Flexible super-redundant mechanical arm calibration method and system, storage medium and computing equipment

Abstract

The invention relates to the field of mechanical arm calibration, and discloses a flexible super-redundant mechanical arm calibration method and system, a storage medium and computing device.The flexible super-redundant mechanical arm calibration method comprises the steps that a nominal positive kinematics model of a redundant mechanical arm is established, and a Jacobian matrix is determined; a matrix of gravity borne by all the joints is obtained, and additional joint rotation angles and elastic coefficients generated by the joints are obtained on the basis of the gravitational torque; through a pose sensor, known mechanical arm nominal MDH parameters and a redundant mechanical arm nominal positive kinematics model, pose error vectors of the joints at the measurement configuration are obtained; and merging the elastic coefficients of all the joints and the MDH parameter errors of all the joints into a vector delta u, establishing a mapping relation from delta u to Ej, defining the solved delta u as a first identification result, and performing iterative asymptotic identification to obtain a final identification result of the MDH parameter and the joint elastic coefficient. And step-by-step classification compensation is carried out on the MDH parameter error and the joint elastic coefficient, and finally compensated corner instructions of all joints are obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of robot arm calibration, and in particular to a highly flexible ultra-redundant robot arm calibration method, system, medium and equipment based on rigid-flexible coupling modeling and iterative identification. Background Art

[0002] Absolute positioning accuracy is crucial to the working performance of the robot. For industrial robot arms, kinematic parameter errors are the main cause of absolute positioning errors, which mainly come from the errors introduced by each link and joint during the manufacturing, assembly and transmission process. Traditional calibration methods can effectively compensate for kinematic parameter errors and improve the absolute positioning accuracy of industrial robot arms, so that they can meet most operating requirements. However, industrial robot arms are limited by strong rigidity, long links and few degrees of freedom, making it difficult to perform some tasks in unstructured spaces. Therefore, super-redundant robot arms with strong joint flexibility, short links and a large number of joints have emerged. Most traditional calibration methods only consider kinematic parameter errors in the modeling process, and the model does not include parameters related to joint flexibility. Some studies have focused on the joint flexibility characteristics, but the modeling object is a six-degree-of-freedom industrial robot arm. Therefore, the corresponding parameter error identification algorithm is only suitable for processing low-dimensional models and small angle errors, and its performance is difficult to match the dramatically increased model dimensions and linearization errors of super-redundant robot arms. In summary, the existing calibration methods can no longer meet the calibration accuracy requirements of highly flexible and ultra-redundant robotic arms, and there is an urgent need to significantly improve the integrity of the calibration model and the performance of the error parameter identification algorithm. Summary of the invention

[0003] In view of the above problems, the purpose of the present invention is to provide a flexible super-redundant robotic arm calibration method, system, storage medium and computing device, which can meet the calibration accuracy requirements of a highly flexible super-redundant robotic arm.

[0004] To achieve the above objectives, in the first aspect, the technical solution adopted by the present invention is: a flexible super redundant manipulator calibration method, which comprises: based on the MDH criterion, establishing a nominal positive kinematics model of the redundant manipulator, and obtaining the Jacobian matrix J of k joints based on differential transformation. k , and the jth measurement configuration {θ 1 ,…,θ k} j The Jacobian matrix Where k is the total number of joints of the serial k-DOF super-redundant manipulator; considering the influence of joint flexibility error on the posture error of the redundant manipulator, the gravity moment M of the i-th joint is calculated Gi , to obtain the gravity matrix M of all joints G , and based on the gravity moment, the additional joint rotation angle δθ generated by the i-th joint is obtained iG =M Gi λi , where λ i is the elastic coefficient of the i-th joint, i = 1, 2, ..., k; in the measurement configuration {θ 1 ,…,θ k} j Under this condition, the position sensor, the known nominal MDH parameters of the manipulator, and the nominal forward kinematics model of the redundant manipulator are used to obtain the measured configuration {θ 1 ,…,θ k} j The pose error vector E at j ; Set the elastic coefficients λ of all joints i The MDH parameter error Δu of all joints i Merge into a vector Δu=[Δu 1 T ,Δu 2 T ,…,Δu k T ,λ 1 ,λ 2 ,…,λ k ] T ; Under the jth measurement configuration, establish Δu to E j The mapping relationship E j =J j Δu, and expands to E = JΔu; where E = [E 1 T ,E 2 T ,…,E n T ] T , J=[J 1 T ,J 2 T ,…,J n T ] T , n is the total number of selected measurement configurations; Δu is the error vector composed of the unknown MDH parameter errors of all joints and the elastic coefficients of all joints; J j The position error vector E is Δu at the jth measurement configuration. j The mapping Jacobian matrix of J k , and M G The mapping Jacobian matrix is ​​constructed; the Δu obtained by solving E=JΔu is defined as the first identification result, and iterative asymptotic identification is performed to obtain the final identification results of the MDH parameters and joint elastic coefficients. The MDH parameter errors and joint elastic coefficients are compensated for in steps and classification based on the final identification results of the MDH parameters and joint elastic coefficients to obtain the final compensated rotation angle instructions for all joints.

[0005] Furthermore, considering the influence of joint flexibility error on the posture error of the redundant manipulator, the gravity moment M of the i-th joint is calculated: Gi ,include:

[0006] Install at least three non-collinear target balls on a regular-shaped bracket and measure the total weight m of the bracket and all the target balls. s , combine the vertical suspension method and the geometric center method to determine the common center of gravity position P of all target balls and brackets gs ;

[0007] According to the measured mass m of each joint i , combine the vertical suspension method and the geometric center method to determine the center of gravity position P of the first k-1 joints gi ;

[0008] According to the common center of gravity position P gs and the center of gravity position P of each joint gi , get the common center of gravity P of all the subsequent joints of joint i g The x, y, and z coordinate values ​​of the rear joint include a sensor and a bracket;

[0009] Determine the common center of gravity P g To the i-th joint axis direction vector Z i The vertical point V g , and based on the measured total weight of the bracket and all target balls m s and the mass m of each joint i , get the total gravity G of all the subsequent joints of joint i i , and then get the total gravity of the rear joint G i In the base coordinate system F 0 The following is expressed as the total gravity vector G of the rear joint g , by the total gravity vector G of the rear joint g and the common center of gravity P g Get vector G g The end point coordinates P G ;

[0010] From the end point coordinates P G and vertical point V g Get G i At the same time, it is perpendicular to the force arm vector L i and the joint axis direction vector Z i The force vector F Gi , and then get the gravity moment M on joint i Gi = ±||F Gi ||·||L i ||.

[0011] Furthermore, in the measurement configuration {θ 1 ,…,θ k} j Under this condition, the position sensor, the known nominal MDH parameters of the manipulator, and the nominal forward kinematics model of the redundant manipulator are used to obtain the measured configuration {θ 1 ,…,θ k} j The pose error vector E at j ,include:

[0012] In the measurement configuration {θ 1 ,…,θ k} j The actual posture P of joint k is measured by the posture sensor ka(j) ;

[0013] Based on the known nominal MDH parameters of the manipulator and the nominal forward kinematics model of the redundant manipulator, in {θ 1 ,…,θ k} j Calculate the nominal pose vector p of joint k k(j) ;

[0014] The actual pose P ka(j) and the nominal pose vector p of joint k k(j) Subtract, and get the joint k in the measurement configuration {θ 1 ,…,θ k} j The pose error vector E at j .

[0015] Further, J j The position error vector E is Δu at the jth measurement configuration. j The mapping Jacobian matrix of J k , and M G The constructed mapping Jacobian matrix includes:

[0016]

[0017] in:

[0018]

[0019] In the formula, C i is the MDH parameter error vector Δu of the i-th joint i To the joint coordinate system F i The mapping matrix of the pose error; is the mapping Jacobian matrix of the DH parameter error of the i-th joint to the pose error of the k-th joint at the end, M is the mapping Jacobian matrix of the i-th joint gravity torque to the end k joint posture error; G is the gravitational moment M acting on all joints Gi The diagonal matrix formed.

[0020] Further, by transforming E=JΔu, the obtained Δu is: Δu=J + E, J + is the generalized inverse matrix of J.

[0021] Furthermore, the Δu obtained by solving E = JΔu is defined as the first identification result, and iterative asymptotic identification is performed to obtain the final identification results of the MDH parameters and joint elastic coefficients, including:

[0022] Define Δu as the first identification result Δu (0) , multiply it by the weight w and then add it to u (0) Add to get u (1) =u (0) +wΔu (0) ; Among them, u (0) is a vector consisting of the nominal values ​​of the MDH parameters and the joint elastic coefficients;

[0023] will u (1) Substitute Δu into E=JΔu and re-establish the formula Δu=J + E is used to identify when u (1) The first iteration identification result Δu is the nominal value (1) ;

[0024] Repeat the above steps. If the ||Δu|| obtained in each iteration shows an upward trend, the iteration diverges. At this time, reduce the weight w and recalculate u (1) ; If ||Δu|| shows a downward trend, the iteration converges until ||Δu||<ε is satisfied, where ε is the threshold set according to the calibration accuracy requirement. At this time, if the number of iterations is q-1, the obtained u (q) =u (q-1) +wΔu (q-1) This is the final identification result of MDH parameters and joint elastic coefficients.

[0025] Furthermore, the MDH parameter errors and joint elastic coefficients are compensated step by step based on the final identification results of the MDH parameters and joint elastic coefficients, and the final compensated rotation angle instructions of all joints are obtained, including:

[0026] Take u at any measurement configuration (q) -u (0) The 4i-1th parameter δθ in i As the zero position error of the i-th joint, all δθ are compensated synchronously in the control system i ;

[0027] Take u (q) Use the nominal MDH parameters of the robot arm to solve the inverse kinematics;

[0028] Subtract λ from the joint i rotation command obtained by inverse solution i(q) M Gi , get the final compensation angle command of all joints; where M Gi is the gravitational moment on joint i at the above inverse solution, λ i(q) is the identification result of the joint elastic coefficient of the qth identification.

[0029] In the second aspect, the technical solution adopted by the present invention is: a flexible super redundant manipulator calibration system, which includes: a first processing module, based on the MDH criterion, establishes a nominal positive kinematics model of the redundant manipulator, and obtains the Jacobian matrix J of k joints based on differential transformation k , and the jth measurement configuration {θ 1 ,…,θ k} j The Jacobian matrix Where k is the total number of joints of the serial k-DOF super-redundant manipulator; the second processing module considers the influence of joint flexibility error on the posture error of the redundant manipulator and calculates the gravity moment M of the i-th joint Gi , to obtain the gravity matrix M of all joints G , and based on the gravity moment, the additional joint rotation angle δθ generated by the i-th joint is obtained iG =M Gi λ i , where λ i is the elastic coefficient of the i-th joint, i = 1, 2, ..., k; the posture error vector module, in the measurement configuration {θ 1 ,…,θ k} j Under this condition, the position sensor, the known nominal MDH parameters of the manipulator, and the nominal forward kinematics model of the redundant manipulator are used to obtain the measured configuration {θ 1 ,…,θ k} j The pose error vector E at j ; Mapping module, which converts the elastic coefficients λ of all joints i The MDH parameter error Δu of all joints i Merge into a vector Δu=[Δu 1 T ,Δu 2 T ,…,Δu k T ,λ 1 ,λ 2 ,…,λk ] T ; Under the jth measurement configuration, establish Δu to E j The mapping relationship E j =J j Δu, and expands to E = JΔu; where E = [E 1 T ,E 2 T ,…,E n T ] T , J=[J 1 T ,J 2 T ,…,J n T ] T , n is the total number of selected measurement configurations; Δu is the error vector composed of the unknown MDH parameter errors of all joints and the elastic coefficients of all joints; J j The position error vector E is Δu at the jth measurement configuration. j The mapping Jacobian matrix of J k , and M G The mapping Jacobian matrix is ​​constructed; the identification and compensation module defines Δu obtained by solving E=JΔu as the first identification result, performs iterative asymptotic identification, and obtains the final identification results of MDH parameters and joint elastic coefficients. The MDH parameter errors and joint elastic coefficients are compensated in steps and categories based on the final identification results of MDH parameters and joint elastic coefficients to obtain the final compensated rotation angle instructions for all joints.

[0030] In a third aspect, the technical solution adopted by the present invention is: a computer-readable storage medium storing one or more programs, wherein the one or more programs include instructions, and when the instructions are executed by a computing device, the computing device executes any one of the above methods.

[0031] In a fourth aspect, the technical solution adopted by the present invention is: a computing device, comprising: one or more processors, a memory and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include instructions for executing any of the above methods.

[0032] The present invention adopts the above technical solution, which has the following advantages:

[0033] 1. The present invention includes two types of error parameters that characterize the rigidity and flexibility characteristics of the hyper-redundant robotic arm in the calibration model at the same time, and aims at the problem of sharp increase in linearization error caused by rigid-flexible coupling modeling, and gradually reduces its influence on the identification accuracy through iterative identification, so that the identification result finally converges to high accuracy.

[0034] 2. The present invention establishes a rigid-flexible coupling error model and iteratively suppresses the model linearization error without making significant changes to the typical industrial robot arm calibration process, so it has good feasibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is an overall flow chart of the flexible super-redundant mechanical arm calibration method in an embodiment of the present invention;

[0036] Figure 2 are the coordinate systems of the hyper-redundant robotic arm with k joints in an embodiment of the present invention;

[0037] Figure 3 is the total weight G of the rear joint of the i-th joint in the embodiment of the present invention i and to the axis Z i Schematic diagram of the lever arm;

[0038] Figure 4 is the total gravity G in the embodiment of the present invention i The force arm L i and its perpendicular to the lever arm L i The force F Gi Schematic diagram;

[0039] Figure 5 In the embodiment of the present invention, the base coordinate system F is determined in the laser tracker coordinate system. 0 and nominal F 1 Schematic diagram of the method;

[0040] Figure 6 is a schematic diagram of a method for determining the coordinate system of the 12th joint of the robot arm in the laser tracker coordinate system in an embodiment of the present invention;

[0041] Figure 7 It is a comparison of the accuracy of MDH identification, single identification of the new method and iterative identification of the new method in the embodiment of the present invention;

[0042] Figure 8 is a distribution diagram of measurement points in an embodiment of the present invention;

[0043] Fig. 9 is a comparison of absolute positioning residuals after using different calibration methods in the embodiments of the present invention;

[0044] Fig.10 is a graph showing the variation trend of the error identification accuracy of each parameter with the number of iterations in an embodiment of the present invention;

[0045] Fig.11 1 is a graph showing the absolute positioning residual changing with the number of iterations in an embodiment of the present invention. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical solution and advantages of the embodiment of the present invention clearer, the technical solution of the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings of the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the described embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field belong to the scope of protection of the present invention.

[0047] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0048] In one embodiment of the present invention, Figure 1 As shown, a flexible super-redundant manipulator calibration method, system, storage medium and computing device are provided. The present invention establishes a rigid-flexible coupling calibration model for a serial super-redundant manipulator with flexible joints, and proposes a high-precision iterative identification algorithm for the error parameters of the model. In this embodiment, the measuring instrument used is an API Radian PLUS laser tracker, the sensor is a laser target ball, and the calibration object is a 12-degree-of-freedom super-redundant manipulator with adjacent joint axes perpendicular to each other. The method includes the following steps:

[0049] 1) Based on the MDH (Modified Denavit-Hartenberg) criterion, the nominal forward kinematics model of the redundant manipulator is established, and the Jacobian matrix J of k joints is obtained based on differential transformation. k , and the jth measurement configuration {θ 1 ,…,θ k} j The Jacobian matrix Wherein, k is the total number of joints of the serial k-DOF hyper-redundant manipulator, j = 1, 2, …, n, and n represents the number of measurement configurations.

[0050] 2) Considering the influence of joint flexibility error on the posture error of redundant manipulator, calculate the gravity moment M of the i-th joint Gi , to obtain the gravity matrix M of all joints G, and based on the gravity moment, the additional joint rotation angle δθ generated by the i-th joint is obtained iG is: δθ ig =M Gi λ i , where λ i is the elastic coefficient of the i-th joint, i = 1, 2, …, k.

[0051] 3) In the measurement configuration {θ 1 ,…,θ k} j Under this condition, the position sensor, the known nominal MDH parameters of the manipulator and the nominal forward kinematics model of the redundant manipulator are used to obtain the measured configuration {θ 1 ,…,θ k} j The pose error vector E at j =P ka(j)- P k(j) .

[0052] 4) Set the elastic coefficients λ of all joints i The MDH parameter error Δu of all joints i Merge into a vector Δu=[Δu 1 T ,Δu 2 T ,…,Δu k T ,λ 1 ,λ 2 ,…,λ k ] T In the jth measurement configuration used for calibration, establish Δu to E j The mapping relationship E j =J j Δu, and expanded to E = JΔu; E = JΔu is the rigid-flexible coupling calibration model;

[0053] Where E=[E 1 T ,E 2 T ,…,E n T ] T , J=[J 1 T ,J 2 T ,…,J n T ] T ; Δu is the error vector composed of the unknown MDH parameter errors of all joints and the elastic coefficients of all joints; J j The position error vector E is Δu at the jth measurement configuration.j The mapping Jacobian matrix of J k , and M G Construct the mapped Jacobian matrix.

[0054] 5) Define Δu obtained by solving E=JΔu as the first identification result, perform iterative asymptotic identification, and obtain the final identification results of MDH parameters and joint elastic coefficients. Use the final identification results of MDH parameters and joint elastic coefficients to perform step-by-step classification compensation for MDH parameter errors and joint elastic coefficients to obtain the final compensated rotation angle instructions for all joints.

[0055] When used, the present invention combines the influence of MDH parameter error and joint flexibility error on the posture error of the super-redundant manipulator, establishes a rigid-flexible coupling calibration model, and improves the integrity of the model. On this basis, the influence of the linearization error of the rigid-flexible coupling model on the identification accuracy is overcome through an iterative identification algorithm, ensuring the accuracy of the calibration.

[0056] In the above step 1), based on the MDH criterion, a nominal forward kinematics model of the redundant manipulator is established, which specifically includes the following steps:

[0057] 1.1) A posture sensor is installed at the end joint k of the serial k-degree-of-freedom super-redundant robot arm, which can output the posture of its own coordinate system in real time, and thus indirectly obtain the actual posture of the end joint.

[0058] 1.2) Select the measurement configuration {θ 1 ,…,θ k} j (j=1,2,…,n). 1 ,…,θ k} represents the set of rotation instructions of k joints corresponding to the measurement configuration, j represents the sequence number of the measurement configuration, and n represents the number of measurement configurations.

[0059] 1.3) Based on the MDH criteria, Figure 2 The base coordinate system F of a serial super redundant manipulator with k degrees of freedom is established as shown in 0 and the joint coordinate system F i (i=1,2,…,k).

[0060] 1.4) Based on the MDH criterion, a nominal positive kinematic model of the redundant manipulator is established.

[0061] Specifically, the implementation method in this embodiment is as follows:

[0062] (1) Figure 5 As shown in the figure, the target ball is made to contact two different points on the upper surface of the robot arm base, and its coordinates A are collected by a laser tracker 1 and A2 , and define the vector v 1 =A 1 A 2 ; Make the target ball contact the two end points A of the first joint axis 3 and A 4 , we get the vector Z 1 =A 3 A 4 ; Base coordinate system origin O 0 Defined as A 1 , X 0 The axis is defined as X 0 =v 1 ×Z 1 , base coordinate system Y 0 The axis is defined as 1 The axes are reversed, thus establishing the base coordinate system F 0 ; Make the target ball contact 6 points evenly distributed along the arc on the outer contour of the cylindrical base of the first joint, and the target ball should contact the upper surface of the base at the same time to ensure that the 6 points are approximately located in the same plane; use a laser tracker to collect the coordinates of these 6 points B 1 , B 2 , …, B 6 , get a circular arc by fitting, and calculate the center of the arc O B ; According to the size of the robot parts, get the rotation center of the first joint and O B The spacing, defined as a 1 ;O B Along X 0 Direction translation a 1 The point after is defined as the origin O of the first joint coordinate system 1 , the first joint coordinate axis X 1 Defined as 0 Overlap; Calculate O 0 Along Z 1 Reverse to O B The distance is defined as d 1 , thus establishing the nominal coordinate system F of the first joint 1 . F 0 to F 1 Transformation 0 T 1 Considered as the nominal transformation matrix of the first joint.

[0063] (2) Install the bracket with the target ball on the 12th joint of the robot arm (make sure each target ball is fixed relative to the 12th joint).

[0064] (3) Figure 6 As shown, only the joint 11 is rotated, and the arc trajectory of the target ball 1 is collected by a laser tracker, and the arc rotation axis vector Z is obtained by fitting. 11The other joint angles remain unchanged, only the joint 12 is rotated, the arc trajectory of the target ball 1 is collected, and the arc rotation axis vector Z is obtained by fitting. 12 , as the Z coordinate system of joint 12 12 Axis; vector X 12 =Z 11 ×Z 12 Defined as the X of the 12th joint coordinate system 12 Axis, Z 11 and Z 12 The common perpendicular line and Z 12 The intersection point is taken as the origin O 12 , thus establishing the coordinate system F 12 ; All joint angles remain unchanged, and the laser tracker is used to collect the coordinates of the three target balls S 1 , S 2 and S 3 ; Establish sensor coordinate system F s , first by S 1 , S 2 and S 3 Get vector v 2 、v 3 , and v 4 =v 2 ×v 3 ; S 1 Defined as the origin O s , v 2 Defined as Z s Axis, v 4 Defined as X s axis. From this, we can get F 12 and F s In F 0 The actual transformation matrix under 0 T 12a and 0 T sa , and then we can get s T 12 = sa T 12a =( 0 T s ) -1 ( 0 T 12a ); In any measurement configuration, use the same method to establish F s , and then the actual value corresponding to the measurement configuration can be calculated 0 T 12a .

[0065] (3) The number of measurement configurations is selected to be 60, that is, {θ 1 ,…,θ 12} j(j=1,2,…,60), the method is random selection. 1 ,…,θ 12} represents the rotation instruction set of 12 joints corresponding to the measurement configuration, and j represents the serial number of the measurement configuration.

[0066] (4) This step begins to establish a kinematic error model for the kinematic parameters that produce errors. Figure 2 As shown in the figure, based on the MDH rule, the coordinate systems of each joint of a serial super-redundant manipulator with 12 degrees of freedom are established, that is, the base coordinate system F of the k=12 super-redundant manipulator. 0 and the joint coordinate system F i (i=1,2,…,12).

[0067] Table 1 Nominal values ​​of MDH parameters of super redundant manipulator

[0068]

[0069] As shown in Table 1, the nominal DH parameters of each joint are as follows. Based on the MDH criterion, the forward kinematic model of the i-th joint of the redundant manipulator is:

[0070] 0 T i = 0 T 1 1 T 2 ... i-1 T i (1)

[0071] In the formula, i-1 T i Yes F i-1 to F i The nominal transformation matrix is

[0072] i-1 T i =R x (α i )D x (a i )R z (θ i )D z (d i ) (2)

[0073] R x (*) and R z (*) are the transformation matrices for translation around the X-axis and Z-axis of the joint coordinate system, respectively. x (*) and D z (*) are the transformation matrices for translation along the X-axis and Z-axis of the joint coordinate system, α i 、a i ,θi and d i is the nominal MDH parameter of joint i, where α i 、a i , and d i is a fixed value related to the structure, θ i is the i-th joint rotation command corresponding to the j-th measurement configuration. The MDH parameter error of the i-th joint can be expressed as Δu i =[δα i ,δa i ,δθ i ,δd i ] T Based on the differential transformation theory (not described here), from Δu i to F i The mapping matrix C of the pose error i for:

[0074]

[0075] The symbols S and C in the matrix elements of formula (3) are simplified expressions of the trigonometric functions sin(*) and cos(*), respectively.

[0076] In the above step 2), consider the arm weight force on the joint angle θ i First, we need to calculate the gravity moment on joint i. Figure 3 As shown, calculate the gravity moment M on joint i Gi The total gravity G of all rear joints (ik joints) needs to be known i and to the axis Z i The force arm. Figure 4 As shown, let the direction vector of the i-th joint axis be Z i =[Z ix ,Z iy ,Z iz ] T (From formula (1) 0 T i The first three elements of the third column), its center (i.e., coordinate system F i The origin is obtained from formula (1) 0 T i The first three elements of the fourth column are P i =[P ix ,P iy ,P iz ] T , the common center of gravity of all its rear joints is P g =[P gx ,P gy ,P gz ] T. Calculate the common center of gravity of all subsequent joints of joint i as P g .

[0077] Specifically, considering the influence of joint flexibility error on the posture error of redundant manipulator, the gravity moment M of the i-th joint is calculated: Gi , including the following steps:

[0078] 2.1) Install at least three non-collinear target balls on a regular-shaped bracket (the bracket is custom-made and has a mechanical interface, such as a threaded hole, for fixing with the 12th joint of the robot arm) and measure the total weight m of the bracket and all the target balls. s , combine the vertical suspension method and the geometric center method to determine the common center of gravity position P of all target balls and brackets gs ;

[0079] 2.2) According to the measured mass m of each joint i , combine the vertical suspension method and the geometric center method to determine the center of gravity position P of the first k-1 joints gi In this embodiment, before the robot arm is assembled, the mass m of each joint is measured i ;

[0080] Since the joints and the target ball mounting device at the end are usually axisymmetric structures, the common center of gravity position is represented by the distance d gs (i.e. O 12 Along X 12 The distance from the center of gravity to the joint center of gravity can be represented by d gi (i.e. the origin of each joint coordinate system O i Along X i distance from the center of gravity).

[0081] Then the center of gravity P gs In F 0 The following calculation is:

[0082] P gs = 0 T 12 D x (d gs ) (4)

[0083] Center of gravity P gi In F 0 The following calculation is:

[0084] P gi = 0 T i D x (d gi ) (5)

[0085] 2.3) According to the common center of gravity position P gsand the center of gravity position P of each joint gi , get the common center of gravity P of all the subsequent joints of joint i g The x, y, and z coordinate values ​​of the rear joint include ik joints, sensors, and brackets;

[0086] Specifically: the common center of gravity P of all the rear joints of joint i (including sensors and brackets) g The three coordinate values ​​of can be calculated as:

[0087]

[0088] The symbols “(1)”, “(2)”, and “(3)” represent the first, second, and third elements of the vector, respectively, and avg(*) means finding the average.

[0089] 2.4) Determine the common center of gravity P g To the i-th joint axis direction vector Z i The vertical point V g , and based on the measured total weight of the bracket and all target balls m s and the mass m of each joint i , get the total gravity G of all the subsequent joints of joint i i , and then get the total gravity of the rear joint G i In the base coordinate system F 0 The following is expressed as the total gravity vector G of the rear joint g , by the total gravity vector G of the rear joint g and the common center of gravity P g Get vector G g The end point coordinates P G ;

[0090] Specifically, P g to Z i The vertical point V g Can be characterized as

[0091] V g =P i +t·Z i (7)

[0092] Where t is a scalar. i Defined as:

[0093] L i =P g -V g (8)

[0094] Because L i Should be with Z i vertical, so we can find t as:

[0095]

[0096] Substituting the above formula into formula (7), we can get V g =[V gx ,V gy ,V gz ] T , then the force arm vector L can be calculated by formula (8): i .

[0097] The total weight of the bracket and three target balls is m s and the mass m of each joint i , then the total gravity G of all the joints after joint i i The specific calculation is:

[0098]

[0099] In formula (10), g is the acceleration due to gravity. i In the base coordinate system F 0 The following is represented as a vector G g =[0,0,-G i ] T , we can get the coordinates of the end point of the vector:

[0100] P G =P g +G g (11)

[0101] 2.5) From the end point coordinates P G and vertical point V g Get G i At the same time, it is perpendicular to the force arm vector L i and the joint axis direction vector Z i The force vector F Gi , and then get the gravity moment M on joint i Gi = ±||F Gi ||·||L i ||. L i is the total gravity G of all the subsequent joints (ik joints) of joint i i and to the axis Z i The lever arm.

[0102] Specifically, define T d =[T dx ,T dy ,T dz ] T For L i and Z i The normal vector of the plane, and let P G The projection point V to the plane G =[VGx ,V Gy ,V Gz ] T Since the vector P i V G With T d perpendicular, and vector V G P G Respectively with Z i and L i Vertical, then the equations can be listed as:

[0103]

[0104] Solving equation (12) yields the vertical point V G , then G i At the same time, it is perpendicular to the force arm vector L i and joint axis Z i The component force vector is:

[0105] F Gi =P G -V G (13)

[0106] If T d With G g If the angle is less than 90°, the gravitational moment on joint i is

[0107] M Gi =||F Gi ||·||L i || (14)

[0108] If T d With G g The angle is not less than 90°, then the gravitational moment on joint i is

[0109] M Gi =-||F Gi ||·||L i || (15)

[0110] In the above step 3), when measuring the measurement configuration {θ 1 ,…,θ k} j Under this condition, the position sensor, the known nominal MDH parameters of the manipulator, and the nominal forward kinematics model of the redundant manipulator are used to obtain the measured configuration {θ 1 ,…,θ k} j The pose error vector E at j , including the following steps:

[0111] 3.1) In the measurement configuration {θ 1 ,…,θk} j The actual posture P of joint k is measured by the posture sensor ka(j) ;

[0112] 3.2) Based on the known nominal MDH parameters of the manipulator and the nominal forward kinematics model of the redundant manipulator, in {θ 1 ,…,θ k} j Calculate the nominal pose vector p of joint k k(j) ;

[0113] 3.3) The actual pose P ka(j) and the nominal pose vector p of joint k k(j) Subtract, and get the joint k in the measurement configuration {θ 1 ,…,θ k} j The pose error vector E at j .

[0114] Specifically, in this embodiment, under the selected measurement configuration, a laser tracker is used to collect {θ 1 ,…,θ 12} j The three target sphere coordinates on the joint 12 at (j = 1, 2, ..., 60) are used to establish the actual (F sa ) j , and then get the actual ( 0 T sa ) j ; Combined with the actual sa T 12a , we can get ( 0 T 12a ) j =[( 0 T sa ) j ] -1sa T 12a ,assumed( 0 T 12a ) j Each element is characterized by:

[0115]

[0116] According to formula (16) 0 T 12a ) j Each element can be calculated according to the following formula to get the corresponding actual posture vector p 12a(j) :

[0117]

[0118] Where atan2(y,x) is the inverse tangent function of two variables.

[0119] Let i = 12, then we can get {θ 1 ,…,θ 12} j The nominal transformation matrix of joint 12 at ( 0 T 12 ) j .assumed( 0 T 12 ) j Each element is characterized by:

[0120]

[0121] Then by ( 0 T 12 ) j The corresponding nominal pose vector p can be obtained 12(j) :

[0122]

[0123] It can be obtained that the joint 12 is in the measurement configuration {θ 1 ,…,θ 12} j The pose error vector E at j

[0124] E j =p 12a(j) -p 12(j) (20)

[0125] In the above step 4), J j The position error vector E is Δu at the jth measurement configuration. j The mapping Jacobian matrix of J k , and M G The constructed mapping Jacobian matrix includes:

[0126]

[0127] in:

[0128]

[0129] In the formula, C i is the MDH parameter error vector Δu of the i-th joint i To the joint coordinate system F i The mapping matrix of the pose error; is the mapping Jacobian matrix of the DH parameter error of the i-th joint to the pose error of the k-th joint at the end, is the Jacobian matrix of the mapping from the gravity moment of the i-th joint to the pose error of the k-th joint at the end. The two are constructed based on the positive kinematics of the manipulator, the nominal values ​​of the MDH parameters of the k joints, {θ 1 ,…,θ k} j and the differential transformation principle; M G is the gravitational moment M acting on all joints Gi The diagonal matrix formed.

[0130] In this embodiment, when k=12, we have:

[0131]

[0132] In formula (21), we have:

[0133]

[0134] In formula (22), we have

[0135]

[0136] In formula (23), we have

[0137]

[0138] The matrix elements in (25) and (26) are derived from the forward kinematics equation:

[0139]

[0140] In the above step 5), E=JΔu is transformed to obtain Δu, which is: Δu=J + E, J + is the generalized inverse matrix of J.

[0141] In the above step 5), the Δu obtained by solving E=JΔu is defined as the first identification result, and iterative asymptotic identification is performed to obtain the final identification results of the MDH parameters and the joint elastic coefficients, including the following steps:

[0142] 5.1) Define Δu as the first identification result Δu (0) , multiply it by the weight w and then add it to u (0) Add to get u (1) =u (0) +wΔu (0) ; Among them, u (0) is a vector consisting of the nominal values ​​of the MDH parameters and the joint elastic coefficients;

[0143] 5.2) will u (1) As Δu (i.e. the first identification result Δu (0) ) into E = JΔu, and re-establish the formula Δu = J+ E is used to identify when u (1) The first iteration identification result Δu is the nominal value (1) ;

[0144] 5.3) Repeat the above step 5.2) and if the ||Δu|| obtained in each iteration shows an upward trend, the iteration diverges. At this time, reduce the weight w and recalculate u (1) , and jump back to step 5.1); if ||Δu|| shows a downward trend, the iteration converges until ||Δu||<ε is satisfied, where ε is the threshold set according to the calibration accuracy requirement. At this time, if the number of iterations is q-1, the obtained u (q) =u (q-1) +wΔu (q-1) This is the final identification result of MDH parameters and joint elastic coefficients.

[0145] Specifically, let u (0) =[α 1 ,a 1 ,θ 1 ,d 1 ,…,α i ,a i ,θ i ,d i ,…,α 12 ,a 12 ,θ 12 ,d 12 ,0 (1×12) ] T is the nominal value vector of the manipulator MDH parameters and joint elastic coefficients at the jth measurement configuration, where {θ 1 ,θ 2 ,…,θ 12} is the joint rotation command at the measurement configuration, and the MDH parameter used for the first time is u (0) The first obtained Δu is defined as the first identification result Δu (0) =[δα 1(0) ,δa 1(0) ,δθ 1(0) ,δd 1(0) ,…,δα i(0) ,δa i(0) ,δθ i(0) ,δd i(0) ,…,δα 12(0) ,δa 12(0) ,δθ 12(0) ,δd 120) ,λ 1(0) ,…,λ 12(0) ] T , where the subscript “(0)” stands for “first identification”. 0Multiply by weight w and u (0) Add to get u (1) :

[0146] u (1) =u (0) +wΔu (0) (28)

[0147] Among them, the weight w needs to be set manually, usually w≤1.

[0148] Using formula (28) to obtain u (1) =[α 1(1) ,a 1(1) ,θ 1(1) ,d 1(1) ,…,α i(1) ,a i(1) ,θ i(1) ,d i(1) ,…,α 12(1) ,a 12(1) ,θ 12(1) ,d 12(1) ,λ 1(1) ,…,λ 12(1) ] T Replace the u used in the previous step (0) , re-establish the formula Δu=J + E is used to identify when u (1) The first iteration identification result Δu is the nominal value (1) , where the subscript “(1)” stands for “first iteration identification”. When replacing, Δu=J + E used {α i ,a i ,d i} is replaced by u (1) {α i(1) ,a i(1) ,d i(1)}, and θ i Replace with θ i(1) +λ i(1) M Gi , M Gi For joint i in the measured configuration {θ 1 ,θ 2 ,…,θ 12} j The location is subject to gravitational moment.

[0149] Repeat the above steps, then the formula Δu=J + E. Formula (28) can be generalized as:

[0150]

[0151] The subscripts “(q-1)” and “(q)” represent “q-1th iterative identification” and “qth iterative identification” respectively. If the Δu obtained by iterating equation (29) is (q-1) The modulus of ||Δu (q-1) || is on an upward trend, indicating that the iteration is divergent. In this case, the weight w in equation (28) needs to be reduced to reduce the linearization error in each iteration step, and the iteration should be restarted from q = 1. (q-1) || is a downward trend, indicating that the iteration converges until ||Δu is satisfied (q-1) The iteration stops when ||<ε. ε is the threshold set according to the calibration accuracy requirement. (q) =[α 1(q) ,a 1(q) ,θ 1(q) ,d 1(q) ,…,α i(q) ,a i(q) ,θ i(q) ,d i(q) ,…,α 12(q) ,a 12(q) ,θ 12(q) ,d 12(q) ,λ 1(q) ,…,λ 12q) ] T That is the final MDH parameter and joint elastic coefficient identification result.

[0152] In the above step 5), the MDH parameter errors and joint elastic coefficients are compensated step by step based on the final identification results of the MDH parameters and joint elastic coefficients to obtain the final compensated rotation angle instructions of all joints, including the following steps:

[0153] 5.4) For i = 1 to 12, take u at any measurement configuration (q) -u (0) The 4i-1th parameter δθ in i As the zero position error of the i-th joint, all δθ are compensated synchronously in the control system i ;

[0154] 5.5) Take u (q) Use the nominal MDH parameters of the robot arm to solve the inverse kinematics;

[0155] 5.6) For i=1-12, subtract λ from the joint i rotation command obtained by inverse solution i(q) M Gi , get the final compensation angle command of all joints; where M Gi is the gravitational moment on joint i at the above inverse solution, λ i(q) is the identification result of the joint elastic coefficient of the qth identification.

[0156] In one embodiment of the present invention, a flexible hyper-redundant robotic arm calibration system is provided, comprising:

[0157] The first processing module, based on the MDH criterion, establishes the nominal forward kinematics model of the redundant manipulator and obtains the Jacobian matrix J of k joints based on differential transformation. k , and the jth measurement configuration {θ 1 ,…,θ k} j The Jacobian matrix Wherein, k is the total number of joints of the serial k-DOF super-redundant manipulator;

[0158] The second processing module considers the influence of joint flexibility error on the posture error of the redundant manipulator and calculates the gravity moment M of the i-th joint. Gi , to obtain the gravity matrix M of all joints G , and based on the gravity moment, the additional joint rotation angle δθ generated by the i-th joint is obtained iG =M Gi λ i , where λ i is the elastic coefficient of the i-th joint, i = 1, 2, …, k;

[0159] The pose error vector module, in the measurement configuration {θ 1 ,…,θ k} j Under this condition, the position sensor, the known nominal MDH parameters of the manipulator, and the nominal forward kinematics model of the redundant manipulator are used to obtain the measured configuration {θ 1 ,…,θ k} j The pose error vector E at j ;

[0160] The mapping module transforms the elastic coefficients λ of all joints i The MDH parameter error Δu of all joints i Merge into a vector Δu=[Δu 1 T ,Δu 2 T ,…,Δu k T ,λ 1 ,λ 2 ,…,λ k ] T ; Under the jth measurement configuration, establish Δu to E j The mapping relationship E j =J j Δu, and expand to E = JΔu;

[0161] Where E=[E 1 T ,E 2 T ,…,E n T ] T , J=[J 1 T ,J 2 T ,…,J n T ] T , n is the total number of selected measurement configurations; Δu is the error vector composed of the unknown MDH parameter errors of all joints and the elastic coefficients of all joints; J j The position error vector E is Δu at the jth measurement configuration. j The mapping Jacobian matrix of J k , and M G Constructed mapping Jacobian matrix;

[0162] The identification and compensation module defines Δu obtained by solving E=JΔu as the first identification result, performs iterative asymptotic identification, obtains the final identification results of the MDH parameters and joint elastic coefficients, and uses the final identification results of the MDH parameters and joint elastic coefficients to perform step-by-step classification compensation on the MDH parameter errors and joint elastic coefficients to obtain the final compensated rotation angle instructions for all joints.

[0163] In the above embodiment, considering the influence of joint flexibility error on the posture error of redundant manipulator, the gravity moment M of the i-th joint is calculated. Gi ,include:

[0164] Install at least three non-collinear target balls on a regular-shaped bracket and measure the total weight m of the bracket and all the target balls. s , combine the vertical suspension method and the geometric center method to determine the common center of gravity position P of all target balls and brackets gs ;

[0165] According to the measured mass m of each joint i , combine the vertical suspension method and the geometric center method to determine the center of gravity position P of the first k-1 joints gi ;

[0166] According to the common center of gravity position P gs and the center of gravity position P of each joint gi , get the common center of gravity P of all the subsequent joints of joint i g The x, y, and z coordinate values ​​of the rear joint include a sensor and a bracket;

[0167] Determine the common center of gravity Pg To the i-th joint axis direction vector Z i The vertical point V g , and based on the measured total weight of the bracket and all target balls m s and the mass m of each joint i , get the total gravity G of all the subsequent joints of joint i i , and then get the total gravity of the rear joint G i In the base coordinate system F 0 The following is expressed as the total gravity vector G of the rear joint g , by the total gravity vector G of the rear joint g and the common center of gravity P g Get vector G g The end point coordinates P G ;

[0168] From the end point coordinates P G and vertical point V g Get G i At the same time, it is perpendicular to the force arm vector L i and the joint axis direction vector Z i The force vector F Gi , and then get the gravity moment M on joint i Gi = ±||F Gi ||·||L i ||.

[0169] In the above embodiment, when measuring the measurement configuration {θ 1 ,…,θ k} j Under this condition, the position sensor, the known nominal MDH parameters of the manipulator, and the nominal forward kinematics model of the redundant manipulator are used to obtain the measured configuration {θ 1 ,…,θ k} j The pose error vector E at j ,include:

[0170] In the measurement configuration {θ 1 ,…,θ k} j The actual posture P of joint k is measured by the posture sensor ka(j) ;

[0171] Based on the known nominal MDH parameters of the manipulator and the nominal forward kinematics model of the redundant manipulator, in {θ 1 ,…,θ k} j Calculate the nominal pose vector p of joint k k(j) ;

[0172] The actual pose P ka(j)and the nominal pose vector p of joint k k(j) Subtract, and get the joint k in the measurement configuration {θ 1 ,…,θ k} j The pose error vector E at j .

[0173] In the above embodiment, J j The position error vector E is Δu at the jth measurement configuration. j The mapping Jacobian matrix of J k , and M G The constructed mapping Jacobian matrix includes:

[0174]

[0175] in:

[0176]

[0177] In the formula, C i is the MDH parameter error vector Δu of the i-th joint i To the joint coordinate system F i The mapping matrix of the pose error; is the mapping Jacobian matrix of the DH parameter error of the i-th joint to the pose error of the k-th joint at the end, M is the mapping Jacobian matrix of the i-th joint gravity torque to the end k joint posture error; G is the gravitational moment M acting on all joints Gi The diagonal matrix formed.

[0178] In the above embodiment, E=JΔu is transformed to obtain Δu, which is: Δu=J + E, J + is the generalized inverse matrix of J.

[0179] In the above embodiment, Δu obtained by solving E=JΔu is defined as the first identification result, and iterative asymptotic identification is performed to obtain the final identification results of the MDH parameters and the joint elastic coefficients, including:

[0180] Define Δu as the first identification result Δu (0) , multiply it by the weight w and then add it to u (0) Add to get u (1) =u (0) +wΔu (0) ; Among them, u (0) is a vector consisting of the nominal values ​​of the MDH parameters and the joint elastic coefficients;

[0181] will u (1)Substitute Δu into E=JΔu and re-establish the formula Δu=J + E is used to identify when u (1) The first iteration identification result Δu is the nominal value (1) ;

[0182] Repeat the above steps. If the ||Δu|| obtained in each iteration shows an upward trend, the iteration diverges. At this time, reduce the weight w and recalculate u (1) ; If ||Δu|| shows a downward trend, the iteration converges until ||Δu||<ε is satisfied, where ε is the threshold set according to the calibration accuracy requirement. At this time, if the number of iterations is q-1, the obtained u (q) =u (q-1) +wΔu (q-1) This is the final identification result of MDH parameters and joint elastic coefficients.

[0183] In the above embodiment, the MDH parameter errors and joint elastic coefficients are compensated step by step based on the final identification results of the MDH parameters and joint elastic coefficients to obtain the final compensated rotation angle instructions of all joints, including:

[0184] Take u at any measurement configuration (q) -u (0) The 4i-1th parameter δθ in i As the zero position error of the i-th joint, all δθ are compensated synchronously in the control system i ;

[0185] Take u (q) Use the nominal MDH parameters of the robot arm to solve the inverse kinematics;

[0186] Subtract λ from the joint i rotation command obtained by inverse solution i(q) M Gi , get the final compensation angle command of all joints; where M Gi is the gravitational moment on joint i at the above inverse solution, λ i(q) is the identification result of the joint elastic coefficient of the qth identification.

[0187] The system provided in this embodiment is used to execute the above-mentioned method embodiments. Please refer to the above-mentioned embodiments for specific processes and detailed contents, which will not be repeated here.

[0188] The following simulation is used to compare the performance of the calibration method based on the rigid-flexible coupling model and iterative identification proposed in the present invention with the typical MDH calibration method.

[0189] (1) Assume that the nominal values ​​of the MDH parameters of the hyper-redundant manipulator are as shown in Table 1, the MDH parameter error values ​​and the joint elastic coefficient values ​​are as shown in Table 2, the initial value of the iteration weight is w = 1, the threshold ε = 0.02, and w is multiplied by a coefficient of 0.1 for reduction each time the iteration diverges.

[0190] Table 2 MDH parameter errors and joint elastic coefficients of the hyper-redundant manipulator

[0191]

[0192] (2) Select the measurement configuration {θ 1 ,…,θ 12} j (j=1,2,…,60).

[0193] (3) Simulate and generate E used in the MDH calibration method. Required pose error E j =[Δx j ,Δy j ,Δz j ,Δα j ,Δβ j ,Δγ j ] T The elements of are obtained by the following formula:

[0194]

[0195] In the formula, 0 T 12a By measuring the configuration {θ 1 ,…,θ 12} j The following formula is obtained:

[0196] 0 T 12a = 0 T 1a 1a T 2a ... (i-1)a T ia ... 12a T 12a (31)

[0197] In the formula, (i-1)a T ia Indicates that Δu i The actual impact (i-1) T i . Replace {α i ,a i ,θ i ,d i} is replaced by {α i +δα i ,ai +δa i ,θ i +δθ i ,d i +δd i} to get (i-1)a T ia In formula (31), 0 T 12 From equation (1) when i = 12 and the measurement configuration {θ 1 ,…,θ 12} j The E at the 60 measurement configurations generated in the specific implementation manner is obtained. j The complete posture error vector E can be established by combining the above. To distinguish it from the E used in the present invention, E is replaced by E MDH Representation.

[0198] (4) Simulate and generate E used in the new calibration method (i.e., the present invention). Similar to the above step (3), 0 T 12a Still by the measurement configuration {θ 1 ,…,θ 12} j The difference is that in the formula (i-1)a T ia Indicates that Δu i With λ i The reality of common impact (i-1) T i Specifically, replace {α i ,a i ,θ i ,d i} is replaced by {α i +δα i ,a i +δa i ,θ i +δθ i ,d i +δd i}, where δθ i The actual value is the assumed δθ i With the calculated λ i M Gi The sum of Gi is the measured configuration {θ 1 ,…,θ 12} j The gravity moment at the location is obtained by step 11 of the specific implementation method. 0 T 12 The above step (3) 0 T 12The E at the 60 measurement configurations generated by the specific implementation method j By combining them, the complete pose error vector E can be established.

[0199] (5) Establish the calibration models used by the MDH calibration method and the new method respectively. Take the first 48 columns of J to form the identification matrix J for the MDH calibration method MDH , take the first 48 parameters of Δu to form the parameter vector Δu to be calibrated by the MDH calibration method MDH , and then combined with the E obtained in step (3) above MDH The model used in the MDH calibration method can be established:

[0200] E MDH =J MDH Δu MDH (32)

[0201] For the new method, the E obtained in the above step (4) is substituted into the calibration model E=JΔu of the specific implementation method.

[0202] (6) According to the formula Δu=J + E and iterative identification Δu of specific implementations MDH When the iterative identification algorithm is used here, Δu is replaced by Δu MDH Then, according to the steps in the specific implementation method, Δu is obtained in sequence. (0) and Δu (q) .

[0203] (7) for Δu MDH , Δu (0) and Δu (q) The oth element in (o represents the sequence number of the error parameter in the Δu vector, Δu MDH δα of each element 1 , δa 1 ,…,δd 12 The serial numbers o are 1, 2, ..., 48, Δu (0) and Δu (q) δα of each element 1 , δa 1 , …, λ 12 The serial numbers o are 1, 2, ..., 60) and the identification accuracy is δu (o) It is expressed and calculated by the following formula:

[0204]

[0205] Among them, Δu ca (o) is the identification result corresponding to the assumed value Δu(o), Δu MDH , Δu (0) and Δu (q)The identification accuracy δu(o) is as follows Figure 7 shown.

[0206] (8) Randomly generate 1000 measurement points in the robot arm motion space, distributed as follows Figure 8 Then, compensate Δu MDH , Δu (0) and Δu (q) The identification results are obtained, and at the test-th measurement point (test=1,2,…,1000), the absolute positioning residual E of the 12th joint of the manipulator after MDH calibration, the first step of the new method iteration calibration, and the complete iteration calibration of the new method are calculated according to the following formula: re :

[0207]

[0208] The method for calculating the residual after MDH calibration is similar to step (3) above. The method for calculating the residual after the first iterative calibration of the new method and the complete iterative calibration of the new method is similar to step (4) above. The difference is that the measurement configuration j used in step (3) and step (4) is replaced by the measurement point test, and the Δu substituted i With λ i are replaced by Δu MDH , Δu (0) and Δu (q) The corresponding identification value in the E of all measurement points re The statistical results are as follows Fig. 9 shown.

[0209] (9) The positioning error of the uncalibrated manipulator at the measurement point test is obtained through step (4) and equation (34), which serves as the control group for the above three groups of residuals. test , Δy test and Δz test are the corresponding components of E obtained in step (4). The statistical results of the control group are as follows Fig. 9 shown.

[0210] (10) For the new method proposed in this invention, the identification accuracy δu(o) of each parameter obtained by each iterative identification is calculated using formula (34). The results are as follows: Fig.10 shown.

[0211] (11) After compensating the identification results of each iteration in the new method proposed by the present invention, the positioning residual of the kth joint of the robot arm is calculated at the above 1000 measurement points using formula (34), and the result is as follows: Fig.11 shown.

[0212] Result analysis: Through Figure 7 It shows that the parameter identification accuracy of the present invention is significantly better than that of the MDH method. Fig. 9 It shows that the MDH method, the single calibration of the present invention and the iterative calibration of the present invention can effectively reduce the residual. Among them, the single calibration of the present invention obtains residuals with smaller variance and smaller median than the MDH method, which shows that considering the joint elastic coefficient during modeling can effectively improve the calibration accuracy. In addition, the iterative calibration of the present invention obtains the smallest residual, which significantly improves the calibration accuracy compared with the other two. Fig.10 It shows that with the increase of iteration times, the identification accuracy of each parameter increases as a whole and eventually tends to be stable. Fig.11 It shows that the absolute positioning residual of the manipulator gradually decreases with the increase of the number of iterations and eventually tends to be stable. The overall results show that the present invention improves the model integrity and more realistically characterizes the rigid and flexible coupling characteristics of the manipulator. In addition, the present invention overcomes the problem of increased linearization error caused by improving the model integrity through an iterative identification algorithm, ensures the accuracy of parameter identification, and achieves the unity of calibration integrity and accuracy.

[0213] In one embodiment of the present invention, a computing device is provided, which may be a terminal, and may include: a processor, a communication interface, a memory, a display screen, and an input device. Among them, the processor, the communication interface, and the memory communicate with each other through a communication bus. The processor is used to provide computing and control capabilities. The memory includes a non-volatile storage medium and an internal memory, and the non-volatile storage medium stores an operating system and a computer program. When the computer program is executed by the processor, the method in each of the above embodiments is implemented; the internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The communication interface is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be implemented through WIFI, a management network, NFC (near field communication) or other technologies. The display screen may be a liquid crystal display screen or an electronic ink display screen, and the input device may be a touch layer covered on the display screen, or a key, trackball or touchpad provided on the housing of the computing device, or an external keyboard, touchpad or mouse, etc. The processor may call the logic instructions in the memory.

[0214] In addition, the logic instructions in the above-mentioned memory can be implemented in the form of software functional units and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0215] In one embodiment of the present invention, a computer program product is provided, wherein the computer program product includes a computer program stored on a non-transitory computer-readable storage medium, wherein the computer program includes program instructions. When the program instructions are executed by a computer, the computer can execute the methods provided by the above-mentioned method embodiments.

[0216] In one embodiment of the present invention, a non-transitory computer-readable storage medium is provided, wherein the non-transitory computer-readable storage medium stores server instructions, and the computer instructions enable a computer to execute the methods provided in the above embodiments.

[0217] The above embodiment provides a computer-readable storage medium, whose implementation principle and technical effect are similar to those of the above method embodiment, and will not be repeated here.

[0218] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0219] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0220] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0221] 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 make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A flexible hyper-redundant robotic arm calibration method, characterized in that: include: Based on the MDH criterion, the nominal forward kinematics model of the redundant manipulator is established, and the Jacobian matrix J of k joints is obtained based on differential transformation. k , and the jth measurement configuration {θ1,…,θ k } j The Jacobian matrix Wherein, k is the total number of joints of the serial k-DOF super-redundant manipulator; Considering the influence of joint flexibility error on the posture error of redundant manipulator, calculate the gravity moment M of the i-th joint Gi , to obtain the gravity matrix M of all joints G , and based on the gravity moment, the additional joint rotation angle δθ generated by the i-th joint is obtained iG =M Gi λ i , where λ i is the elastic coefficient of the i-th joint, i = 1, 2, …, k; In the measurement configuration {θ1,…,θ k } j Under this condition, the position sensor, the known nominal MDH parameters of the manipulator, and the nominal forward kinematics model of the redundant manipulator are used to obtain the joint k in the measurement configuration {θ1,…,θ k } j The pose error vector E at j ; The elastic coefficients λ of all joints i The MDH parameter error Δu of all joints i Merge into a vector Δu=[Δu1 T ,Δu2 T ,…,Δu k T ,λ1,λ2,…,λ k ] T ; Under the jth measurement configuration, establish Δu to E j The mapping relationship E j =J j Δu, and expanded to E = JΔu; Where E=[E1 T ,E2 T ,…,E n T ] T , J=[J1 T ,J2 T ,…,J n T ] T , n is the total number of selected measurement configurations; Δu is the error vector composed of the unknown MDH parameter errors of all joints and the elastic coefficients of all joints; J j The position error vector E is Δu at the jth measurement configuration. j The mapping Jacobian matrix of J k , and M G Constructed mapping Jacobian matrix; The Δu obtained by solving E=JΔu is defined as the first identification result, and iterative asymptotic identification is performed to obtain the final identification results of the MDH parameters and joint elastic coefficients. The MDH parameter errors and joint elastic coefficients are compensated step by step based on the final identification results to obtain the final compensated rotation angle instructions for all joints.

2. The flexible hyper-redundant robotic arm calibration method according to claim 1, characterized in that: Considering the influence of joint flexibility error on the posture error of redundant manipulator, calculate the gravity moment M of the i-th joint Gi ,include: Install at least three non-collinear target balls on a regular-shaped bracket and measure the total weight m of the bracket and all the target balls. s , combine the vertical suspension method and the geometric center method to determine the common center of gravity position P of all target balls and brackets gs ; According to the measured mass m of each joint i , combine the vertical suspension method and the geometric center method to determine the center of gravity position P of the first k-1 joints gi ; According to the common center of gravity position P gs and the center of gravity position P of each joint gi , get the common center of gravity P of all the subsequent joints of joint i g The x, y, and z coordinate values ​​of the rear joint include a sensor and a bracket; Determine the common center of gravity P g To the i-th joint axis direction vector Z i The vertical point V g , and based on the measured total weight of the bracket and all target balls m s and the mass m of each joint i , get the total gravity G of all the subsequent joints of joint i i , and then get the total gravity of the rear joint G i In the base coordinate system F0, it is expressed as the total gravity vector G of the rear joint g , by the total gravity vector G of the rear joint g and the common center of gravity P g Get vector G g The end point coordinates P G ; From the end point coordinates P G and vertical point V g Get G i At the same time, it is perpendicular to the force arm vector L i and the joint axis direction vector Z i The force vector F Gi , and then get the gravity moment M on joint i Gi = ±||F Gi ||·||L i ||.

3. The flexible super-redundant manipulator calibration method according to claim 1, characterized in that: In the measurement configuration {θ1,…,θ k } j Under this condition, the position sensor, the known nominal MDH parameters of the manipulator, and the nominal forward kinematics model of the redundant manipulator are used to obtain the joint k in the measurement configuration {θ1,…,θ k } j The pose error vector E at j , include: In the measurement configuration {θ1,…,θ k } j The actual posture P of joint k is measured by the posture sensor ka(j) ; Based on the known nominal MDH parameters of the manipulator and the nominal forward kinematics model of the redundant manipulator, in {θ1,…,θ k } j Calculate the nominal pose vector p of joint k k(j) ; The actual pose P ka(j) and the nominal pose vector p of joint k k(j) Subtract them and get the joint k in the measurement configuration {θ1,…,θ k } j The pose error vector E at j .

4. The flexible super-redundant manipulator calibration method according to claim 1, characterized in that: J j The position error vector E is Δu at the jth measurement configuration. j The mapping Jacobian matrix of J k , and M G The constructed mapping Jacobian matrix includes: in: In the formula, C i is the MDH parameter error vector Δu of the i-th joint i To the joint coordinate system F i The mapping matrix of the pose error; is the mapping Jacobian matrix of the DH parameter error of the i-th joint to the pose error of the k-th joint at the end, M is the mapping Jacobian matrix of the i-th joint gravity torque to the end k joint posture error; G is the gravitational moment M acting on all joints Gi The diagonal matrix formed.

5. The flexible super-redundant manipulator calibration method according to claim 1, characterized in that: Transforming E=JΔu, the obtained Δu is: Δu=J + E, J + is the generalized inverse matrix of J.

6. The flexible hyper-redundant manipulator calibration method according to claim 1, characterized in that: The Δu obtained by solving E=JΔu is defined as the first identification result, and iterative asymptotic identification is performed to obtain the final identification results of the MDH parameters and joint elastic coefficients, including: Define Δu as the first identification result Δu (0) , multiply it by the weight w and then add it to u (0) Add to get u (1) =u (0) +wΔu (0) ; Among them, u (0) is a vector consisting of the nominal values ​​of the MDH parameters and the joint elastic coefficients; will u (1) Substitute Δu into E=JΔu and re-establish the formula Δu=J + E is used to identify when u (1) The first iteration identification result Δu is the nominal value (1) ; Repeat the above steps. If the ||Δu|| obtained in each iteration shows an upward trend, the iteration diverges. At this time, reduce the weight w and recalculate u (1) ; If ||Δu|| shows a downward trend, the iteration converges until ||Δu||<ε is satisfied, where ε is the threshold set according to the calibration accuracy requirement. At this time, if the number of iterations is q-1, the obtained u (q) =u (q-1) +wΔu (q-1) This is the final identification result of MDH parameters and joint elastic coefficients.

7. The flexible hyper-redundant robotic arm calibration method according to claim 1, characterized in that: The final identification results of the MDH parameters and joint elastic coefficients are used to classify and compensate the MDH parameter errors and joint elastic coefficients in steps to obtain the final compensated rotation angle instructions of all joints, including: Take u at any measurement configuration (q) -u (0) The 4i-1th parameter δθ in i As the zero position error of the i-th joint, all δθ are compensated synchronously in the control system i ; Take u (q) Use the nominal MDH parameters of the robot arm to solve the inverse kinematics; Subtract λ from the joint i rotation command obtained by inverse solution i(q) M Gi , get the final compensation angle command of all joints; where M Gi is the gravitational moment on joint i at the above inverse solution, λ i(q) is the identification result of the joint elastic coefficient of the qth identification.

8. A flexible super-redundant robotic arm calibration system, characterized in that: include: The first processing module, based on the MDH criterion, establishes the nominal forward kinematics model of the redundant manipulator and obtains the Jacobian matrix J of k joints based on differential transformation. k , and the jth measurement configuration {θ1,…,θ k } j The Jacobian matrix Wherein, k is the total number of joints of the serial k-DOF super-redundant manipulator; The second processing module considers the influence of joint flexibility error on the posture error of the redundant manipulator and calculates the gravity moment M of the i-th joint. Gi , to obtain the gravity matrix M of all joints G , and based on the gravity moment, the additional joint rotation angle δθ generated by the i-th joint is obtained iG =M Gi λ i , where λ i is the elastic coefficient of the i-th joint, i = 1, 2, …, k; The pose error vector module measures the measurement configuration {θ1,…,θ k } j Under this condition, the position sensor, the known nominal MDH parameters of the manipulator, and the nominal forward kinematics model of the redundant manipulator are used to obtain the joint k in the measurement configuration {θ1,…,θ k } j The pose error vector E at j ; The mapping module transforms the elastic coefficients λ of all joints i The MDH parameter error Δu of all joints i Merge into a vector Δu=[Δu1 T ,Δu2 T ,…,Δu k T ,λ1,λ2,…,λ k ] T ; Under the jth measurement configuration, establish Δu to E j The mapping relationship E j =J j Δu, and expanded to E = JΔu; Where E=[E1 T ,E2 T ,…,E n T ] T , J=[J1 T ,J2 T ,…,J n T ] T , n is the total number of selected measurement configurations; Δu is the error vector composed of the unknown MDH parameter errors of all joints and the elastic coefficients of all joints; J j The position error vector E is Δu at the jth measurement configuration. j The mapping Jacobian matrix of J k , and M G Constructed mapping Jacobian matrix; The identification and compensation module defines Δu obtained by solving E=JΔu as the first identification result, performs iterative asymptotic identification, obtains the final identification results of the MDH parameters and joint elastic coefficients, and uses the final identification results of the MDH parameters and joint elastic coefficients to perform step-by-step classification compensation on the MDH parameter errors and joint elastic coefficients to obtain the final compensated rotation angle instructions for all joints.

9. A computer-readable storage medium storing one or more programs, characterized in that: The one or more programs include instructions, which, when executed by a computing device, cause the computing device to perform any one of the methods of claims 1 to 7.

10. A computing device, characterized in that: include: One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include instructions for executing any one of the methods described in claims 1 to 7.

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