Hybrid robot dynamics modeling and friction parameter identification method

Abstract

The invention provides a hybrid robot dynamic modeling and friction parameter identification method. The hybrid robot dynamic modeling and friction parameter identification method comprises the following steps that a Newton-Euler method and a spiral theory are used for establishing a dynamic model considering active and passive joint friction for a hybrid robot; carrying out global sensitivity analysis on friction parameters of the hybrid robot by adopting a summation function variance and covariance decomposition method; an identification and verification circular trajectory of the hybrid robot is planned according to a quintic polynomial; the driving torque of a servo motor in the moving process of the robot is collected; and carrying out friction parameter identification on the hybrid robot by using a Gaussian quantum particle swarm algorithm. The method has the beneficial effects that the established model can accurately predict the driving torques under different configurations, and a reliable dynamic basis is provided for trajectory planning and real-time control of the robot.

Description

Technical Field

[0001] This invention relates to the field of industrial robot dynamics, and in particular to a method for dynamic modeling and friction parameter identification of hybrid robots. Background Technology

[0002] Hybrid robots combine the advantages of serial robots (large workspace) and parallel robots (high rigidity and strong load-bearing capacity), demonstrating significant application value in high-end industrial fields such as aerospace component processing and high-end equipment manufacturing. As the foundation for achieving high-precision control, the dynamic model must accurately reflect the force and motion relationships of each component during robot movement. Joint friction, as one of the key factors affecting the accuracy of the dynamic model, plays a significant role in the robot's pose error, trajectory tracking performance, and stability.

[0003] Currently, research on robot dynamics modeling has made some progress, but there are still significant gaps in the comprehensiveness of friction considerations and the accuracy of the models. On the one hand, most existing dynamics modeling methods focus on modeling the friction parameters of active joints, often ignoring the friction effects of passive joints. However, in hybrid robots, passive joints are key links in motion transmission, and their friction will accumulate errors as the motion configuration changes. Especially during high-speed or complex trajectory motion, this error will significantly reduce the accuracy of the dynamics model. On the other hand, traditional modeling processes often treat joint friction as a constant value or simplify calculations using empirical formulas, without considering the dynamic influence of joint constraint forces on friction, making it difficult for the dynamics model to accurately match actual working conditions.

[0004] In terms of friction parameter identification, existing identification methods have two prominent problems: First, there is a lack of systematic screening of friction parameters. Usually, all parameters in the model are uniformly identified, but in reality, some friction parameters have low sensitivity to driving torque, and blindly including them in the identification will increase computational redundancy. Second, the identification process is not sufficiently coupled with the dynamic model. It does not take into account the constraint force changes under the actual configuration of the robot, resulting in poor adaptability of the identified parameters under different motion conditions, making it difficult to directly apply them to high-precision dynamic models. Summary of the Invention

[0005] In view of this, the present invention aims to propose a method for dynamic modeling and friction parameter identification of hybrid robots to solve at least one of the above-mentioned problems in the prior art.

[0006] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0007] A method for dynamic modeling and friction parameter identification of a hybrid robot includes the following steps:

[0008] S1. A dynamic model considering the friction of active and passive joints is established for the hybrid robot using the Newton-Euler method and the spiral theory.

[0009] S2, global sensitivity analysis of friction parameters of hybrid robots is carried out by using the summation function variance and covariance decomposition method;

[0010] S3, Identification and verification of circular trajectories of hybrid robots according to fifth-order polynomial programming;

[0011] S4, operate the hybrid robot to move along a predetermined trajectory and collect the driving torque of the servo motor during the robot's movement;

[0012] S5 uses the Gaussian quantum particle swarm optimization algorithm to identify friction parameters of a hybrid robot.

[0013] Furthermore, S1 includes the following sub-steps:

[0014] S11, based on the inverse kinematics model, through the end-point reference point The pose, velocity, and acceleration are used to obtain the variables of each active joint of the hybrid robot. , Velocity amplitude , ; acceleration amplitude , ;

[0015] S12, for the hybrid robot, the component numbers that need to consider inertia, where the active arm can be disassembled into a sleeve, a lead screw and motor assembly (excluding the moment of inertia of the lead screw about its own axis), and a push rod assembly, in the branch... The sleeve, lead screw and motor assembly are component 1, and the push rod assembly is component 2; in the branch chain 4, the rotating bracket is component 0, the universal ring assembly is component 1, the driven support arm is component 2, and the moving platform is component 3; the first swing head, the second swing head and the cutter are component 4, component 5 and component 6 respectively;

[0016] S13, from the velocities and accelerations of all joints, obtain the relationships between all components and points. Instantaneous overlap point (like , ;like , ) velocity / acceleration spiral / ;

[0017] S14, calculate all components about point using the following formula. The resultant force of inertial force / torque and gravity spirals :

[0018] ;

[0019] In the formula, This indicates that the component is about the point. The spatial inertia matrix; Represents a spiral The cross product operator; This indicates that the component is about the point. The gravity spiral;

[0020] S15, According to the Newton-Euler method, all components are considered as free bodies under force, and their forces are analyzed. Each component is subjected to gravity, inertial force / torque, constraint force / torque from the kinematic pairs at both ends, and frictional force / torque. If the kinematic pairs are active, driving force / torque is also included. Let the reference point of the kinematic pairs at both ends of any component be... The constraint resultant force helical can be written using the following formula. ( Indicates component reference point The constraint spiral, Indicates component reference point (constraint screw)

[0021] = ;

[0022] In the formula, Point Unit vectors in three orthogonal directions; Point Time The direction vector; The magnitude matrix representing the constraint screw in the three orthogonal directions is expressed as follows:

[0023] ;

[0024] In the formula, , , and They represent the reference points respectively. along the direction The amplitudes of the constraint force, friction force, constraint torque, and friction torque, where, if Indicates the reference point of the active secondary and Let the axis vector of the active pair be... (Active sliding joint) indicates the driving force. (Active rotating joint) indicates the driving torque;

[0025] S16 uses the Stribeck model to model the frictional force / torque of the kinematic pair, and its expression is:

[0026] ;

[0027] In the formula, Indicates frictional force / torque. , , and These represent the Coulomb coefficient of friction, the maximum static friction coefficient, the viscous friction coefficient, and the Stribeck velocity, respectively. This represents the radius of the friction circle of a kinematic pair, where the sliding pair... ; This indicates the magnitude of the constraint force on the plane perpendicular to the axis of the kinematic pair; Indicates the joint velocity amplitude; sign represents the sign function;

[0028] S17, list all components about points using the following formula. Newton-Euler equations:

[0029] ;

[0030] S18, organize the Newton-Euler equations for all components, containing a total of 78 equations and 80 unknown constraint forces / moments. Combine these with the two equations for constraint deformation and compatibility conditions, forming a linear system of 80 equations and 80 unknowns:

[0031] ;

[0032] In the formula, Represents the coefficient matrix. Represents a constant vector. This represents a vector of unknown parameters containing joint constraint forces / torques and driving forces / torques;

[0033] S19, obtained by solving the system of linear equations And extract the joint driving force of the 1T2R parallel mechanism from it. And the joint driving torque of the first and second swing heads and the cutting tool. ;

[0034] S110, the joint driving force is calculated using the following formula. Converted to driving torque:

[0035] ;

[0036] In the formula, This indicates the lead of the ball screw. This indicates the frictional torque at the leadscrew-nut junction;

[0037] Furthermore, S19 includes the following sub-steps:

[0038] S191, neglecting the influence of joint friction, solve the linear equation system of S18 to obtain the constraint forces / torques of each joint;

[0039] S192, Substitute the obtained joint constraint forces into the Stribeck friction model in S16 to obtain the friction force / torque of each joint;

[0040] S193. Considering the impact of neglecting joint friction on the accuracy of joint constraint force solution in S191, the joint friction force / torque obtained in S192 is incorporated into the force analysis. Using the linear equations in S1-8, the initial corrected joint constraint force is obtained.

[0041] S194, repeat S192 and S193 to obtain the joint drive and constraint forces after secondary correction;

[0042] Furthermore, the hybrid robot comprises 6 active joints and 12 passive joints. Since the active joints play a dominant role in the friction effect, they are directly incorporated into the identification process. All passive joints are located in the 1T2R parallel mechanism. S2 includes the following sub-steps:

[0043] S21 classifies the friction parameters of all passive joints into four categories: Coulomb friction, viscous friction, static friction, and Stribeck velocity.

[0044] S22, taking Coulomb friction parameters as an example, constructs three driving forces for a 1T2R parallel mechanism using the following formula. Three sets of summation functions:

[0045] , ;

[0046] In the formula, This represents a combination vector of the 12 parameters in the Coulomb friction parameters;

[0047] S23, will , It can be represented by a high-dimensional model as the sum of a series of low-dimensional functions. and The variance can be expressed as:

[0048] ;

[0049] S24, using the Latin hypersampling method, the Coulomb friction parameters are sampled twice independently within its sampling space to generate... A sample matrix with 12 rows and 12 columns and Sample size Set it to 15000, then swap them. and The Columns, constructing matrices Here, Indicates using The Column substitution No. Therefore, , The variance of the variance and the variance of its subfunctions can be expressed as:

[0050] , ;

[0051] ;

[0052] S25 will determine the total fluctuation of the system. Defined as:

[0053] ;

[0054] S26, Coulomb friction parameters Individual fluctuations and their interaction with other Coulomb friction parameters Apart from the partial fluctuations caused by the interaction, the sum of all partial fluctuations caused by other Coulomb friction parameters is defined as:

[0055] ;

[0056] In the formula, express Except for containing The sum of the variances of all sub-functions other than the first one. express Except for containing The sum of the variances of all sub-functions other than the first one;

[0057] S27, Define Coulomb friction parameters global sensitivity index for:

[0058] ;

[0059] S28, repeating S22 to S27, yields global sensitivity indices for viscous friction, static friction, and Stribeck velocity. ;

[0060] S29, based on four types of friction We select highly sensitive friction parameters for the passive joint and incorporate them into the friction parameter process, while ignoring the influence of low-sensitivity friction parameters.

[0061] Furthermore, S3 includes the following sub-steps:

[0062] S31, Assume: the robot's velocity and acceleration at the start and stop are 0, and the initial angle is... Termination angle The start time is The termination time is ,point The line connecting the center of the circular trajectory to the coordinate system The angle between the y-axis and the y-axis It satisfies the rule of fifth-degree polynomial transformation:

[0063] ;

[0064] In the formula, These are the coefficients of the terms from degree 0 to degree 5 corresponding to the fifth-degree polynomial;

[0065] S32, point obtained from S31 Speed ​​Spiral ,right Differentiation yields the acceleration spiral .

[0066] Furthermore, S4 includes the following steps:

[0067] S41, utilizing the inverse kinematics of a hybrid robot, based on points The position, velocity, and acceleration are used to calculate the displacement, velocity, and acceleration of each active joint;

[0068] S42, the acquired active joint kinematic information is written into G code and then input into the Power PMAC IDE software to drive the hybrid robot to move according to the identified and verified circular trajectory;

[0069] S43, during the movement of the hybrid robot, synchronously collects the drive current signals of each servo motor on both tracks. ;

[0070] S44 converts the drive current signal into drive torque using the following formula:

[0071] ;

[0072] In the formula, The reduction ratio of the speed reducer connected to the servo motor. The torque constant of the servo motor. This represents the servo motor current.

[0073] Furthermore, S5 includes the following sub-steps:

[0074] S51, Determine the number of particles Initialize the friction parameter population in the friction parameter value space. ,in This represents the combination of friction parameters to be identified;

[0075] S52, the sum of the mean square error of the theoretical driving torque of each active joint S111 and S112 and the collected driving torque of S44 is used as the fitness function, and the minimum of the fitness function is set as the optimization objective. Its expression is:

[0076] ;

[0077] In the formula, This indicates the number of sampling points in parameter identification. , These represent the theoretical driving torque value and the acquired driving torque value of the i-th active joint at the j-th sampling point, respectively.

[0078] S53, calculate the fit value for each particle, comparing each particle before... The fit values ​​of the previous and current generations are used to update the local optimal combination of friction parameters for individual particles. Compare the fit values ​​of all particles in the previous t generations with those in the current generation to update the globally optimal combination of friction parameters for the particles. ;

[0079] S54, calculate the variable using the following formula. :

[0080] ;

[0081] In the formula, and It is a Gaussian mutation operator and follows a Gaussian distribution with mean 0 and variance 1;

[0082] S55, contraction-expansion factor Dynamic adjustment is achieved through a linear decreasing strategy, the expression of which is:

[0083] ;

[0084] In the formula, and These represent the initial and final values ​​of the inertia weight, respectively. Indicates the maximum number of iterations. Indicates the current iteration number;

[0085] S56, calculate the local optimal combination of friction parameters for all particles using the following formula. arithmetic mean vector :

[0086] ;

[0087] S57 updates the state of all particles using the following formula:

[0088] ;

[0089] In the formula, Represents a random number;

[0090] S58, jump to S53, until the maximum iteration number is reached, then the last generation... The corresponding globally optimal combination of friction parameters is used as the identification result of the friction parameters.

[0091] Furthermore, it also includes S6, which verifies and evaluates the dynamic model through experiments based on the identified parameters, and corrects the dynamic model of the hybrid robot.

[0092] Furthermore, S6 includes the following sub-steps:

[0093] S61, calculate the driving torque of each active joint using the identified friction parameters, and draw a comparison chart of the theoretical driving torque and the collected driving torque;

[0094] S62, Using the coefficient of determination The dynamic model is evaluated, and its expression is as follows:

[0095] ;

[0096] In the formula, Indicates the first The average value of the driving torque collected by each active joint over N sampling points;

[0097] S63, to further verify the generalization ability of the dynamic model and friction parameter identification results, calculate the driving torque of each active joint under the verification trajectory, plot a comparison chart of the theoretical driving torque and the collected driving torque, and use S62's... The dynamic model is evaluated.

[0098] Compared with existing technologies, the hybrid robot dynamics modeling and friction parameter identification method of this invention has the following advantages: 1. Addressing the limitation of existing technologies that ignore passive joint friction, this invention simultaneously incorporates the frictional effects of both active and passive joints. Compared with traditional models that only consider active joint friction, this method can accurately capture the coupling effect of active and passive joint friction under different configurations; 2. Overcoming the shortcomings of traditional models that treat friction as a constant value or simplify calculations, this invention incorporates joint constraint forces into the friction modeling system. By integrating the Newton-Euler method with the spiral theory, a mathematical correlation is established for the dynamic changes of constraint forces with configuration, load, and running speed, thereby accurately characterizing the nonlinear characteristics of friction; 3. Addressing the parameter redundancy problem of existing identification methods, this invention uses global sensitivity analysis based on variance and covariance decomposition to screen key friction parameters with high sensitivity to driving force, and uses the Gaussian quantum particle swarm optimization algorithm to optimize parameters, ensuring that the identified parameters have strong adaptability under different configurations and loads. In summary, the dynamic model established by this invention can accurately predict the driving torque under different configurations, greatly improving the accuracy of the dynamic model of hybrid robots and providing a reliable dynamic basis for robot trajectory planning and real-time control. Attached Figure Description

[0099] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0100] Figure 1 This is a front view schematic diagram of the hybrid robot three-dimensional mechanism described in an embodiment of the present invention;

[0101] Figure 2 This is a rear view schematic diagram of the hybrid robot three-dimensional mechanism described in an embodiment of the present invention;

[0102] Figure 3 This is a simplified schematic diagram of the hybrid robot described in an embodiment of the present invention;

[0103] Figure 4 This is a flowchart illustrating the global sensitivity analysis process described in an embodiment of the present invention.

[0104] Figure 5 This is a flowchart illustrating the Gaussian quantum particle swarm optimization algorithm for identifying friction parameters according to an embodiment of the present invention.

[0105] Figure 6 This represents the fitness function value variation curve described in the embodiments of the present invention;

[0106] Figure 7 This represents the driving torque curves collected and calculated by all active joints of the hybrid robot described in this embodiment of the invention during the identification of the circular trajectory;

[0107] Figure 8 This represents the driving torque curves collected and calculated by all active joints of the hybrid robot described in this embodiment of the invention during the verification circular trajectory;

[0108] Explanation of reference numerals in the attached figures:

[0109] 1-First servo motor; 2-Second servo motor; 3-Third servo motor; 4-First sleeve; 5-Second sleeve; 6-Third sleeve; 7-First push rod; 8-Second push rod; 9-Third push rod; 10-Rotating bracket; 11-Universal ring; 12-Driven support arm; 13-Moving platform; 14-First swing head; 15-Second swing head; 16-Cutting tool.

[0110] Figure 3 middle:

[0111] : Corresponds to branch The intersection of the axis and the axis of the rotating support;

[0112] : The intersection of the driven support arm axis and the rotating bracket;

[0113] : Corresponds to branch The intersection of the axis and the moving platform;

[0114] For the dynamic platform Point and Midpoint of a point;

[0115] : This is the fixed connection point between the driven support arm and the moving platform;

[0116] : The intersection of the axes of the first and second oscillating heads;

[0117] : refers to the tip of the cutting tool;

[0118] : Corresponds to branch Displacement of the sliding joint ( Click (distance between points)

[0119] : for the displacement of the sliding joint of the driven support arm ( Click (distance between points)

[0120] : The rotation angle of the first swing head around the axis of the moving platform;

[0121] : The angle of rotation of the second pendulum head around the axis of the first pendulum head;

[0122] : is the angle of rotation of the tool around the axis of the second oscillating head. Detailed Implementation

[0123] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0124] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0125] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0126] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0127] Please see Figures 1 to 8 A method for dynamic modeling and friction parameter identification of hybrid robots, comprising the following steps:

[0128] S1. A dynamic model considering the friction of active and passive joints is established for the hybrid robot using the Newton-Euler method and the spiral theory.

[0129] S2, global sensitivity analysis of friction parameters of hybrid robots is carried out by using the summation function variance and covariance decomposition method;

[0130] S3, Identification and verification of circular trajectories of hybrid robots according to fifth-order polynomial programming;

[0131] S4, operate the hybrid robot to move along a predetermined trajectory and collect the driving torque of the servo motor during the robot's movement;

[0132] S5 uses the Gaussian quantum particle swarm optimization algorithm to identify friction parameters of a hybrid robot.

[0133] In a preferred embodiment, S1 includes the following sub-steps:

[0134] S11, such as Figure 3 As shown, based on the inverse kinematics model, through the end reference point The pose, velocity, and acceleration are used to obtain the variables of each active joint of the hybrid robot. , Velocity amplitude , ; acceleration amplitude , ;

[0135] S12, for the hybrid robot, the component numbers that need to consider inertia, where the active arm can be disassembled into a sleeve, a lead screw and motor assembly (excluding the moment of inertia of the lead screw about its own axis), and a push rod assembly, in the branch... The sleeve, lead screw and motor assembly are component 1, and the push rod assembly is component 2; in the branch chain 4, the rotating bracket is component 0, the universal ring assembly is component 1, the driven support arm is component 2, and the moving platform is component 3; the first swing head, the second swing head and the cutter are component 4, component 5 and component 6 respectively;

[0136] S13, from the velocities and accelerations of all joints, obtain the relationships between all components and points. Instantaneous overlap point (like , ;like , ) velocity / acceleration spiral / ;

[0137] S14, calculate all components about point using the following formula. The resultant force of inertial force / torque and gravity spirals :

[0138] ;

[0139] In the formula, This indicates that the component is about the point. The spatial inertia matrix; Represents a spiral The cross product operator; This indicates that the component is about the point. The gravity spiral;

[0140] S15, According to the Newton-Euler method, all components are considered as free bodies under force, and their forces are analyzed. Each component is subjected to gravity, inertial force / torque, constraint force / torque from the kinematic pairs at both ends, and frictional force / torque. If the kinematic pairs are active, driving force / torque is also included. Let the reference point of the kinematic pairs at both ends of any component be... The constraint resultant force helical can be written using the following formula. ( Indicates component reference point The constraint spiral, Indicates component reference point (constraint screw)

[0141] = ;

[0142] In the formula, Point Unit vectors in three orthogonal directions; Point Time The direction vector; The magnitude matrix representing the constraint screw in the three orthogonal directions is expressed as follows:

[0143] ;

[0144] In the formula, , , and They represent the reference points respectively. along the direction The amplitudes of the constraint force, friction force, constraint torque, and friction torque, where, if Indicates the reference point of the active secondary and Let the axis vector of the active pair be... (Active sliding joint) indicates the driving force. (Active rotating joint) indicates the driving torque;

[0145] S16 uses the Stribeck model to model the frictional force / torque of the kinematic pair, and its expression is:

[0146] ;

[0147] In the formula, Indicates frictional force / torque. , , and These represent the Coulomb coefficient of friction, the maximum static friction coefficient, the viscous friction coefficient, and the Stribeck velocity, respectively. This represents the radius of the friction circle of a kinematic pair, where the sliding pair... ; This indicates the magnitude of the constraint force on the plane perpendicular to the axis of the kinematic pair; Indicates the joint velocity amplitude; sign represents the sign function;

[0148] S17, list all components about points using the following formula. Newton-Euler equations:

[0149] ;

[0150] S18, organize the Newton-Euler equations for all components, containing a total of 78 equations and 80 unknown constraint forces / moments. Combine these with the two equations for constraint deformation and compatibility conditions, forming a linear system of 80 equations and 80 unknowns:

[0151] ;

[0152] In the formula, Represents the coefficient matrix. Represents a constant vector. This represents a vector of unknown parameters containing joint constraint forces / torques and driving forces / torques;

[0153] S19, obtained by solving the system of linear equations And extract the joint driving force of the 1T2R parallel mechanism from it. And the joint driving torque of the first and second swing heads and the cutting tool. ;

[0154] S110, the joint driving force is calculated using the following formula. Converted to driving torque:

[0155] ;

[0156] In the formula, This indicates the lead of the ball screw. This indicates the frictional torque at the leadscrew-nut junction;

[0157] In a preferred embodiment, S19 includes the following sub-steps:

[0158] S191, neglecting the influence of joint friction, solve the linear equation system of S18 to obtain the constraint forces / torques of each joint;

[0159] S192, Substitute the obtained joint constraint forces into the Stribeck friction model in S16 to obtain the friction force / torque of each joint;

[0160] S193. Considering the impact of neglecting joint friction on the accuracy of joint constraint force solution in S191, the joint friction force / torque obtained in S192 is incorporated into the force analysis. Using the linear equations in S18, the initial corrected joint constraint force is obtained.

[0161] S194, repeat S192 and S193 to obtain the joint drive and constraint forces after secondary correction;

[0162] In a preferred embodiment, the hybrid robot includes 6 active joints and 12 passive joints. Since the active joints play a dominant role in the friction effect, they are directly incorporated into the identification process. All passive joints are located in a 1T2R parallel mechanism, such as... Figure 4 As shown, S2 includes the following sub-steps:

[0163] S21 classifies the friction parameters of all passive joints into four categories: Coulomb friction, viscous friction, static friction, and Stribeck velocity.

[0164] S22, taking Coulomb friction parameters as an example, constructs three driving forces for a 1T2R parallel mechanism using the following formula. Three sets of summation functions:

[0165] , ;

[0166] In the formula, This represents a combination vector of the 12 parameters in the Coulomb friction parameters;

[0167] S23, will , It can be represented by a high-dimensional model as the sum of a series of low-dimensional functions. and The variance can be expressed as:

[0168] ;

[0169] S24, using the Latin hypersampling method, the Coulomb friction parameters are sampled twice independently within its sampling space to generate... A sample matrix with 12 rows and 12 columns and Sample size Set it to 15000, then swap them. and The Columns, constructing matrices Here, Indicates using The Column substitution No. Therefore, , The variance of the variance and the variance of its subfunctions can be expressed as:

[0170] , ;

[0171] ;

[0172] S25 will determine the total fluctuation of the system. Defined as:

[0173] ;

[0174] S26, Coulomb friction parameters Individual fluctuations and their interaction with other Coulomb friction parameters Apart from the partial fluctuations caused by the interaction, the sum of all partial fluctuations caused by other Coulomb friction parameters is defined as:

[0175] ;

[0176] In the formula, express Except for containing The sum of the variances of all sub-functions other than the first one. express Except for containing The sum of the variances of all sub-functions other than the first one;

[0177] S27, Define Coulomb friction parameters global sensitivity index for:

[0178] ;

[0179] S28, repeating S22 to S27, yields global sensitivity indices for viscous friction, static friction, and Stribeck velocity. ;

[0180] S29, based on four types of friction We select highly sensitive friction parameters for the passive joint and incorporate them into the friction parameter process, while ignoring the influence of low-sensitivity friction parameters.

[0181] In a preferred embodiment, S3 includes the following sub-steps:

[0182] S31, Assume: the robot's velocity and acceleration at the start and stop are 0, and the initial angle is... Termination angle The start time is The termination time is ,point The line connecting the center of the circular trajectory to the coordinate system The angle between the y-axis and the y-axis It satisfies the rule of fifth-degree polynomial transformation:

[0183] ;

[0184] In the formula, These are the coefficients of the terms from degree 0 to degree 5 corresponding to the fifth-degree polynomial;

[0185] S32, point obtained from S31 Speed ​​Spiral ,right Differentiation yields the acceleration spiral .

[0186] In a preferred embodiment, S4 includes the following steps:

[0187] S41, utilizing the inverse kinematics of a hybrid robot, based on points Given the pose, velocity, and acceleration, calculate the displacement, velocity, and acceleration of each active joint;

[0188] S42, the acquired active joint kinematic information is written into G code and then input into the Power PMAC IDE software to drive the hybrid robot to move according to the identified and verified circular trajectory;

[0189] S43, during the movement of the hybrid robot, synchronously collects the drive current signals of each servo motor on both tracks. ;

[0190] S44 converts the drive current signal into drive torque using the following formula:

[0191] ;

[0192] In the formula, The reduction ratio of the speed reducer connected to the servo motor. The torque constant of the servo motor. This represents the servo motor current.

[0193] In a preferred embodiment, such as Figure 5 As shown, S5 includes the following sub-steps:

[0194] S51, Determine the number of particles Initialize the friction parameter population in the friction parameter value space. ,in This represents the combination of friction parameters to be identified;

[0195] S52, the sum of the mean square error of the theoretical driving torque of each active joint S19 and S110 and the collected driving torque of S44 is used as the fitness function, and the minimum of the fitness function is set as the optimization objective. Its expression is:

[0196] ;

[0197] In the formula, This indicates the number of sampling points in parameter identification. , These represent the theoretical driving torque value and the acquired driving torque value of the i-th active joint at the j-th sampling point, respectively.

[0198] S53, calculate the fit value for each particle, comparing each particle before... The fit values ​​of the previous and current generations are used to update the local optimal combination of friction parameters for individual particles. Compare the fit values ​​of all particles in the previous t generations with those in the current generation to update the globally optimal combination of friction parameters for the particles. ;

[0199] S54, calculate the variable using the following formula. :

[0200] ;

[0201] In the formula, and It is a Gaussian mutation operator and follows a Gaussian distribution with mean 0 and variance 1;

[0202] S55, contraction-expansion factor Dynamic adjustment is achieved through a linear decreasing strategy, the expression of which is:

[0203] ;

[0204] In the formula, and These represent the initial and final values ​​of the inertia weight, respectively. Indicates the maximum number of iterations. Indicates the current iteration number;

[0205] S56, calculate the local optimal combination of friction parameters for all particles using the following formula. arithmetic mean vector :

[0206] ;

[0207] S57 updates the state of all particles using the following formula:

[0208] ;

[0209] In the formula, Represents a random number;

[0210] S58, jump to S53, until the maximum iteration number is reached, then the last generation... The corresponding globally optimal combination of friction parameters is used as the identification result of the friction parameters.

[0211] In a preferred embodiment, S6 includes the following sub-steps:

[0212] S61, such as Figure 7 As shown, the driving torque of each active joint is calculated using the identified friction parameters, and a comparison chart of the theoretical driving torque and the collected driving torque is drawn.

[0213] S62, Using the coefficient of determination The dynamic model is evaluated, and its expression is as follows:

[0214] ;

[0215] In the formula, Indicates the first The average value of the driving torque collected by each active joint over N sampling points;

[0216] S63, to further verify the generalization ability of the dynamic model and friction parameter identification results, the driving torque of each active joint under the verification trajectory is calculated, such as... Figure 8 As shown, a comparison chart of the theoretical driving torque and the collected driving torque is plotted, and S62's... The dynamic model is evaluated.

[0217] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for dynamic modeling and friction parameter identification of a hybrid robot, characterized in that, Includes the following steps: S1. A dynamic model considering the friction of active and passive joints is established for the hybrid robot using the Newton-Euler method and the spiral theory. S2, global sensitivity analysis of friction parameters of hybrid robots is carried out by using the summation function variance and covariance decomposition method; S3, Identification and verification of circular trajectories of hybrid robots according to fifth-order polynomial programming; S4, operate the hybrid robot to move along a predetermined trajectory and collect the driving torque of the servo motor during the robot's movement; S5 uses the Gaussian quantum particle swarm optimization algorithm to identify friction parameters of a hybrid robot.

2. The method for dynamic modeling and friction parameter identification of a hybrid robot according to claim 1, characterized in that, S1 includes the following steps: S11, based on the inverse kinematics model, through the end-point reference point The pose, velocity, and acceleration are used to obtain the variables of each active joint of the hybrid robot. , Velocity amplitude , ; acceleration amplitude , ; S12, for hybrid robots, all component numbers need to be considered for inertia. The active arm is broken down into a sleeve, lead screw, motor assembly, and push rod assembly, in the branch... The sleeve, lead screw, and motor assembly are designated as component 1, and the push rod assembly is designated as component 2. In the branch chain 4, the rotating bracket is designated as component 0, the universal ring assembly is designated as component 1, the driven support arm is designated as component 2, the moving platform is designated as component 3, the first swing head is designated as component 4, the second swing head is designated as component 5, and the cutting tool is designated as component 6. S13, based on the velocity and acceleration of all joints, obtain the relationship between all components and points. Instantaneous overlap point Velocity / Acceleration Spiral / , In the middle, if , ;like , ; S14, calculate all components about point using the following formula. The resultant force of inertial force / torque and gravity spirals : ； In the formula, This indicates that the component is about the point. The spatial inertia matrix; Represents a spiral The cross product operator; This indicates that the component is about the point. The gravity spiral; S15, According to the Newton-Euler method, all components are considered as free bodies under force, and their forces are analyzed. Each component is subjected to gravity, inertial force / torque, constraint force / torque from the kinematic pairs at both ends, and frictional force / torque. If the kinematic pairs are active, driving force / torque is also included. Let the reference point of the kinematic pairs at both ends of any component be... The constraint resultant force helical can be written using the following formula. ,in, Indicates component reference point The constraint spiral, Indicates component reference point Constraint screw: = ； In the formula, Point Unit vectors in three orthogonal directions; Point Time The direction vector; The magnitude matrix representing the constraint screw in the three orthogonal directions is expressed as follows: ； In the formula, , , and They represent the reference points respectively. along the direction The amplitudes of the constraint force, friction force, constraint torque, and friction torque, where, if Indicates the reference point of the active secondary and If the axis vector of the active translator is represented, then the primary translator... Indicates driving force, active rotating pair Indicates driving torque; S16 uses the Stribeck model to model the frictional force / torque of the kinematic pair, and its expression is: ； In the formula, Indicates frictional force / torque. , , and These represent the Coulomb coefficient of friction, the maximum static friction coefficient, the viscous friction coefficient, and the Stribeck velocity, respectively. This represents the radius of the friction circle of a kinematic pair, where the sliding pair... ; This indicates the magnitude of the constraint force on the plane perpendicular to the axis of the kinematic pair; Indicates the joint velocity amplitude; sign represents the sign function; S17, list all components about points using the following formula. Newton-Euler equations: ； S18, organize the Newton-Euler equations for all components, containing a total of 78 equations and 80 unknown constraint forces / moments. Combine these with the two equations for constraint deformation and compatibility conditions, forming a linear system of 80 equations and 80 unknowns: ； In the formula, Represents the coefficient matrix. Represents a constant vector. This represents a vector of unknown parameters containing joint constraint forces / torques and driving forces / torques; S19, obtained by solving the system of linear equations And extract the joint driving force of the 1T2R parallel mechanism from it. And the joint driving torque of the first and second swing heads and the cutting tool. ; S110, the joint driving force is calculated using the following formula. Converted to driving torque: ； In the formula, This indicates the lead of the ball screw. This indicates the frictional torque at the lead screw and nut.

3. The method for dynamic modeling and friction parameter identification of a hybrid robot according to claim 2, characterized in that, S19 includes the following sub-steps: S191, neglecting the influence of joint friction, solve the linear equation system of S18 to obtain the constraint forces / torques of each joint; S192, Substitute the obtained joint constraint forces into the Stribeck friction model in S16 to obtain the friction force / torque of each joint; S193. Considering the impact of neglecting joint friction on the accuracy of joint constraint force solution in S191, the joint friction force / torque obtained in S192 is incorporated into the force analysis. Using the linear equations in S18, the initial corrected joint constraint force is obtained. S194, repeat S192 and S193 to obtain the joint drive and constraint forces after secondary correction.

4. A method for dynamic modeling and friction parameter identification of a hybrid robot, wherein the hybrid robot comprises 6 active joints and 12 passive joints, and since the active joints play a dominant role in the friction effect, they are directly included in the identification process; all passive joints are located in a 1T2R parallel mechanism, characterized in that... Applying S2 according to any one of claims 1-3 includes the following sub-steps: S21 classifies the friction parameters of all passive joints into four categories: Coulomb friction, viscous friction, static friction, and Stribeck velocity. S22, taking Coulomb friction parameters as an example, constructs three driving forces for a 1T2R parallel mechanism using the following formula. Three sets of summation functions: ， ； In the formula, This represents a combination vector of the 12 parameters in the Coulomb friction parameters; S23, will , It can be represented by a high-dimensional model as the sum of a series of low-dimensional functions. and The variance can be expressed as: ； S24, using the Latin hypersampling method, the Coulomb friction parameters are sampled twice independently within its sampling space to generate... A sample matrix with 12 rows and 12 columns and Sample size Set it to 15000, then swap them. and The Columns, constructing matrices Here, Indicates using The Column substitution No. Therefore, , The variance of the variance and the variance of its subfunctions can be expressed as: , ； ； S25 will determine the total fluctuation of the system. Defined as: ； S26, Coulomb friction parameters Individual fluctuations and their interaction with other Coulomb friction parameters Apart from the partial fluctuations caused by the interaction, the sum of all partial fluctuations caused by other Coulomb friction parameters is defined as: ； In the formula, express Except for containing The sum of the variances of all sub-functions other than the first one. express Except for containing The sum of the variances of all sub-functions other than the first one; S27, Define Coulomb friction parameters global sensitivity index for: ； S28, repeating S22 to S27, yields global sensitivity indices for viscous friction, static friction, and Stribeck velocity. ; S29, based on four types of friction We select highly sensitive friction parameters for the passive joint and incorporate them into the friction parameter process, while ignoring the influence of low-sensitivity friction parameters.

5. The method for dynamic modeling and friction parameter identification of a hybrid robot according to claim 1, characterized in that, S3 includes the following steps: S31, Assume the robot's velocity and acceleration are 0 at the start and stop times, and the initial angle is... Termination angle The start time is The termination time is ,point The line connecting the center of the circular trajectory to the coordinate system The angle between the y-axis and the y-axis It satisfies the rule of fifth-degree polynomial transformation: ； In the formula, These are the coefficients of the terms from degree 0 to degree 5 corresponding to the fifth-degree polynomial; S32, point obtained from S31 Speed ​​Spiral ,right Differentiation yields the acceleration spiral .

6. The method for dynamic modeling and friction parameter identification of a hybrid robot according to claim 1, characterized in that, S4 includes the following steps: S41, utilizing the inverse kinematics of a hybrid robot, based on points Given the pose, velocity, and acceleration, calculate the displacement, velocity, and acceleration of each active joint; S42, the acquired active joint kinematic information is written into G code and then input into the Power PMAC IDE software to drive the hybrid robot to move according to the identified and verified circular trajectory; S43, during the movement of the hybrid robot, synchronously collects the drive current signals of each servo motor on both tracks. ; S44 converts the drive current signal into drive torque using the following formula: ； In the formula, The reduction ratio of the speed reducer connected to the servo motor. The torque constant of the servo motor. This represents the servo motor current.

7. The method for dynamic modeling and friction parameter identification of a hybrid robot according to claim 1, characterized in that, S5 includes the following steps: S51, Determine the number of particles Initialize the friction parameter population in the friction parameter value space. ,in This represents the combination of friction parameters to be identified; S52, the sum of the mean square error of the theoretical driving torque of each active joint S19 and S110 and the collected driving torque of S44 is used as the fitness function, and the minimum of the fitness function is set as the optimization objective. Its expression is: ； In the formula, This indicates the number of sampling points in parameter identification. , These represent the theoretical driving torque value and the acquired driving torque value of the i-th active joint at the j-th sampling point, respectively. S53, calculate the fit value for each particle, comparing each particle before... The fit values ​​of the previous and current generations are used to update the local optimal combination of friction parameters for individual particles. Compare the fit values ​​of all particles in the previous t generations with those in the current generation to update the globally optimal combination of friction parameters for the particles. ; S54, calculate the variable using the following formula. : ； In the formula, and It is a Gaussian mutation operator and follows a Gaussian distribution with mean 0 and variance 1; S55, contraction-expansion factor Dynamic adjustment is achieved through a linear decreasing strategy, the expression of which is: ； In the formula, and These represent the initial and final values ​​of the inertia weight, respectively. Indicates the maximum number of iterations. Indicates the current iteration number; S56, calculate the local optimal combination of friction parameters for all particles using the following formula. arithmetic mean vector : ； S57 updates the state of all particles using the following formula: ； In the formula, Represents a random number; S58, jump to S53, until the maximum iteration number is reached, then the last generation... The corresponding globally optimal combination of friction parameters is used as the identification result of the friction parameters.

8. The method for dynamic modeling and friction parameter identification of a hybrid robot according to claim 1, characterized in that, It also includes S6, which verifies and evaluates the dynamic model through experiments based on the identified parameters, and corrects the dynamic model of the hybrid robot.

9. The method for dynamic modeling and friction parameter identification of a hybrid robot according to claim 8, characterized in that, S6 includes the following steps: S61, calculate the driving torque of each active joint using the identified friction parameters, and draw a comparison chart of the theoretical driving torque and the collected driving torque; S62, Using the coefficient of determination The dynamic model is evaluated, and its expression is as follows: ； In the formula, Indicates the first The average value of the driving torque collected by each active joint over N sampling points; S63, to further verify the generalization ability of the dynamic model and friction parameter identification results, calculate the driving torque of each active joint under the verification trajectory, plot a comparison chart of the theoretical driving torque and the collected driving torque, and use S62's... The dynamic model is evaluated.

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