A kinematic calibration method for hybrid robots optimized for work area

Abstract

This invention discloses a kinematic calibration method for hybrid robots with optimized working areas. The method includes: analyzing geometric error sources affecting the end-effector accuracy of the hybrid robot and establishing a kinematic model containing error terms; using a laser tracker to collect the difference between the actual coordinates of the end-effector and the output coordinates of the error model within the reachable range of the hybrid robot to generate a residual function; weighting the residual function according to the distribution of measurement points in the working area within the maximum reachable range of the hybrid robot to generate an improved particle swarm optimization (PSO) fitness function; using the improved PSO iteratively to identify geometric errors in the hybrid robot; and compensating the identified errors to the controller to complete the robot's kinematic calibration. The kinematic calibration method proposed in this invention is simple and efficient, and can be applied to most parallel and hybrid robots.

Description

Technical Field

[0001] This invention relates to the field of robot calibration, and more particularly to a kinematic calibration method for hybrid robots optimized for the working area. Background Technology

[0002] With the development of industrial robot technology, more and more industrial sectors are using robots to replace traditional manual operations, which places higher demands on the working accuracy of robots. Regarding robot positioning accuracy, geometric errors generated during robot manufacturing and assembly can cause deviations between the position of the robot's end effector and its actual position during operation. Therefore, improving the absolute positioning accuracy of robots by calibrating their geometric parameters has become an urgent problem to be solved.

[0003] Traditional robot kinematic calibration algorithms face three main problems when applied to hybrid robots: First, compared to the relatively simple open-chain structure of serial robots, hybrid robots have a large number of joints, each with multiple sources of error. Furthermore, due to the various structural errors between joints, the number of error sources is enormous, making systematic error identification difficult. Second, the error identification process suffers from ill-conditioned identification matrices and unstable identification results, hindering high-precision error compensation. Finally, when using external measurement techniques to compensate for robot kinematic errors, the relationship between the distribution of selected measurement points and the robot's workspace is not considered in conjunction with the actual working conditions, resulting in limited improvement in the positioning accuracy of the compensated work area.

[0004] A search of existing literature revealed two invention patents: Chinese Invention Patent Publication No. CN104517297A, entitled "A Robot Calibration Method Based on Particle Swarm Optimization," which describes a method for robot kinematic calibration using the particle swarm optimization algorithm. This method constructs a fitness function for the robot's end-effector position and posture, and identifies end-effector pose errors using extrinsic parameters. However, this method does not incorporate compensation based on the robot's kinematic error model and does not consider the influence of robot body structural errors on end-effector pose errors. Another invention patent, Chinese Invention Patent Publication No. CN112775935A, entitled "A Parallel Robot Calibration Method Based on a Subset of End-Effect Error Detection Information," describes a method for accurately, quickly, and reliably identifying structural errors based on the kinematic error model of a parallel robot using a subset of end-effector error detection information. However, this method uses the least squares method for branch error model identification, which is susceptible to outliers, leading to unstable identification results. Chinese invention patent publication number CN114147726A, entitled "A Robot Calibration Method Combining Geometric and Non-Geometric Errors," utilizes singular value decomposition to eliminate coupling parameters and employs particle swarm optimization to compensate for position errors, thereby improving calibration accuracy and saving computation time. However, this method does not increase the weight of measurement points within the robot's working area, resulting in limited improvement in positioning accuracy within that area. Summary of the Invention

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

[0006] The technical solution to achieve the purpose of this invention is as follows:

[0007] A kinematic calibration method for a hybrid robot optimized for its working area, characterized in that the strategy includes 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. Construct a residual function based on the difference between the measured coordinates of the end point of the hybrid robot and the output coordinates of the error model;

[0011] S4. Based on the distribution of measurement points within the working area of ​​the hybrid robot within its reachable range, weight the residual function and construct the fitness function.

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

[0013] S6. Compensate the geometric error identification results to the hybrid robot controller;

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

[0015] Furthermore, in step S1, the kinematic model of the hybrid robot consists of a kinematic model of the parallel part and a kinematic model of the series part; the kinematic model of the parallel part of the hybrid robot is performed using the space vector method; the position vector of the center o′ of the moving platform in the parallel part in the hybrid robot's base coordinate system o-xyz is r1, and the sum of the vector from the origin o of the base coordinate system to the center of the rotation axis of the active arm and the vector from the center of the ball joint of the active arm to the center of the moving platform is b. i The lengths of the driving arm and the driven arm are l respectively. 1i l 2i The unit direction vector of the driving 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 kinematic modeling of the serial part of the hybrid robot is performed using the DH method. The starting end of the serial part is fixedly connected to the center of the moving platform of the parallel part. Here, the offset part of the fixed connection is regarded as link 4. The coordinates of the end point of the serial part are r2. The homogeneous transformation matrix between link i-1 and link i is established according to the DH rule. The length of the connecting rod is a i The joint twist angle is α i The link offset is d i The joint angle is θ i Where i = 5, 6, 7; Link 4 is the connection point between the series part base and the parallel part moving platform, the link offset is d4, the joint torsion angle α4 is 0, the joint angle θ4 is 0, and the link 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 end-effector 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 and serial parts of the hybrid robot, the kinematic model f(q, p) of the hybrid robot can be obtained, where q represents the six active joint variables of the hybrid robot, i.e., θ i (i = 1, 2, 3, 5, 6, 7); p is the set of ideal geometric parameters:

[0021]

[0022] Furthermore, in step S2, the kinematic error model of the hybrid robot consists of a kinematic error model for the parallel part and a kinematic error model for the serial part; the position vector error of the center o′ of the parallel part of the hybrid robot's moving platform in the hybrid robot's base coordinate system o-xyZ is Δr1, and the axes of the coordinate system where the rotation center of the active arm is located are x i y i , z i Zero-point error Δθ of the active arm joint angle 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 during the manufacturing and installation of static and dynamic platforms i Manufacturing error Δl in the length of the active arm 1i Manufacturing error Δl in boom length 2i The unit direction vector error between the driving 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 parts of the hybrid robot are the link torsion angle errors Δα from link 4 to link 7. i Link length error Δa i Linkage offset error Δd i The zero-point error of the active joint Δθ i The coordinate error at the end of the series connection is Δr2, where i = 4, 5, 6, 7; J2 is the Jacobian matrix of the kinematic error of the series connection of the hybrid robot, and ε2 is its error term matrix. The kinematic error model of the series connection is:

[0032] Δr2=J2·ε2;

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

[0034]

[0035] By integrating the error models of the parallel and series components of the hybrid robot, the overall error Jacobian matrix of the hybrid robot is obtained as J, which can be calculated from the geometric parameters. ε represents 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] Furthermore, in step S3, the active joint θ of the hybrid robot is controlled. i (i = 1, 2, 3, 5, 6, 7) ensures that the end points of the target ball are evenly distributed within the reachable area, and the true coordinates of the end points are recorded using a laser tracker [x]. n y n , z n ] T The six active joint angles at the time of measurement were recorded. Based on the established kinematic model f(q, p) of the hybrid robot, combined with the six active joint angles q at this time... n The ideal coordinates are obtained; the difference between the three is used as the residual function δ. n The specific expression is as follows:

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

[0043] Furthermore, in step S4, the residual function δ between the obtained n measured point coordinates and the ideal model is used... n and the weight k to be assigned to the measurement points n Construct an improved fitness function L for the particle swarm optimization algorithm:

[0044]

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

[0046]

[0047] Furthermore, in step S4, a three-dimensional Gaussian distribution is used to assign weights to the measurement points (x, y, z) within 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 taken as 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:

[0048]

[0049] Furthermore, in step S5, an initial value for the ideal geometric parameter set p of the hybrid robot is set; the upper and lower limits of the geometric parameter identification error are set at 3% above and below the actual parameters; and an improved particle swarm optimization algorithm is used to identify the geometric error of the hybrid robot; the improved particle swarm optimization algorithm update formula is as follows, where v i The particle's current velocity, x i The current position of the particle, c1 and c2 are individual cognitive factors and group cognitive factors, r1 and r2 are random numbers between 0 and 1, pbest i gbest is the best position ever achieved by the current individual. iLet w be the current best position reached by the current group, and w be the current particle inertia coefficient. After error identification, the overall error term ε of the hybrid robot is obtained, and 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 optimization algorithm introduces exponentially decaying dynamic weight updates, where iter is the iteration number and maxiter is the maximum iteration number. The weight update rule is as follows:

[0053]

[0054] Furthermore, in step S6, the identified geometric error value of the hybrid robot is used to compensate the 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 coordinates of the detection point are [x r y r , z r ] T After compensation, the end point f(q) of the hybrid robot n The evaluation function fval is as follows: (p+ε)

[0056]

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

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

[0059] (1) This invention addresses the working area distribution of hybrid robots by proposing 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, increasing the importance of the working area during calibration, and improving the positioning accuracy of the robot during operation.

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

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

[0062] (4) This invention establishes a kinematic model of a hybrid robot and a kinematic error model of a hybrid robot, which facilitates subsequent kinematic research and experiments. Attached Figure Description

[0063] Figure 1 A flowchart of a kinematic calibration method for a hybrid robot optimized for the work area;

[0064] Figure 2 This is a structural diagram of the hybrid robot body according to the present invention;

[0065] Figure 3 A schematic diagram illustrating the kinematic calibration of a robot using a laser tracker;

[0066] Figure 4 A schematic diagram showing the maximum reachable range of the hybrid robot;

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

[0068] Figure 6 A schematic diagram illustrating the weighting of Gaussian distributions for measurement points within the working area within the maximum reachable range;

[0069] Figure 7 A schematic diagram illustrating the iterative optimization process for improving the particle swarm optimization algorithm. Detailed Implementation

[0070] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0071] Furthermore, those skilled in the art should understand that the accompanying drawings provided herein are for illustrative purposes only and are not necessarily drawn to scale.

[0072] like Figure 1 The diagram shown is a flowchart of a kinematic calibration method for a hybrid robot optimized for the working area, as described in this invention. The method includes 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. Construct a residual function based on the difference between the measured coordinates of the end point of the hybrid robot and the output coordinates of the error model;

[0076] S4. Based on the distribution of measurement points within the working area of ​​the hybrid robot within its reachable range, weight the residual function and construct the fitness function.

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

[0078] S6. Compensate the geometric error identification results to the hybrid robot controller;

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

[0080] like Figure 2 The diagram shown is a structural diagram of the hybrid robot body in this embodiment. In step S1, the kinematic model of the hybrid robot consists of a kinematic model of the parallel part and a kinematic model of the serial part. The kinematic model of the parallel part of the hybrid robot is performed using the space vector method. The position vector of the center o′ of the moving platform in the parallel part in the hybrid robot's base coordinate system o-xtz is r1, and the sum of the vector from the origin o of the base coordinate system to the center of the rotation axis of the active arm and the vector from the center of the ball joint of the active arm to the center of the moving platform is b. i The lengths of the driving arm and the driven arm are 1. 1i l 2i The unit direction vector of the driving 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 kinematic modeling of the serial part of the hybrid robot is performed using the DH method. The starting end of the serial part is fixedly connected to the center of the moving platform of the parallel part. Here, the offset part of the fixed connection is regarded as link 4. The coordinates of the end point of the serial part are r2. The homogeneous transformation matrix between link i-1 and link i is established according to the DH rule. The length of the connecting rod is a i The joint twist angle is α i The link offset is d i The joint angle is θ i Where i = 5, 6, 7; Link 4 is the connection point between the series part base and the parallel part moving platform, the link offset is d4, the joint torsion angle α4 is 0, the joint angle θ4 is 0, and the link 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 end-effector 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 and serial parts of the hybrid robot, the kinematic model f(q,p) of the hybrid robot can be obtained, where q represents the six active joint variables of the hybrid robot, i.e., θ i (i = 1, 2, 3, 4, 5, 6); p is the 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°, 0°, 120°, 120°, 120°, 0, 0, 0, 0, -90°, 90°, 0°, 100, 0, 0, 200}. The length unit in p is mm.

[0087] In step S2, the kinematic error model of the hybrid robot consists of a kinematic error model for the parallel part and a kinematic error model for the serial part; the position vector error of the center o′ of the parallel part of the hybrid robot's moving platform in the hybrid robot's base coordinate system o-xyz is Ar1, and the axes of the coordinate system containing the rotation center of the active arm are x and xyz respectively. i y i , z i Zero-point error Δθ of the active arm joint angle 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 during the manufacturing and installation of static and dynamic platforms i Manufacturing error Δl in the length of the active arm 1i Manufacturing error Δl in boom length 2iThe unit direction vector error between the driving 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 components of the hybrid robot are represented by the link torsion angle error Δα, which is the value of links 4 to 7. i Link length error Δa i Linkage offset error Δd i The zero-point error of the active joint Δθ i The coordinate error at the end of the series connection is Δr2, where i = 4, 5, 6, 7; J2 is the Jacobian matrix of the kinematic error of the series connection of the hybrid robot, and ε2 is its error term matrix. The kinematic error model of the series connection is:

[0097] Δr2=J2·ε2;

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

[0099]

[0100] By integrating the error models of the parallel and series components of the hybrid robot, the overall error Jacobian matrix of the hybrid robot is obtained as J, which can be calculated from the geometric parameters. ε represents 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 The diagram shows a kinematic calibration of a robot using a laser tracker; in step S3, the active joint θ of the hybrid robot is controlled. i (i = 1, 2, 3, 5, 6, 7) ensures that the end points of the target ball are evenly distributed within the reachable area, and the true coordinates of the end points are recorded using a laser tracker [x]. n y n , z n ] T And record the 6 active joint angles during measurement; such as Figure 4 The diagram shows 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. Based on the established kinematic model f(q, p) of the hybrid robot, combined with the angles q of the six active joints at this time... n The ideal coordinates are obtained; in this embodiment, 50 points are sampled within the maximum reachable range of the hybrid robot, and the difference between the three is used as the residual function δ. n The specific expression is 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 used. n and the weight k to be assigned to the measurement points n Construct an improved fitness function L for the particle swarm optimization algorithm:

[0109]

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

[0111]

[0112] In step S4, the measurement points within the working area are weighted using a three-dimensional Gaussian probability density function within the maximum reachable range of the hybrid robot; for example... Figure 6 The diagram shows a Gaussian distribution weighting of measurement points within the maximum reachable range of the working area; (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, in meters; (x, y, z) is any point within the maximum reachable range of the hybrid robot; σ0 is the standard deviation of the Gaussian distribution, taken as 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:

[0113]

[0114]

[0115] In step S5, a scalar of the ideal geometric parameter set p of the hybrid robot is set as an initial value; and the upper and lower limits of the geometric parameter identification error are set to 3% above and below the scalar value; such as Figure 7 The diagram shows an iterative optimization process using the improved particle swarm optimization algorithm. The improved particle swarm optimization algorithm is used to identify the geometric errors of the hybrid robot. The updated formula for the improved particle swarm optimization algorithm is as follows, where v i The particle's current velocity, x i The current position of the particle, c1 and c2 are individual cognitive factors and group cognitive factors, r1 and r2 are random numbers between 0 and 1, pbest i gbest is the best position ever achieved by the current individual. i Let w be the current best position reached by the current group, and w be the current particle inertia coefficient. After error identification, the overall error term of the hybrid robot is ε, and 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 optimization algorithm introduces exponentially decaying dynamic weight updates, where iter is the iteration number and maxiter is the maximum iteration number. In this embodiment, the maximum iteration number is set to 100. The update rule is 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); In this embodiment, after error identification, the overall error term of the hybrid robot is obtained as 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°,0.08°,0.08°,0°,3.26,0,0,2.12,0.09°,0.032°,0.048°,0,0.0782°,0.008°,0.054°}, with the length unit being 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 coordinates of the detection point are [x r y r , z r ] T After compensation, the robot's end-effector position is f(q). n The evaluation function fval is as follows: (p+ε)

[0122]

[0123] If the value of fval is less than 0.2 mm, it indicates that the kinematic calibration is successful. In this embodiment, the value of fval is 0.1052 mm. The average end-effector positioning error of the hybrid robot before calibration reached 5 mm, and the average end-effector error after calibration reached 0.105 mm, indicating that the kinematic calibration of the hybrid robot was successful.

[0124] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions 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 its 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. Construct a residual function based on the difference between the measured coordinates of the end point of the hybrid robot and the output coordinates of the error model; S4. Based on the distribution of measurement points within the working area of ​​the hybrid robot within its reachable range, weight the residual function and construct the fitness function. S5. Use an improved particle swarm optimization algorithm to identify the geometric errors of the hybrid robot; S6. Compensate the geometric error identification results to the hybrid robot controller; S7. Establish an error compensation evaluation function to assess the compensation effect.

2. The kinematic calibration method for a hybrid robot with optimized working area according to claim 1, characterized in that, In step S1, the kinematic model of the hybrid robot consists of a kinematic model of the parallel part and a kinematic model of the serial part; the kinematic model of the parallel part of the hybrid robot is performed using the space vector method; the position vector of the center o′ of the moving platform in the parallel part in the hybrid robot's base coordinate system o-xyz is r1, and the sum of the vectors from the origin o of the base coordinate system to the center of the rotation axis of the active arm and from the center of the ball joint of the active arm to the center of the moving platform is b. i The lengths of the driving arm and the driven arm are l respectively. 1i l 2i The unit direction vector of the driving 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 kinematic modeling of the serial part of the hybrid robot is performed using the DH method. The starting end of the serial part is fixedly connected to the center of the moving platform of the parallel part. Here, the offset part of the fixed connection is regarded as link 4. The coordinates of the end point of the serial part are r2. The homogeneous transformation matrix between link i-1 and link i is established according to the DH rule. The length of the connecting rod is a i The joint twist angle is α i The link offset is d i The joint angle is θ i Where i = 5, 6, 7; Link 4 is the connection point between the series part base and the parallel part moving platform, the link offset is d4, the joint torsion angle α4 is 0, the joint angle θ4 is 0, and the link 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 end-effector 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 and serial parts of the hybrid robot, the kinematic model f(q, p) of the hybrid robot can be obtained, where q represents the six active joint variables of the hybrid robot, i.e., θ i (i = 1, 2, 3, 5, 6, 7); p is the set of ideal geometric parameters:

3. The kinematic calibration method for a hybrid robot with optimized working area according to claim 1, characterized in that, In step S2, the kinematic error model of the hybrid robot consists of a kinematic error model for the parallel part and a kinematic error model for the serial part; the position vector error of the center o′ of the parallel part of the hybrid robot's moving platform in the hybrid robot's base coordinate system o-xyz is Δr1, and the axes of the coordinate system containing the rotation center of the active arm are x and y. i y i , z i Zero-point error Δθ of the active arm joint angle 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 during the manufacturing and installation of static and dynamic platforms i Manufacturing error Δl in the length of the active arm 1i Manufacturing error Δl in boom length 2i The unit direction vector error between the driving 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 parts of the hybrid robot are the link torsion angle error Δα from link 4 to link 7. i Link length error Δa i Linkage offset error Δd i The zero-point error of the active joint Δθ i The coordinate error at the end of the series connection is Δr2, where i = 4, 5, 6, 7; J2 is the Jacobian matrix of the kinematic error of the series connection of the hybrid robot, and ε2 is its error term matrix. The kinematic error model of the series connection is: Δr2=J2·ε2; ε2=[Δa4,…,Δa7,Δd4,…,Δd7,Δθ4,…,Δθ7,Δα4,…,Δα7] T ; By integrating the error models of the parallel and series components of the hybrid robot, the overall error Jacobian matrix of the hybrid robot is obtained as J, which can be calculated from the geometric parameters. ε represents 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 for a hybrid robot with optimized working area according to claim 1, characterized in that, In step S3, the active joint θ of the hybrid robot is controlled. i (i = 1, 2, 3, 5, 6, 7) ensures that the end points of the target ball are evenly distributed within the reachable area, and the true coordinates of the end points are recorded using a laser tracker [x]. n y n , z n ] T The six active joint angles at the time of measurement were recorded. Based on the established kinematic model f(q,P) of the hybrid robot, combined with the six active joint angles q at this time... n The ideal coordinates are obtained; the difference between the three is used as the residual function δ. n The specific expression is as follows: δ n =|[x n ,y n ,z n ] T -f(q n ,p)-J·ε|。 5. The kinematic calibration method for a hybrid robot with optimized 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 used. n and the weight k to be assigned to the measurement points n Construct an improved fitness function L for the particle swarm optimization algorithm:

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

7. The kinematic calibration method for a hybrid robot with optimized working area according to claim 1, characterized in that, In step S4, a three-dimensional Gaussian distribution is used to assign weights to the measurement points (x, y, z) within 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 taken as 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 for a hybrid robot with optimized working area according to claim 1, characterized in that, In step S5, an initial value for the ideal geometric parameter set p of the hybrid robot is set; the upper and lower limits of the geometric parameter identification error are set at 3% above and below the actual parameters; and an improved particle swarm optimization algorithm is used to identify the geometric error of the hybrid robot. The improved particle swarm optimization algorithm update formula is as follows, where v i The particle's current velocity, x i The current position of the particle, c1 and c2 are individual cognitive factors and group cognitive factors, r1 and r2 are random numbers between 0 and 1, pbest i gbest is the best position ever achieved by the current individual. i w represents the best position reached by the current group. i Given the current particle motion inertia coefficient, after error identification, the overall error term ε of the hybrid robot is obtained, and 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 optimization algorithm introduces exponentially decaying dynamic weight updates, where iter is the iteration number and maxiter is the maximum iteration number. The weight update rule is as follows:

9. The kinematic calibration method for a hybrid robot with optimized 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 which point the end point position is f(q). n ,p+ε).

10. The kinematic calibration method for a hybrid robot with optimized working area according to claim 1, characterized in that, 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 coordinates of the detection point are [x r y r , z r ] T After compensation, the robot end-effector position f(q) n The evaluation function fval is as follows: (p+ε) If the value of fval is less than 0.2mm, it indicates that the kinematic calibration of the hybrid robot is successful.

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