracy of parameter identification.

5. The robot dynamic parameter identification method based on physical consistency constraint and load-related friction model as claimed in claim 4, characterized in that: The S4 specifically includes: Basis parameter χ and standard kinetic parameters The corresponding relationship is as follows: Among them, F1 represents Functions for performing parameter substitution and linear recombination; In the inertial principal axis system, the three inertial products of the object are all zero. In the inertial principal axis system {O} with the center of mass as the origin, the physical consistency constraint based on positive density can be expressed by the following formula: in: They represent the moment of inertia of joint k about the x-axis, y-axis and z-axis in {O}, m k represents the mass of joint k; The above physical consistency constraints are simplified as follows: In the center-of-mass principal system {O k }Next, remember According to the definition of moment of inertia: Then the above physical consistency constraint with positive density can be expressed as: Standard kinetic parameters The inertia and moment of inertia parameters in are reparameterized as follows: Among them: There are 6n inertia moment parameters in total, the re-parameterized parameter is η, and the left side parameters represent the standard dynamic parameters The moment of inertia and product of inertia of joint k, α k ,β k ,γ k They represent the center of mass principal system of joint k {O k } to DH / MDH coordinate system {V k }Three rotation angles: {O k }First rotate angle γ around the Z axis k , and then rotate around the Y axis by an angle β k , and finally rotate around the X axis by an angle α k Get {V k }Right now: in, Indicates {O k } to {V k }'s rotation matrix; So the parameter The 6n different inertia parameters in the parameter η have the following corresponding relationship: According to the above formula, we can establish the center of mass principal system {O k } to the standard kinetic parameters Relationship: then: Consider the maximum material density on joint k to be ρ m,k , so the joint k can be equivalently considered as a joint with density ρ m,k The constant density object is composed of, for the joint k, the density is less than ρ m,k It can be considered that it consists of a cavity with a density of 0 and a cavity with a density of ρ m,k Objects are composed of mixtures; For a constant density ρ m,k , mass is m k The joints k are: In the above formula, a, b, and c represent any positive numbers. When the integral on the right side is the smallest, the object is an ellipsoid, and its density is ρ m,k The mass is m k , and the ratio of the three polar semi-axes is a:b:c, and the calculation is based on the ellipsoid: For any a, b, c>0, the above equation becomes The upper half of a plane of the formula, the upper half of the surface formed by the intersection of the upper halves of all planes in the above formula, the surface satisfies: the plane in the above formula is the tangent plane of the surface, and the density upper limit ρ is obtained by solving the surface m,k The constraints formed are as follows: Consider the radius of the circumscribed sphere on joint k to be r k , then: Therefore, considering the physical consistency constraints of density upper and lower limits and spatial distribution, the parameter η of the center-of-mass principal system {O} is expressed as follows:

6. The robot dynamic parameter identification method based on physical consistency constraint and load-related friction model as claimed in claim 5, characterized in that: The S5 specifically includes: According to the data set A, the parameter η of the center of mass principal system {O} is optimized and solved: Where: W is the joint weight, and all elements in W are 1 initially; Compute the residual: Where: ε∈R (6m)×1 represents the moment residual; According to joints 1 to n, the residual ε is reconstructed as [ε1,…,ε n ], where ε n ∈R m×1 Represents the torque residual of joint n, and updates the weight according to the following formula: W new =[W1,…,W1] T Where: C new ∈R n×n represents the new covariance matrix, C old ∈R n×n represents the old covariance matrix, C old Initially, it is the unit matrix. cov() means to find the covariance of the matrix. diag() means to extract the diagonal elements of the matrix. W1∈R 1×n Represents the weights of the six joints, stacking W1 to get the new weight W new ∈R (mn)×1 ; The joint parameters are recalculated using the updated weights, and the above process is repeated iteratively until the covariance matrix reaches the following standard: in, is the tolerance for covariance changes; Calculate the standard parameters based on the converged η And basis parameters χ = F1(F2(η)).

7. The robot dynamic parameter identification method based on physical consistency constraint and load-related friction model as claimed in claim 6, characterized in that: The S6 specifically includes: The observation matrix W is divided into the friction parameter observation matrix and the inertia parameter observation matrix: Among them: Y2 is the observation matrix corresponding to the friction parameters, Y1 is the observation matrix corresponding to the non-friction parameters, χ1 and χ2 represent the basis parameter parts corresponding to the inertia parameters and friction parameters; Extract the joint friction as follows: f=τ-Y1χ1 Where f∈R n×1 Indicates the calculated friction of the joint, and the joint load τ can also be obtained Load : t Load =Y1x1 According to the load range, select the data set B1 for preliminary friction identification in data set B: in: is the load threshold; The friction model without considering the load is modeled as follows: Among them, a 1,k ~a 7,k is the nonlinear friction parameter of joint k, F k is the nonlinear friction force of joint k, sgn() is the sign function, F k ′ is the simplified friction force, where Describes the Coulomb friction phenomenon, Describes the viscous friction phenomenon. Since the temperature increases with the speed, a straight line fit is not used. Describes the Stribeck friction phenomenon; The friction parameters were preliminarily identified using the optimization algorithm using data set B1: in, is the nonlinear friction parameter of the joint, F and F′ are the friction torques calculated according to different joint friction models, λ1 and λ2 are the weights of the simple and complex friction models, so as to avoid the friction model parameters losing their original meaning; The load is considered to affect only the Coulomb friction force, that is, only the a in the nonlinear friction model. 1,k : Among them, b 1,k , b 2,k is the load-related friction model parameter, A 1,k For b 1,k , b 2,k Determine the parameters and replace a in the original friction model 1,k Replace with A 1,k The load-related friction force F can be obtained k ″; The nonlinear friction parameters are fixed and the load-dependent friction model is identified using data set B: in, represents the load-related friction parameter matrix, F″ is the friction force F associated with each joint load k The friction torque obtained.

8. The robot dynamic parameter identification method based on physical consistency constraint and load-related friction model as claimed in claim 7, characterized in that: The S7 specifically includes: The identified friction parameters are fixed and given as a function of load and speed: The load-related friction model parameters are fixed and divided into three parts, giving new linear friction parameters: Among them, F k ″′ is the load-related friction after linearization, ξ 1,k ~ξ 3,k is the new linear friction parameter, friction parameter a 1,k ~a 7,k and b 1,k ~b 2,k is considered a constant here; Calculation of joint load τ Load , and then replace the original linear friction part with the new linear load-dependent friction model: Among them, χ2′∈R (3n)×1 and To associate friction parameters and their observation matrix with the load after replacement; Then, the standard dynamic parameters and basis parameters of the joints are calculated by iterative weighting according to step S5; It should be noted that since the parameter changes after each iteration will cause the calculated value of the joint load to change, the joint load needs to be recalculated and the observation matrix of the load-associated friction parameters needs to be updated in each iteration.

9. The robot dynamic parameter identification method based on physical consistency constraint and load-related friction model as claimed in claim 8, characterized in that: The S8 specifically includes: After completing S7, the obtained nonlinear friction parameters and dynamic parameters are used to establish the joint torque prediction model, and the predicted torque is calculated using data set C, which is compared with the actual torque to calculate the torque prediction error value: Where: ξ is the torque prediction error, τ real is the actual torque of data set C, τ cacu is the calculated torque obtained using the position, velocity, and acceleration of data set C; Return to step S6 to iterate, calculate the prediction error of data set C in each iteration, stop iteration when the prediction error converges, and obtain the final inertia parameter and load-associated friction parameter: Where: new is the error of the latest iteration, ξ old is the error of the last iteration, is the threshold of error change.

10. A robot dynamic parameter identification system based on the method according to any one of claims 1 to 9, based on physical consistency constraints and load-related friction model, characterized in that: The system specifically includes: The parameterization processing module establishes the robot dynamic parameter model under the linear friction model based on the Newton-Euler method, the Lagrange method, etc., performs linear parameterization processing on the parameters in the model, and converts the model into a minimum parameter set to obtain the basis parameters and its observation matrix; The excitation trajectory design module is connected with the parameterized processing module and designs the excitation trajectory based on the finite Fourier series to meet the physical limit constraints and physical boundary constraints; The data processing module is connected to the excitation trajectory design module, runs multiple excitation trajectories, collects joint position, velocity, acceleration, and current information, performs data processing, and divides the data set into three parts; The constraint establishment module is connected with the data processing module to establish the upper and lower density constraints and spatial distribution constraints based on the center of mass inertia principal axis coordinate system to obtain a complete physical consistency constraint; The parameter acquisition module is connected with the constraint establishment module, and obtains the standard dynamic parameters and basic parameters of the dynamics by using the weighted least square method based on the physical consistency constraint; optimizes and calculates the load-related friction parameters based on the identified inertial parameters; establishes a linearly separated joint torque model based on the load-related friction parameters, and obtains the standard dynamic parameters and basic parameters of the dynamics by using the weighted least square method based on the physical consistency constraint; The iteration module is connected with the parameter acquisition module and iteratively identifies the inertia parameters and the load-related friction parameters.

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