CN115741697A - Optimized moment feedback method, system and equipment for mechanical arm joint - Google Patents
Optimized moment feedback method, system and equipment for mechanical arm joint Download PDFInfo
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Abstract
The application provides an optimized moment feedback method, system and equipment for a mechanical arm joint, which comprise the following steps: the input signal controls a servo motor to drive a mechanical arm joint to perform grabbing action, and a coder at the tail end of the servo motor is used for collecting the moving position, speed and torque data of the motor; the feedback signal of the encoder in the S1 and the motor current are transmitted to a servo motor control module, the control module obtains the data of the permanent magnet synchronous motor and combines the voltage sum of the permanent magnet synchronous motorThe electromagnetic torque T of the motor is calculated by a flux linkage equation E The size and direction of (a); respectively combining the data of the permanent magnet synchronous motor in the S2 to obtain a friction torque compensation model at the speed reducer; calculating viscous friction T in an electric machine n (ii) a Deducing a moment operation model; using calculated T E 、T j 、T n And a moment operation model deduced by the joint kinematics model obtains more accurate joint moment, and the more accurate joint moment is output by the control module to complete a moment feedback process and improve the numerical precision of the fed-back joint moment.
Description
Technical Field
The application relates to the technical field of robot control, in particular to a method, a system and equipment for optimizing torque feedback of a mechanical arm joint.
Background
Industrial robots are multi-joint manipulators or multi-degree-of-freedom machine devices widely used in the industrial field, have a certain degree of automation, and can realize various industrial processing and manufacturing functions depending on the power energy and control capability of the industrial robots. Industrial robots are widely used in various industrial fields such as electronics, logistics, and chemical industry. The industrial robot can realize various industrial processing and manufacturing functions through self power and control algorithms, and assist human beings to finish a large amount of complicated and repeated flow operations.
However, in the conventional technology, because a feedback estimation value of a moment joint at the end of an actuator has a large relative error, most industrial robots can only support dragging, lifting and other works and cannot further complete finer industrial cooperation, which limits further application and development of the industrial robots to a certain extent. Because the influence of friction torque in the operation of a machine is not considered, the existing joint torque estimated value is only obtained by the measured value and the angle estimation of the motor current, and the accuracy is relatively low.
Therefore, how to realize a torque feedback design fully considering the friction torque of the speed reducer and improve the joint precision of the industrial robot is a technical problem to be solved urgently in the field.
Disclosure of Invention
In view of this, the present application provides a method, a system, and a device for optimizing torque feedback of a mechanical arm joint, so as to solve the problems in the prior art.
In a first aspect, an embodiment of the present application provides a method for optimizing torque feedback of a robot arm joint, where the method includes:
s1, controlling a servo motor to drive a mechanical arm joint to perform grabbing action by an input signal, and acquiring moving position, speed and torque data of the motor by using an encoder at the tail end of the servo motor;
s2, transmitting a feedback signal of the encoder in the S1 and the motor current to a servo motor control module, obtaining data of the permanent magnet synchronous motor by the control module, and calculating the electromagnetic torque T of the motor by combining the voltage and the flux linkage equation of the permanent magnet synchronous motor E The size and direction of (d);
s3, establishing friction torque T at the speed reducer in the torque feedback process by using the data of the permanent magnet synchronous motor in the S2 and applying a Gaussian mixture model j A compensation model;
s4, performing parameter identification on the speed reducer friction torque model established in the S3 through a differential evolution algorithm to obtain a specific mathematical function expression of the friction torque compensation model at the speed reducer;
s5, calculating viscous friction T in the motor by using the data of the permanent magnet synchronous motor in the S2 n ；
S6, deducing a moment operation model by utilizing the data of the permanent magnet synchronous motor in the S2 and establishing a kinematic model for the joint;
s7, T calculated by utilizing S2, S3, S4 and S5 E 、T j 、T n And combining with the S6 moment operation model deduced from the joint kinematics model to obtain more accurate joint moment, outputting the more accurate joint moment through the control module, completing a moment feedback process, and improving the accuracy of the feedback joint moment value.
A possible implementation mode is that a feedback signal of an encoder in S1 and a motor current are transmitted to a servo motor control module, the control module obtains permanent magnet synchronous motor data, and the data are combined with the permanent magnet synchronous motorThe voltage and flux linkage equation calculates the electromagnetic torque T of the motor E Including:
the control terminal signal obtains the size and the direction of the electromagnetic torque borne by the motor by the following operations:
the voltage and flux linkage equations for a permanent magnet synchronous machine are generally expressed as:
in the formula, V abcs Is the voltage of the permanent magnet synchronous motor; lambda [ alpha ] abcs Is a flux linkage of the permanent magnet synchronous motor; r is s Is a stator phase winding resistor; i.e. i abcs Is the current of the permanent magnet synchronous motor; l is ls Leakage inductance of the stator phase winding; l is ms Magnetizing the inductor for the stator phase winding; theta r Is the rotor electrical angle; phi is a m Magnetic linkage caused by permanent magnets;
the motor voltage and flux equations are simplified as:
λ qs ＝L qs i qs +φ m (4)
in the formula, v qs Stator speed for the q-axis; v. of ds Stator speed for d-axis; i.e. i qs Stator current for the q-axis; lambda [ alpha ] qs A flux linkage for the q-axis; lambda [ alpha ] ds A flux linkage for the d-axis; omega r Is the rotor angular velocity;
since the d-and q-axis inductive circuits are identical, it can be seen that
In the formula, L s A stator phase winding inductor; l is qs Is a q-axis stator phase wound inductor; l is a radical of an alcohol ds D-axis stator phase wound inductors;
the inductance is represented by:
in the formula, L 1s Phase wound inductance of a stator which is any one of the three stators; l is 2s A phase winding inductance of a stator which is an optional one of the remaining two stators;
expressions describing the electromagnetic torque of the permanent magnet synchronous motor that can be obtained from expressions (1) to (7) are as follows
In the formula, T e Is the motor torque;
the power average of the three stators is shown.
One possible implementation way is to utilize the data of the permanent magnet synchronous motor in S2 and establish the friction torque T at the speed reducer in the torque feedback process by applying a Gaussian mixture model j A compensation model, comprising:
when the speed reducer and the machine member have relative movement trend but do not rotate, the static friction is generated at the moment, and the functional relation is as follows:
in the formula: f j Is the static friction moment of the reducer; f i Is an external moment; f m Maximum static friction moment; sign () is a sign function (F) i >0，sign(F i )＝1；F i ＝0，sign(F i )＝0；F i <0，sign(F i )＝-1)；
Alternatively, the first and second electrodes may be,
when the mechanical arm joint rotates at a low speed, the Stribeck friction effect occurs, and the friction of the speed reducer is represented as sliding boundary friction at the moment, and the functional relation is as follows:
in the formula: f j Friction torque of the speed reducer; f c Coulomb friction torque; f s The maximum static friction moment of the reducer; b is a viscosity coefficient; v. of s Stribeck speed for a reducer; v is the speed of the reducer when in motion.
The utility model provides a possible implementation, carry out parameter identification to the speed reducer friction torque model that S3 established through differential evolution algorithm, obtain the concrete mathematical function expression of speed reducer department friction torque compensation model, include:
f in friction torque model of speed reducer established by pair formula (11) c ，F s B and v s Distinguishing the parameters;
taking 4 parameters to be identified as individuals, producing an initial group, adopting real number coding, and taking identification error index
In the formula, N is the number of test data; y is i The output of the ith test sample for the model;
the differential evolution algorithm obtains the identification value of the friction model parameter in each step of iteration as
Wherein M =1,2, …, M is the number of initial populations;
parameters in the friction model to be identified;
the identification value of the friction torque model parameter of the speed reducer by the corresponding equation (11):
in the formula (I), the compound is shown in the specification,
the value of (b) can be obtained from the established friction model;
the fitness function of the differential evolution algorithm is taken as:
one possible implementation manner, the differential evolution algorithm implementation process is as follows:
generating an initial population, randomly generating M individuals meeting constraint conditions in a four-dimensional space, and implementing the following measures:
in the formula (I), the compound is shown in the specification,
and
respectively the upper and lower bounds, rand, of the jth individual ij (0,1) is [0,1]Random decimal between;
mutation operation, randomly selecting 3 individuals x from the population p1 、x p2 And x p3 Carrying out mutation operation:
h ij (t+1)＝x p1j (t)+F(x p2j (t)-x p3j (t)) (17)
in the formula, x p2j (t)-x p3j (t) is a differentiation vector, and F is a scaling factor;
crossover operations, introducing new individuals to increase the diversity of the population based on crossover probability factors:
in the formula, randl ij Is [0,1]Random decimal between, CR is the cross probability, and CR is E [0,1 ]]；
Selecting operation, using fitness function of formula (15) as evaluation standard, determining x i (t) whether or not to become the next generation;
and (5) repeatedly executing the operation from 2 steps to 4 steps until the maximum iteration times are reached, obtaining an optimal individual and taking the optimal individual as optimal output, namely obtaining the optimal identification value of the friction torque model parameter of the speed reducer in the formula (11).
In one possible implementation manner, the viscous friction T in the motor is calculated by using the data of the permanent magnet synchronous motor in S2 n The method comprises the following steps:
establishing a fluid-solid coupling model to calculate the viscous friction torque in the motor, wherein the shear stress between the surface of the rotor and the cooling water is as follows:
τ＝CρU 2 (19)
wherein C is the coefficient of friction; rho is the density of the cooling liquid; u is the relative speed of the cooling fluid and the rotor surface;
wherein:
wherein Re is Relo number;
Re＝Rωδν (21)
wherein R is the radius of the rotor; omega is the rotation angular velocity of the rotor; delta is the length of the single-sided air gap; ν is the kinematic viscosity of the cooling water;
viscous friction torque T between rotor surface and cooling water n Comprises the following steps:
T n ＝2ΠCνR 2 U 2 L (22)
wherein L is the rotor length.
One possible implementation manner of deriving a moment operation model by establishing a kinematic model for a joint by using the permanent magnet synchronous motor data in S2 includes:
the friction torque in the torque feedback process can be expressed as the sum of several components, and the friction model is expressed as follows:
T J ＝T j +T n (23)
in the formula, T J For the friction torque during the torque feedback process,
the friction torque of the reducer obtained by the GMM model; t is n Is viscous friction torque inside the motor;
the dynamic equation established for the mechanical arm joint is as follows
In the formula, T e The electromagnetic torque determined for the equations (8) and (9); t is J A compensation torque determined for the friction model (24); theta m Is the high-speed shaft angle;
a low speed shaft angle; j = n 2 J 1 +J 2 Representing an equivalent moment of inertia; m l (q) represents the equivalent rotational inertia term of the load end;
the centripetal force and the Coriolis force items of the load end are represented; g l (q) represents a gravity term at the load end;
the speed reducer is divided into a high-speed side and a low-speed side according to the speed, a motor shaft is a high-speed shaft, an output shaft of the speed reducer is a low-speed shaft, the speed reducer is structured by a joint transmission chain, and the dynamic equation of the high-speed shaft obtained by the combined formula (24) is as follows:
the kinetic equation for the low-speed shaft can be obtained by the same method as follows:
in the formula, T m Calculating the accurate joint moment;
a compensation torque calculated for the friction model; j. the design is a square 1 Moment of inertia for high speed shafts; j. the design is a square 2 Is the moment of inertia of the low-speed shaft, T r Is the load moment;
wherein, based on Lagrange's equation, load T r Can be expressed as
In a second aspect, an embodiment of the present application provides an optimized torque feedback system for a robot arm joint, including:
the first acquisition module is used for inputting signals to control the servo motor to drive the mechanical arm joint to perform grabbing action, and acquiring the moving position, speed and torque data of the motor by utilizing an encoder at the tail end of the servo motor;
the first calculation module is used for transmitting the feedback signal of the encoder and the motor current to the servo motor control module, and the control module acquires the data of the permanent magnet synchronous motor and combines the data with the permanent magnet synchronous motorCalculating motor electromagnetic torque T by voltage and flux linkage equation of magnetic synchronous motor E The size and direction of (d);
a model establishing module for establishing friction torque T at the speed reducer in the torque feedback process by using the data of the permanent magnet synchronous motor and applying a Gaussian mixture model j A compensation model;
the second acquisition module is used for carrying out parameter identification on the established friction torque model of the speed reducer through a differential evolution algorithm to acquire a specific mathematical function expression of the friction torque compensation model at the speed reducer;
a second calculation module for calculating viscous friction T in the motor by using the data of the permanent magnet synchronous motor n ；
The model acquisition module is used for deducing a moment operation model by establishing a kinematic model for the joint by utilizing the data of the permanent magnet synchronous motor;
an output control module for utilizing the calculated T E 、T j 、T n The more accurate joint moment is obtained by combining a moment operation model derived from the joint kinematics model and is output through the control module to complete a moment feedback process and improve the accuracy of the feedback joint moment value
In a third aspect, an embodiment of the present application provides an electronic device, including:
a processor;
a memory;
and a computer program, wherein the computer program is stored in the memory, the computer program comprising instructions that, when executed by the processor, cause the electronic device to perform the method of any of the possible implementations of the first aspect.
In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium, where the computer-readable storage medium includes a stored program, where the program, when executed, controls an apparatus in which the computer-readable storage medium is located to perform the method described in any possible implementation manner of the first aspect
In the embodiment of the application, the influence of friction of a speed reducer and viscous friction inside a motor during the operation of the mechanical arm joint is fully considered, a Gaussian mixture model and a fluid-solid coupling model are established for friction torque, and error compensation is performed through a torque operation model, so that a torque feedback estimation value is more accurate, the precision of the mechanical arm joint is improved, and the mechanical arm joint can be applied to a more precise industrial control environment.
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In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive labor.
FIG. 1 is a schematic structural diagram of an optimized moment feedback design applied to a robot joint according to an embodiment of the present disclosure;
fig. 2 is a schematic flowchart of a method for optimizing torque feedback of a robot arm joint according to an embodiment of the present disclosure;
fig. 3 is a schematic view of an optimized moment feedback device for a robot arm joint according to an embodiment of the present disclosure;
fig. 4 is a schematic structural diagram of an electronic device according to an embodiment of the present application.
Detailed Description
For better understanding of the technical solutions of the present application, the following detailed descriptions of the embodiments of the present application are provided with reference to the accompanying drawings.
It should be understood that the embodiments described are only a few embodiments of the present application, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
The terminology used in the embodiments of the present application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. As used in the examples of this application and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
It should be understood that the term "and/or" as used herein is merely one type of associative relationship that describes an associated object, meaning that three types of relationships may exist, e.g., A and/or B, may mean: a exists alone, A and B exist simultaneously, and B exists alone. In addition, the character "/" herein generally indicates that the former and latter related objects are in an "or" relationship.
Fig. 1 is a schematic structural diagram of an optimized torque feedback design applied to a mechanical arm joint according to an embodiment of the present application, and as shown in the figure, the optimized torque feedback design structure applied to the mechanical arm joint includes a servo motor, a servo motor control module, an encoder, a torque feedback operation, a differential evolution operation, a speed reducer, a motor angle sensor, a control module, and a gear transmission structure. The input signal controls the servo motor to drive the joint to operate, an encoder at the tail end of the motor detects data such as speed, angle, torque, rotary displacement and the like of the joint and transmits the data to a servo motor control module, the control module reads encoder information and motor current, and the electromagnetic torque T of the motor is calculated by utilizing a flux linkage equation E Calculating the viscous friction T inside the motor n Calculating a joint moment feedback value T through a joint moment operation model deduced by a dynamic model m And the torque is output through the control module to complete the torque feedback process.
Fig. 2 is a schematic flow chart of a method for feedback of an optimized torque of a joint of a robot arm according to an embodiment of the present disclosure, and referring to fig. 2, the method for feedback of an optimized torque of a joint of a robot arm according to the present embodiment includes:
s1, inputting signals to control a servo motor to drive a mechanical arm joint to perform grabbing action, and collecting data of the moving position, speed and torque of the motor by using an encoder at the tail end of the servo motor.
S2, transmitting a feedback signal of the encoder in the S1 and the motor current to a servo motor control module, obtaining data of the permanent magnet synchronous motor by the control module, and calculating the electromagnetic torque T of the motor by combining the voltage and the flux linkage equation of the permanent magnet synchronous motor E The size and direction of the light beam.
The control terminal signal obtains the size and the direction of the electromagnetic torque borne by the motor by the following operations:
the voltage and flux linkage equations for a permanent magnet synchronous machine are generally expressed as:
in the formula, V abcs Is the voltage of the permanent magnet synchronous motor; lambda [ alpha ] abcs Is a flux linkage of the permanent magnet synchronous motor; r is s Is a stator phase winding resistor; i.e. i abcs Is the current of the permanent magnet synchronous motor; l is ls Leakage inductance of the stator phase winding; l is ms Magnetizing the inductor for the stator phase winding; theta r Is the rotor electrical angle; phi is a m Magnetic linkage caused by permanent magnets;
equations (1) and (2) are time-varying and a function of the electromagnetic and load torques, the three stator fluxes being coupled to each other because they depend on the rotor position. The following frame of reference theory simplifies the equations of motion by changing a set of variables to mean a stator number component, directly along the 90 ° axis, with rotation synchronized with the rotor and vice versa.
The motor voltage and flux equations are simplified as:
λ qs ＝L qs i qs +φ m (4)
in the formula, v qs Stator speed for the q-axis; v. of ds Stator speed for d-axis; i all right angle qs Stator current for the q-axis; lambda [ alpha ] qs A flux linkage for the q-axis; lambda [ alpha ] ds A flux linkage for the d-axis; omega r Is the rotor angular velocity;
since the d-and q-axis inductive circuits are identical, it can be seen that
In the formula, L s A stator phase winding inductor; l is a radical of an alcohol qs Is a q-axis stator phase wound inductor; l is ds D-axis stator phase wound inductors;
the permanent magnet synchronous motor has a remarkable magnetic structure, and therefore, the inductance is expressed as follows:
in the formula, L 1s Phase wound inductance of a stator which is any one of the three stators; l is a radical of an alcohol 2s A phase winding inductance of a stator which is an optional one of the remaining two stators;
expressions describing the electromagnetic torque of the permanent magnet synchronous motor that can be obtained from expressions (1) to (7) are as follows
In the formula, T e Is the motor torque; p is the average of the power of the three stators.
However, the motor torque calculated in this way is the electromagnetic torque of the motor, and is not the output torque. It has an error within 5% from the output torque.
S3, establishing friction torque T at the speed reducer in the torque feedback process by using the data of the permanent magnet synchronous motor in the S2 and applying a Gaussian mixture model j And (5) compensating the model.
Based on a Gaussian mixture model, the friction torque of the speed reducer is considered, and the process of establishing a friction torque compensation model at the speed reducer in the torque feedback process is as follows:
the friction force between the speed reducer at the joint and the machine element is considered in 10 cases.
When the speed reducer and the machine member have relative movement trend but do not rotate, the static friction is generated at the moment, and the functional relation is as follows:
in the formula: f j Is the static friction moment of the reducer; f i Is an external moment; f m Maximum static friction moment; sign () is a sign function (F) i >0，sign(F i )＝1；F i ＝0，sign(F i )＝0；F i <0，sign(F i )＝-1)；
Alternatively, the first and second electrodes may be,
when the mechanical arm joint rotates at a low speed, the Stribeck friction effect occurs, and the friction of the speed reducer is represented as sliding boundary friction. In consideration of accurate numerical values, simplicity and practicality, the Gaussian mixture model is applied to fully express the conversion process, and the negative slope friction phenomenon is fully considered by the model, so that the model can fit the friction applied to the speed reducer at the moment with the precision of nearly 90%. The functional relationship is as follows:
in the formula: f j Friction torque of the speed reducer; f c Coulomb friction torque; f s The maximum static friction moment of the reducer; b is a viscosity coefficient; v. of s Stribeck speed for a reducer; v is the speed of the reducer when in motion.
And S4, performing parameter identification on the friction torque model of the speed reducer established in the S3 through a differential evolution algorithm to obtain a specific mathematical function expression of the friction torque compensation model at the speed reducer.
For obtaining the specific mathematical function expression of the friction model, F in the friction torque model of the speed reducer established by the formula (11) c ，F s B and v s And the parameters are identified. The differential evolution algorithm has stronger global convergence capability and robustness, and reduces the complexity of modeling the friction torque.
Taking 4 parameters to be identified as individuals, producing an initial group, adopting real number coding, and taking identification error index
In the formula, N is the number of test data; y is i The output of the ith test sample for the model;
the differential evolution algorithm iterates at each step to obtain the identification value of the friction model parameter as
Wherein M =1,2, …, M is the number of initial populations;
parameters in the friction model to be identified;
the identification value of the friction torque model parameter of the speed reducer by the corresponding formula (11):
the fitness function of the differential evolution algorithm is taken as:
specifically, the differential evolution algorithm is implemented as follows:
generating an initial population, and randomly generating M individuals meeting constraint conditions in a four-dimensional space, wherein the implementation measures are as follows:
in the formula (I), the compound is shown in the specification,
and
respectively the upper and lower bounds, rand, of the jth individual ij (0,1) is [0,1]Random decimal in between;
mutation operation, randomly selecting 3 individuals x from the population p1 、x p2 And x p3 Carrying out mutation operation:
h ij (t+1)＝x p1j (t)+F(x p2j (t)-x p3j (t)) (17)
in the formula, x p2j (t)-x p3j (t) is a differentiation vector, and F is a scaling factor;
crossover operations, introducing new individuals to increase the diversity of the population based on crossover probability factors:
in the formula, randl ij Is [0,1]Random decimal between them, CR is the cross probability, CR belongs to [0,1 ]]；
Selecting operation, using fitness function of formula (15) as evaluation standard, determining x i (t) whether or not to become the next generation;
and (4) repeatedly executing the operation from 2 steps to 4 steps until the maximum iteration times is reached, obtaining an optimal individual and taking the optimal individual as optimal output, namely obtaining the optimal identification value of the friction torque model parameter of the speed reducer in the formula (11).
S5, calculating viscous friction T in the motor by using the data of the permanent magnet synchronous motor in the S2 n 。
Because the motor is filled with cooling liquid, the motor rotor and the cooling liquid can move relatively during operation, viscous friction loss is generated, and the torque feedback process is influenced. This application calculates the inside viscous friction moment of motor through establishing the fluid-solid coupling model, and the shear stress between rotor surface and the cooling water is:
τ＝CρU 2 (19)
wherein C is the coefficient of friction; ρ is the coolant density; u is the relative speed of the cooling fluid and the rotor surface;
wherein:
wherein Re is Relo number;
Re＝Rωδν (21)
wherein R is the radius of the rotor; omega is the rotation angular velocity of the rotor; delta is the length of the single-sided air gap; ν is the kinematic viscosity of the cooling water;
viscous friction torque T between rotor surface and cooling water n Comprises the following steps:
T n ＝2ΠCνR 2 U 2 L (22)
wherein L is the rotor length.
And S6, deducing a moment operation model by establishing a kinematic model for the joint by using the data of the permanent magnet synchronous motor in the S2.
The friction torque in the torque feedback process can be expressed as the sum of several components, and the friction model is expressed as follows:
T J ＝T j +T n (23)
in the formula, T J For the friction torque during the torque feedback process,
the friction torque of the reducer obtained for the GMM; t is n Is viscous friction torque inside the motor;
considering that most industrial robots cannot be provided with joint torque and angle sensors due to the cost problem at present, the existing equipment with the design can only acquire torque and angle data of the servo motor. Based on the above, the dynamic equation established for the mechanical arm joint is as follows
In the formula, T e The electromagnetic moments determined for equations (8) and (9); t is J A compensation torque determined for the friction model (24); theta m Is the high-speed shaft angle;
a low speed shaft angle; j = n 2 J 1 +J 2 Representing an equivalent moment of inertia; m l (q) represents the equivalent rotational inertia term of the load end;
the centripetal force and the Coriolis force items of the load end are represented; g l (q) a gravity term representing a load end;
the speed reducer is divided into a high-speed side and a low-speed side according to the speed, a motor shaft is a high-speed shaft, an output shaft of the speed reducer is a low-speed shaft, the speed reducer is structured by a joint transmission chain, and the dynamic equation of the high-speed shaft obtained by the combined formula (24) is as follows:
the kinetic equation of the low-speed shaft can be obtained by the same method as follows:
in the formula, T m Calculating the accurate joint moment;
compensation obtained for friction modelMoment of force; j. the design is a square 1 Moment of inertia for high speed shafts; j. the design is a square 2 Moment of inertia for low speed shafts; t is r Is the load moment;
wherein, based on Lagrange's equation, load T r Can be expressed as
S7, calculating the obtained T by using the S2, the S3, the S4 and the S5 E 、T j 、T n And combining with the S6 moment operation model deduced from the joint kinematics model to obtain more accurate joint moment, outputting the more accurate joint moment through the control module, completing a moment feedback process, and improving the accuracy of the feedback joint moment value.
Compared with the optimized moment feedback method of the mechanical arm joint provided by the embodiment, the application also provides an embodiment of an optimized moment feedback system of the mechanical arm joint.
Referring to fig. 3, the optimized moment feedback system 20 for a robotic arm joint includes:
the first acquisition module 201 is used for inputting signals to control the servo motor to drive the mechanical arm joint to perform grabbing actions, and acquiring the moving position, speed and torque data of the motor by using an encoder at the tail end of the servo motor;
the first calculation module 202 is used for transmitting the feedback signal of the encoder and the motor current to the servo motor control module, the control module obtains the data of the permanent magnet synchronous motor, and the motor electromagnetic torque T is calculated by combining the voltage and the flux linkage equation of the permanent magnet synchronous motor E The size and direction of (d);
a model establishing module 203 for establishing the friction torque T at the speed reducer in the torque feedback process by applying the Gaussian mixture model according to the data of the permanent magnet synchronous motor j A compensation model;
the second obtaining module 204 is configured to perform parameter identification on the established speed reducer friction torque model through a differential evolution algorithm, and obtain a specific mathematical function expression of the friction torque compensation model at the speed reducer;
a second calculation module 205 for calculating the viscous friction T in the motor using the data of the permanent magnet synchronous motor n ；
The model acquisition module 206 is configured to derive a torque operation model by establishing a kinematic model for the joint using the permanent magnet synchronous motor data;
an output control module 207 for utilizing the calculated T E 、T j 、T n And a more accurate joint moment is obtained by combining a moment operation model derived from the joint kinematics model and is output through the control module, so that a moment feedback process is completed, and the accuracy of the fed-back joint moment value is improved.
It should be noted that specific contents of the method for optimizing torque feedback of a robot arm joint according to the embodiment of the present application may be referred to in the description of the above embodiment, and for brevity, no further description is provided herein.
Corresponding to the embodiment, the embodiment of the application also provides the electronic equipment.
Fig. 4 is a schematic structural diagram of an electronic device according to an embodiment of the present application. As shown in fig. 4, the electronic device 300 may include: a processor 301, a memory 302, and a communication unit 303. The components communicate via one or more buses, and those skilled in the art will appreciate that the electronic device structures shown in the figures do not constitute a limitation on the embodiments of the present application, and may be bus-type structures, star-type structures, or include more or less components than those shown, or some components in combination, or a different arrangement of components.
The communication unit 303 is configured to establish a communication channel, so that the electronic device can communicate with other devices.
The processor 301, which is a control center of the electronic device, connects various parts of the entire electronic device using various interfaces and lines, and performs various functions of the electronic device and/or processes data by operating or executing software programs and/or modules stored in the memory 302 and calling data stored in the memory. The processor may be composed of Integrated Circuits (ICs), for example, a single packaged IC, or a plurality of packaged ICs connected to the same or different functions. For example, the processor 301 may include only a Central Processing Unit (CPU). In the embodiments of the present application, the CPU may be a single arithmetic core or may include multiple arithmetic cores.
A memory 302 for storing instructions executed by the processor 301, the memory 302 may be implemented by any type of volatile or non-volatile storage device or combination thereof, such as Static Random Access Memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic or optical disk.
The execution instructions in the memory 302, when executed by the processor 301, enable the electronic device 300 to perform some or all of the steps in the above-described method embodiments.
Corresponding to the above embodiments, the present application further provides a computer-readable storage medium, where the computer-readable storage medium may store a program, and when the program runs, the apparatus in which the computer-readable storage medium is located may be controlled to perform some or all of the steps in the above method embodiments. In a specific implementation, the computer-readable storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM), a Random Access Memory (RAM), or the like.
Corresponding to the above embodiments, the present application also provides a computer program product, which contains executable instructions, and when the executable instructions are executed on a computer, the computer is caused to execute some or all of the steps in the above method embodiments.
In the embodiments of the present application, "at least one" means one or more, "a plurality" means two or more. "and/or" describes the association relationship of the associated objects, and means that there may be three relationships, for example, a and/or B, and may mean that a exists alone, a and B exist simultaneously, and B exists alone. Wherein A and B can be singular or plural. The character "/" generally indicates that the former and latter associated objects are in an "or" relationship. "at least one of the following" and similar expressions refer to any combination of these items, including any combination of singular or plural items. For example, at least one of a, b, and c may represent: a, b, c, a-b, a-c, b-c, or a-b-c, wherein a, b, c may be single or multiple.
Those of ordinary skill in the art will appreciate that the various elements and algorithm steps described in connection with the embodiments disclosed herein can be implemented as electronic hardware, computer software, or combinations of electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present application.
It is clear to those skilled in the art that, for convenience and brevity of description, the specific working processes of the above-described systems, apparatuses and units may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
The above description is only for the specific embodiments of the present application, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present disclosure, and all the changes or substitutions should be covered by the protection scope of the present application. The protection scope of the present application shall be subject to the protection scope of the claims.
Claims (10)
1. An optimized moment feedback method for a mechanical arm joint is characterized by comprising the following steps:
s1, inputting signals to control a servo motor to drive a mechanical arm joint to perform grabbing action, and acquiring moving position, speed and torque data of the motor by using an encoder at the tail end of the servo motor;
s2, transmitting a feedback signal of the encoder in the S1 and the motor current to a servo motor control module, obtaining data of the permanent magnet synchronous motor by the control module, and combining the voltage and the flux linkage of the permanent magnet synchronous motorThe electromagnetic torque T of the motor is calculated by an equation E The size and direction of (d);
s3, establishing friction torque T at the speed reducer in a torque feedback process by using the data of the permanent magnet synchronous motor in the S2 through applying a Gaussian mixture model j A compensation model;
s4, performing parameter identification on the friction torque model of the speed reducer established in the S3 through a differential evolution algorithm to obtain a specific mathematical function expression of the friction torque compensation model at the speed reducer;
s5, calculating viscous friction T in the motor by using the data of the permanent magnet synchronous motor in the S2 n ；
S6, deducing a moment operation model by establishing a kinematic model for the joint by using the data of the permanent magnet synchronous motor in the S2;
s7, calculating the obtained T by using S2, S3, S4 and S5 E 、T j 、T n And combining with the S6 moment operation model deduced from the joint kinematics model to obtain more accurate joint moment, outputting the more accurate joint moment through the control module, completing a moment feedback process, and improving the accuracy of the feedback joint moment value.
2. The method for optimizing torque feedback of a mechanical arm joint according to claim 1, wherein the feedback signal of the encoder in S1 and the motor current are transmitted to a servo motor control module, the control module obtains data of the permanent magnet synchronous motor, and the motor electromagnetic torque T is calculated by combining the voltage and flux linkage equation of the permanent magnet synchronous motor E Including:
the control terminal signal obtains the size and the direction of the electromagnetic torque borne by the motor by the following operations:
the voltage and flux linkage equations for a permanent magnet synchronous machine are generally expressed as:
in the formula (I), the compound is shown in the specification,
is the voltage of the permanent magnet synchronous motor;
is a flux linkage of the permanent magnet synchronous motor; r is s A stator phase winding resistor;
is the current of the permanent magnet synchronous motor; l is a radical of an alcohol ls Leakage inductance of the stator phase winding; l is ms Magnetizing the inductor for the stator phase winding; theta r Is the rotor electrical angle; phi is a m Magnetic flux linkage caused for permanent magnets;
the motor voltage and flux equations are simplified as:
λ qs ＝L qs i qs +φ m (4)
in the formula, v qs Stator speed for the q-axis; v. of ds Stator speed for d-axis; i.e. i qs Stator current for the q-axis; lambda [ alpha ] qs A flux linkage for the q-axis; lambda [ alpha ] ds A flux linkage for the d-axis; omega r Is the rotor angular velocity;
since the d-and q-axis inductive circuits are identical, it can be seen that
In the formula, L s A stator phase winding inductor; l is qs Is a q-axis stator phase wound inductor; l is ds D-axis stator phase wound inductors;
the inductance is represented by:
in the formula, L 1s A phase wound inductance of a stator which is any one of the three stators; l is 2s A phase winding inductance of a stator which is an optional one of the remaining two stators;
expressions describing the electromagnetic torque of the permanent magnet synchronous motor that can be obtained from expressions (1) to (7) are as follows
In the formula, T e Is the motor torque;
the power average of the three stators is shown.
3. The optimized torque feedback method for mechanical arm joint according to claim 2, wherein the friction torque T at the speed reducer in the torque feedback process is established by applying a gaussian mixture model by using the data of the permanent magnet synchronous motor in S2 j A compensation model, comprising:
when the speed reducer and the machine member have relative movement trend but do not rotate, the static friction is generated at the moment, and the functional relation is as follows:
in the formula: f j Is the static friction moment of the reducer; f i Is an external moment; f m Maximum static friction moment; sign () is a sign function (F) i >0，sign(F i )＝1；F i ＝0，sign(F i )＝0；F i <0，sign(F i )＝-1)；
Alternatively, the first and second electrodes may be,
when the mechanical arm joint rotates at a low speed, the Stribeck friction effect occurs, and the friction of the speed reducer is represented as sliding boundary friction at the moment, and the functional relation is as follows:
in the formula: f j Friction torque of the speed reducer; f c Coulomb friction torque; f s The maximum static friction moment of the reducer; b is a viscosity coefficient; v. of s Stribeck speed for a reducer; v is the speed of the reducer when in motion.
4. The method for optimizing the torque feedback of the mechanical arm joint according to claim 3, wherein the parameter identification is performed on the speed reducer friction torque model established in the step S3 through a differential evolution algorithm to obtain a specific mathematical function expression of the friction torque compensation model at the speed reducer, and the method comprises the following steps:
f in friction torque model of speed reducer established by pair formula (11) c ，F s B and v s Distinguishing the parameters;
taking 4 parameters to be identified as individuals, producing an initial group, adopting real number coding, and taking identification error index
In the formula, N is the number of test data; y is i The output of the ith test sample for the model;
the differential evolution algorithm iterates at each step to obtain the identification value of the friction model parameter as
Wherein M =1,2, …, M is the number of initial populations;
parameters in the friction model to be identified;
the identification value of the friction torque model parameter of the speed reducer by the corresponding formula (11):
in the formula (I), the compound is shown in the specification,
the value of (b) can be obtained from the established friction model;
the fitness function of the differential evolution algorithm is taken as:
5. the optimized moment feedback method for the mechanical arm joint according to claim 4, wherein the differential evolution algorithm is implemented as follows:
generating an initial population, and randomly generating M individuals meeting constraint conditions in a four-dimensional space, wherein the implementation measures are as follows:
in the formula (I), the compound is shown in the specification,
and
respectively the upper and lower bounds, rand, of the jth individual ij (0,1) is [0,1]Random decimal between;
mutation operation, randomly selecting 3 individuals x from the population p1 、x p2 And x p3 Carrying out mutation operation:
h ij (t+1)＝x p1j (t)+F(x p2j (t)-x p3j (t)) (17)
in the formula, x p2j (t)-x p3j (t) is a differentiation vector, and F is a scaling factor;
crossover operations, introducing new individuals to increase the diversity of the population based on crossover probability factors:
in the formula, randl ij Is [0,1]Random decimal between them, CR is the cross probability, CR belongs to [0,1 ]]；
Selecting operation, using fitness function of formula (15) as evaluation standard, determining x i (t) whether or not to become the next generation;
and (4) repeatedly executing the operation from 2 steps to 4 steps until the maximum iteration times is reached, obtaining an optimal individual and taking the optimal individual as optimal output, namely obtaining the optimal identification value of the friction torque model parameter of the speed reducer in the formula (11).
6. The method for optimizing torque feedback of a mechanical arm joint according to claim 5, wherein the viscous friction T in the motor is calculated by using the data of the permanent magnet synchronous motor in S2 n The method comprises the following steps:
establishing a fluid-solid coupling model to calculate the viscous friction torque in the motor, wherein the shear stress between the surface of the rotor and the cooling water is as follows:
τ＝CρU 2 (19)
wherein C is the coefficient of friction; rho is the density of the cooling liquid; u is the relative speed of the cooling fluid and the rotor surface;
wherein:
wherein Re is Relog;
Re＝Rωδν (21)
wherein R is the rotor radius; omega is the rotation angular velocity of the rotor; delta is the length of the single-sided air gap; ν is the kinematic viscosity of the cooling water;
viscous friction torque T between rotor surface and cooling water n Comprises the following steps:
T n ＝2ΠCνR 2 U 2 L (22)
wherein L is the rotor length.
7. The method for optimizing the torque feedback of the mechanical arm joint according to claim 6, wherein the step of deriving the torque operation model by establishing a kinematic model for the joint by using the PMSM data in the step S2 comprises the following steps:
the friction torque in the torque feedback process can be expressed as the sum of several components, and the friction model is expressed as follows:
T J ＝T j +T n (23)
in the formula, T J For the friction torque during the torque feedback process,
friction torque of the reducer is obtained by a Gaussian Mixture Model (GMM); t is n Is viscous friction torque inside the motor;
the dynamic equation established for the mechanical arm joint is as follows
In the formula, T e The electromagnetic moments determined for equations (8) and (9); t is J A compensation torque determined for the friction model (24); theta m Is the high-speed shaft angle;
a low speed shaft angle; j = n 2 J 1 +J 2 Representing an equivalent moment of inertia; m is a group of l (q) represents the equivalent rotational inertia term of the load end;
the centripetal force and the Coriolis force items of the load end are represented; g l (q) represents a gravity term at the load end;
the speed reducer is divided into a high-speed side and a low-speed side according to the speed, a motor shaft is a high-speed shaft, an output shaft of the speed reducer is a low-speed shaft, the speed reducer is structured by a joint transmission chain, and the dynamic equation of the high-speed shaft obtained by the combined formula (24) is as follows:
the kinetic equation of the low-speed shaft can be obtained by the same method as follows:
in the formula, T m Calculating the accurate joint moment;
a compensation torque calculated for the friction model; j. the design is a square 1 Moment of inertia for high speed shafts; j. the design is a square 2 Moment of inertia for the low speed shaft; t is r Is the load moment;
wherein, based on Lagrange's equation, load T r Can be expressed as
8. An optimized torque feedback system for a mechanical arm joint, comprising:
the first acquisition module is used for inputting signals to control the servo motor to drive the mechanical arm joint to perform grabbing action, and acquiring the moving position, speed and torque data of the motor by using an encoder at the tail end of the servo motor;
the first calculation module is used for transmitting a feedback signal of the encoder and the motor current to the servo motor control module, the control module obtains the data of the permanent magnet synchronous motor, and the motor electromagnetic torque T is calculated by combining the voltage and the flux linkage equation of the permanent magnet synchronous motor E The size and direction of (d);
a model establishing module for establishing the friction torque T at the speed reducer in the torque feedback process by using the data of the permanent magnet synchronous motor and a Gaussian mixture model j A compensation model;
the second acquisition module is used for carrying out parameter identification on the established friction torque model of the speed reducer through a differential evolution algorithm to acquire a specific mathematical function expression of the friction torque compensation model at the speed reducer;
a second calculation module for calculating viscous friction T in the motor by using the data of the permanent magnet synchronous motor n ；
The model acquisition module is used for deducing a moment operation model by establishing a kinematic model for the joint by utilizing the data of the permanent magnet synchronous motor;
an output control module for utilizing the calculated T E 、T j 、T n And a more accurate joint moment is obtained by combining a moment operation model derived from the joint kinematics model and is output through the control module, so that a moment feedback process is completed, and the accuracy of the fed-back joint moment value is improved.
9. An electronic device, comprising:
a processor;
a memory;
and a computer program, wherein the computer program is stored in the memory, the computer program comprising instructions that, when executed by the processor, cause the electronic device to perform the method of any of claims 1 to 7.
10. A computer-readable storage medium, comprising a stored program, wherein the program, when executed, controls an apparatus in which the computer-readable storage medium is located to perform the method of any one of claims 1 to 7.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116922401A (en) * | 2023-09-18 | 2023-10-24 | 苏州艾利特机器人有限公司 | Control method for improving joint peak speed, robot and electronic equipment |
| CN117872955A (en) * | 2024-01-04 | 2024-04-12 | 超同步股份有限公司 | Online servo friction compensation method, device, equipment and storage medium |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116922401A (en) * | 2023-09-18 | 2023-10-24 | 苏州艾利特机器人有限公司 | Control method for improving joint peak speed, robot and electronic equipment |
| CN116922401B (en) * | 2023-09-18 | 2023-11-28 | 苏州艾利特机器人有限公司 | Control method for improving joint peak speed, robot and electronic equipment |
| CN117872955A (en) * | 2024-01-04 | 2024-04-12 | 超同步股份有限公司 | Online servo friction compensation method, device, equipment and storage medium |
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