A method for identifying dynamics parameters of an articulated industrial robot

Abstract

The application discloses a kind of industrial robot dynamics identification method with nonlinear viscous friction, it is related to robot dynamics modeling and control field.The method is considered in robot modeling, nonlinear term of viscous friction, different from traditional coulomb viscous friction model, its content includes robot friction model construction, excitation trajectory model selection, parameter optimization and dynamics parameter solving.In excitation trajectory selection optimization, the trajectory model of five order Fourier series and five polynomials is selected, and the genetic algorithm with penalty function is used to optimize the parameters of excitation trajectory;In solving process, based on interior point method, iteration fitting is carried out, and complete dynamics parameters of robot are obtained.The friction model considered in the application has higher modeling accuracy, and the problem of system jitter at start and end position is overcome, the efficiency and accuracy of robot dynamics parameter identification are improved, and can be used in robot mobile handling, polishing and polishing and heavy load hydraulic industrial scene.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of robot dynamics modeling and control, in particular to a joint type industrial robot dynamics parameter identification method. BACKGROUND

[0002] With the development of industrial robots towards high speed, high precision and high load capacity, higher and higher requirements are put forward for the control precision of the robot. Industrial robots are nonlinear, strongly coupled and uncertain systems, and there is nonlinear friction between the joints. Therefore, in order to realize accurate positioning and tracking operation of the industrial robot, the dynamics parameters of the robot need to be estimated in real time so as to enable high-precision motion control.

[0003] In some cases, the influence of nonlinear viscous friction on identification needs to be considered, and a robot identification model with a friction term needs to be established. At the same time, the model selection of the excitation trajectory and the parameter optimization are also the main reasons affecting the accuracy of the identified parameters. Selecting a suitable excitation trajectory can more fully excite the dynamic characteristics of the robot system. In order to make the robot not vibrate at the start and end times when running according to the excitation trajectory, a combination of a quintic polynomial and a fifth-order Fourier series excitation trajectory model can be selected. In the selection of excitation trajectory optimization index, the minimum condition number of observation matrix is usually selected as the optimization target. In order to improve the quality of data, filtering is usually performed. The traditional solving method is to use the least square method, which has low calculation accuracy and long solving process, so it is a development trend to study intelligent solving method SUMMARY

[0004] In order to overcome the shortcomings of the above prior art, the purpose of the present application is to provide a joint type industrial robot dynamics parameter identification method, which improves joint friction, optimizes excitation trajectory and improves identification algorithm, so as to more accurately establish an industrial robot dynamics model and improve the parameter identification precision.

[0005] In order to achieve the above purpose, the technical scheme adopted by the present application is:

[0006] A joint type industrial robot dynamics parameter identification method, comprising the following steps:

[0007] S1, for the joint type industrial robot, considering the existing nonlinear viscous friction term, the minimum inertia parameter set containing the to-be-identified dynamics parameters is calculated; the to-be-identified dynamics parameters are coulomb friction, viscous friction coefficient and positive and negative friction force asymmetry bias;

[0008] S2, the constant term of the Fourier series is replaced by a quintic polynomial, and a combined excitation trajectory model of a quintic polynomial and a fifth-order Fourier series is used to drive the robot movement, so that the robot does not vibrate at the starting time and the ending time when running according to the excitation trajectory;

[0009] S3, selecting the minimum condition number of the observation matrix as the optimization objective, and using a genetic algorithm to solve the optimal excitation trajectory parameters, so that the excitation trajectory sufficiently excites the robot;

[0010] S4, collecting the joint angle, angular velocity and torque data of the robot, calculating the estimated friction term, and selecting an interior point method to iteratively solve the dynamic parameters.

[0011] In one embodiment, S1, a robot dynamics model containing a nonlinear viscous friction term is established, and linearization processing is performed to obtain a minimum inertia parameter set.

[0012] In one embodiment, for the jth joint, the joint friction model is as follows:

[0013]

[0014] Where, F cj is the Coulomb friction force, F vj is the viscous friction coefficient, B j is the positive and negative friction force asymmetry bias, alpha j is the nonlinear index parameter for forming viscous friction; All are coefficients corresponding to the friction parameters in the joint friction model.

[0015] In one embodiment, the established dynamics model is converted into the product of a regression matrix and a minimum inertia parameter vector by using matrix transformation, to obtain a minimum inertia parameter set P B containing the to-be-identified dynamic parameters.

[0016] Gamma = WP B + epsilon

[0017] Where, Y B is a regression matrix composed of linearly independent columns of the industrial robot dynamics parameter identification matrix Y, is the value of the joint angle, angular velocity and angular acceleration of the robot at the rth sampling, and epsilon represents a random error introduced, which is subject to a normal distribution with a mean of 0.

[0018] In one embodiment, S2, the excitation trajectory model is as follows:

[0019]

[0020] Where, qi (t) represents the position of the i-th joint at time t, ω f is the fundamental frequency of the Fourier series, k is the number of harmonics, m is the m-th term of the quintic polynomial, a i,k and b i,k are the Fourier series coefficients, c i,k is the constant term coefficient.

[0021] In one embodiment, the S3, the condition number of the observation matrix is represented as f(W) = Cond(W), and the smaller the value, the more useful the data information collected in the robot motion is for parameter identification; a genetic algorithm is used to solve the constrained nonlinear optimization problem min{f(W) = Cond(W)}.

[0022] In one embodiment, the penalty function is selected as:

[0023]

[0024] where a is the penalty factor, b is the empirical constant, r(x) is the number of individuals that satisfy the nonlinear constraints and linear constraints, and x is the to-be-identified parameter matrix, taking the excitation trajectory parameters as individuals;

[0025] By initializing the population, the initial population, the maximum evolution generation, the crossover probability, and the genetic mutation probability, the fitness of each individual in the population is calculated, and the optimal individual x best is selected as the optimization solution of the excitation trajectory parameters, i.e., the optimal excitation trajectory parameters; where F(X) = f(W) + g(X), X is the decision variable, i.e., the unknown coefficient in the excitation trajectory model expression, and g(X) is the adaptive penalty function designed in the genetic algorithm.

[0026] In one embodiment, the S4, the collected data is filtered according to the optimized excitation trajectory, the robot dynamics parameters are obtained by least squares identification, and the estimated friction term is calculated; the nonlinear viscous friction parameters are obtained by iterative fitting using the interior point method, and the robot dynamics parameters The estimated friction force is obtained as:

[0027]

[0028] The established joint friction force model is used to solve and iteratively fit the estimated friction force using the interior point method, and the F cj , F vj , B j and the last α jAs the initial solution of the problem, the exponential parameter optimization is carried out by using the iterative method until the global optimal solution is converged to obtain the nonlinear exponential parameter alpha of the viscous friction j .

[0029] In one embodiment, the collected angle data is processed by a combination of Butterworth low-pass filter and zero-phase digital filter; the angular velocity and angular acceleration are obtained by using the second-order central difference method; and the joint torque value is processed by using smoothing filtering.

[0030] Compared with the prior art, in the robot modeling, the nonlinear term of viscous friction is considered, which is different from the traditional Coulomb viscous friction model, including the robot friction model, the excitation trajectory model selection and the solution of the dynamic parameters. In the excitation trajectory selection optimization, the trajectory model combining the fifth-order Fourier series and the quintic polynomial is selected, and the genetic algorithm with a penalty function is used for parameter optimization of the excitation trajectory; in the solution process, the iterative fitting is carried out based on the interior point method to obtain the complete dynamic parameters of the robot. The friction model considered in the application has higher modeling accuracy, and at the same time, the problems of system jitter at the starting and ending positions are overcome, the efficiency and accuracy of the robot dynamic parameter identification are improved, and the application can be used in robot mobile handling, polishing and polishing and heavy load hydraulic industrial scenes. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 is the identification algorithm flowchart of the application.

[0032] Figure 2 is the genetic algorithm flowchart of the excitation trajectory optimization of the application.

[0033] Figure 3 is the interior point iterative algorithm flowchart of the application.

[0034] Figure 4 is the comparison of the calculated torque and the sampled torque of the joint 1 axis corresponding to the optimal excitation trajectory of the six-degree-of-freedom robot of the application.

[0035] Figure 5 is the comparison of the calculated torque and the sampled torque of the joint 2 axis corresponding to the optimal excitation trajectory of the six-degree-of-freedom robot of the application. DETAILED DESCRIPTION

[0036] In order to make the purpose, technical scheme and advantages of the application clearer, the application will be further described in detail below with reference to the drawings. It should be understood that the specific embodiments described herein are only used to explain the application and do not limit the application.

[0037] In addition, the technical features involved in each embodiment of the application described below can be combined with each other as long as they do not conflict with each other.

[0038] The application provides a joint type industrial robot dynamics parameter identification method, for a linear parameter part of an inertia parameter set obtained after linearization of a robot, least square fitting algorithm is used for identification; according to a friction torque and a friction model in an industrial robot dynamics model, an interior point method is used for iteration to obtain a nonlinear viscous friction force parameter, and a complete friction force model is identified.

[0039] As shown in Figure 1 The joint type industrial robot dynamics parameter identification method of the application comprises the following steps:

[0040] S1, for a joint type industrial robot, a joint friction model of the robot is established by a friction torque on the basis of considering a nonlinear viscous friction term, a robot dynamics model containing the nonlinear viscous friction term is established and linearized, and further minimum inertia parameter set is obtained. The dynamics parameter to be identified in the application is contained in the minimum inertia parameter set. In the application, the dynamics parameter to be identified is coulomb friction, viscous friction coefficient and positive and negative friction asymmetry bias.

[0041] In some embodiments of the application, S1 can specifically comprise the following sub-steps:

[0042] S11, a friction considered industrial robot dynamics model is established according to Newton Euler recursion method by acquiring each axis number.

[0043] S12, a joint friction model of the industrial robot is established, and the joint friction model is part of the robot dynamics model. For the j joint, the joint friction model is expressed as:

[0044]

[0045] Wherein F cj is coulomb friction, F vj is viscous friction coefficient, B j is positive and negative friction asymmetry bias, α j is a nonlinear index parameter for forming viscous friction; All are coefficients corresponding to friction parameters in the joint friction model, and do not have specific physical meaning. The friction model can be more accurate by using the coefficients to construct the friction model.

[0046] The nonlinear model is expanded on the basis of a traditional friction force model. It can be noted that the viscous friction maintains a nonlinear relationship with the joint speed in the model, and the model can more comprehensively characterize the nonlinear error between joints.

[0047] S13, linearize the established complete robot dynamics equation, and obtain the minimum regression matrix expression and the minimum inertia parameter set expression by using QR decomposition parameter reorganization method. For the joint type robot dynamics model converted into linearized dynamics model, as follows:

[0048]

[0049] where Y ∈ R n×(13×n) is the industrial robot dynamics parameter identification matrix, P ∈ R 13×n is the complete dynamics parameter, Y b is the regression matrix of the basic dynamics part of the robot, Y f is the regression matrix of the joint friction force part, P b is the basic dynamics parameter, P f is the dynamics parameter corresponding to the friction force;

[0050] From formula (2), P is the complete dynamics parameter set, and the classical dynamics parameter of the ith link is:

[0051] P i = [m i ,m i x i ,m i y i ,m i z i ,I xxi ,I yyi ,I zzi ,I xyi ,I xzi ,I yzi ,F ci ,F vi ,B j ] (3)

[0052] where m i is the mass of the ith link, (x i , y i , z i ) is the center of mass coordinates of the ith link; I xxi , I yyi , I zzi is the inertia moment of the ith link in the ith coordinate system, I xyi is the inertia product of the ith link in the ith coordinate system to x, y axis, I xzi , I yzi Similarly. The complete dynamics parameter vector P is an n × 1 vector, P = [p1, p2, …, p n ] T , n is the number of joints.

[0053] S14, due to the dynamic parameter identification matrix in formula (2) It is not a full-rank matrix, meaning that not all parameters in P affect the dynamic model. Therefore, a set of minimal parameters, called the minimal inertia parameter set, is needed. If a certain column of Y(·) (let's say the i*j-th column) is effective for any... If all are 0, then the corresponding P ij This will not affect the model, given randomness. Let's simply evaluate these columns and remove them, assuming only column c remains, then we call it Y(·). Given e random groups... And generate the regression sequence w r×c The observation matrix after removing columns with no influence is: The observation matrix can then be decomposed into:

[0054] w = [w1 w2] = [Q1R1 Q2R2] (4)

[0055] From the above equation, we can derive w1 = w2β, β = R1 -1 R2 means that column (cb) of w2 is a linear combination of column b of w1. Therefore, the minimum set of inertia parameters is:

[0056] P B =P1+βP2 (5)

[0057] By using the above steps to reorganize the inertial parameters of the dynamic parameter identification matrix Y through QR decomposition, and separating the linearly dependent and linearly independent columns, the following linearized model is obtained:

[0058]

[0059] Among them, Y B The matrix Y, used for identifying the dynamic parameters of industrial robots, is composed of linearly independent columns and is also called the regression matrix. B That is, it is the smallest set of inertial parameters containing the basic inertial parameters and friction parameters of each link and the dynamic parameters to be identified, which is a column vector;

[0060] S15, in order to identify good P B The value must be sampled multiple times, and the number of samplings is denoted as . r We can obtain the following two matrices:

[0061]

[0062]

[0063] W is a data set obtained after multiple sampling, also called an observation matrix, and by using matrix transformation, the established dynamic model can be converted into the product of W and the minimum inertia parameter vector to obtain the minimum inertia parameter set P B According to the formula (6) in S14, the matrix relationship after the linearization of the dynamic model is represented as:

[0064] Γ=WP B +ε (9)

[0065] wherein, is the value of the joint angle, angular velocity and angular acceleration of the robot at the rth sampling, and ε represents the random error introduced in the sampling process, and generally, the error obeys the normal distribution with a mean of 0. Since the joint angle value and joint torque value collected in the data collection process are affected by noise interference, in order to minimize the influence of noise interference on the identification result, a proper excitation trajectory is selected, so that when the robot runs according to the excitation trajectory, the measured values in the motion process are collected to realize the calculation of the dynamic model parameters.

[0066] S2, an optimal excitation trajectory for identification experiment is designed, and a quintic polynomial is used to compensate and improve the start boundary problem of the single Fourier series as the excitation trajectory.

[0067] In order to select a proper excitation trajectory while satisfying the boundary condition that the angular velocity and angular acceleration are 0 at the initial time, the constant term of the Fourier series is replaced by a quintic polynomial, and a combination excitation trajectory model of the quintic polynomial and the fifth-order Fourier series is adopted to drive the robot to move, so that no jitter occurs at the initial time and the terminal time when the robot runs according to the excitation trajectory. In this step, minimizing the condition number of the observation matrix is selected as the optimization target of the excitation trajectory.

[0068] In some embodiments of the present application, S2 can specifically include the following sub-steps:

[0069] S21, the selected identification trajectory should be able to minimize the influence of disturbance error on the identification result, while satisfying the boundary condition that the angular velocity and angular acceleration are 0 at the initial time, the constant term of the Fourier series is replaced by a quintic polynomial, and a combination excitation trajectory model of the quintic polynomial and the fifth-order Fourier series is selected, as follows:

[0070]

[0071] wherein, q i (t) represents the position of the ith joint at time t, ω f is the fundamental frequency of the Fourier series, k is the number of harmonics, m is the mth term of the quintic polynomial, a i,k and b i,k are the Fourier series coefficients, and c i,kThe number of unknown parameters of each joint excitation trajectory expression is 16 for the constant term coefficient. For the ith joint, the unknown parameters are respectively: i,0 i,1 i,2 i,3 i,4 i,5 i,1 i,2 i,3 i,4 i,5 i,1 i,2 i,3 i,4 i,5 .

[0072] S22, the influence of disturbance on the identification result is evaluated by the condition number of matrix W, the smaller the condition number of W, the smaller the influence of disturbance error on the result. Therefore, the minimum observation matrix condition number is used as the optimization index of the excitation trajectory. According to equation (7) in S15, the observation matrix condition number is as follows:

[0073] f(W) = Cond(W) (11)

[0074] Wherein, Cond(W) is the observation matrix condition number, the smaller the value, the more useful the collected data information is for parameter identification in robot motion.

[0075] S3, after the optimization index is determined, the excitation trajectory parameters can be optimized by optimization algorithm. For this constrained nonlinear optimization problem min{f(W) = Cond(W)}, genetic algorithm is used to solve the optimal excitation trajectory parameters, so that the excitation trajectory can fully excite the robot.

[0076] S31, according to the constraint conditions of the robot in the Cartesian space and each joint position, velocity and acceleration, the optimal excitation trajectory can be converted into a constrained multivariable parameter optimization problem, and genetic algorithm is used to optimize the excitation trajectory parameters.

[0077] S32, the penalty function is selected as follows:

[0078]

[0079] ​​​​​​​​​​​​​​​wherein a is a penalty factor, b is an empirical constant, r(x) is the number of individuals satisfying the nonlinear constraint and the linear constraint, and x is the parameter matrix to be identified. The penalty value of the penalty function g(x) in the above formula (12) varies with the number of individuals satisfying the constraint condition, and when an individual does not satisfy the constraint condition, the penalty value is large, i.e. the individual is removed from the population; on the contrary, when an individual satisfies the constraint condition, the penalty value is small; when all the constraint conditions are satisfied, the penalty value is 0, and the function returns to the case of seeking the minimum of the objective function. In the present application, the excitation trajectory parameters are taken as individuals.

[0080] S33, the selected individual evaluation function is as follows:

[0081] F(X) = f(W) + g(X) (13)

[0082] wherein X is a decision variable, i.e. an unknown coefficient in the expression of the excitation trajectory model, g(X) is an adaptive penalty function in the designed genetic algorithm, and F(X) is an objective function. The excitation trajectory is known in mathematical form, but the coefficients therein are unknown, and these coefficients are the decision variables. The system selects the optimal excitation trajectory parameters by optimizing the decision variables.

[0083] S34, the genetic algorithm is used to optimize and solve the excitation trajectory parameters.

[0084] As shown in Figure 2 , the optimization condition is to minimize the individual evaluation function, i.e. minF(X), and the optimal individual x best is selected in the maximum evolution generation, which is taken as the optimal solution of the excitation trajectory parameters, i.e. the optimal excitation trajectory parameters. It is known from S21 that for the i joint, the number of unknown parameters in the expression of the excitation trajectory is 16, and when n = 6, the number of unknown parameters in the expression of the excitation trajectory of the six-joint industrial robot is 16n. It is known that the individual dimension of the genetic algorithm is 16n.

[0085] Further preferably, the steps of solving the motion planning problem with constraints by using the genetic algorithm are as follows:

[0086] S341, the unknown coefficients of the expression of the excitation trajectory are taken as decision variables X, i.e. the individuals of the genetic algorithm. The population is initialized, and the population size N p , the mutation probability p, the crossover probability CR, the maximum evolution generation g max and other algorithm control parameters are determined.

[0087] S342, an initial population p0 is generated;

[0088] S343, the crossover and mutation operations are performed on the g generation population;

[0089] S344, the fitness values of the parent population and the population after the crossover and mutation are calculated, and the Np Each individual generates a next generation population p g+1 ;

[0090] S345, if the maximum evolution number is reached, terminate, select the optimal individual X in the current population best,g+1 is the solution of the motion planning, i.e., the optimized coefficient of the excitation trajectory; otherwise, g = g + 1, go to S443.

[0091] Figure 2 The flow chart of the genetic algorithm optimizing the excitation trajectory parameters shows this process.

[0092] S4, identification of the minimum inertia parameter set of the robot dynamics. Joint angle, angular velocity and torque data of the robot are collected, the estimated friction term is calculated, and the interior point method is used to iteratively solve the dynamics parameters.

[0093] In some embodiments of the present application, the robot body dynamics parameters are identified by least squares, and the friction model parameters considering the nonlinear viscous friction term are obtained by iterative fitting, which can specifically include the following sub-steps:

[0094] S41, obtain the sampling data, operate the robot according to the optimized excitation trajectory to obtain the robot motion data and torque data after data preprocessing.

[0095] Specifically, for experimental current data and joint torque data, a Butterworth low-pass filter and a zero-phase digital filter are used for filtering processing, and for speed and acceleration, a zero-phase filter is used to remove noise by using a numerical differential central difference format;

[0096] S42, filter the collected data according to the optimized excitation trajectory, and obtain the robot dynamics parameters by least squares identification;

[0097] Initially, the elements of the viscous friction index parameter α in the joint friction model in formula (1) in S12 are all 1, i.e., the friction force model is degenerated into the traditional Coulomb viscous friction model. Assuming that there are r data points, i.e., r times of sampling, the observation matrix W and the observation response Γ are calculated according to formulae (7) and (8) in S15, and the minimum inertia parameter set P is directly obtained by using the least squares fitting algorithm based on the linearized dynamics model obtained by formula (9) in S15. B When solving the overdetermined linear equation, considering that the number of actual sampling points is much larger than the column number of Y B and there is no linear relationship between each sampling point, Y B is considered to be column full rank, which meets the use condition of least squares. The results of parameter identification by least squares are as follows:

[0098] P B_LS = (WT W) -1 W T Γ (14)

[0099] wherein, its length is p = m + 3n, m is the minimum inertia parameter set of the body dynamics, and n is the number of links.

[0100] S43, as shown, according to the constructed joint friction model, the friction model parameters are solved by using the interior point method fitting iterative method, and the friction force estimation method is: Figure 3

[0101]

[0102] In order to estimate and update α j , according to the friction model proposed in formula (1) in S12, the estimated friction is iteratively fitted by using the interior point method, and according to each estimation, after finding the global optimal solution, a new α is obtained. According to the updated α, the regression matrix Y B and the observation matrix W are recalculated by using (7) in S15, and the step S42 is jumped to, so that a new round of linear regression analysis continues.

[0103] Further preferably, the step of identifying the friction force parameter by using the iterative method is as follows:

[0104] S431, if it is initial, the elements of the viscous friction index parameter α in the friction model in formula (1) in S12 are all 1, that is, the friction model is degenerated into the traditional friction model at this time, otherwise the viscous friction index parameter α in the friction model is the value after fitting and updating. Then the size of the estimated friction is calculated according to formula (14) in S42 and formula (15) in S43;

[0105] S432, update of the nonlinear viscous friction index parameter α, this step uses the interior point iterative method to estimate, and the objective function is:

[0106]

[0107] In the formula, τ j is the nonlinear friction force model described in S12 (2), is the estimated friction in S43, and the jth joint is considered here. In the optimization process, all these parameters are constrained to be greater than zero.

[0108] According to the robot dynamics parameters the estimated friction is obtained: ​The established joint friction model is used to solve the estimated friction force by using the interior point method and iterative fitting, and each iteration α is updated in the fitting. Since the linear regression analysis in formula (14) in S42 obtains F cj ,F vj ,B j and the last α j As the initial solution of the estimation problem of formula (16), the exponential parameter optimization is performed by using the iterative method, and finally the solution of the estimation problem of formula (16) can finally converge to the global optimal solution. After finding the global optimal solution, a new α new , i.e. the nonlinear exponential parameter α of viscous friction j is obtained, which is returned to S431 to calculate the matrix W, so that the next round of linear regression analysis can proceed, and the complete iteration step is completed.

[0109] With the iteration, α gradually converges and approaches the true value, so that the friction model is more accurate, and the identified model parameters have higher precision. Each time α changes, W needs to be recalculated until the nonlinear exponential parameter α of viscous friction tends to be stable, the iterative fitting ends, and the complete dynamic parameters are calculated using the α at this time to end the identification.

[0110] Figure 3 The iterative fitting friction parameter identification algorithm shows this process.

[0111] S5, verification of robot dynamics parameters.

[0112] Further preferably, the verification step is as follows:

[0113] S51, verification of robot dynamics identification parameters. A trajectory different from the excitation trajectory is selected as the verification trajectory, the robot is operated to run the verification trajectory, and the angle data and joint torque of the motion are collected.

[0114] S52, the complete dynamics parameters are calculated to obtain the corresponding calculated torque as follows:

[0115]

[0116] S53, the difference between the sampled torque value and the calculated torque value is compared, and the accuracy of the parameter identification is measured by calculating the root mean square (RMS) of the deviation between the calculated torque and the sampled torque. The RMS calculation method is as follows:

[0117]

[0118] Where N is the number of sampling points.

[0119] In a specific embodiment of the application, UR10e is used as a collaborative industrial robot with a high payload of 12.5 kg, so a six-degree-of-freedom industrial robot UR10e is selected for the dynamic parameter identification experiment. Through repeated experiments, 18 parameters in the nonlinear friction model of the six joints and 40 minimum inertia parameters in the linearized dynamic model are determined.

[0120] By optimizing and solving the excitation trajectory with different periods T and harmonic number N=5, it is obtained that when N=12, the best estimation of the root mean square error of torque prediction is obtained. By using genetic algorithm for multiple calculations and result screening, an ideal excitation trajectory is selected, in which the condition number cond(W b (·))≈90.78<100. The required data set is obtained by using the optimal excitation trajectory, and the estimated friction force is obtained according to the measured data, the calculated friction force is obtained according to the friction force model, and the nonlinear index coefficient of viscous friction is solved by using the interior point iterative optimization algorithm. Among them, the corresponding joint 1 axis is alpha1=0.5482, and the joint 2 axis is alpha2=0.4060. In order to verify the effectiveness, the application requires that the root mean square error of torque prediction is minimum, and the calculated torque of joint 1 axis and joint 2 axis which meets the requirements is compared with the sampling torque. It can be seen from the figure that the predicted torque of the application is highly consistent with the actual torque trend, which shows that the application greatly improves the parameter identification efficiency and accuracy.

Claims

1. A method for identifying the dynamics parameters of an articulated industrial robot, characterized in that ,including the following steps: S1,for joint industrial robot,considering the existence of nonlinear viscous friction term,establish joint friction model,for the j joint,its joint friction model is: ； ； wherein, is the Coulomb friction force, is the viscous friction coefficient, is the positive-negative friction asymmetry bias, is the nonlinear exponential parameter for the formation of viscous friction; , are coefficients corresponding to the friction parameters in the joint friction model; The established dynamic model is transformed into the product of regression matrix and minimum inertia parameter vector by matrix transformation, and the minimum inertia parameter set containing the dynamic parameters to be identified is obtained The dynamic model is expressed as: ； wherein, , is an industrial robot dynamics parameter identification matrix is a regression matrix composed of linearly independent columns, is the value of each joint angle, angular velocity, angular acceleration of the robot at the rth sampling, denotes the introduced random error, which is subject to a normal distribution with a mean of 0; S2,replace the Fourier series constant term with five polynomial,using the following excitation trajectory model: ； wherein denotes the time instant the position of the joint, is the fundamental frequency of the Fourier series, is the number of the harmonic, is the term of the quintic polynomial, and is the Fourier series coefficient, is the constant term coefficient; Drive robot movement,make the robot according to the excitation trajectory operation starting time and termination time do not occur jitter; S3, Genetic algorithm is used to solve the constrained nonlinear optimization problem, and the minimum condition number of observation matrix is selected For optimization, the adaptive penalty function is selected: ； wherein, is a penalty factor, is an empirical constant, is the number of individuals satisfying the nonlinear constraints and the linear constraints, is a parameter matrix to be identified, with the trajectory parameters as individuals; By initializing the population, the initial population, the maximum evolution generation, the crossover probability, and the genetic mutation probability are set, the fitness of each individual in the population is calculated, and the individual evaluation function is minimized For optimization conditions, the optimal individual within the maximum evolution generation is selected As the optimized solution of the excitation trajectory parameters, i.e., the optimal excitation trajectory parameters; wherein , is a decision variable, i.e., an unknown coefficient in the expression of the excitation trajectory model, is an adaptive penalty function in the designed genetic algorithm; the optimal excitation trajectory parameters are solved by using the genetic algorithm, so that the excitation trajectory fully excites the robot; S4, collect the joint angle, angular velocity and torque data of the robot, filter the collected data according to the optimized excitation trajectory, obtain the robot dynamics parameters by least square identification, and calculate the estimated friction term; use the interior point method for iterative fitting to obtain the nonlinear viscous friction parameters, and obtain the estimated friction force according to the robot dynamics parameters ​ ； Using the established joint friction model, the estimated friction force is solved by the interior point method and iterative fitting, and the linear regression analysis is obtained , , and the last as the starting solution of the problem, using iterative method for exponential parameter optimization, until converging to the global optimal solution, get the nonlinear exponential parameters of viscous friction , select the interior point method to solve the dynamic parameters iteratively.

2. The method of claim 1, wherein ,The smaller the value of the S3,observation matrix condition number,indicates that in the robot movement,the data collected is more useful for parameter identification.

3. The method of claim 1, wherein The collected angle data is processed by combining Butterworth low-pass filter and zero-phase digital filter; The angular velocity and angular acceleration are obtained by using the second-order central difference method; The joint torque value is processed by using smoothing filter.

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