Kinetic parameter identification method, device and equipment of collaborative robot considering uncertainty factors

Abstract

The invention discloses a kinetic parameter identification method, device and equipment of a collaborative robot considering uncertain factors, and relates to the technical field of robots, the method comprises the following steps: constructing an improved kinetic friction model considering uncertain factors and multi-factor coupling, and obtaining friction torques borne by joints according to the model; constructing a kinetic equation; solving the kinetic equation to obtain a recursive expression; the collaborative robot is driven according to the excitation track, an output parameter matrix is obtained, the joint angular velocity of the collaborative robot is calculated according to the output parameter matrix and the recursion expression, and high-order terms of the joint angular velocity are calculated step by step; when the error of the expansion values of two adjacent orders is smaller than an iteration convergence coefficient, outputting the angular velocity; and judging a motion stage to which the angular velocity belongs according to the velocity judgment coefficient, and dividing a parameter identification stage according to a judgment result to realize segmented identification of the kinetic parameters of the collaborative robot. According to the method, the identification precision and calculation efficiency of the kinetic model are improved.

Description

Technical Field

[0001] The present application relates to the field of robotics, and in particular to a method, device, and apparatus for identifying dynamic parameters of a collaborative robot taking uncertainty factors into consideration. Background Art

[0002] In the field of robot dynamics research, dynamic model construction mainly relies on the Lagrangian method and the Newton-Euler method to build a model that includes inertia terms, Coriolis force terms, gravity terms, and friction terms. The accuracy of the friction model has a significant impact on the overall dynamic model construction. Friction modeling has evolved from basic linear models to complex nonlinear models. The LuGre model introduces internal state variables to accurately describe the friction characteristics of the pre-slip stage. In terms of solving dynamic models, there are explicit integration methods such as the Runge-Kutta algorithm, as well as hybrid integration methods that improve stability by decomposing rigid and non-rigid parts. In the field of parameter identification, least squares methods and intelligent optimization algorithms are commonly used. Intelligent optimization algorithms improve parameter search efficiency by simulating natural evolution mechanisms.

[0003] However, existing technologies still have many shortcomings. In parameter identification, due to the strong coupling of parameters, the objective function is prone to multiple local extreme points, making the optimization prone to falling into local optimality. The varying sensitivity of different parameters to system responses also increases the uncertainty of the identification results, making it difficult to meet the high-precision requirements of dynamic models. Therefore, innovative methods are urgently needed to overcome the bottlenecks of existing technologies. Summary of the Invention

[0004] The present application provides a method, device and equipment for identifying the dynamic parameters of a collaborative robot taking uncertainty factors into consideration, which can improve the identification accuracy and computational efficiency of the dynamic model.

[0005] To achieve the above objectives, this application adopts the following technical solutions: In a first aspect, the application provides a method for identifying dynamic parameters of a collaborative robot considering uncertainty factors, the method comprising: constructing an improved dynamic friction model considering multi-factor coupling, obtaining a friction torque acting on a joint according to the improved dynamic friction model; constructing a dynamic equation of a dynamic model based on a Newton-Euler method and the friction torque acting on the joint; solving the dynamic equation based on a time-domain segmentation algorithm to obtain a recursive expression of the dynamic equation; setting an excitation trajectory required for segmented identification of the collaborative robot based on the expression of the dynamic equation; driving the collaborative robot according to the excitation trajectory to obtain an output parameter matrix, calculating a joint angular velocity of the collaborative robot according to the output parameter matrix and the recursive expression of the dynamic equation, and calculating high-order terms of the joint angular velocity step by step; setting an iterative convergence coefficient, and outputting the angular velocity when an error of expanded values of adjacent two orders is less than the iterative convergence coefficient; wherein the error of the expanded values of the adjacent two orders is obtained through the high-order terms; setting a speed judgment coefficient, determining a motion phase to which the angular velocity belongs according to the speed judgment coefficient, dividing phases of parameter identification according to a determination result, and realizing segmented identification of dynamic parameters of the collaborative robot.

[0006] In some possible implementation manners, the constructing the improved dynamic friction model considering multi-factor coupling comprises: According to asymmetry of forward and reverse friction, stiffness disturbance coefficients are introduced, friction coefficients of the model under forward and reverse velocity motion trends are respectively set, a non-symmetrical viscous friction term is constructed according to the friction coefficients, and a basic friction model is constructed according to the stiffness disturbance coefficients and the non-symmetrical viscous friction term; Based on periodic disturbance of gear engagement and inertial impact effect, a position harmonic term capable of describing friction fluctuation caused by assembly error and gear engagement error is constructed with a joint position of the collaborative robot as a variable; With a joint acceleration of the collaborative robot as a variable, a smoothing factor is introduced to construct an acceleration compensation term; The improved dynamic friction model considering multi-factor coupling is constructed in combination of the basic friction model, the position harmonic term, the acceleration compensation term and uncertainty factors.

[0007] In some possible implementation manners, the solving the dynamic equation based on the time-domain segmentation algorithm to obtain the recursive expression of the dynamic equation comprises: A time variable of joint motion of the collaborative robot is normalized to obtain a first time variable; The joint position of the collaborative robot is subjected to high-order Taylor expansion, an expansion order is determined according to the first time variable, a high-order Taylor expansion formula is obtained, and an expansion formula containing derivatives of the joint position at each order is obtained; Determining an expansion of a first parameter in a dynamic equation based on the high-order Taylor expansion and an expansion including derivatives of various orders of joint positions; The expanded expression of the first parameter is introduced into the kinetic equation and simplified to obtain the recursive expression of the kinetic equation.

[0008] In some possible implementations, setting the excitation trajectory required for segmented identification of the collaborative robot based on the expression of the dynamic equation includes: Divide the stages of segmented identification of collaborative robots into first-stage identification, second-stage identification, and third-stage identification; designing a stepped velocity trajectory for the first stage, and when it is determined that the stepped velocity trajectory includes a plurality of fixed velocity values, using the stepped velocity trajectory as the excitation trajectory for the first stage; Designing a second-stage sinusoidal function trajectory, wherein the frequency of the sinusoidal function trajectory linearly increases from an initial value to a set upper frequency limit, and using the sinusoidal function trajectory as the excitation trajectory of the second stage; Design the fifth-order Fourier series trajectory of the third stage, set constraints, solve the trajectory parameters by combining the correlation function, and use the fifth-order Fourier series trajectory as the excitation trajectory of the third stage; Design a transition function, and connect the excitation trajectories set in each stage in the order of the first stage, the second stage, and the third stage through the transition function, and set them as the excitation trajectory required for the collaborative robot segmented identification.

[0009] In some possible implementations, the method further includes: When the error between the expansion values ​​of two adjacent orders is not less than the iterative convergence coefficient, continue the iteration.

[0010] In some possible implementations, setting the speed determination coefficient includes: Based on the maximum static friction torque, joint stiffness coefficient and joint natural frequency of the collaborative robot, the speed judgment coefficient of the second stage and the speed judgment coefficient of the third stage are calculated.

[0011] In some possible implementations, the segmented identification of the collaborative robot's dynamic parameters includes: The collaborative robot is controlled to move along the excitation trajectory corresponding to the first stage, and the recursive least squares method is used to identify the gravity term, the maximum static friction parameter, and the uncertainty factors influencing the quasi-static stage. The collaborative robot is controlled to move along the excitation trajectory corresponding to the second stage, and the recursive least squares method is used to identify the Coulomb friction parameters, Stribeck characteristic parameters, asymmetric viscous friction parameters, and uncertainty factors in the quasi-static stage. The collaborative robot is controlled to move according to the excitation trajectory corresponding to the third stage, and the recursive least squares method is used to identify the parameters of the inertia term, Coriolis force term, harmonic disturbance term and the uncertainty influencing factors in the high-speed stage.

[0012] In some possible implementations, the recursive least squares method constructs a regression matrix based on the output parameter matrix, and initializes the parameter matrix and the covariance matrix; Calculate the gain matrix and update the parameter matrix and covariance matrix according to the gain matrix; The relative change rate of the parameter matrix between two adjacent iterations is calculated. When the relative change rate is less than the set convergence judgment coefficient, the iteration is stopped and the optimal parameter matrix is ​​output.

[0013] In a second aspect, the present application provides a device for identifying dynamic parameters of a collaborative robot that takes uncertainty factors into account, the device comprising: a construction module for constructing an improved dynamic friction model that takes into account the coupling of multiple factors, and obtaining the friction torque exerted on the joint according to the improved dynamic friction model; and constructing a dynamic equation of the dynamic model based on the Newton-Euler method and the friction torque exerted on the joint; A calculation module is configured to solve the dynamic equation based on a time-domain segmentation algorithm to obtain a recursive expression of the dynamic equation; set an excitation trajectory required for segmented identification of the collaborative robot based on the expression of the dynamic equation; drive the collaborative robot according to the excitation trajectory, obtain an output parameter matrix, calculate the joint angular velocity of the robot according to the output parameter matrix and the recursive expression of the dynamic equation, and calculate high-order terms of the joint angular velocity step by step; set an iterative convergence coefficient, and output the angular velocity when the error between the expansion values ​​of two adjacent orders is less than the iterative convergence coefficient; wherein the error between the expansion values ​​of two adjacent orders is obtained through the high-order terms; The identification module is used to set the speed judgment coefficient, determine the motion stage to which the angular velocity belongs based on the speed judgment coefficient, divide the parameter identification stages according to the judgment results, and realize the segmented identification of the collaborative robot's dynamic parameters.

[0014] In a third aspect, the present application provides a computing device, including a memory and a processor; One or more computer programs are stored in the memory, and the one or more computer programs include instructions; when the instructions are executed by the processor, the computing device executes the method as described in any one of the first aspects.

[0015] In a fourth aspect, the present application provides a computer-readable storage medium for storing a computer program for executing the method as described in any one of the first aspects.

[0016] In a fifth aspect, the present application provides a computer program product, which includes one or more computer instructions. When the computer instructions are executed by a computer, the computer executes the method as described in any one of the first aspects.

[0017] It can be seen from the above technical solution that this application has at least the following beneficial effects: In the present application, an improved dynamic friction model considering uncertainty factors and multi-factor coupling is constructed, and the friction torque acting on the joint is obtained according to the improved dynamic friction model; the dynamic equation of the dynamic model is constructed based on the Newton-Euler method and the friction torque acting on the joint; the dynamic equation is solved based on the time domain segmentation algorithm to obtain the recursive expression of the dynamic equation; the excitation trajectory required for the segmented identification of the collaborative robot is set based on the expression of the dynamic equation; the collaborative robot is driven according to the excitation trajectory, and the output parameter matrix is ​​obtained, and the joint angular velocity of the collaborative robot is calculated according to the output parameter matrix and the recursive expression, and the high-order terms of the joint angular velocity are calculated step by step; the iterative convergence coefficient is set, and the angular velocity is output when the error of the expanded values ​​of two adjacent orders is less than the iterative convergence coefficient; the speed judgment coefficient is set, and the motion stage to which the angular velocity belongs is judged according to the speed judgment coefficient, and the parameter identification stages are divided according to the judgment result to realize the segmented identification of the dynamic parameters of the collaborative robot.

[0018] In the existing technology, a single friction model is often used to ignore coupling factors such as assembly errors and stiffness fluctuations, or a global excitation trajectory cannot adapt to the parameter characteristics of each stage, resulting in low parameter identification accuracy, large deviation between the model and the actual motion, and difficulty in meeting the needs of collaborative robots for fine operations. It can be seen that this application accurately depicts complex friction by constructing an improved dynamic friction model that couples uncertainty factors with multiple factors, uses a time-domain segmented algorithm to decompose the dynamic equations for efficient solution, designs segmented excitation trajectories to cover all motion stages, combines recursive iteration with stage judgment to achieve accurate segmented parameter identification, and improves the accuracy of the collaborative robot dynamics model, providing more reliable parameter support for trajectory planning and force control of collaborative operations, and solving the problems of large identification errors and poor adaptability caused by rough models and single excitation in traditional methods.

[0019] It should be understood that the description of technical features, technical solutions, beneficial effects or similar language in this application does not imply that all features and advantages can be realized in any single embodiment. On the contrary, it is understood that the description of a feature or beneficial effect means that a specific technical feature, technical solution or beneficial effect is included in at least one embodiment. Therefore, the description of a technical feature, technical solution or beneficial effect in this specification does not necessarily refer to the same embodiment. Furthermore, the technical features, technical solutions and beneficial effects described in the present embodiment can also be combined in any appropriate manner. Those skilled in the art will understand that the embodiment can be implemented without one or more specific technical features, technical solutions or beneficial effects of a specific embodiment. In other embodiments, additional technical features and beneficial effects can also be identified in specific embodiments that do not embody all embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A flowchart of a method for identifying dynamic parameters of a collaborative robot taking uncertainty factors into account provided in an embodiment of the present application; Figure 2 A schematic diagram comparing the output torque accuracy of the improved dynamic friction model and the Lugre model under the excitation trajectory drive provided in the embodiment of the present application; Figure 3 A schematic diagram comparing the solution results of the time domain segmentation algorithm under different step size settings and the Runge-Kutta algorithm under fixed step size provided in an embodiment of the present application; Figure 4 A schematic diagram comparing the solution results of the Runge-Kutta algorithm under different step size settings and the time domain segmentation algorithm under fixed step size provided in an embodiment of the present application; Figure 5 A schematic diagram comparing the joint angle solution results of the time-domain segmentation algorithm and the Runge-Kutta algorithm under the excitation trajectory drive provided in an embodiment of the present application; Figure 6 Flowchart for solving dynamic models based on time domain segmentation algorithm; Figure 7 This is a diagram showing the excitation trajectory of a six-degree-of-freedom collaborative robot obtained through MATLAB optimization according to an embodiment of the present application; Figure 8 A schematic diagram comparing the theoretical torque and actual torque results of the dynamic model parameter identification provided in the embodiment of the present application; Figure 9 A schematic diagram of a device for identifying dynamic parameters of a collaborative robot taking uncertainty factors into consideration, provided in an embodiment of the present application; Figure 10 A schematic diagram of a computing device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0021] The terms "first", "second" and "third" in this application specification and the accompanying drawings are used to distinguish different objects rather than to limit a specific order.

[0022] In the embodiments of this application, words such as "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of this application should not be interpreted as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0023] To make the description of the following embodiments clear and concise, a brief introduction to the related technologies is first given: The dynamic parameter identification of collaborative robots is the core link to achieve precise control, which relies on accurate friction models, efficient solution of dynamic equations and adaptive identification strategies.

[0024] At present, traditional dynamic identification methods mostly use simplified friction models, such as a single Coulomb-viscous friction model that ignores uncertainty factors such as assembly errors and stiffness fluctuations. This model is difficult to adapt to the multi-factor coupled friction characteristics of collaborative robots under complex working conditions. The solution of dynamic equations often suffers from nonlinear and strong coupling problems, and the use of global numerical solutions leads to low computational efficiency and cannot meet real-time control requirements. The excitation trajectory design is mostly a single global trajectory, which cannot specifically cover different motion stages such as quasi-static, low and high speed, resulting in uneven distribution of parameter identification accuracy, especially in the low-speed Stribeck effect and high-speed inertia term identification. The errors are significant.

[0025] However, the existing segmented identification strategy lacks deep adaptation to the multi-factor coupling of the friction model. The trajectory transition between each stage is prone to motion mutations, and parameter iterative optimization is not achieved through recursion of the dynamic equations, resulting in poor parameter consistency in segmented identification. The overall accuracy of the model still cannot meet the high requirements of the dynamic model for the precise operation of collaborative robots.

[0026] In view of this, an embodiment of the present application provides a method for identifying the dynamic parameters of a collaborative robot taking into account uncertainty factors, in which an improved dynamic friction model that takes into account uncertainty factors and multi-factor coupling is constructed, and the friction torque acting on the joint is obtained according to the improved dynamic friction model; the dynamic equation of the dynamic model is constructed based on the Newton-Euler method and the friction torque acting on the joint; the dynamic equation is solved based on the time domain segmentation algorithm to obtain a recursive expression of the dynamic equation; the excitation trajectory required for the segmented identification of the collaborative robot is set based on the expression of the dynamic equation; the collaborative robot is driven according to the excitation trajectory, and an output parameter matrix is ​​obtained; the joint angular velocity of the collaborative robot is calculated according to the output parameter matrix and the recursive expression, and the high-order terms of the joint angular velocity are calculated step by step; an iterative convergence coefficient is set, and when the error of the expanded values ​​of two adjacent orders is less than the iterative convergence coefficient, the angular velocity is output; a speed judgment coefficient is set, and the motion stage to which the angular velocity belongs is judged according to the speed judgment coefficient, and the parameter identification stages are divided according to the judgment result to realize the segmented identification of the dynamic parameters of the collaborative robot.

[0027] It can be seen that this application accurately depicts complex friction by constructing an improved dynamic friction model with multi-factor coupling, decomposes the dynamic equations with a time-domain segmentation algorithm to achieve efficient solution, designs segmented excitation trajectories to cover the entire motion stage, combines recursive iteration with stage judgment to achieve accurate segmented identification of parameters, and improves the accuracy of the collaborative robot dynamic model, providing more reliable parameter support for trajectory planning and force control of collaborative operations, and solving the problems of large identification errors and poor adaptability caused by rough models and single excitation in traditional methods.

[0028] In order to make the technical solution of this application clearer and easier to understand, the following describes a method for identifying the dynamic parameters of a collaborative robot taking uncertainty factors into consideration, provided by an embodiment of this application, in conjunction with the accompanying drawings. Figure 1 As shown in the figure, this figure is a flow chart of a method for identifying dynamic parameters of a collaborative robot taking uncertainty factors into consideration, provided in an embodiment of the present application.

[0029] The method for identifying dynamic parameters of a collaborative robot considering uncertainty factors is applied to a processing device, and the method includes: S101. Construct an improved dynamic friction model that takes into account uncertainty factors and multi-factor coupling, and obtain the friction torque acting on the joint based on the improved dynamic friction model.

[0030] According to the asymmetry of forward and reverse friction, a stiffness perturbation coefficient is introduced, and the friction coefficient of the model under the forward and reverse velocity motion trends is set respectively. The asymmetric viscous friction term is constructed according to the friction coefficient, and the basic friction model is constructed according to the stiffness perturbation coefficient and the asymmetric viscous friction term; based on the gear meshing periodic perturbation and inertial impact effect, the joint position of the collaborative robot is used as a variable to construct a position harmonic term that can describe the friction fluctuation caused by assembly error and gear meshing error; the joint acceleration of the collaborative robot is used as a variable, and a smoothing factor is introduced to construct an acceleration compensation term; considering the modeling error and measurement error, this application adds an uncertainty factor to characterize this error; therefore, the basic friction model, position harmonic term, acceleration compensation term and uncertainty factor are combined to construct an improved dynamic friction model that considers the coupling of uncertainty factors and multiple factors. Specifically including: Considering that the friction of collaborative robot joints exhibits complex characteristics such as speed-dependent nonlinearity and position-related harmonic disturbance, an improved Lugre friction model is proposed based on the friction characteristic curve of collaborative robots under actual working conditions and related influencing factors to accurately describe the friction force exerted on collaborative robots under actual working conditions. First, considering that in actual mechanical systems, due to assembly tolerances or uneven lubrication, the forward and reverse friction often presents asymmetry, that is, the friction forces generated during the forward and reverse motion processes are not mutually inverse. In order to accurately describe the manifestation of the friction model under actual working conditions, the friction coefficients of the model under the forward and reverse velocity motion trends are set respectively, and an asymmetric viscous friction term is constructed; considering that the stiffness of collaborative robots will produce random changes due to material deformation and temperature fluctuations, adding uncertainty factors can effectively reduce the prediction residual of the model. Therefore, the stiffness perturbation coefficient is introduced on the basis of the Lugre model and the basic friction model is constructed as shown in formula (1): (1) Where, is the basic friction model function, is the contact stiffness coefficient, is the microscopic damping coefficient, is the Heaviside step function, is the step function of the reverse motion, is the joint angular velocity, Obeying the standard normal distribution, it is used to describe the random perturbation of the stiffness coefficient. and It is the symmetric interval of asymmetric viscous friction.

[0031] Secondly, considering that the Lugre model does not consider the friction fluctuations caused by gear meshing periodic disturbances and inertial impact effects, the position harmonic terms caused by assembly errors and gear meshing errors are constructed: (2) Where, is the position harmonic term, is the first harmonic amplitude error caused by gear meshing periodic disturbance, is the harmonic order, is the joint angle, is the first phase offset error due to assembly error, e is the maximum order of sine harmonics, f is the maximum order of cosine harmonics, is an integer greater than or equal to 1 and less than or equal to e and f, is the second harmonic amplitude error caused by gear meshing periodic disturbance, is the second phase offset error caused by assembly error.

[0032] Considering the inertial impact caused by commutation when the collaborative robot moves at high speed, introducing an acceleration compensation term at the start and stop moments can effectively reduce the probability of acceleration waveform distortion. In order to smooth this phenomenon and avoid the singularity that may occur at zero acceleration, the acceleration compensation term is constructed: (3) Where, is the acceleration compensation term, is the acceleration compensation coefficient, is the joint acceleration, is a smoothing factor used to avoid zero-speed singularity, The improved dynamic friction model considering uncertainty factors and multi-factor coupling is obtained by comprehensive analysis of formula (1), formula (2), and formula (3): (4) Where, is the friction torque on the joint, The uncertainty factors are represented, thereby realizing the construction of an improved dynamic friction model that considers the uncertainty factors and the coupling of multiple factors.

[0033] In order to verify the accuracy of the improved dynamic friction model that takes into account uncertainty factors and multi-factor coupling, a parameter identification study of a six-degree-of-freedom collaborative robot was carried out. The specific operations are as follows: Drive the collaborative robot so that the target joint moves in a direction parallel to the direction of gravity, and lock the remaining joints while keeping the joint running at a constant speed. In this state, the influence of the inertia term, Coriolis force term, and gravity term in the dynamic model can be ignored. At this time, the torque value measured can be approximately determined as the friction torque value of the joint. The unknown parameters of the joint are identified based on the least squares method, and then the identified unknown parameters are substituted into the improved dynamic friction model to solve for the theoretical output torque. The theoretical output torque is compared with the actual torque obtained by experimental measurement to verify the construction accuracy of the improved dynamic friction model. The relevant identification results are shown in Figure 2. Figure 2 As shown in Figure 3, the simulation results show that the identification torque calculated by the proposed improved dynamic friction model has higher accuracy and is more consistent with the friction characteristics under actual working conditions.

[0034] S102. Construct the dynamic equations of the dynamic model based on the Newton-Euler method and the friction torque acting on the joint.

[0035] The construction of the dynamic model is based on the Newton-Euler method to construct the dynamic equation of the dynamic model, which can be expressed as formula (5): (5) Where, is the u×u mass matrix of the manipulator, where u is an integer greater than or equal to 1, are the centrifugal force and Coriolis force vectors of u×1, is the gravity vector of u×1, represents the friction torque on the joint, is the joint output torque, q is the joint angle, is the joint angular velocity, is the joint acceleration, and the specific expressions of several matrices are formulas (6) to (8): (6) (7) (8) Where, is the i-th row and j-th column element of the inertia matrix, T is the homogeneous transformation matrix, is the homogeneous transformation matrix of the base joint, are the elements of the Coriolis force matrix, are the elements of the gravity matrix, is the angle value of the i-th joint, is the angle value of the jth joint, represents the w-th joint angle value, is the joint angular velocity of the w-th joint, is the Coriolis force matrix element, is the second harmonic amplitude error caused by the periodic disturbance of gear meshing, is the second phase shift error caused by assembly error, is the i-th row, w-th column element of the inertia matrix, is the j-th row, w-th column element of the inertia matrix, is the inertia tensor of the i-th joint, and tr represents the rank of the matrix, represents the mass of the j-th link, is the i-th joint gravity torque component, and g represents the gravity acceleration vector, is the center of mass position of the j-th link, , i, j and w are integers.

[0036] In the formula, the inertia term can be obtained by relevant physical parameters of the joint, the Coriolis force term depends on the change of speed during joint movement, and when the collaborative robot joint is driven to move at a certain speed, the term can be ignored, and the gravity term is mainly affected by the change of gravitational potential energy during joint movement, and through the analysis, only the friction term in the above dynamics expression cannot be accurately modeled, so the friction model is improved to obtain an improved dynamics friction model considering multi-factor coupling, and the specific improvement steps are in S101, which will not be repeated here.

[0037] In order to verify the solving accuracy and convenience of the proposed time domain segmentation algorithm, a three-degree-of-freedom collaborative robot dynamics model solving experiment is designed based on MATLAB Simulink software, the solving results of the time domain segmentation algorithm under different step conditions and the Runge-Kutta algorithm under fixed step are compared, the simulation results are shown in Figure 3 , and the solving results of the Runge-Kutta algorithm under different step conditions and the time domain segmentation algorithm under fixed step are compared, the simulation results are shown in Figure 4 , the results verify that the solving accuracy and convergence of the time domain segmentation algorithm are not limited by the set time step. At the same time, the simulation results of the time domain segmentation algorithm and the Runge-Kutta algorithm under the same excitation trajectory driving are viewed, the simulation results are shown in Figure 5 , and the results verify that the solving accuracy of the proposed time domain segmentation algorithm is higher.

[0038] S103, solving the dynamics equation based on the time domain segmentation algorithm to obtain the recursive expression of the dynamics equation.

[0039] ​The time variables of the collaborative robot's joint motion are normalized to obtain a first time variable; a high-order Taylor expansion is performed on the collaborative robot's joint positions, and the expansion order is determined based on the first time variable to obtain a high-order Taylor expansion, and an expansion containing various order derivatives of the joint positions is obtained; the expansion of the first parameter in the dynamic equation is determined based on the high-order Taylor expansion and the expansion containing various order derivatives of the joint positions; the expansion of the first parameter is introduced into the dynamic equation and simplified to obtain a recursive expression of the dynamic equation. Specifically, it includes: High-precision solution of dynamic models based on time-domain segmentation algorithm. This method transforms continuous time-domain nonlinear differential equations into discretized polynomial forms through normalized time variables, high-order Taylor expansion and parameter separation method to achieve the solution of dynamic models. The specific process is as follows Figure 6 shown.

[0040] S601. Define initial parameters based on experience.

[0041] The initial parameters required for solving the dynamic model are set based on experience. These parameters provide the basis for subsequent calculations, affect the starting state of the entire solution process, and are a prerequisite for solving the model.

[0042] S602: Calculate the output value a at time t.

[0043] At the current time t, the output value a is calculated based on the defined initial parameters and the relevant formulas of the dynamic model. This output value a may contain relevant physical quantity information such as joint position, velocity, acceleration, etc. It is a quantitative expression of the model state at the current moment and provides basic data for subsequent calculations.

[0044] S603: Calculate the output value c of order n.

[0045] Based on time t, a higher-order Taylor expansion of the joint positions is performed, with the expansion order being n. Following the Taylor series calculation rules and combining the relationships between the various parameters in the dynamic model, the output value c is calculated. The output value c contains information about the joint positions in the n-order expansion, which is used to more accurately describe the state of the system at that moment.

[0046] S604: Calculate the output value d of order n+1.

[0047] After calculating the nth-order output value c, the Taylor expansion order is further increased to n+1, and the output value d is calculated based on the Taylor series calculation rules and the relationship between the dynamic model parameters. Increasing the expansion order can more accurately characterize the system state and improve calculation accuracy.

[0048] S605: Calculate error values ​​p at different orders.

[0049] Compare the output value d of order n+1 with the output value c of order n and calculate the error p between them. Error p reflects the degree of change in the calculation result after increasing the Taylor expansion order and is used to determine whether to increase the expansion order to improve calculation accuracy.

[0050] S606: Determine whether p is less than the order threshold.

[0051] Compare the calculated error value p with the pre-set order threshold. If p is less than the order threshold, further increasing the Taylor expansion order will no longer significantly improve the calculation results. At this point, stop increasing the expansion order and proceed to the next step. If p is not less than the order threshold, return to the step of calculating the output value d of order n+1 and continue increasing the expansion order to achieve higher accuracy.

[0052] S607: Calculate the output value b at time t+1.

[0053] When the error value p is less than the order threshold, a preset time step is added to the current time step to obtain a new time step, and prepare to calculate the next time step, so that the calculation process advances in the time dimension.

[0054] At the new time step, the output value b at time t+1 is calculated based on the updated time and the relevant formulas of the dynamic model, combined with the calculation results of the previous time step. The output value b also contains relevant physical quantity information such as joint position, velocity, acceleration, etc., reflecting the state of the system at the new time step.

[0055] S608: Calculate the error value q at different times.

[0056] Compare the output value b at time t+1 with the output value at the previous time step (e.g., output value a) and calculate the error value q at different times. The error value q is used to evaluate the stability and accuracy of the model over time and reflects the changes in the system state over time.

[0057] S609: Determine whether q is less than a time threshold.

[0058] Compare the calculated error value q with a pre-set time threshold. If q is less than the time threshold, the model's changes over time are within an acceptable range, the calculation process meets expectations, and the calculation can be terminated. If q is not less than the time threshold, return to the step of calculating the output value b at time t+1, add a time step, and continue the calculation for the next time step to ensure the stability and accuracy of the model calculation results in the time dimension.

[0059] S610: End calculation.

[0060] When the error value q is less than the time threshold, the entire dynamic model solving process based on the time domain segmentation algorithm ends, and the final calculation results are output. These calculation results can be used to analyze the dynamic characteristics of the collaborative robot and provide data support for subsequent parameter identification and motion control.

[0061] First, define the normalized time variable as shown in equation (9): (9) In the formula, △K is the time step, is the actual time, is the starting time of the first time step, and s is the time variable. Through normalization, any time interval can be mapped to a unified scale, facilitating subsequent analysis. On this basis, the joint position is expanded by a high-order Taylor series as shown in equation (10): Equation (10):

[0062]

[0063] In the formula, is a high-order Taylor expansion, m is the expansion order of the high-order Taylor expansion, and by introducing the Taylor series, the continuous dynamic equation can be discretized into a polynomial form, represents the n-order Taylor coefficient at time t, n is greater than or equal to 1 and less than or equal to m, and m is an integer, where equation (11) is as follows: Equation (11):

[0064] Similarly, the Taylor expansion of velocity and acceleration is shown in equations (12) and (13): (12) (13) At the same time, the inertia force term, Coriolis force term, gravity term and friction term coefficients in the dynamic model are expanded into polynomials as shown in equations (14) to (17): (14) (15) (16) (17) In the formula, is a summation index variable, is the l-order Taylor coefficient of the inertia matrix at the kth time step, and r represents the summation index variable of the velocity term, is the r-order Taylor coefficient of the joint position at the k-th time step, is the l-order Taylor coefficient of the joint Coriolis moment at the k-th time step, is the v-order Taylor coefficient of the joint position at the k-th time step, , is the (nl-r+1)th order Taylor coefficient of the joint position at the kth time step, is the n-order Taylor coefficient of the joint gravity torque at the k-th time step, is the n-order Taylor coefficient of the joint friction term at the k-th time step.

[0065] Substituting equations (14), (15), (16) and (17) into equation (5), and aligning them according to the powers of the Taylor series, we obtain the corresponding function expression as shown in equation (18): Formula (18):

[0066] By simplifying formula (18), the recursive expression of the dynamic equation is obtained as shown in formula (19): (19) Among them, the position update and velocity update expressions are formula (20): (20) Through the above steps, the construction of the dynamic model is completed.

[0067] S104. Set the excitation trajectory required for segmented identification of the collaborative robot based on the expression of the dynamic equation.

[0068] The stages of segmented identification of collaborative robots are divided into first-stage identification, second-stage identification, and third-stage identification; a stepped velocity trajectory is designed for the first stage, and when it is determined that the stepped velocity trajectory contains multiple fixed speed values, the stepped velocity trajectory is used as the excitation trajectory for the first stage; a sinusoidal function trajectory is designed for the second stage, and the frequency of the sinusoidal function trajectory linearly increases from the initial value to the set upper limit frequency, and the sinusoidal function trajectory is used as the excitation trajectory for the second stage; a fifth-order Fourier series trajectory is designed for the third stage, constraints are set, and trajectory parameters are solved in combination with related functions, and the fifth-order Fourier series trajectory is used as the excitation trajectory for the third stage; the design of the trajectories of the above stages needs to be carried out around the characteristics of the collaborative robot dynamics model and the requirements of the parameters to be identified. The excitation trajectories of different stages must adapt to the parameter identification logic, and the segmented identification can be carried out in an orderly manner through reasonable connection, thereby laying a solid foundation for the complete identification process.

[0069] Next, we design a transition function, which connects the excitation trajectories set in each stage in the order of the first stage, the second stage, and the third stage, and sets the excitation trajectory required for the collaborative robot's segmented identification. Specifically, it includes: The expression for the excitation trajectory required for the segmented identification of the collaborative robot is set. For the dynamic model built above, the parameters that need to be identified are mainly divided into: (1) Inertia coefficient: including the mass m of each connecting rod i , center of mass position c ix 、c iy 、c iz and the independent components of the inertia tensor I xx , I yy , I zz , I xy , I xz , I yz These parameters determine the composition of the inertia term M(q) and have a significant impact on the system acceleration response.

[0070] (2) Coriolis force coefficient: It is composed of the partial derivative of the inertia term with respect to position, reflects the velocity coupling relationship between robot joints, and is usually associated with the inertia parameters.

[0071] (3) Gravity parameters: mainly related to mass, which is reflected in the influence of gravity torque on each connecting rod in different postures. It belongs to static or quasi-static characteristics.

[0072] (4) Friction parameters: Based on the extended Lugre model, it includes static friction, dynamic friction, asymmetric viscosity term, periodic disturbance term, acceleration compensation term and possible random disturbance term.

[0073] In this application, the first stage is a quasi-static stage, the second stage is a low-speed motion stage, and the third stage is a high-speed motion stage. In order to ensure that the above parameters can be accurately estimated, targeted excitation trajectories are designed for different identification tasks.

[0074] Among them, the first stage of the step velocity trajectory identification, that is, the parameters to be identified in the quasi-static stage, is adopted. This process mainly ensures that the identification and analysis of static friction and sliding friction parameters can be realized under the premise of step-changing low-speed motion. The joint velocity-position trajectory function expression is defined as shown in formula (21): (twenty one) Where, is the joint angle function in the quasi-static stage, is the joint angular velocity trajectory function, is the set value of the zxth speed step, is the set value of the zx+1th speed step, ϵ{0,±0.05,±0.1,±0.2,±0.5}, is the initial position of the joint, is the starting time of the zx speed segment, is the transition time from segment zx to segment zx+1, is an interval characteristic function, when When , it is 1, otherwise it is 0. R is the ramp transition function, and the specific expression is: (twenty two) For the parameters to be identified in the second stage, that is, the low-speed motion stage, the low-speed motion stage refers to the situation where the vehicle speed is lower than the set threshold speed. In this application, the threshold speed can be set to 40 km / h. The sine function expression is used as the excitation trajectory, where the speed symmetry of the sine function can be used to realize the identification of asymmetric friction parameters in forward and reverse motion. The linear growth frequency is used to ensure that the motion range of the Stribeck effect can be effectively covered. The running trajectory is shown in formula (23): (twenty three) Where, is the joint angle function at low speed, is the amplitude, and the frequency f(t) increases linearly from 0.1Hz to 10Hz.

[0075] The fifth-order Fourier series is used to excite the inertia and Coriolis terms to identify the parameters to be identified in the third stage, that is, the high-speed motion stage. The high-speed motion stage refers to the situation where the vehicle speed is lower than the set threshold speed during operation. In this application, the threshold speed can be set to 40 km / h. Its function expression is shown in formula (24): (twenty four) Where, is the joint angle function in the high-speed stage, It refers to the first coefficient to be solved of the excitation trajectory in the form of the fifth-order Fourier series. It refers to the second coefficient to be solved of the excitation trajectory in the form of a fifth-order Fourier series. It refers to the third coefficient to be solved of the excitation trajectory in the form of the fifth-order Fourier series, ω is the fundamental frequency of the Fourier series, and there are 5 2+1=11 unknown coefficients.

[0076] In order to solve this expression, it is necessary to construct a constraint equation and add constraints to the above fifth-order Fourier series. Under the premise of ensuring that the joint moves within the specified range of motion, the observation matrix condition number is minimized to ensure the stability of the numerical solution. The constraint conditions are shown in formula (25): Formula (25):

[0077] wherein, to minimize the condition number of the observation matrix W, is the minimum value of the joint angle, is the maximum value of the joint angle, is the minimum value of the joint angular velocity, is the maximum value of the joint angular velocity, is the minimum value of the joint acceleration, is the maximum value of the joint acceleration, is the joint angle value of the yth joint, is the joint angular velocity value of the yth joint, is the joint acceleration value of the yth joint, is to perform inverse kinematics calculation on the joint to verify whether the trajectory point is in the working range, is the working range that the robot arm can reach, is the yth joint.

[0078] The constraint optimization (fmincon) function of matlab is combined to analyze the to-be-solved parameters of the Fourier series, and the excitation trajectory image obtained is as shown in Figure 7 The excitation trajectory function in the image can effectively cover the entire working range and can be used to effectively excite the to-be-identified parameters. The excitation trajectory expression obtained by combining the excitation trajectory expressions (21), (23) and (24) used in the three-stage identification is: (26) In the formula, is the trajectory setting time of the low-speed motion stage, is the trajectory setting time of the high-speed motion stage; and is the first transition function of adjacent stages, is the second transition function of adjacent stages; the angle, angular velocity and acceleration values at adjacent nodes can be ensured to be consistent, and the polynomial is expressed in the form of a quintic polynomial: (27) For example, the polynomial needs to meet the boundary conditions, and the edge angle condition is as shown in formula (28): (28) The unknown coefficients of the polynomial (27) are obtained by solving the polynomial boundary condition of formula (28): (29) In the formula, c0, c1, …, c5 are polynomial coefficients, and △t is the set transition time, is the starting time of the transition phase, The end of the transition phase.

[0079] The unknown parameters obtained by the solution are substituted into the polynomial expression, and the collaborative robot is driven to run according to the desired excitation trajectory function. The parameters required for identification are output by the encoder to realize the identification of all unknown parameters.

[0080] S105. Drive the collaborative robot according to the excitation trajectory, obtain the output parameter matrix, calculate the joint angular velocity of the collaborative robot according to the output parameter matrix and the recursive expression, and calculate the high-order terms of the joint angular velocity step by step.

[0081] Based on the identification stage judgment of the time domain segmentation algorithm, the collaborative robot is driven by the excitation trajectory to obtain a series of physical parameters that are convenient for parameter identification. The output parameter matrix Y of the collaborative robot driven by the excitation trajectory is defined. Then, combined with the recursive expression of the dynamic equation, one set of data Y0 is taken as an example, which includes the parameters required for identification: joint torque τ0, joint angle q0 (0) 、Joint angular velocity q0 (1) , and calculate the joint acceleration q0 (2) : (30) On this basis, the high-order terms are calculated step by step, as shown in formula (31): Formula (31):

[0082] in, is the third-order derivative function of the joint angle value at the initial time step, is the fourth-order derivative function of the joint angle value at the initial time step, is the m-order derivative function of the joint angle value at the initial time step, is the first-order derivative function of the joint friction matrix at the initial time step, is the second-order derivative function of the joint friction matrix at the initial time step, is the m-2 derivative function of the joint friction matrix at the initial time step.

[0083] S106: Set an iterative convergence coefficient. When the error between the expansion values ​​of two adjacent orders is less than the iterative convergence coefficient, output the angular velocity.

[0084] When the error between the expansion values ​​of two adjacent orders is not less than the iterative convergence coefficient, continue the iteration.

[0085] Set the iterative convergence coefficient ɛ. When the error of the expansion value of two adjacent orders is less than the convergence coefficient, where the error of the expansion value of two adjacent orders is obtained through the high-order term, as shown in formula (32), stop the iteration of the expansion order: (32) After completing the expansion iteration of the current time step, calculate the output result of the next time step: (33) When the time step threshold is reached, the iteration stops and the final angular velocity solution is output. .

[0086] S107: Set a speed determination coefficient, and determine the motion stage to which the angular velocity belongs based on the speed determination coefficient.

[0087] Based on the maximum static friction torque, joint stiffness coefficient and joint natural frequency of the collaborative robot, the speed judgment coefficient of the first stage and the speed judgment coefficient of the third stage are calculated.

[0088] The speed judgment coefficient of the second stage and the speed judgment coefficient of the third stage are used to make the judgment in the identification stage, as shown in formula (34): (34) Where, is the speed judgment coefficient in the low-speed motion stage, is the speed judgment coefficient in the high-speed motion stage. The specific expressions of these two speed judgment coefficients are shown in formula (35): Formula (35):

[0089] In the formula is the maximum static friction torque, is the joint stiffness coefficient, is the natural frequency of the joint, calculated in this application The value is 0.03rad / s, The value is taken as 4.28rad / s, and the parameters required for parameter identification are divided through this process.

[0090] S108. Divide the stages of parameter identification according to the determination result to achieve segmented identification of the dynamic parameters of the collaborative robot.

[0091] The collaborative robot is controlled to move according to the excitation trajectory corresponding to the first stage, and the recursive least squares method is used to identify the gravity term, the maximum static friction parameter, and the uncertainty influencing factors of the quasi-static stage; the collaborative robot is controlled to move according to the excitation trajectory corresponding to the second stage, and the recursive least squares method is used to identify the Coulomb friction parameters, Stribeck characteristic parameters, and asymmetric viscous friction parameters; the collaborative robot is controlled to move according to the excitation trajectory corresponding to the third stage, and the recursive least squares method is used to identify the inertia term, Coriolis force term, and harmonic disturbance term parameters.

[0092] Among them, the recursive least squares method constructs a regression matrix based on the output parameter matrix, initializes the parameter matrix and covariance matrix; calculates the gain matrix, updates the parameter matrix and covariance matrix according to the gain matrix; calculates the relative change rate of the parameter matrix between two adjacent iterations, and when the relative change rate is less than the set convergence judgment coefficient, stops the iteration and outputs the optimal parameter matrix. Specifically including: The study of segmented identification of unknown parameters of the dynamic model first focuses on the joint motion under static conditions. At this time, the gravity term, maximum static friction, sliding friction parameters, and uncertainty influencing factors in the quasi-static stage are mainly identified to provide initial values ​​for further dynamic identification and narrow the search space. The model required for identification in this process is shown in formula (36): (36) in, The output torque required for identification of the joint in the quasi-static stage is: is the Coulomb friction coefficient, is the maximum static friction coefficient, is the gravity vector of u×1, It is the uncertainty influencing factor in the quasi-static stage.

[0093] After completing the static parameter identification, the identified gravity term, maximum static friction, sliding friction parameters, and the uncertainty influencing factors in the quasi-static stage are substituted into the dynamic model as known quantities to carry out the parameter identification of the low-speed motion stage. The parameters that need to be identified in this stage are the Coulomb friction parameter, Stribeck characteristic parameter, asymmetric viscous friction parameter, and the uncertainty influencing factors in the low-speed stage. The model that needs to be identified in this process is shown in formula (37): (37) in, To identify the output torque required for the joint at low speed, and is the symmetric interval of asymmetric viscous friction, is the contact stiffness, is the Heaviside step function, is the step function of the reverse motion, is the micro damping, is the internal state variable, is the Stribeck function, It is the uncertainty influencing factor in the low-speed stage.

[0094] The results obtained from the above identification are substituted into the dynamic model as known parameters to carry out the identification of the high-speed motion stage, and the uncertainty influencing factors of the inertia term, Coriolis force term, harmonic disturbance term parameters and high-speed stage are solved. The model required for identification in this process is shown in formula (38): (38) in, To identify the output torque required for high-speed stage, is the u×u mass matrix of the manipulator, where u is an integer greater than or equal to 1, are the centrifugal force and Coriolis force vectors of u×1, is the gravity vector of u×1, is the first harmonic amplitude error caused by gear meshing periodic disturbance, is the joint angle value, is the first phase offset error due to assembly error, e is the maximum order of sine harmonics, f is the maximum order of cosine harmonics, is the harmonic order, is the second harmonic amplitude error caused by gear meshing periodic disturbance, is the second phase offset error caused by assembly error, It is the uncertainty influencing factor in the high-speed stage.

[0095] The three-stage identification process uses the recursive least squares method to perform parameter identification analysis, and the parameters to be identified are output through the parameter update matrix to achieve the solution of the dynamic model. The calculation expression of the gain matrix is ​​shown in formula (39): (39) Where Y is the regression matrix obtained by the excitation trajectory, which includes the specific parameters measured such as angle and angular velocity. is the identity matrix, is the forgetting factor, the initial covariance matrix Set to 10 -3 , the gain matrix K(1) is calculated by combining the regression matrix Y(1) obtained by the first set of identification, and the parameter matrix θ(1) in the current iteration state is calculated based on the empirical definition of the initial parameter matrix θ(0). The calculation expression is shown in formula (40): (40) Where, is the parameter matrix at time t, is the parameter matrix at time t-1, is the gain matrix, which is used to control the parameter update step size.

[0096] At the same time, the covariance matrix P(1) of the current iteration process is calculated to facilitate the calculation of the parameter matrix of the next process. The calculation formula of the covariance matrix is ​​shown in formula (41): (41) The parameter matrix is ​​obtained by iterative output calculation of the above process, and the relative change rate of the parameter matrix under two adjacent iterations is calculated to see whether it meets the convergence condition, as shown in formula (42): (42) Where ɛ1 is the parameter matrix convergence judgment coefficient, and ɛ1 is taken as 1e-4. When the convergence requirement is reached, the calculation is stopped and the optimal parameter matrix θ(t) is output as the final parameter obtained by identification. The identification parameters are substituted into the dynamic model, and the regression matrix Y(t) obtained in this iterative process is substituted into the dynamic model to obtain the current identification torque τ model , combined with the experimental torque τ obtained from the current process excitation trajectory model Calculate the RMSE accuracy error value and judge the accuracy of the current identification process by the RMSE indicator as shown in formula (43): (43) Where, is the experimental measured torque at time t, is the model predicted torque at time t, is the precision error value.

[0097] In order to verify the feasibility of the proposed segmented identification algorithm, a collaborative robot parameter identification simulation analysis was carried out. The identification parameters obtained under the excitation trajectory were solved based on the time domain segmented algorithm. According to the results, the array was divided into three stages for step-by-step identification analysis. The unknown parameters in the dynamic model were identified by the recursive least squares method. After the identification was completed, the unknown parameters were substituted into the dynamic model. The identification accuracy was identified based on the difference between the identification torque parameters and the experimental data. The identification results are shown in Figure 2. Figure 8 As shown in the figure, the error between the theoretical torque and the experimental torque is small, and the proposed segmented identification strategy can effectively improve the accuracy of identification.

[0098] Based on the above content, an improved dynamic friction model considering uncertainty factors and multi-factor coupling is constructed, and the friction torque acting on the joint is obtained according to the improved dynamic friction model; the dynamic equation of the dynamic model is constructed based on the Newton-Euler method and the friction torque acting on the joint; the dynamic equation is solved based on the time domain segmentation algorithm to obtain the recursive expression of the dynamic equation; the excitation trajectory required for the segmented identification of the collaborative robot is set based on the expression of the dynamic equation; the collaborative robot is driven according to the excitation trajectory, and the output parameter matrix is ​​obtained. The joint angular velocity of the collaborative robot is calculated according to the output parameter matrix and the recursive expression, and the high-order terms of the joint angular velocity are calculated step by step; the iterative convergence coefficient is set, and the angular velocity is output when the error of the expanded values ​​of two adjacent orders is less than the iterative convergence coefficient; the speed judgment coefficient is set, and the motion stage to which the angular velocity belongs is judged according to the speed judgment coefficient, and the parameter identification stages are divided according to the judgment result to realize the segmented identification of the dynamic parameters of the collaborative robot.

[0099] It can be seen that this application accurately depicts complex friction by constructing an improved dynamic friction model with multi-factor coupling, decomposes the dynamic equations with a time-domain segmentation algorithm to achieve efficient solution, designs segmented excitation trajectories to cover the entire motion stage, combines recursive iteration with stage judgment to achieve accurate segmented identification of parameters, and improves the accuracy of the collaborative robot dynamic model, providing more reliable parameter support for trajectory planning and force control of collaborative operations, and solving the problems of large identification errors and poor adaptability caused by rough models and single excitation in traditional methods.

[0100] Combined with the above Figures 1 to 8 The method for identifying the dynamic parameters of a collaborative robot taking into account uncertainty factors provided in an embodiment of the present application is introduced in detail. The apparatus and equipment provided in the embodiment of the present application will be introduced below in conjunction with the accompanying drawings.

[0101] The embodiment of the present application also provides a device for identifying the dynamic parameters of a collaborative robot taking uncertainty factors into consideration, such as Figure 9 As shown in FIG, this figure is a schematic diagram of a dynamic parameter identification device of a collaborative robot considering uncertainty factors provided by an embodiment of the present application, the device comprising: Construction module 901 is used to construct an improved dynamic friction model that considers multi-factor coupling, obtain the friction torque on the joint according to the improved dynamic friction model; and construct the dynamic equation of the dynamic model based on the Newton-Euler method and the friction torque on the joint; The calculation module 902 is configured to solve the dynamic equation based on a time domain segmentation algorithm to obtain a recursive expression of the dynamic equation; set an excitation trajectory required for segmentation identification of the collaborative robot based on the expression of the dynamic equation; drive the collaborative robot according to the excitation trajectory, obtain an output parameter matrix, calculate joint angular velocity of the collaborative robot according to the output parameter matrix and the recursive expression of the dynamic equation, and calculate high-order terms of the joint angular velocity step by step; set an iterative convergence coefficient, and when an expansion value error of adjacent two orders is less than the iterative convergence coefficient, output the angular velocity; wherein the expansion value error of the adjacent two orders is obtained through the high-order terms. The identification module 903 is configured to set a speed judgment coefficient, determine a motion stage to which the angular velocity belongs according to the speed judgment coefficient, divide stages of parameter identification according to a determination result, and realize segmentation identification of dynamic parameters of the collaborative robot.

[0102] In some possible implementation manners, the construction module 901 is specifically configured to introduce a stiffness disturbance coefficient according to asymmetry of forward and reverse friction, set friction coefficients of the model under forward and reverse speed motion trends respectively, construct an asymmetric viscous friction term according to the friction coefficients, and construct a basic friction model according to the stiffness disturbance coefficient and the asymmetric viscous friction term; based on periodic disturbance of gear engagement and inertial impact effect, construct a position harmonic term capable of describing friction fluctuation caused by assembly error and gear engagement error with the joint position of the collaborative robot as a variable; introduce a smoothing factor to construct an acceleration compensation term with the joint acceleration of the collaborative robot as a variable; and construct an improved dynamic friction model considering multi-factor coupling by combining the basic friction model, the position harmonic term, the acceleration compensation term, and an uncertainty factor.

[0103] In some possible implementation manners, the calculation module 902 is specifically configured to perform normalization processing on a time variable of joint motion of the collaborative robot to obtain a first time variable; perform high-order Taylor expansion on the joint position of the collaborative robot, determine an expansion order according to the first time variable, obtain a high-order Taylor expansion formula, and obtain an expansion formula containing derivatives of the joint position of each order; determine an expansion formula of a first parameter in the dynamic equation according to the high-order Taylor expansion formula and the expansion formula containing the derivatives of the joint position of each order; bring the expansion formula of the first parameter into the dynamic equation, and perform simplification processing to obtain the recursive expression of the dynamic equation.

[0104] In some possible implementation manners, the calculation module 902 is specifically configured to divide the stages of the collaborative robot segmented identification based on the expression of the dynamic equation, into a first stage identification, a second stage identification, and a third stage identification; design a stair velocity trajectory for the first stage, and when it is determined that the stair velocity trajectory contains a plurality of fixed velocity values, take the stair velocity trajectory as an excitation trajectory for the first stage; design a sinusoidal function trajectory for the second stage, the frequency of the sinusoidal function trajectory is linearly increased from an initial value to a set upper limit frequency, and take the sinusoidal function trajectory as an excitation trajectory for the second stage; design a five-order Fourier series trajectory for the third stage, set a constraint condition, solve a trajectory parameter in combination with a related function, and take the five-order Fourier series trajectory as an excitation trajectory for the third stage; design a transition function, sequentially connect the excitation trajectories set for the stages in sequence through the transition function according to the first stage, the second stage, and the third stage, and set the excitation trajectories as excitation trajectories required by the collaborative robot segmented identification.

[0105] In some possible implementation manners, the device further includes: The iteration module is configured to continue iteration when the error of the expansion values of two adjacent orders is not less than an iteration convergence coefficient.

[0106] In some possible implementation manners, the identification module 903 is specifically configured to calculate a velocity judgment coefficient of the second stage and a velocity judgment coefficient of the third stage based on a maximum static friction torque of the collaborative robot, a joint stiffness coefficient, and a joint inherent frequency.

[0107] In some possible implementation manners, the identification module 903 is specifically configured to control the collaborative robot to move according to the excitation trajectory corresponding to the first stage, and identify a gravity term, a maximum static friction parameter, and an uncertainty influencing factor in a quasi-static stage by using a recursive least square method; control the collaborative robot to move according to the excitation trajectory corresponding to the second stage, and identify a Coulomb friction parameter, a Stribeck characteristic parameter, an asymmetric viscous friction parameter, and an uncertainty influencing factor in a quasi-static stage by using a recursive least square method; control the collaborative robot to move according to the excitation trajectory corresponding to the third stage, and identify an inertia term, a Coriolis force term, a harmonic disturbance term parameter, and an uncertainty influencing factor in a high-speed stage by using a recursive least square method.

[0108] In some possible implementation manners, the recursive least square method is based on an output parameter matrix to construct a regression matrix, initialize a parameter matrix and a covariance matrix; calculate a gain matrix, and update the parameter matrix and the covariance matrix according to the gain matrix; The relative change rate of the parameter matrix between two adjacent iterations is calculated. When the relative change rate is less than the set convergence judgment coefficient, the iteration is stopped and the optimal parameter matrix is ​​output.

[0109] According to the embodiment of the present application, the dynamic parameter identification device of the collaborative robot considering uncertainty factors can correspond to the method described in the embodiment of the present application, and the above-mentioned other operations and / or functions of each module / unit of the dynamic parameter identification device of the collaborative robot considering uncertainty factors are respectively for realizing Figure 1 For the sake of brevity, the corresponding processes of the various methods in the illustrated embodiments are not described again here.

[0110] The present application also provides a computing device. Figure 10 As shown, this figure is a schematic diagram of a computing device provided by an embodiment of the present application, wherein the computing device 400 includes a bus 401, a processor 402, a communication interface 403, and a memory 404. The processor 402, the memory 404, and the communication interface 403 communicate with each other via the bus 401.

[0111] The bus 401 may be a peripheral component interconnect (PCI) bus or an extended industry standard architecture (EISA) bus. The bus may be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 9 Only one thick line is used in the diagram, but this does not mean that there is only one bus or one type of bus.

[0112] The processor 402 may be any one or more of a central processing unit (CPU), a graphics processing unit (GPU), a microprocessor (MP), or a digital signal processor (DSP).

[0113] The communication interface 403 is used for communicating with the outside.

[0114] Memory 404 may include volatile memory, such as random access memory (RAM). Memory 404 may also include non-volatile memory, such as read-only memory (ROM), flash memory, hard disk drive (HDD), or solid state drive (SSD).

[0115] The memory 404 stores executable codes, and the processor 402 executes the executable codes to perform the aforementioned method for identifying dynamic parameters of the collaborative robot taking uncertainty factors into consideration.

[0116] Specifically, in the implementation Figure 8 In the case of the embodiment shown, and Figure 8 When each module or unit of the dynamic parameter identification device of the collaborative robot considering uncertainty factors described in the embodiment is implemented by software, the execution Figure 8 The software or program code required for the functions of each module / unit in the system may be partially or completely stored in the memory 404. The processor 402 executes the program code corresponding to each unit stored in the memory 404 to perform the aforementioned method for identifying the dynamic parameters of the collaborative robot considering uncertainty factors.

[0117] Embodiments of the present application also provide a computer-readable storage medium. The computer-readable storage medium can be any available medium capable of being stored by a computing device, or a data storage device such as a data center that contains one or more available media. The available medium can be a magnetic medium (e.g., a floppy disk, hard disk, or magnetic tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive). The computer-readable storage medium includes instructions that instruct the computing device to execute the above-described method for identifying the dynamic parameters of a collaborative robot that takes uncertainty factors into account.

[0118] The present application also provides a computer program product comprising one or more computer instructions that, when loaded and executed on a computing device, fully or partially generate the process or function described in the present application.

[0119] The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions can be transmitted from one website, computer or data center to another website, computer or data center via wired (e.g., coaxial cable, optical fiber) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0120] When the computer program product is executed by a computer, the computer performs any of the aforementioned methods for identifying the dynamic parameters of a collaborative robot taking uncertainty factors into account. The computer program product may be a software installation package, which can be downloaded and executed on a computer when any of the aforementioned methods for identifying the dynamic parameters of a collaborative robot taking uncertainty factors into account is required.

[0121] The descriptions of the processes or structures corresponding to the above figures have different emphases. For parts that are not described in detail in a certain process or structure, please refer to the relevant descriptions of other processes or structures.

[0122] The above description is only a specific implementation method of the present application, but the protection scope of the present application is not limited thereto. Any changes or replacements within the technical scope disclosed in the present application should be included in the protection scope of the present application.

Claims

1. A method for identifying the dynamic parameters of a collaborative robot considering uncertainty factors, characterized in that: The method comprises: An improved dynamic friction model considering multi-factor coupling is constructed, and the friction torque acting on the joint is obtained according to the improved dynamic friction model; constructing a dynamic equation of the dynamic model based on the Newton-Euler method and the friction torque acting on the joint; Solving the kinetic equation based on a time-domain segmentation algorithm to obtain a recursive expression of the kinetic equation; Setting the excitation trajectory required for segmented identification of the collaborative robot based on the expression of the dynamic equation; driving the collaborative robot according to the excitation trajectory, obtaining an output parameter matrix, calculating the joint angular velocity of the collaborative robot according to the output parameter matrix and a recursive expression of the dynamic equation, and calculating high-order terms of the joint angular velocity step by step; Set the iterative convergence coefficient. When the error between the expansion values ​​of two adjacent orders is less than the iterative convergence coefficient, output the angular velocity. The error between the expansion values ​​of two adjacent orders is obtained through the high-order terms. The speed judgment coefficient is set, and the motion stage to which the angular velocity belongs is determined according to the speed judgment coefficient. The parameter identification stages are divided according to the judgment results to realize the segmented identification of the dynamic parameters of the collaborative robot.

2. The method according to claim 1, characterized in that The improved dynamic friction model considering multi-factor coupling is constructed, including: According to the asymmetry of forward and reverse friction, a stiffness perturbation coefficient is introduced, and the friction coefficient of the model under the forward and reverse velocity motion trends is set respectively. An asymmetric viscous friction term is constructed based on the friction coefficient, and a basic friction model is constructed based on the stiffness perturbation coefficient and the asymmetric viscous friction term. Based on the gear meshing periodic disturbance and inertial impact effect, the joint position of the collaborative robot is used as a variable to construct a position harmonic term that can describe the friction fluctuation caused by assembly error and gear meshing error. The joint acceleration of the collaborative robot is used as a variable, and a smoothing factor is introduced to construct the acceleration compensation term. An improved dynamic friction model considering multi-factor coupling is constructed by combining the basic friction model, the position harmonic term, the acceleration compensation term and uncertainty factors.

3. The method according to claim 1, characterized in that The method of solving the kinetic equation based on the time domain segmentation algorithm to obtain a recursive expression of the kinetic equation includes: Normalizing the time variables of the joint motion of the collaborative robot to obtain a first time variable; Performing a high-order Taylor expansion on the joint positions of the collaborative robot, determining the expansion order according to the first time variable, obtaining a high-order Taylor expansion, and obtaining an expansion including derivatives of various orders of the joint positions; Determining an expansion of a first parameter in a dynamic equation based on the high-order Taylor expansion and an expansion including derivatives of various orders of joint positions; The expanded expression of the first parameter is introduced into the kinetic equation and simplified to obtain the recursive expression of the kinetic equation.

4. The method according to claim 1, wherein The step of setting the excitation trajectory required for segmented identification of the collaborative robot based on the dynamic equation expression includes: Dividing the stages of segmented identification of the collaborative robot based on the dynamic equation expression into first stage identification, second stage identification, and third stage identification; designing a stepped velocity trajectory for the first stage, and when it is determined that the stepped velocity trajectory includes a plurality of fixed velocity values, using the stepped velocity trajectory as the excitation trajectory for the first stage; Designing a second-stage sinusoidal function trajectory, wherein the frequency of the sinusoidal function trajectory linearly increases from an initial value to a set upper frequency limit, and using the sinusoidal function trajectory as the excitation trajectory of the second stage; Design the fifth-order Fourier series trajectory of the third stage, set constraints, solve the trajectory parameters by combining the correlation function, and use the fifth-order Fourier series trajectory as the excitation trajectory of the third stage; Design a transition function, and connect the excitation trajectories set in each stage in the order of the first stage, the second stage, and the third stage through the transition function, and set them as the excitation trajectory required for the collaborative robot segmented identification.

5. The method according to claim 1, wherein The method further comprises: When the error between the expansion values ​​of two adjacent orders is not less than the iterative convergence coefficient, continue the iteration.

6. The method according to claim 1, characterized in that The setting speed judgment coefficient includes: Based on the maximum static friction torque, joint stiffness coefficient and joint natural frequency of the collaborative robot, the speed judgment coefficient of the second stage and the speed judgment coefficient of the third stage are calculated.

7. The method according to claim 1, characterized in that The segmented identification of the collaborative robot's dynamic parameters includes: The collaborative robot is controlled to move along the excitation trajectory corresponding to the first stage, and the recursive least squares method is used to identify the gravity term, the maximum static friction parameter, and the uncertainty factors influencing the quasi-static stage. The collaborative robot is controlled to move along the excitation trajectory corresponding to the second stage, and the recursive least squares method is used to identify the Coulomb friction parameters, Stribeck characteristic parameters, asymmetric viscous friction parameters, and uncertainty factors in the quasi-static stage. The collaborative robot is controlled to move according to the excitation trajectory corresponding to the third stage, and the recursive least squares method is used to identify the parameters of the inertia term, Coriolis force term, harmonic disturbance term and the uncertainty influencing factors in the high-speed stage.

8. The method according to claim 7, characterized in that The recursive least squares method constructs a regression matrix based on the output parameter matrix, and initializes the parameter matrix and the covariance matrix; Calculate the gain matrix and update the parameter matrix and covariance matrix according to the gain matrix; The relative change rate of the parameter matrix between two adjacent iterations is calculated. When the relative change rate is less than the set convergence judgment coefficient, the iteration is stopped and the optimal parameter matrix is ​​output.

9. A device for identifying dynamic parameters of a collaborative robot taking uncertainty factors into consideration, characterized in that: The device comprises: A construction module is used to construct an improved dynamic friction model that considers the coupling of multiple factors, obtain the friction torque exerted on the joint according to the improved dynamic friction model; and construct the dynamic equation of the dynamic model based on the Newton-Euler method and the friction torque exerted on the joint; A calculation module is configured to solve the dynamic equation based on a time-domain segmented algorithm to obtain a recursive expression of the dynamic equation; set an excitation trajectory required for segmented identification of the collaborative robot based on the expression of the dynamic equation; drive the collaborative robot according to the excitation trajectory, obtain an output parameter matrix, calculate the joint angular velocity of the collaborative robot according to the output parameter matrix and the recursive expression of the dynamic equation, and calculate high-order terms of the joint angular velocity step by step; set an iterative convergence coefficient, and output the angular velocity when the error between the expanded values ​​of two adjacent orders is less than the iterative convergence coefficient; wherein the error between the expanded values ​​of two adjacent orders is obtained through the high-order terms; The identification module is used to set the speed judgment coefficient, determine the motion stage to which the angular velocity belongs based on the speed judgment coefficient, divide the parameter identification stages according to the judgment results, and realize the segmented identification of the collaborative robot's dynamic parameters.

10. A computing device, characterized in that including memory and processor; One or more computer programs are stored in the memory, and the one or more computer programs include instructions; when the instructions are executed by the processor, the computing device executes the method according to any one of claims 1 to 8.

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