Series-parallel robot kinematics calibration method for working area optimization

Abstract

The invention discloses a series-parallel robot kinematics calibration method for working area optimization. The method comprises the following steps: analyzing a geometric error source influencing the tail end precision of the hybrid robot, and establishing a kinematic model containing error terms; a laser tracker is used for collecting the difference value between the real coordinates of the tail end point and the output coordinates of the error model in the reachable range of the hybrid robot to generate a residual function; according to the distribution of the measurement points in the working area in the maximum reachable range of the hybrid robot, weighting operation is carried out on the residual function, and an improved particle swarm algorithm fitness function is generated; using an improved particle swarm algorithm to iteratively identify geometric errors of the hybrid robot; the identified error is compensated to a controller, and kinematics calibration of the robot is completed; the kinematics calibration method provided by the invention is simple and efficient, and can be applied to most parallel and hybrid robots.

Description

Technical Field

[0001] The present invention relates to the field of robot calibration, and in particular to a kinematic calibration method of a hybrid robot optimized for a working area. Background Art

[0002] With the development of industrial robot technology, more and more industrial fields use robots to replace traditional manual operations, which puts higher requirements on the working accuracy of robots. In terms of robot positioning accuracy, due to the geometric errors generated during the manufacturing and assembly of robots, the position of the robot end effector will deviate from the actual position during operation. How to improve the absolute positioning accuracy of robots by calibrating the error of robot geometric parameters has become an urgent problem to be solved.

[0003] There are three main problems when applying traditional robot kinematics calibration algorithms to hybrid robots: First, compared with the simpler open-chain structure of serial robots, hybrid robots have more joints, and each joint has multiple sources of error. In addition, due to the multiple structural errors between the joints, the number of error sources is huge, making it difficult to perform systematic error identification; second, in the error identification link, there are problems such as morbid identification matrix and unstable identification results, making it difficult to achieve high-precision error compensation; finally, in the process of using external measurement technology to achieve robot kinematic error compensation, the relationship between the distribution of selected measurement points and the robot workspace is not considered in combination with the actual working situation, resulting in limited improvement in the positioning accuracy of the working area after compensation.

[0004] A search of the literature on the prior art revealed that the Chinese invention patent publication number CN104517297A, entitled A robot calibration method based on particle swarm optimization, introduces a method for robot kinematic calibration using a particle swarm algorithm. This method can construct a fitness function for the robot's terminal position and posture, and use external parameters to identify the terminal posture error. However, this method does not combine the robot kinematic error model for compensation, and does not consider the impact of the robot's body structural error on the terminal posture error; the Chinese invention patent publication number CN1 12775935A, entitled A parallel robot calibration method based on a terminal error detection information subset, introduces the use of a terminal error detection information subset to accurately, quickly, and reliably identify structural errors based on the parallel robot kinematic error model. However, this method uses the least squares method to identify the error model of the branch chain, which is easily affected by outliers, resulting in unstable identification results. China's invention patent publication number is CN114147726A, and its name is a robot calibration method combining geometric error and non-geometric error. This patent uses singular value decomposition to eliminate coupling parameters and uses particle swarm algorithm to compensate for position errors, thereby improving calibration accuracy and saving calculation time. However, this method does not increase the weight of measurement points in the robot's working area, resulting in limited improvement in positioning accuracy in the working area. Summary of the invention

[0005] The purpose of the present invention is to provide a kinematic calibration method for a hybrid robot optimized for a working area, which can quickly and efficiently detect geometric errors of the hybrid robot and compensate for the working area, with accurate identification results and a simple process.

[0006] The technical solution to achieve the purpose of the present invention is:

[0007] A kinematic calibration method for a hybrid robot optimized for a working area, characterized in that the strategy comprises the following steps:

[0008] S1. Establish the kinematic model of the hybrid robot;

[0009] S2. Establish a kinematic error model for the hybrid robot;

[0010] S3, constructing a residual function according to the difference between the measured coordinates of the end point of the hybrid robot and the output coordinates of the error model;

[0011] S4, weighting the residual function according to the distribution of the measurement points in the working area of ​​the hybrid robot within its reachable range, and constructing a fitness function;

[0012] S5. Use improved particle swarm algorithm to identify the geometric error of the hybrid robot;

[0013] S6, compensating the geometric error identification result to the hybrid robot controller;

[0014] S7. Establish an error compensation evaluation function to evaluate the compensation effect.

[0015] Furthermore, in step S1, the kinematic model of the hybrid robot consists of a parallel part kinematic model and a serial part kinematic model; the space vector method is used to perform kinematic modeling on the parallel part of the hybrid robot; the position vector of the center o′ of the parallel part moving platform in the hybrid robot base coordinate system o-xyz is r1, and the sum of the vectors from the base coordinate origin o to the center of the active arm rotation axis and from the center of the moving arm ball joint to the center of the moving platform is b i The lengths of the active arm and the driven arm are l 1i , l 2i , the unit direction vector of the active arm and the driven arm is u i 、w i , the active joint variable is θ i , the structural angle formed by the axis of the active arm and the xy plane is γ i , the structural angle between the axis of the active arm and the yz plane is Where i = 1, 2, 3; the kinematic model of the parallel part of the hybrid robot is:

[0016] r1=b i +l 1i u i +l 2i w i ;

[0017]

[0018] The DH method is used to perform kinematic modeling of the serial part of the hybrid robot; the starting end of the serial part is fixedly connected to the center of the moving platform of the parallel part, and the fixed offset part is regarded as link 4 here; the coordinate of the end point of the serial part is r2; according to the DH rule, the homogeneous transformation matrix between link i-1 and link i is established The length of the connecting rod is a i , the joint torsion angle is α i , the connecting rod offset is d i , the joint angle is θ i , where i = 5, 6, 7; the connecting rod 4 is the connection between the base of the series part and the dynamic platform of the parallel part, the connecting rod offset is d4, the joint torsion angle α4 is 0, the joint angle θ4 is 0, and the connecting rod length a4 is 0; the lower half length of the series part is d7, the active joint rotation angles are θ5, θ6, θ7, the joint torsion angle α5 is -90°, and α6 is 90°; r2 is the terminal coordinate of the hybrid robot, and the kinematic model of the series part of the hybrid robot is:

[0019]

[0020] By integrating the kinematic models of the parallel part and the serial part of the hybrid robot, the kinematic model of the hybrid robot f(q, p) can be obtained, where q is the six active joint variables of the hybrid robot, that is, θ i (i=1, 2, 3, 5, 6, 7); p is the ideal geometric parameter set:

[0021]

[0022] Furthermore, in step S2, the kinematic error model of the hybrid robot is composed of a parallel part kinematic error model and a serial part kinematic error model; the position vector error of the center o′ of the parallel part moving platform of the hybrid robot in the hybrid robot base coordinate system o-xyZ is Δr1, and the axes of the coordinate system where the active arm rotation center is located are x i ,y i , z i ; Active arm joint angle zero point error Δθ i , the structural angle error Δγ formed by the axis of the active arm and the xy plane i , the structural angle error between the active arm axis and the yz plane is Vector error Δb generated by the static platform and the dynamic platform during manufacturing and installation i , manufacturing error of active arm length Δl 1i , manufacturing error of the length of the follower arm Δl 2i , the unit direction vector error between the active arm and the driven arm is Δu i , Δw i , where i = 1, 2, 3; J1 is the Jacobian matrix of the kinematic error of the parallel part of the hybrid robot, ε1 is its error term matrix, and the kinematic error model of the parallel part is:

[0023] Δr1=J1·ε1;

[0024]

[0025]

[0026] Δc=1 1i Δa i ;

[0027] Δu i =D i Δa i ;

[0028] Δa i =[Δα i Δγ i Δθ i ];

[0029]

[0030] e2=[0 1 0] T ;

[0031] The kinematic errors of the serial part of the hybrid robot are: i , connecting rod length error Δa i , connecting rod offset error Δd i , active joint zero point error Δθ i , the coordinate error of the end of the series part is Δr2, where i = 4, 5, 6, 7; J2 is the Jacobian matrix of the kinematic error of the series part of the hybrid robot, ε2 is its error term matrix, and the kinematic error model of the series part is:

[0032] Δr2=J2·ε2;

[0033] ε2=[Δa4,...,Δa7,Δd4,...,Δd7,Δθ4,...,Δθ7,Δα4,...,Δα7] T ;

[0034]

[0035] Integrating the parallel and series error models of the hybrid robot, the overall error Jacobian matrix of the hybrid robot is J, which can be calculated from the geometric parameters. ε is the overall error term:

[0036]

[0037] The overall end position error is Δr, and the error model is as follows:

[0038] Δr=J·ε;

[0039] J = [J1 J2];

[0040]

[0041] Further, in step S3, by controlling the active joint θ of the hybrid robot i (i=1, 2, 3, 5, 6, 7) Make the end measuring points of the target ball evenly distributed in the reachable area, and use the laser tracker to record the real coordinates of the end points [x n ,y n , z n ] T , and record the 6 active joint angles during measurement; according to the established hybrid robot kinematic model f(q, p), combined with the 6 active joint angles q n Get the ideal coordinates; take the difference between the three as the residual function δ n , specifically expressed as follows:

[0042] δ n =|[x n ,y n , z n ] T -f(q n , p)-J·ε|.

[0043] Furthermore, in step S4, according to the residual function δ between the obtained n measured point coordinates and the ideal model n and the weight k to be assigned to the measurement point n , construct the fitness function L of the improved particle swarm algorithm:

[0044]

[0045] Furthermore, in step S4, the measurement points in the working area are weighted using a probability density function of a three-dimensional spatial distribution within the maximum reachable range of the hybrid robot; the weight k adopted is n It is related to the distribution of the measurement points (x, y, z) in the working area within the maximum reachable range of the hybrid robot. The closer the measurement point is to the center of the working area (x0, y0, z0), the greater the weight assigned, and the corresponding residual function has a more prominent proportion in the error identification process. The calibration result will be more inclined to compensate for the error in the working area. σ is the speed parameter of the control function attenuation.

[0046]

[0047] Furthermore, in step S4, a three-dimensional Gaussian distribution is used to weight the measurement points (x, y, z) in the working area; (x0, y0, z0) is the center of the working area of ​​the hybrid robot, σ0 is the standard deviation of the Gaussian distribution, which is 0.2; r is the distance between the measurement point within the reachable range of the hybrid robot and the center of the working area; the weight distribution expression is:

[0048]

[0049] Furthermore, in step S5, the initial value of the ideal geometric parameter set p of the hybrid robot is set; the upper and lower limits of the geometric parameter identification error are 3% of the actual parameters, and the improved particle swarm algorithm is used to identify the geometric error of the hybrid robot; the improved particle swarm algorithm update formula is as follows, where v i The particle's current velocity, x i is the current position of the particle, c1 and c2 are the individual cognitive factor and the group cognitive factor, r1 and r2 are random numbers between 0 and 1, and pbest i is the best position that the current individual has ever reached, gbest iis the best position reached by the current group, w is the inertia coefficient of the current particle motion, and the overall error term ε of the hybrid robot is obtained after error identification. The update equation is as follows:

[0050] v i+1 =v i ·w+c1·r1·(pbest i -x i )+c2·r2·(gbest i -x i );

[0051] x i+1 =x i +v i+1 ;

[0052] The improved particle swarm algorithm introduces exponential decay to dynamically update the weight, where iter is the number of iterations, maxiter is the maximum number of iterations, and the weight update rules are as follows:

[0053]

[0054] Furthermore, in step S6, the identified geometric error value of the hybrid robot is used to compensate the identified overall error term ε of the hybrid robot to the controller. At this time, the end point position of the hybrid robot is f(q n , p+ε).

[0055] Furthermore, in step S7, the coordinates of n points are measured using a laser tracker, and the six joint variables of the robot at each point in the workspace are q n , the detection point coordinates are [x r ,y r , z r ] T , after compensation, the hybrid robot end point f(q n , p+ε), the evaluation function fval is as follows:

[0056]

[0057] If the value of fval is less than 0.2 mm, it means that the kinematic calibration of the hybrid robot is successful.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] (1) Aiming at the distribution of the working area of ​​the hybrid robot, the present invention proposes to use Gaussian distribution to describe the characteristics of the entire working area and perform weighting operations, thereby optimizing the fitness function in the particle swarm algorithm, thereby increasing the importance of the working area during the calibration process and improving the positioning accuracy of the robot during operation;

[0060] (2) The present invention introduces an improved particle swarm algorithm with the advantages of high solution efficiency, strong adaptability, and good robustness, which simplifies the calibration process of the hybrid robot, effectively identifies the motion parameters, and accurately compensates for the errors;

[0061] (3) The present invention establishes an error compensation evaluation function to evaluate the compensation effect, and evaluates whether the absolute positioning accuracy of the hybrid robot can meet the requirements after compensating for the geometric error;

[0062] (4) The present invention establishes a kinematic model of a hybrid robot and a kinematic error model of a hybrid robot, which is convenient for subsequent kinematic research and experiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 It is a flow chart of a kinematic calibration method of a hybrid robot optimized for the working area;

[0064] Figure 2 The main structure diagram of the hybrid robot implemented in the present invention;

[0065] Figure 3 Schematic diagram of kinematic calibration of robot using laser tracker;

[0066] Figure 4 Schematic diagram of the maximum reachable range of the hybrid robot;

[0067] Figure 5 This is a schematic diagram of the relationship between the maximum reachable range and working area of ​​the hybrid robot;

[0068] Figure 6 Schematic diagram of weighting the Gaussian distribution of the measurement points in the working area within the maximum reachable range;

[0069] Figure 7 Schematic diagram of iterative optimization for improving particle swarm algorithm. DETAILED DESCRIPTION

[0070] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0071] In addition, persons of ordinary skill in the art will appreciate that the drawings provided herein are for illustration purposes and are not necessarily drawn to scale.

[0072] like Figure 1 FIG. 1 is a flow chart of a kinematic calibration method for a hybrid robot optimized for a working area according to the present invention, and the method comprises the following steps:

[0073] S1. Establish the kinematic model of the hybrid robot;

[0074] S2. Establish a kinematic error model for the hybrid robot;

[0075] S3, constructing a residual function according to the difference between the measured coordinates of the end point of the hybrid robot and the output coordinates of the error model;

[0076] S4, weighting the residual function according to the distribution of the measurement points in the working area of ​​the hybrid robot within its reachable range, and constructing a fitness function;

[0077] S5. Use improved particle swarm algorithm to identify the geometric error of the hybrid robot;

[0078] S6, compensating the geometric error identification result to the hybrid robot controller;

[0079] S7. Establish an error compensation evaluation function to evaluate the compensation effect.

[0080] like Figure 2 As shown, it is a structural diagram of the hybrid robot in this embodiment; in the step S1, the kinematic model of the hybrid robot consists of a parallel part kinematic model and a serial part kinematic model; the space vector method is used to perform kinematic modeling on the parallel part of the hybrid robot; the position vector of the center o′ of the parallel part moving platform in the base coordinate system o-xtz of the hybrid robot is r1, and the sum of the vectors from the base coordinate origin o to the center of the active arm rotation axis and from the center of the moving arm ball joint to the center of the moving platform is b i The lengths of the active arm and the driven arm are 1 1i , l 2i , the unit direction vector of the active arm and the driven arm is u i 、w i , the active joint variable is θ i , the structural angle formed by the axis of the active arm and the xy plane is γ i , the structural angle between the axis of the active arm and the yz plane is Where i = 1, 2, 3; the kinematic model of the parallel part of the hybrid robot is:

[0081] r1=b i +l 1i u i +l 2i w i ;

[0082]

[0083]

[0084] The DH method is used to perform kinematic modeling of the serial part of the hybrid robot; the starting end of the serial part is fixedly connected to the center of the moving platform of the parallel part, and the fixed offset part is regarded as link 4 here; the coordinate of the end point of the serial part is r2; according to the DH rule, the homogeneous transformation matrix between link i-1 and link i is established The length of the connecting rod is a i , the joint torsion angle is α i , the connecting rod offset is d i , the joint angle is θ i , where i = 5, 6, 7; the connecting rod 4 is the connection between the base of the series part and the dynamic platform of the parallel part, the connecting rod offset is d4, the joint torsion angle α4 is 0, the joint angle θ4 is 0, and the connecting rod length a4 is 0; the lower half length of the series part is d7, the active joint rotation angles are θ5, θ6, θ7, the joint torsion angle α5 is -90°, and α6 is 90°; r2 is the terminal coordinate of the hybrid robot, and the kinematic model of the series part of the hybrid robot is:

[0085]

[0086] By integrating the kinematic models of the parallel part and the serial part of the hybrid robot, the kinematic model of the hybrid robot f(q,p) can be obtained, where q is the six active joint variables of the hybrid robot, that is, θ i (i=1, 2, 3, 4, 5, 6); p is a set of ideal geometric parameters. In this embodiment, the scalar of the ideal geometric parameter p is {51, 51, 51, 400, 400, 400, 950, 950, 950, 0°, 0°, 120°, 120°, 120°, 0, 0, 0, 0°, -90°, 90°, 0°, 100, 0, 0, 200}, and the length unit in p is mm.

[0087] In step S2, the kinematic error model of the hybrid robot consists of a parallel part kinematic error model and a serial part kinematic error model; the position vector error of the center o′ of the parallel part moving platform of the hybrid robot in the hybrid robot base coordinate system o-xyz is Ar1, and the axes of the coordinate system where the active arm rotation center is located are x i ,y i , z i ; Active arm joint angle zero point error Δθ i , the structural angle error Δγ formed by the axis of the active arm and the xy plane i , the structural angle error between the active arm axis and the yZ plane is Vector error Δb generated by the static platform and the dynamic platform during manufacturing and installation i , manufacturing error of active arm length Δl 1i , manufacturing error of the length of the follower arm Δl 2i, the unit direction vector error between the active arm and the driven arm is Δu i , Δw i , where i = 1, 2, 3; J1 is the Jacobian matrix of the kinematic error of the parallel part of the hybrid robot, ε1 is its error term matrix, and the kinematic error model of the parallel part is:

[0088] Δr1=J1·ε1;

[0089]

[0090]

[0091] Δc=l li Δa i ;

[0092] Δu i =D i Δa i ;

[0093] Δa i =[Δα i Δγ i Δθ i ];

[0094]

[0095] e2=[0 1 0] T ;

[0096] The kinematic errors of the series part of the hybrid robot are respectively the link torsion angle errors Δα from link 4 to link 7 i , connecting rod length error Δa i , connecting rod offset error Δd i , active joint zero point error Δθ i , the coordinate error of the end of the series part is Δr2, where i = 4, 5, 6, 7; J2 is the Jacobian matrix of the kinematic error of the series part of the hybrid robot, ε2 is its error term matrix, and the kinematic error model of the series part is:

[0097] Δr2=J2·ε2;

[0098] ε2=[Δa4,...,Δa7,Δd4,...,Δd7,Δθ4,...,Δθ7,Δα4,...,Δα7] T ;

[0099]

[0100] Integrating the parallel and series error models of the hybrid robot, the overall error Jacobian matrix of the hybrid robot is J, which can be calculated from the geometric parameters. ε is the overall error term:

[0101]

[0102] The overall end position error is Δr, and the error model is as follows:

[0103] Δr=J·ε;

[0104] J = [J1 J2];

[0105]

[0106] like Figure 3 As shown in FIG. 1 , it is a schematic diagram of kinematic calibration of a robot using a laser tracker; in the step S3, by controlling the active joint θ of the hybrid robot i (i=1, 2, 3, 5, 6, 7) Make the end measuring points of the target ball evenly distributed in the reachable area, and use the laser tracker to record the real coordinates of the end points [x n ,y n , z n ] T , and record the 6 active joint angles during measurement; Figure 4 As shown in the figure, it is a schematic diagram of the maximum reachable range of the hybrid robot. In this embodiment, a 1×1×0.5m cube space is taken as the maximum reachable range of the hybrid robot. According to the established kinematic model f(q, p) of the hybrid robot, combined with the 6 active joint angles q n Get the ideal coordinates; In this embodiment, 50 points are sampled in the maximum reachable range of the hybrid robot, and the difference between the three is used as the residual function δ n , specifically expressed as follows:

[0107] δ n =|[x n ,y n , z n ] T -f(q n , p)-J·ε|.

[0108] In step S4, the residual function δ between the obtained n measured point coordinates and the ideal model is n and the weight k to be assigned to the measurement point n , construct the fitness function L of the improved particle swarm algorithm:

[0109]

[0110] In step S4, the measurement points in the working area are weighted using a probability density function of a three-dimensional spatial distribution within the maximum reachable range of the hybrid robot; the weight k nIt is related to the distribution of the measurement points (x, y, z) in the maximum reachable range of the hybrid robot. The closer the measurement point is to the center of the working area (x0, y0, z0), the greater the weight assigned. The corresponding residual function has a more prominent proportion in the error identification process, and the calibration result will be more inclined to compensate for the error in the working area. σ is the speed parameter of the control function attenuation.

[0111]

[0112] In step S4, the measurement points in the working area are weighted using a probability density function of a three-dimensional Gaussian distribution within the maximum reachable range of the hybrid robot; Figure 6 As shown, it is a schematic diagram of Gaussian distribution weighting of the measurement point in the working area within the maximum reachable range; (x0, y0, z0) is the center of the working area of ​​the hybrid robot; in this embodiment, (0.2, 0.7, 0.4) is taken as the center of the working area, and the unit is m; (x, y, z) is any point within the maximum reachable range of the hybrid robot; σ0 is the standard deviation of the Gaussian distribution, which is 0.2; r is the distance between the measurement point within the reachable range of the hybrid robot and the center of the working area; the weight distribution expression is:

[0113]

[0114]

[0115] In step S5, the scalar of the ideal geometric parameter set p of the hybrid robot is set as the initial value; the upper and lower limits of the geometric parameter identification error are 3% above and below the scalar value; Figure 7 As shown in the figure, it is a schematic diagram of iterative optimization of the improved particle swarm algorithm; the improved particle swarm algorithm is used to identify the geometric error of the hybrid robot; the update formula of the improved particle swarm algorithm is as follows, where v i The particle's current velocity, x i is the current position of the particle, c1 and c2 are the individual cognitive factor and the group cognitive factor, r1 and r2 are random numbers between 0 and 1, and pbest i is the best position that the current individual has ever reached, gbest i is the best position reached by the current group, w is the inertia coefficient of the current particle motion, and after error identification, the overall error term of the hybrid robot is obtained as ε. The update equation is as follows:

[0116] v i+1 =v i ·w+c1·r1·(pbest i -x i )+c2·r2·(gbest i -x i );

[0117] x i+1 =x i +v i+1 ;

[0118] The improved particle swarm algorithm introduces exponential decay to dynamically update the weight, where iter is the number of iterations, maxiter is the maximum number of iterations, and in this embodiment the maximum number of iterations is set to 100; the update rules are as follows:

[0119]

[0120] In step S6, the overall geometric error term ε of the hybrid robot identified in step S5 is compensated to the controller. At this time, the end point position is f(q n , p+ε); After error identification in this embodiment, the overall error term of the hybrid robot is ε{0,5.42,8.67,-5.26,-5.26,-5.26,4.67,4.67,4.67,0°,0.173°,-0.293°,0.2°,-0.08°,-0.12°,0,0,0,0°,0.08°,0.08°,0°,3.26,0,0,2.12,0.09°,0.032°,0.048°,0,0.0782°,0.008°,0.054°}, and the length unit is mm.

[0121] In step S7, the measurement process in step S4 is repeated, and the coordinates of 10 points are measured using a laser tracker. The six joint variables of the robot at each point in the workspace are q n , the detection point coordinates are [x r ,y r , z r ] T , the robot end point after compensation is f(q n , p+ε), the evaluation function fval is as follows:

[0122]

[0123] If the value of fval is less than 0.2mm, it means that the kinematic calibration is successful; in this embodiment, the value of fval is 0.1052mm; the average terminal positioning error of the hybrid robot before calibration reaches 5mm, and the average terminal error after calibration reaches 0.105mm, indicating that the kinematic calibration of the hybrid robot is successful.

[0124] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A kinematic calibration method for a hybrid robot optimized for a working area, characterized in that: The strategy includes the following steps: S1. Establish the kinematic model of the hybrid robot; S2. Establish a kinematic error model for the hybrid robot; S3, constructing a residual function according to the difference between the measured coordinates of the end point of the hybrid robot and the output coordinates of the error model; S4, weighting the residual function according to the distribution of the measurement points in the working area of ​​the hybrid robot within its reachable range, and constructing a fitness function; S5. Use improved particle swarm algorithm to identify the geometric error of the hybrid robot; S6, compensating the geometric error identification result to the hybrid robot controller; S7. Establish an error compensation evaluation function to evaluate the compensation effect.

2. A kinematic calibration method for a hybrid robot optimized for a working area according to claim 1, characterized in that: In the step S1, the kinematic model of the hybrid robot consists of a parallel part kinematic model and a serial part kinematic model; the space vector method is used to perform kinematic modeling on the parallel part of the hybrid robot; the position vector of the center o′ of the parallel part moving platform in the hybrid robot base coordinate system o-xyz is r1, and the sum of the vectors from the base coordinate origin o to the center of the active arm rotation axis and from the center of the moving arm ball joint to the center of the moving platform is b i The lengths of the active arm and the driven arm are l 1i , l 2i , the unit direction vector of the active arm and the driven arm is u i 、w i , the active joint variable is θ i , the structural angle formed by the axis of the active arm and the xy plane is γ i , the structural angle between the axis of the active arm and the yz plane is Where i = 1, 2, 3; the kinematic model of the parallel part of the hybrid robot is: r1=b i +l 1i u i +l 2i w i ; The DH method is used to perform kinematic modeling of the serial part of the hybrid robot; the starting end of the serial part is fixedly connected to the center of the moving platform of the parallel part, and the fixed offset part is regarded as link 4 here; the coordinate of the end point of the serial part is r2; according to the DH rule, the homogeneous transformation matrix between link i-1 and link i is established The length of the connecting rod is a i , the joint torsion angle is α i , the connecting rod offset is d i , the joint angle is θ i , where i = 5, 6, 7; the connecting rod 4 is the connection between the base of the series part and the dynamic platform of the parallel part, the connecting rod offset is d4, the joint torsion angle α4 is 0, the joint angle θ4 is 0, and the connecting rod length a4 is 0; the lower half length of the series part is d7, the active joint rotation angles are θ5, θ6, θ7, the joint torsion angle α5 is -90°, and α6 is 90°; r2 is the terminal coordinate of the hybrid robot, and the kinematic model of the series part of the hybrid robot is: By integrating the kinematic models of the parallel part and the serial part of the hybrid robot, the kinematic model of the hybrid robot f(q, p) can be obtained, where q is the six active joint variables of the hybrid robot, that is, θ i (i=1, 2, 3, 5, 6, 7); p is the ideal geometric parameter set:

3. A kinematic calibration method for a hybrid robot optimized for a working area according to claim 1, characterized in that: In step S2, the kinematic error model of the hybrid robot consists of a parallel part kinematic error model and a serial part kinematic error model; the position vector error of the center o′ of the parallel part moving platform of the hybrid robot in the hybrid robot base coordinate system o-xyz is Δr1, and the axes of the coordinate system where the active arm rotation center is located are x i ,y i , z i ; Active arm joint angle zero point error Δθ i , the structural angle error Δγ formed by the axis of the active arm and the xy plane i , the structural angle error between the active arm axis and the yz plane is Vector error Δb generated by the static platform and the dynamic platform during manufacturing and installation i , manufacturing error of active arm length Δl 1i , manufacturing error of the length of the follower arm Δl 2i , the unit direction vector error between the active arm and the driven arm is Δu i , Δw i , where i = 1, 2, 3; J1 is the Jacobian matrix of the kinematic error of the parallel part of the hybrid robot, ε1 is its error term matrix, and the kinematic error model of the parallel part is: Δr1=J1·ε1; Δc=l 1i Δa i ; Thu i =D i Da i ; Da i =[Da i Dg i Dth i ]; e2＝[0 1 0] T ； The kinematic errors of the serial part of the hybrid robot are: i , connecting rod length error Δa i , connecting rod offset error Δd i , active joint zero point error Δθ i , the coordinate error of the end of the series part is Δr2, where i = 4, 5, 6, 7; J2 is the Jacobian matrix of the kinematic error of the series part of the hybrid robot, ε2 is its error term matrix, and the kinematic error model of the series part is: Δr2=J2·ε2; ε2=[Δa4,…,Δa7,Δd4,…,Δd7,Δθ4,…,Δθ7,Δα4,…,Δα7] T ; Integrating the parallel and series error models of the hybrid robot, the overall error Jacobian matrix of the hybrid robot is J, which can be calculated from the geometric parameters. ε is the overall error term: The overall end position error is Δr, and the error model is as follows: Δr=J·ε; J = [J1 J2]; 4. The kinematic calibration method of a hybrid robot optimized for a working area according to claim 1, characterized in that: In step S3, by controlling the active joint θ of the hybrid robot i (i=1, 2, 3, 5, 6, 7) Make the end measuring points of the target ball evenly distributed in the reachable area, and use the laser tracker to record the real coordinates of the end points [x n ,y n , z n ] T , and record the 6 active joint angles during measurement; according to the established hybrid robot kinematic model f(q,P), combined with the 6 active joint angles q n Get the ideal coordinates; take the difference between the three as the residual function δ n , specifically expressed as follows: δ n =|[x n ,y n ,z n ] T -f(q n ,p)-J·ε|。 5. The kinematic calibration method of a hybrid robot optimized for a working area according to claim 1, characterized in that: In step S4, the residual function δ between the obtained n measured point coordinates and the ideal model is n and the weight k to be assigned to the measurement point n , construct the fitness function L of the improved particle swarm algorithm:

6. The kinematic calibration method of a hybrid robot optimized for a working area according to claim 1, characterized in that: In step S4, the measurement points in the working area are weighted using the probability density function of the three-dimensional space distribution within the maximum reachable range of the hybrid robot; the weight k taken by the measurement point (x, y, z) is n It is related to the distribution of the measurement points in the maximum reachable range of the hybrid robot. The closer the measurement point is to the center of the working area (x0, y0, z0), the greater the weight assigned. The corresponding residual function has a more prominent proportion in the error identification process, and the calibration result will be more inclined to compensate for the error in the working area. σ is the speed parameter of the control function attenuation.

7. The kinematic calibration method of a hybrid robot optimized for a working area according to claim 1, characterized in that: In step S4, a three-dimensional Gaussian distribution is used to weight the measurement points (x, y, z) in the working area; (x0, y0, z0) is the center of the working area of ​​the hybrid robot, σ0 is the standard deviation of the Gaussian distribution, which is 0.2; r is the distance from the measurement point within the reachable range of the hybrid robot to the center of the working area; the weight distribution expression is:

8. The kinematic calibration method of a hybrid robot optimized for a working area according to claim 1, characterized in that: In step S5, the initial value of the ideal geometric parameter set p of the hybrid robot is set; the upper and lower limits of the geometric parameter identification error are 3% of the actual parameters, and the improved particle swarm algorithm is used to identify the geometric error of the hybrid robot; the improved particle swarm algorithm update formula is as follows, where v i The particle's current velocity, x i is the current position of the particle, c1 and c2 are the individual cognitive factor and the group cognitive factor, r1 and r2 are random numbers between 0 and 1, and pbest i is the best position that the current individual has ever reached, gbest i is the best position reached by the current group, w i is the inertia coefficient of the current particle motion. After error identification, the overall error term ε of the hybrid robot is obtained. The update equation is as follows: v i+1 =v i ·w i +c1·r1·(pbest i -x i )+c2·r2·(gbest i -x i ); x i+1 =x i +v i+1 ; The improved particle swarm algorithm introduces exponential decay to dynamically update the weight, where iter is the number of iterations, maxiter is the maximum number of iterations, and the weight update rule is as follows:

9. The kinematic calibration method of a hybrid robot optimized for a working area according to claim 1, characterized in that: In step S6, the identified overall geometric error term ε of the hybrid robot is compensated to the controller. At this time, the end point position is f(q n , p+ε).

10. The kinematic calibration method of a hybrid robot optimized for a working area according to claim 1, characterized in that: In step S7, the laser tracker is used to measure the coordinates of n points. The six joint variables of the robot at each point in the workspace are q n , the detection point coordinates are [x r ,y r , z r ] T , the robot end point after compensation f(q n , p+ε), the evaluation function fval is as follows: If the value of fval is less than 0.2 mm, it means that the kinematic calibration of the hybrid robot is successful.

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