CN112109084A - End position compensation method based on robot joint angle compensation and its application - Google Patents

Abstract

The invention discloses a terminal position compensation method based on robot joint angle compensation and application thereof, wherein the method comprises the following steps: constructing a kinematic model of the robot and an error model of the robot; outputting the optimal individual as an initial solution of a tabu search algorithm by adopting a fitness function; performing robot kinematic error model identification by adopting a tabu search algorithm; and (4) realizing the error compensation of the tail end of the robot by using a Newton-Raphson iteration method. The method realizes accurate identification of model errors by using the global search capability of a genetic algorithm and the local search capability of a tabu search algorithm, so as to correct various parameters of the robot model, and compensates joint angle values of the robot for multiple times by using Newton-Raphson iteration, so that the robot can be positioned to a required position.

Description

End position compensation method based on robot joint angle compensation and its application

technical field

The invention relates to the technical field of robot kinematics calibration error compensation, in particular to an end position compensation method based on robot joint angle compensation and its application.

Background technique

Due to the deformation of the robot due to processing, assembly, and load, errors will inevitably occur, which have a greater impact on the positioning accuracy of the robot, thereby reducing the positioning accuracy of the robot. Modern robots require higher precision, reliability, and movement speed. In recent years, with the advancement of technology, especially the significant improvement of AC servo motor control technology, the repeatability of robots can be made very high, generally reaching 0.05mm. The application of robots is not only limited to traditional welding robots, handling robots and assembly robots, but also has wider applications in many fields such as medical service robots, underwater robots and space robots. In these applications, the accuracy of robots is often required. It is not only satisfied with the repeated positioning accuracy, but also requires the robot to have sufficient absolute positioning accuracy. The research on error compensation of industrial robot mainly includes four aspects: establishment of error model, measurement of error, identification of error parameters and error compensation technology;

Error compensation of robots is the ultimate goal of robot error measurement, kinematic error identification and non-geometric error analysis. However, there are many researches on parameter identification and less research on error compensation. The accuracy improvement is very important. Whitney's research can compensate errors in the forward kinematics equation and inverse kinematics equation of the robot, but does not give a specific compensation method; Vuskovic also studied and proposed two compensation methods, forward kinematics compensation and inverse kinematics compensation, but proposed The forward kinematics compensation needs to repeatedly solve the inverse kinematics solution twice, and the solution of the inverse kinematics equation requires multiple judgments and selection of the inverse solution because the obtained motion variables are multiple solutions, so the actual calculation of this method is more complicated.

The current position error and attitude error can be detected at the same time, so it is necessary to design a model that can identify the error parameters uniformly for the position error and attitude error. The model needs to satisfy the integrity, continuity and independence of the selected parameters; on the other hand, the robot The error parameter identification of the 2000 model ignores the working space of the robot. Due to factors such as the force of the robot, many selected measurement points are not used in actual work. Therefore, the unified error identification model needs to consider the actual working space of the fitting point.

For the selection of measurement points in the compensation process, it is generally believed that the number of measurement points should be sufficient, but the measurement of large sample size also requires cost, so it is necessary to use statistical methods to give a minimum measurement point, thereby reducing the workload of measurement.

After the kinematic error compensation, whether the compensation of the non-geometric error of the robot is effective, especially the robot end error caused by the random error of the robot's kinematic error parameters is larger than the end error caused by the non-geometric error. All joints perform non-geometric error compensation, which often cannot achieve the expected compensation effect.

SUMMARY OF THE INVENTION

In view of the closedness of the existing industrial robot control system, the error model inside the controller cannot be changed. In order to overcome the defects and deficiencies of the existing technology, the present invention provides an end position compensation method based on the compensation of the robot joint angle. The pose error compensation is realized by means of each joint angle, and the iterative method based on the Newton-Raphson method (NR method) realizes the compensation of the robot motion parameter error.

The second object of the present invention is to provide an end position compensation system based on robot joint angle compensation.

A third object of the present invention is to provide a storage medium.

A fourth object of the present invention is to provide a computing device.

In order to achieve the above object, the present invention adopts the following technical solutions:

The present invention provides an end position compensation method based on robot joint angle compensation, comprising the following steps:

Build the kinematics model of the robot and the error model of the robot;

Set the population size and randomly generate the initial population;

Calculate the fitness of each individual in the population by taking the inverse of the sum of the squares of the errors of the actual position and the theoretical position of the robot end as the fitness function;

Use the fitness function to output the best individual as the initial solution of the tabu search algorithm;

Using the tabu search algorithm to identify the robot kinematic error model;

Enter the desired pose of the robot end;

According to the kinematic model parameters of the tandem robot and the method of obtaining the inverse kinematics solution of the tandem robot, the nominal joint angle of each joint of the 6-DOF tandem robot is obtained;

Establish the actual kinematic model of the robot according to the identified error of the robot kinematic model;

Using the nominal joint angle and the actual kinematic model of the robot to obtain the approximate correct pose of the robot end by using the method of finding the positive solution of the robot kinematics;

Find the change in joint angle:

The compensated joint angle is used to control the robot, so that the actual position of the end of the robot is the same as the set position.

As a preferred technical solution, the specific calculation formula for calculating the variation of the joint angle is:

As a preferred technical solution, using the tabu search algorithm to identify the robot kinematic error model, the specific steps include:

Build a neighborhood set: generate a neighborhood ring according to the neighborhood rules, and randomly select multiple points in the neighborhood ring as the neighborhood set of the initial solution X;

Take the identified parameters as the kinematic parameters of the robot, use the known joint angles to obtain the theoretical position of the robot end, and take the mean of the square sum of the coordinate differences between the actual position and the theoretical position of all points as the fitness, and calculate the neighborhood according to the fitness. Set the fitness of each point and the fitness of the current point;

The fitness of each point in the neighborhood set is sorted from small to large, and the point with the smallest fitness is taken as the best point in the neighborhood, marked as X';

Judging whether the fitness of X' is less than the fitness of the initial solution X, if it is not less than the number of times of taboo in the tabu table, if it is less than, replace the current solution with X', and update the taboo table;

Judgment of taboo times: judge whether the taboo times of X' in the taboo table is greater than or equal to the set value, if it is greater than or equal to the set value, sort according to the fitness of each point in the neighborhood, and take the next best point of the neighborhood as X'; If it is less than the set value, replace the current solution with X', and update the taboo table;

Judging whether the last point in the neighborhood has been exceeded, if it exceeds, the average value of all points in the neighborhood is taken as X', if not, the number of taboos is judged;

Determine whether the maximum number of iterations of the tabu search has been reached, if not, return to build a neighborhood set, and output the best solution and the fitness of the best solution if it is reached.

As a preferred technical solution, the neighborhood ring is generated according to the neighborhood rule, and the neighborhood rule is set to: dynamically adjust the neighborhood radius by multiplying the fitness by the difference vector of the upper and lower bounds of the individual.

As a preferred technical solution, after calculating the fitness of each individual in the population, it also includes binary coding, evolutionary population and binary decoding steps, specifically:

Binary coding of each individual in the population;

Set the selection probability, crossover probability and mutation probability, first perform the selection operation on the binary-coded chromosomes, then perform the single-point crossover operation on the selected chromosomes, and then perform the single-point bitwise inversion operation on the crossed chromosomes to obtain evolution population;

It is judged whether the maximum number of iterations has been reached. If the maximum number of iterations is not reached, the fitness of each individual in the population is calculated. When the maximum number of iterations is reached, each chromosome in the resulting population is binary decoded.

As a preferred technical solution, the kinematics model of the robot adopts the MD-H kinematics model, and the steps of establishing the joint axis reference coordinate system by the MD-H kinematics model include:

Determine the z-axis direction, the origin of the coordinate system and the x-axis direction;

Determine the z-axis direction: The coordinate system established at joint i is named coordinate system i-1. If joint i is a rotation axis joint, the z-axis direction is consistent with the axis of the joint's rotation axis; if joint i is a moving joint, change its moving direction Set as the z-axis axis direction;

Determine the origin of the coordinate system and the x-axis direction:

When two adjacent joint axes zi _-1 and _zi are straight lines that are different from each other, there is only one shortest common perpendicular between the two axes, and the direction of the x-axis is the shortest common perpendicular from zi _-1 to z The direction of _i , the origin of the coordinate system is the intersection of the z-axis and the x-axis;

When two adjacent joint axes zi _-1 and _zi are parallel lines, there are multiple common vertical lines with the same length between the two axes, and the common vertical line intersecting with the origin of the previous joint coordinate system is selected as the shortest common vertical line , the direction of the x-axis is the direction of the shortest common perpendicular from zi _-1 to _zi , and the origin of the coordinate system is the intersection of the z-axis and the x-axis;

When two adjacent joint axes zi _-1 and _zi are perpendicular to each other, select the normal of the plane where the two axes are located as the common perpendicular, the direction of the x-axis is the direction of the common perpendicular, and the origin of the coordinate system is the common perpendicular the intersection with the two axes;

Determine the direction of the y-axis: Determine the direction of the y-axis by the right-hand rule.

As a preferred technical solution, the MD-H kinematics model adds a rotation β around the y-axis to each joint coordinate system in the classic DH model, and when the axes of two adjacent joints are parallel, replace with β _i d _i , at this time d _i is zero; when the axes of two adjacent joints are not parallel, define β _i to be zero;

The homogeneous transformation matrix of the adjacent joint reference coordinate system is constructed as:

According to the homogeneous transformation matrix at each joint, the error model of the robot is obtained, which is expressed as:

P _G -P=M _θ Δθ+M _α Δα+M _a Δa+M _d Δd+M _β Δβ

Δθ=[Δθ ₁ ,Δθ ₂ ,...,Δθ ₆ ]'

Δα=[Δα ₁ ,Δα ₂ ,…,Δα ₆ ]′

Δa=[Δa ₁ ,Δa ₂ ,...,Δa ₆ ]′

Δd=[Δd ₁ ,Δd ₂ ,...,Δd ₆ ]'

Δβ=Δβ ₃

Among them, c represents cos(), s represents sin(), _PG represents the actual position of the base coordinate system established by the robot end under the laser tracker, and P represents the theoretical position of the end based on the robot kinematic model and joint angle, M _θ , M _α , _{Ma , M d ,} and M _β are coefficient matrices of Δθ, Δα, Δa, Δd, and Δβ, respectively.

In order to achieve the above-mentioned second purpose, the present invention adopts the following technical solutions:

An end position compensation system based on robot joint angle compensation, comprising: an error model building module, an initial population building module, a population individual fitness calculation module, an initial solution building module, an error model identification module, a desired pose input module, and a nominal joint Angle solution module, kinematic model establishment module, pose solution module, joint angle change calculation module and output control module;

The error model building module is used to construct the kinematic model of the robot and the error model of the robot;

The initial population building module is used to set the population size and randomly generate the initial population;

The population individual fitness calculation module is used to calculate the fitness of each individual in the population by using the inverse of the sum of the squares of the errors of the actual position and the theoretical position of the robot end x, y, and z as the fitness function;

The initial solution building module is used to output the best individual as the initial solution of the tabu search algorithm using the fitness function;

The error model identification module is used to identify the robot kinematic error model by using the tabu search algorithm;

The desired pose input module is used to input the desired pose of the robot end;

The nominal joint angle solving module is used to obtain the nominal joint angle of each joint of the six-degree-of-freedom serial robot according to the kinematic model parameters of the serial robot and the method for obtaining the inverse kinematics solution of the robot;

The kinematic model establishment module is used for establishing the actual kinematics model of the robot according to the identified error of the robot kinematic model;

The pose solving module is used to obtain the approximate correct pose of the end of the robot by using the nominal joint angle and the actual kinematics model of the robot by using the method of finding the positive solution of the robot kinematics;

The joint angle change calculation module is used to obtain the change of the joint angle:

The output control module is used to control the robot with the compensated joint angle, so that the actual position of the end of the robot is the same as the set position.

In order to reach the above-mentioned third purpose, the present invention adopts the following technical solutions:

A storage medium storing a program, when the program is executed by a processor, realizes the above-mentioned end position compensation method based on the angle compensation of a robot joint.

In order to reach the above-mentioned fourth purpose, the present invention adopts the following technical solutions:

A computing device includes a processor and a memory for storing a program executable by the processor. When the processor executes the program stored in the memory, the above-mentioned method for compensating an end position based on angle compensation of a robot joint is implemented.

Compared with the prior art, the present invention has the following advantages and beneficial effects:

(1) The present invention uses the global search ability of the genetic algorithm and the local search ability of the tabu search algorithm to realize the accurate identification of the model error, so as to correct the parameters of the robot model, and then use the Newton-Raphson iteration to compensate the robot for many times. The human joint angle value enables it to meet the positioning of the robot end to the required position and realize the error compensation of the robot end.

Description of drawings

FIG. 1 is a schematic flowchart of an end position compensation method based on robot joint angle compensation.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

Example

As shown in FIG. 1 , this embodiment provides an end position compensation method based on robot joint angle compensation, including the following steps:

First, establish the MD-H kinematics model of the six-degree-of-freedom robot. The establishment of the coordinate system is the selection of the coordinate axis direction and the origin. The method of establishing the joint axis reference coordinate system for the D-H model is as follows:

(1) Establishment of the z-axis direction

The coordinate system established at joint i is named as coordinate system i-1. If joint i is a rotation axis joint, the z-axis direction is the same as the axis of the joint rotation axis; if joint i is a moving joint, its moving direction is set as the z-axis axis direction;

(2) Establishment of the origin of the coordinate system and the x-axis direction

The axes of two adjacent joints may have three geometric relationships: different plane lines, parallel lines and mutually perpendicular. Therefore, the origin of the coordinate system and the direction of the x-axis are also considered in three cases;

When two adjacent joint axes zi _-1 and _zi are straight lines that are different from each other, there is only one shortest common perpendicular between the two axes, and the direction of the x-axis is this shortest common perpendicular from zi _-1 Pointing in the direction of _zi , the origin of the coordinate system is the intersection of the z-axis and the x-axis.

When two adjacent joint axes zi _-1 and _zi are parallel lines, there are countless common perpendiculars with the same length between the two axes, and the common perpendicular that intersects with the origin of the previous joint coordinate system is selected as the shortest common perpendicular, The direction of the x-axis is the direction of the shortest common perpendicular from zi _-1 to _zi , and the origin of the coordinate system is the intersection of the z-axis and the x-axis.

When two adjacent joint axes zi _-1 and _zi are perpendicular to each other, select the normal of the plane where the two axes are located as the common perpendicular, the direction of the x-axis is the direction of the common perpendicular, and the origin of the coordinate system is the common perpendicular The intersection with the two axes.

The direction of the y-axis is determined by the right-hand rule.

The joint axis reference coordinate system is established through the above method. There are four parameters describing the model between joint i-1 and joint i: α _i , θ _i , a _i and d _i ; α _i is the torsion angle, namely zi _i The angle between the _-1 axis and the _zi axis, θ _i is the joint rotation angle, that is, the angle between the x _i-1 axis and the x _i axis, a _i is the length of the connecting rod, that is, the common perpendicular line between the zi _-1 axis and the _zi axis , d _i is the pie offset that represents the distance that the x _i-1 axis moves along the z _i axis to the x _i axis.

Therefore, the transformation from the reference coordinate system of the joint axis i-1 to the reference coordinate system of the joint axis i can be described as follows: the coordinate system i-1 first rotates θ _i around the zi _-1 axis, and then translates d _i along the zi _-1 axis, Then translate a _i along the x _i-1 axis, and finally rotate α _i around the x _i-1 axis. The MD-H model adds a rotation β around the y-axis to each joint coordinate system in the classic DH model. When two adjacent joint axes are parallel, replace d _i with β _i , and d _i is zero at this time; When two adjacent joint axes are not parallel, β _i is defined as zero. At this time, the homogeneous transformation matrix of the adjacent joint reference coordinate system is:

where c stands for cos() and s stands for sin().

According to the homogeneous transformation matrix at each joint, the error model of the robot can be obtained as shown in the following formula:

P _G -P=M _θ Δθ+M _α Δα+M _a Δa+M _d Δd+M _β Δβ

P _G represents the actual position of the base coordinate system of the robot end under the laser tracker, P represents the theoretical position of the end based on the robot kinematic model and joint angle, and Δθ=[Δθ ₁ ,Δθ ₂ ,...,Δθ ₆ ]', Δα=[Δα ₁ , Δα ₂ ,...,Δα ₆ ]', Δa=[Δa ₁ ,Δa ₂ ,...,Δa ₆ ]', Δd=[Δd ₁ ,Δd ₂ ,...,Δd ₆ ]' , Δβ=Δβ ₃ , are all the parameter errors to be identified of the robot MD-H model, M _θ , M _α , M _a , M _d , M _β are the coefficient matrices of Δθ, Δα, Δa, Δd, Δβ, respectively, the robot error Model calibration is to solve Δθ, Δα, Δa, Δd, Δβ;

Secondly, the genetic taboo search algorithm is used to identify the parameters of the above errors. The specific steps include:

Step 1: Take the 25 parameter errors as the individuals of the population in the genetic algorithm, set the population size to 50, and randomly initialize the population;

Step 2: Calculate the fitness of each individual in the population by taking the inverse of the sum of the squares of the x, y, and z errors of the actual position and the theoretical position of the robot end as the fitness function;

Step 3: Binary coding for each individual in the population;

Step 4: The selection probability is set to 0.5, the crossover probability is set to 0.8, and the mutation probability is set to 0.1. The selection operation is performed on the binary-coded chromosomes. Here, the method of roulette is used, and then the single-point crossover is performed on the selected chromosomes. operation, and then perform a single-point bitwise inversion operation on the crossed chromosomes to obtain a new population;

Step 5: judge whether the maximum iteration number is 100, if not, go to step 2, and yes, go to step 6;

Step 6: perform binary decoding on each chromosome in the resulting population, and use the fitness function to output the best individual as the initial solution of the tabu search algorithm;

The initial solution of the tabu search algorithm is very important for optimization. In this example, the optimal solution obtained by the genetic algorithm is used as the initial solution of the tabu search algorithm; the length of the tabu table is very important in the tabu search algorithm system, it can determine the tabu search algorithm. The time that the individual stays in the taboo list, the length of the taboo list is set to 5 in this embodiment; the rule of neighborhood setting, this embodiment dynamically adjusts the neighborhood radius by multiplying the fitness by the difference vector between the upper and lower bounds of the individual; iterative termination rule This embodiment uses a fixed number of iterations, which is set to 200. Next, the steps of the tabu search algorithm in the genetic tabu search algorithm are described in detail:

Step 7: Generate a neighborhood ring according to the neighborhood rule, and randomly select 6 points in the neighborhood ring as the neighborhood set of the initial solution X;

Step 8: The fitness function of the tabu search algorithm is defined in this way. The identified parameters are used as the kinematic parameters of the robot, and the theoretical position of the robot end is obtained by using the known joint angles. The mean is used as the fitness, and according to the fitness, the fitness of each point in the neighborhood set and the fitness of the current point are calculated;

Step 9: Sort the fitness of each point in the neighborhood set from small to large, take the point with the smallest fitness as the best point in the neighborhood, and mark it as X';

Step 10: Determine whether the fitness of X' is less than the fitness of the initial solution X, if not, go directly to step 11, if yes, go to step 14;

Step 11: Determine whether the number of taboo times of X' in the taboo list is greater than or equal to 1, if yes, go directly to step 12, if not, go to step 14;

Step 12: According to the fitness of each point in the neighborhood, take the next best point of the neighborhood as X', and judge whether it has exceeded the last point in the neighborhood. If yes, go to step 13, if not, go to step 11;

Step 13: Take the average value of all points in the neighborhood as X';

Step 14: Replace the current solution with X', that is, make X=X', and update the taboo table;

Update the taboo table as follows: if the taboo table is not full, directly add the optimal solution of this iteration to the end of the taboo table, and add 1 to the number of taboos; if the taboo table is full, then randomly select a record that has been lifted. It is replaced by the new optimal solution. Whenever the taboo table is updated, the banned times of all individuals whose taboo times are greater than 0 will be reduced by 1 in turn. When the taboo times is 0, it means that the individual is released from the ban;

Step 15: Determine whether the maximum number of iterations of the taboo search is reached, if not, go to Step 7, if yes, go to Step 16;

Step 16: Output the best solution X and the fitness of X, and end the algorithm flow.

After completing the above sixteen steps, the identification of the robot kinematic error model is completed. The modified kinematic parameters are obtained by subtracting the original theoretical kinematic parameters of the robot from the error. The absolute positioning accuracy of the robot end.

The specific steps of using the NR method to realize pose compensation with joint angle compensation are as follows:

Step 17: Input the desired pose of the robot end;

Step 18: Calculate the nominal joint angle of each joint of the six-degree-of-freedom serial robot according to the kinematic model parameters of the serial robot and the method for obtaining the inverse kinematics solution of the robot;

Step 19: establish the actual kinematics model of the robot according to the errors of the robot kinematics model identified in steps 1 to 16;

Step 20: Use the nominal joint angle and the actual kinematics model of the robot to obtain the approximate correct pose of the robot end by using the method of finding the positive solution of the robot kinematics;

Step 21: Calculate the variation Δθ _i of the joint angle according to the following partial derivative formula:

用于控制实际机器人，使机器人的末端实际位置和设定的位置相同。Step 22: Adjust the compensated joint angles

It is used to control the actual robot, so that the actual position of the end of the robot is the same as the set position.

The existing research on the redundant error parameters of robot kinematics, aiming at the research on the geometric relationship of each kinematic parameter of the robot, omits the random error in the robot compensation process. Under the same manufacturing process level, some kinematic parameters are more accurate. However, it is very difficult for some kinematic parameters to ensure the same accuracy. When two sets of kinematic error parameters are linearly correlated, one set of kinematic error parameters needs to be eliminated, and the randomness of these two sets of kinematic error parameters should be comprehensively considered. error.

The invention uses the global search ability of the genetic algorithm and the local search ability of the tabu search algorithm to realize the accurate identification of the model error, so as to correct the parameters of the robot model, and then uses the Newton-Raphson iteration method to realize the error compensation of the robot end. Newton-Raphson iterations compensate the joint angle value of the robot many times so that the robot end can be positioned to the required position.

This embodiment also provides an end position compensation system based on robot joint angle compensation, including: an error model building module, an initial population building module, a population individual fitness calculation module, an initial solution building module, an error model identification module, a desired pose Input module, nominal joint angle solution module, kinematic model establishment module, pose solution module, joint angle change calculation module and output control module;

The error model building module is used to construct the kinematic model of the robot and the error model of the robot;

The initial population building module is used to set the population size and randomly generate the initial population;

The population individual fitness calculation module is used to calculate the fitness of each individual in the population by using the inverse of the sum of the squares of the errors of the actual position and the theoretical position of the robot end x, y, and z as the fitness function;

The initial solution building module is used to output the best individual as the initial solution of the tabu search algorithm using the fitness function;

The error model identification module is used to identify the robot kinematic error model by using the tabu search algorithm;

The desired pose input module is used to input the desired pose of the robot end;

The nominal joint angle solving module is used to obtain the nominal joint angle of each joint of the six-degree-of-freedom serial robot according to the kinematic model parameters of the serial robot and the method for obtaining the inverse kinematics solution of the robot;

The kinematic model establishment module is used for establishing the actual kinematics model of the robot according to the identified error of the robot kinematic model;

The pose solving module is used to obtain the approximate correct pose of the end of the robot by using the nominal joint angle and the actual kinematics model of the robot by using the method of finding the positive solution of the robot kinematics;

The joint angle change calculation module is used to obtain the change of the joint angle:

The output control module is used to control the robot with the compensated joint angle, so that the actual position of the end of the robot is the same as the set position.

This embodiment also provides a storage medium. The storage medium may be a storage medium such as a ROM, a RAM, a magnetic disk, an optical disk, etc., and the storage medium stores one or more programs. When the programs are executed by the processor, the above-mentioned robot joint-based End position compensation method for angle compensation.

This embodiment also provides a computing device. The computing device may be a desktop computer, a notebook computer, a smart phone, a PDA handheld terminal, a tablet computer, or other terminal device with a display function. The computing device includes a processing A processor and a memory, the memory stores one or more programs, and when the processor executes the programs stored in the memory, the above-mentioned end position compensation method based on robot joint angle compensation is implemented.

The above-mentioned embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited by the above-mentioned embodiments, and any other changes, modifications, substitutions, combinations, The simplification should be equivalent replacement manners, which are all included in the protection scope of the present invention.

Claims (10)

1. a terminal position compensation method based on robot joint angle compensation, is characterized in that, comprises the following steps: Build the kinematics model of the robot and the error model of the robot; Set the population size and randomly generate the initial population; Calculate the fitness of each individual in the population by taking the inverse of the sum of the squares of the errors of the actual position and the theoretical position of the robot end as the fitness function; Use the fitness function to output the best individual as the initial solution of the tabu search algorithm; Using the tabu search algorithm to identify the robot kinematic error model; Enter the desired pose of the robot end; According to the kinematic model parameters of the tandem robot and the method of obtaining the inverse kinematics solution of the tandem robot, the nominal joint angle of each joint of the 6-DOF tandem robot is obtained; Establish the actual kinematic model of the robot according to the identified error of the robot kinematic model; Using the nominal joint angle and the actual kinematic model of the robot to obtain the approximate correct pose of the robot end by using the method of finding the positive solution of the robot kinematics; Find the change in joint angle: The compensated joint angle is used to control the robot, so that the actual position of the end of the robot is the same as the set position. 2. The end position compensation method based on robot joint angle compensation according to claim 1, is characterized in that, described to find the variation of joint angle, the specific calculation formula is:

3. The end position compensation method based on robot joint angle compensation according to claim 1, is characterized in that, described adopting tabu search algorithm to carry out robot kinematics error model identification, and concrete steps comprise: Build a neighborhood set: generate a neighborhood ring according to the neighborhood rules, and randomly select multiple points in the neighborhood ring as the neighborhood set of the initial solution X; Take the identified parameters as the kinematic parameters of the robot, use the known joint angles to obtain the theoretical position of the robot end, and take the mean of the square sum of the coordinate differences between the actual position and the theoretical position of all points as the fitness, and calculate the neighborhood according to the fitness. Set the fitness of each point and the fitness of the current point; The fitness of each point in the neighborhood set is sorted from small to large, and the point with the smallest fitness is taken as the best point in the neighborhood, marked as X'; Judging whether the fitness of X' is less than the fitness of the initial solution X, if it is not less than the number of times of taboo in the tabu table, if it is less than, replace the current solution with X', and update the taboo table; Judgment of taboo times: judge whether the taboo times of X' in the taboo table is greater than or equal to the set value, if it is greater than or equal to the set value, sort according to the fitness of each point in the neighborhood, and take the next best point of the neighborhood as X'; If it is less than the set value, replace the current solution with X', and update the taboo table; Judging whether the last point in the neighborhood has been exceeded, if it exceeds, the average value of all points in the neighborhood is taken as X', if not, the number of taboos is judged; Determine whether the maximum number of iterations of the tabu search has been reached, if not, return to build a neighborhood set, and output the best solution and the fitness of the best solution if it is reached. 4. The end position compensation method based on robot joint angle compensation according to claim 3, wherein the neighborhood ring is generated according to the neighborhood rule, and the neighborhood rule is set as: by multiplying the individual upper and lower bounds by the fitness The difference vector of the dynamically adjusts the neighborhood radius. 5. The end position compensation method based on robot joint angle compensation according to claim 3, characterized in that, after calculating the fitness of each individual in the population, it also includes binary coding, evolutionary population and binary decoding steps, specifically: : Binary encoding of each individual in the population; Set the selection probability, crossover probability and mutation probability, first perform the selection operation on the binary-coded chromosomes, then perform the single-point crossover operation on the selected chromosomes, and then perform the single-point bitwise inversion operation on the crossed chromosomes to obtain evolution population; It is judged whether the maximum number of iterations has been reached. If the maximum number of iterations is not reached, the fitness of each individual in the population is calculated. When the maximum number of iterations is reached, each chromosome in the resulting population is binary decoded. 6. the end position compensation method based on robot joint angle compensation according to claim 3, is characterized in that, the kinematics model of described robot adopts MD-H kinematics model, and described MD-H kinematics model establishes joint axis reference The steps for a coordinate system include: Determine the z-axis direction, the origin of the coordinate system and the x-axis direction; Determine the z-axis direction: The coordinate system established at joint i is named coordinate system i-1. If joint i is a rotation axis joint, the z-axis direction is consistent with the axis of the joint's rotation axis; if joint i is a moving joint, change its moving direction Set as the z-axis axis direction; Determine the origin of the coordinate system and the x-axis direction: When the adjacent two joint axes z _{i -1} and zi are different plane lines, there is only one shortest common perpendicular between the two axes, and the direction of the x-axis is the shortest common perpendicular from z _i-1 to z The direction of _i , the origin of the coordinate system is the intersection of the z-axis and the x-axis; When two adjacent joint axes zi _-1 and _zi are parallel lines, there are multiple common vertical lines with the same length between the two axes, and the common vertical line intersecting with the origin of the previous joint coordinate system is selected as the shortest common vertical line , the direction of the x-axis is the direction of the shortest common perpendicular from zi _-1 to _zi , and the origin of the coordinate system is the intersection of the z-axis and the x-axis; When two adjacent joint axes zi _-1 and _zi are perpendicular to each other, select the normal of the plane where the two axes are located as the common perpendicular, the direction of the x-axis is the direction of the common perpendicular, and the origin of the coordinate system is the common perpendicular the intersection with the two axes; Determine the direction of the y-axis: Determine the direction of the y-axis by the right-hand rule. 7. The end position compensation method based on robot joint angle compensation according to claim 3, wherein the MD-H kinematics model adds a y-axis on each joint coordinate system in the classic DH model. Rotate β, when two adjacent joint axes are parallel, replace d _i with β _i , and d _i is zero at this time; when two adjacent joint axes are not parallel, define β _i to be zero; The homogeneous transformation matrix of the adjacent joint reference coordinate system is constructed as:

According to the homogeneous transformation matrix at each joint, the error model of the robot is obtained, which is expressed as: P _G -P=M _θ Δθ+M _α Δα+M _a Δa+M _d Δd+M _β Δβ Δθ=[Δθ ₁ ,Δθ ₂ ,...,Δθ ₆ ]' Δα=[Δα ₁ ,Δα ₂ ,...,Δα ₆ ]' Δa=[Δa ₁ ,Δa ₂ ,...,Δa ₆ ]' Δd=[Δd ₁ ,Δd ₂ ,...,Δd ₆ ]' Δβ=Δβ ₃ Among them, c represents cos(), s represents sin(), _PG represents the actual position of the base coordinate system established by the robot end under the laser tracker, and P represents the theoretical position of the end based on the robot kinematic model and joint angle, M _θ , M _α , _{Ma , M d ,} and M _β are coefficient matrices of Δθ, Δα, Δa, Δd, and Δβ, respectively. 8. An end position compensation system based on robot joint angle compensation, characterized in that it comprises: an error model building module, an initial population building module, a population individual fitness calculation module, an initial solution building module, an error model identification module, an expected position Attitude input module, nominal joint angle solution module, kinematic model establishment module, pose solution module, joint angle change calculation module and output control module; The error model building module is used to construct the kinematic model of the robot and the error model of the robot; The initial population building module is used to set the population size and randomly generate the initial population; The population individual fitness calculation module is used to calculate the fitness of each individual in the population by using the inverse of the sum of the squares of the errors of the actual position and the theoretical position of the robot end x, y, and z as the fitness function; The initial solution building module is used to output the best individual as the initial solution of the tabu search algorithm using the fitness function; The error model identification module is used to identify the robot kinematic error model by using the tabu search algorithm; The desired pose input module is used to input the desired pose of the robot end; The nominal joint angle solving module is used to obtain the nominal joint angle of each joint of the six-degree-of-freedom serial robot according to the kinematic model parameters of the serial robot and the method for obtaining the inverse kinematics solution of the robot; The kinematic model establishment module is used for establishing the actual kinematics model of the robot according to the identified error of the robot kinematic model; The pose solving module is used to obtain the approximate correct pose of the end of the robot by using the nominal joint angle and the actual kinematics model of the robot by using the method of finding the positive solution of the robot kinematics; The joint angle change calculation module is used to obtain the change of the joint angle: The output control module is used to control the robot with the compensated joint angle, so that the actual position of the end of the robot is the same as the set position. 9 . A storage medium storing a program, wherein when the program is executed by a processor, the end position compensation method based on the angle compensation of a robot joint according to any one of claims 1 to 7 is implemented. 10 . 10. A computing device, comprising a processor and a memory for storing a program executable by the processor, wherein when the processor executes the program stored in the memory, the processor according to any one of claims 1-7 is implemented. End position compensation method based on robot joint angle compensation.

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