Flexible hyper-redundant robot arm calibration method, system, storage medium and computing device

Abstract

The present application relates to the field of mechanical arm calibration, and discloses a flexible super-redundant mechanical arm calibration method, system, storage medium and computing device, which comprises: establishing a nominal forward kinematics model of a redundant mechanical arm, and determining a Jacobian matrix; obtaining a gravity matrix suffered by all joints, and obtaining additional joint rotation angles and elastic coefficients generated by the joints on the basis of the gravity torque; obtaining a pose error vector of the joints at a measurement configuration through a pose sensor and known nominal MDH parameters of the mechanical arm and the nominal forward kinematics model of the redundant mechanical arm; merging the elastic coefficients of all joints and the MDH parameter errors of all joints into a vector Delta u, establishing a mapping relationship of Delta u to E j , and defining the obtained Delta u as a first identification result; performing iterative asymptotic identification to obtain final identification results of the MDH parameters and the joint elastic coefficients, so as to perform step-by-step classified compensation on the MDH parameter errors and the joint elastic coefficients, and obtain final compensated rotation angle instructions of all joints.

Description

Technical Field

[0001] The present invention relates to the technical field of robotic arm calibration, and in particular to a highly flexible and ultra-redundant robotic 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 operational performance of robotic arms. For industrial robotic arms, kinematic parameter errors are the primary cause of absolute positioning error, primarily due to errors introduced by the various links and joints during manufacturing, assembly, and transmission. Traditional calibration methods can effectively compensate for kinematic parameter errors, improving the absolute positioning accuracy of industrial robotic arms and enabling them to meet most operational requirements. However, due to their high rigidity, long links, and limited degrees of freedom, industrial robotic arms struggle to perform tasks in unstructured spaces. Consequently, hyper-redundant robotic arms with highly flexible joints, short links, and a large number of joints have emerged. Most traditional calibration methods only consider kinematic parameter errors during modeling, omitting parameters related to joint flexibility. Some studies have focused on joint flexibility, but these models target six-degree-of-freedom industrial robotic arms. Consequently, the corresponding parameter error identification algorithms are only suitable for low-dimensional models and small angular errors, and their performance is insufficient to match the dramatically increased model dimensionality and linearization errors of hyper-redundant robotic 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 includes: establishing a nominal forward kinematic model of the redundant manipulator based on the MDH criterion, obtaining the Jacobian matrix J of k joints based on differential transformation k , and the jth measurement configuration {θ1,…,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 on 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 λ i , where λi 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 joint k in the measurement configuration {θ1,…,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=[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 pose error vector E is Δu at the jth measurement configuration. j The mapping Jacobian matrix, based on 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 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.

[0005] Furthermore, 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:

[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 the sensor and the bracket;

[0009] Determine the common center of gravity P g To the direction vector Z of the i-th joint axis 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 ;

[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 component force vector F Gi , and then we can get the gravitational moment M on joint i Gi =±||F Gi ||·||L i ||.

[0011] Furthermore, in the measurement configuration {θ1,…,θ k} j Under this condition, the joint k in the measurement configuration {θ1,…,θ k} ja pose error vector E j , comprising:

[0012] an actual pose P k of joint k at the measurement configuration {θ1,…,θ j} ka(j) ;

[0013] based on the known nominal MDH parameters of the robot arm and the nominal forward kinematics model of the redundant robot arm, a nominal pose vector p k of joint k at the measurement configuration {θ1,…,θ j} k(j) is calculated;

[0014] subtracting the actual pose P ka(j) from the nominal pose vector p k(j) of joint k, a pose error vector E k of joint k at the measurement configuration {θ1,…,θ j} j is obtained.

[0015] Further, J j is the mapping Jacobian matrix of Δu to the pose error vector E j at the jth measurement configuration, based on the mapping Jacobian matrix J k , and M G , comprising:

[0016]

[0017] wherein:

[0018]

[0019] wherein, C i is the mapping matrix of the MDH parameter error vector Δu i of the ith joint to the pose error of the joint coordinate system F i ; is the mapping Jacobian matrix of the DH parameter error of the ith joint to the pose error of the end joint k, is the mapping Jacobian matrix of the gravity moment of the ith joint to the pose error of the end joint k; M G is a diagonal matrix composed of the gravity moments M Gi suffered by all joints.

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

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

[0022] Define Δu as the first identification result Δu (0) , multiply it by weight w, and add it to u (0) to obtain u (1) = u (0) +wΔu (0) ; wherein u (0) is a vector composed of nominal values of MDH parameters and joint elastic coefficients;

[0023] Bring u (1) into E=JΔu as Δu, and re-establish the formula Δu=J + E for the first iterative identification result Δu (1) when u (1) is the nominal value;

[0024] Repeat the above steps, if ||Δu|| shows an upward trend in each iteration, the iteration diverges, at this time, reduce the weight w to recalculate u (1) ; if ||Δu|| shows a downward trend, the iteration converges, until ||Δu||<ε, ε is a threshold value 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) is the final identification result of MDH parameters and joint elastic coefficients.

[0025] Further, the MDH parameter error and the joint elastic coefficient are classified and compensated step by step with the final identification result of the MDH parameter and the joint elastic coefficient to obtain the final compensated angle command of all joints, including:

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

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

[0028] Subtract λ i(q) M Gi from the joint i angle command obtained by the inverse solution to obtain the final compensated angle command of all joints; wherein M Gi is the gravity moment of joint i at the above inverse solution, and 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 kinematic 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 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 pose error vector module, in the measurement configuration {θ1, ..., θ k} j Under this condition, the joint k in the measurement configuration {θ1,…,θ k} j The pose error vector E at j ; Mapping module, the elastic coefficient 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; Au is an error vector composed of MDH parameter errors of all joints and elastic coefficients of all joints; J j is a mapping Jacobian matrix of Au to the pose error vector E j at the jth measurement configuration, which is constructed based on J k , and M G ; the identification compensation module defines Au solved by E=JAu as a first identification result, performs iterative asymptotic identification to obtain a final identification result of the MDH parameters and the joint elastic coefficients, and performs step-by-step compensation on the MDH parameter errors and the joint elastic coefficients with the final identification result of the MDH parameters and the joint elastic coefficients to obtain final compensated rotation angle instructions of all joints.

[0030] In a third aspect, a computer-readable storage medium storing one or more programs includes instructions that, when executed by a computing device, cause the computing device to perform any of the above methods.

[0031] In a fourth aspect, a computing device includes one or more processors, memory, and one or more programs stored in the memory and configured to be executed by the one or more processors, the one or more programs including instructions for performing any of the above methods.

[0032] The present application has the following advantages due to the above technical solutions:

[0033] 1. The present application simultaneously includes two types of error parameters representing rigid and flexible characteristics of a hyper-redundant robot arm in the calibration model, and gradually reduces the influence of linearization error caused by rigid-flexible coupling modeling on identification accuracy through iterative identification, so that the identification result finally converges to high precision.

[0034] 2. The present application establishes a rigid-flexible coupling error model and iteratively suppresses the linearization error of the model without making obvious changes to the typical industrial robot arm calibration process, and therefore has good realizability. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 is a whole flow block diagram of the flexible hyper-redundant robot arm calibration method in the embodiment of the present application;

[0036] Figure 2 is each coordinate system of the hyper-redundant robot arm with k joints in the embodiment of the present application;

[0037] Figure 3G is the total gravity of the post-joint of the i th joint in the embodiment of the present application i and the force arm to the axis Z i schematic diagram;

[0038] Figure 4 G is the total gravity of the post-joint of the i th joint in the embodiment of the present application i L is the force arm of the total gravity G i in the embodiment of the present application i F is the component force of L Gi schematic diagram;

[0039] Figure 5 is the method schematic diagram for determining the base coordinate system F0 and the nominal F1 in the laser tracker coordinate system in the embodiment of the present application;

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

[0041] Figure 7 is the precision comparison of MDH identification, new method single identification and new method iterative identification in the embodiment of the present application;

[0042] Figure 8 is the measurement point distribution diagram in the embodiment of the present application;

[0043] Figure 9 is the absolute positioning residual error comparison after using different calibration methods in the embodiment of the present application;

[0044] Figure 10 is the parameter error identification precision trend graph with the number of iterations in the embodiment of the present application;

[0045] Figure 11 is the absolute positioning residual error trend graph with the number of iterations in the embodiment of the present application. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme of the embodiments of the present application will be described clearly and completely below in combination with the drawings of the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all. Based on the described embodiments of the present application, all other embodiments obtained by those skilled in the art belong to the scope of protection of the present application.

[0047] It is to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, steps, operations, elements, components, and / or groups thereof, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof.

[0048] In one embodiment of the present application, as shown in Figure 1 A flexible super-redundant robot arm calibration method, system, storage medium and computing device are provided, the present application is to establish a rigid-flexible coupling calibration model for a series type super-redundant robot arm with flexible joints, and to propose a high-precision iterative identification algorithm for the error parameters of the model. In the present embodiment, the measuring instrument used is API Radian PLUS laser tracker, the sensor is laser target ball, and the calibration object is a 12-degree-of-freedom super-redundant robot arm with adjacent joint axes perpendicular to each other. The method comprises the following steps:

[0049] 1) Based on the MDH (Modified Denavit-Hartenberg) criterion, a nominal forward kinematics model of the redundant robot arm is established, and the Jacobian matrix J k of the k joints is obtained based on differential transformation, and the Jacobian matrix J k of the selected jth measurement configuration {θ1,…,θ j} is selected. Wherein, k is the total number of joints of the series type k-degree-of-freedom super-redundant robot arm, j = 1, 2, …, n, and n represents the number of measurement configurations.

[0050] 2) Considering the influence of joint flexibility error on the pose error of the redundant robot arm, the gravity moment M Gi of the ith joint is calculated to obtain the gravity matrix M G of all joints, and on the basis of the gravity moment, the additional joint rotation angle δθ iG of the ith joint is obtained as follows: δθ ig = M Gi λ i , wherein λ i is the elastic coefficient of the ith joint, i = 1, 2, …, k.

[0051] 3) In the measurement configuration {θ1,…,θ k}, the pose error vector E j of the joint k in the measurement configuration {θ1,…,θ k} is obtained through the pose sensor, and the known nominal MDH parameters of the robot arm and the nominal forward kinematics model of the redundant robot arm. j j ​= P ka(j)- P k(j) .

[0052] 4) the elastic coefficients λ of all joints i and the MDH parameter errors Δu of all joints i are merged into a vector Δu = [Δu1 T , Δu2 T , …, Δu k T , λ1, λ2, …, λ k ] T Under the jth measurement configuration used for calibration, a mapping relationship E j of Δu to E j is established, E j = J T Δu, and is extended to E = JΔu; E = JΔu is a rigid-flexible coupled calibration model;

[0053] wherein E = [E1 T , E2 n , …, E T T ] T , J = [J1 T , J2 n , …, J T T ; Δu is an error vector composed of unknown MDH parameter errors of all joints and elastic coefficients of all joints; J j is a mapping Jacobian matrix of Δu at the jth measurement configuration to the pose error vector E j , and is constructed based on J k , and M G .

[0054] 5) Δu obtained by solving E = JΔu is defined as a first identification result, iterative asymptotic identification is performed, final MDH parameter and joint elastic coefficient identification results are obtained, and the MDH parameter error and the joint elastic coefficient are step-by-step classified and compensated based on the final MDH parameter and joint elastic coefficient identification results, so that the final compensated rotation angle instructions of all joints are obtained.

[0055] When the present application is used, the influence of the MDH parameter error and the joint flexibility error on the pose error of the hyper-redundant robot arm is comprehensively considered, a rigid-flexible coupled calibration model is established, and the model integrity is improved. On this basis, the influence of the linearization error of the rigid-flexible coupled model on the identification accuracy is overcome through an iterative identification algorithm, and the accuracy of the calibration is ensured.

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

[0057] 1.1) A pose sensor is installed at the end joint k of a serial k-DOF hyper-redundant manipulator, which can output the pose of its own coordinate system in real time and indirectly obtain the actual pose of the end joint.

[0058] 1.2) Select the measurement configuration {θ1,…,θ k} j (j=1,2,…,n). 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 As shown in the figure, a base coordinate system F0 and joint coordinate system F of a serial super redundant manipulator with k degrees of freedom are established. i (i=1,2,…,k).

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

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

[0062] (1) Figure 5 As shown, the target ball is made to contact two different points on the upper surface of the robot arm base, and its coordinates A1 and A2 are collected by a laser tracker, and the vector v1=A1A2 is defined; the target ball is made to contact the two end points A3 and A4 of the axis of the first joint, and the vector Z1=A3A4 is obtained; the origin O0 of the base coordinate system is defined as A1, the X0 axis is defined as X0=v1×Z1, and the Y0 axis of the base coordinate system is defined as opposite to the Z1 axis, thereby establishing the base coordinate system F0; the target ball is made to contact 6 points evenly distributed along the arc on the outer contour of the cylindrical base of the first joint, and the target ball must contact the upper surface of the base at the same time to ensure that the 6 points are approximately in the same plane; the coordinates B1, B2, ..., B6 of these 6 points are collected by a laser tracker, and a circular arc is obtained by fitting, and the center O of the arc is calculated. B ; According to the size of the robot arm parts, get the rotation center of the first joint and O B Spacing, defined as a1; O B The point after translation a1 along the X0 direction is defined as the origin O1 of the first joint coordinate system, and the first joint coordinate axis X1 is defined as coinciding with X0; calculate O0 along Z1 in the reverse direction to O B The distance is negative and defined as d1, thus establishing the nominal coordinate system F1 of the first joint. Transformation from F0 to F1 0 T1 is regarded as the nominal transformation matrix of the first joint.

[0063] (2) Install the bracket with the target ball on the 12th joint of the robotic arm (ensure that 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. 11 ; The 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 coordinate system of the 12th joint 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 rotation angles remain unchanged, and the three target ball coordinates S1, S2 and S3 are collected by laser tracker respectively; the sensor coordinate system F is established s First, we get vectors v2, v3, and v4 = v2 × v3 from S1, S2, and S3; S1 is defined as the origin O s , v2 is defined as Z s Axis, v4 defined as X s axis. From this, we can get F 12 and F s The actual transformation matrix under F0 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 as 60, namely {θ1,…,θ 12} j (j=1,2,…,60), the method is random selection. 12Tj represents the joint angle command set of 12 joints corresponding to the measurement configuration, and j represents the serial number of the measurement configuration.

[0066] (4) This step starts to establish a kinematic error model for the kinematic parameters that generate errors. As shown in Figure 2 , based on the MDH rule, the coordinate system of each joint of a serial type hyper-redundant robot with 12 degrees of freedom is established, that is, the base coordinate system F0 and the joint coordinate system F i (i = 1, 2, …, 12) of the k = 12 hyper-redundant robot.

[0067] Table 1 MDH parameter nominal value of hyper-redundant robot

[0068]

[0069] Based on the MDH rule, the forward kinematic model of the i-th joint of the redundant robot is

[0070] 0 T i = 0 T1 1 T2... i-1 T i (1)

[0071] In the formula, i-1 T i is the nominal transformation matrix from F i-1 to F i , and 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 (*) in the above formula are translation matrices around the X axis and the Z axis of the joint coordinate system, respectively, D x (*) and D z (*) are translation matrices along the X axis and the Z axis of the joint coordinate system, respectively, and α i , a i , θ i , and d i are nominal MDH parameters of the joint i, where α i , a i , and d iis a fixed value related to the structure, θ i is the ith joint rotation command corresponding to the jth measurement configuration. The MDH parameter error of the ith joint can be represented as Δu i =[δα i ,δa i ,δθ i ,δd i ] T Based on the differential transformation theory (not detailed 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 effect of arm weight on joint angle θ i First, we need to calculate the gravitational 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 axis of the i-th joint 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. the 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, calculate the gravity moment M of the i-th jointGi , including the following steps:

[0078] 2.1) Mount at least three non-collinear target balls on a regularly shaped bracket (the bracket is custom-made and has a mechanical interface, such as a threaded hole, for connection to the 12th joint of the robotic arm). Measure the total weight m of the bracket and all 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 The calculation under F0 is:

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

[0083] Center of gravity P gi The calculation under F0 is:

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

[0085] 2.3) 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 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 averaging.

[0089] 2.4) Determine the common center of gravity P g To the direction vector Z of the i-th joint axis 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 ;

[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 t is:

[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 is i The specific calculation is:

[0098]

[0099] In formula (10), g is the acceleration due to gravity. i In the base coordinate system F0, it is represented as 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 component force vector F Gi , and then we can get the gravitational 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 Projection point V onto the plane G =[V Gx ,V Gy ,V Gz ] T Since the vector P i V G With T d perpendicular, and vector V G P GRespectively with Z i and L i Vertical, then the equations can be listed:

[0103]

[0104] Solving equations (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 {θ1,…,θ k} j Under this condition, the joint k in the measurement configuration {θ1,…,θ k} j The pose error vector E at j , including the following steps:

[0111] 3.1) In the measurement configuration {θ1,…,θ k} j The actual pose P of joint k is measured by the pose sensor ka(j) ;

[0112] 3.2) Based on the known nominal MDH parameters of the manipulator and the nominal forward kinematic model of the redundant manipulator, in {θ1,…,θ k} j Calculate the nominal pose vector p of joint k k(j) ;

[0113] 3.3) The actual pose P ka(j) and joint k nominal pose vector p k(j) Subtract and get the joint k in the measurement configuration {θ1,…,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 {θ1,…,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 obtain the corresponding actual posture vector p 12a(j) :

[0117]

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

[0119] Let i = 12, then we can get {θ1,…,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 the corresponding nominal pose vector p 0 T 12 ) j can be obtained 12(j) :

[0122]

[0123] From the above, the pose error vector E 12} j of joint 12 at the measurement configuration {θ1,…,θ j}

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

[0125] In the above step 4), J j is the mapping Jacobian matrix of Δu to the pose error vector E j at the jth measurement configuration, which is constructed based on J k , and M G , including:

[0126]

[0127] wherein:

[0128]

[0129] In the formula, C i is the mapping matrix of the MDH parameter error vector Δu i of the ith joint to the pose error of the joint coordinate system F i ; is the mapping Jacobian matrix of the DH parameter error of the ith joint to the pose error of the end k joint, is the mapping Jacobian matrix of the gravity moment of the ith joint to the pose error of the end k joint, both of which are constructed according to the forward kinematics of the robot arm, the nominal values of the MDH parameters of the k joints, {θ1,…,θ k} j and the differential transformation principle; M G is a diagonal matrix composed of the gravity moments M Gi experienced by all joints.

[0130] In this embodiment, when k = 12, there are:

[0131]

[0132] In formula (21), there are:

[0133]

[0134] In formula (22), there are

[0135]

[0136] In formula (23), there are

[0137]

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

[0139]

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

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

[0142] 5.1) Δu is defined as the first identification result Δu (0) , which is multiplied by the weight w and added to u (0) to obtain u (1) = u (0) + wΔu (0) ; wherein u (0) is a vector composed of the nominal values of the MDH parameters and the joint elastic coefficient.

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

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

[0145] Specifically, let u (0) =[α1,a1,θ1,d1,…,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 {θ1,θ2,…,θ 12} is the joint angle command at the measurement configuration, and the MDH parameter used for the first time is u (0) The parameters of sequence numbers 1 to 48 are 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)" represents "first identification". According to the following formula, Δu0 is multiplied by the weight w and then combined with u (0) Add up 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) ,a12(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 iterative 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 measurement configuration {θ1,θ2,…,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] Wherein, the subscripts “(q-1)” and “(q)” represent “q-1th iterative identification” and “qth iterative identification” respectively. If the Δu obtained by the iteration of formula (29) is (q-1) The modulus of ||Δu (q-1) If || is an upward trend, it indicates that the iteration is diverging. In this case, the weight w in formula (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, which means that the iteration converges until ||Δu is satisfied (q-1) The iteration stops when ||<ε. Among them, ε is the threshold set according to the calibration accuracy requirement. At this time, the obtained u (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 This is the final identification result of MDH parameters and joint elastic coefficients.

[0152] In step 5), the MDH parameter errors and joint elastic coefficients are compensated step by step using the final identification results of the MDH parameters and joint elastic coefficients to obtain the final compensated rotation angle instructions for 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) Used as 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 angle 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 establishes the nominal forward kinematics model of the redundant manipulator based on the MDH criterion 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 hyper-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 λi is the elastic coefficient of the i-th joint, i = 1, 2, ..., k;

[0159] The pose error vector module measures the measurement configuration {θ1,…,θ k} j Under this condition, the joint k in the measurement configuration {θ1,…,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=[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;

[0161] 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 pose error vector E is Δu at the jth measurement configuration. j The mapping Jacobian matrix, based on 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, and obtains the final identification results of the MDH parameters and joint elastic coefficients. The final identification results of the MDH parameters and joint elastic coefficients are used to perform step-by-step classification compensation on the MDH parameter errors and joint elastic coefficients to obtain the final compensated rotation angle instructions of all joints.

[0163] In the above embodiment, the influence of joint flexibility error on the posture error of the redundant manipulator is considered, and 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 the sensor and the bracket;

[0167] Determine the common center of gravity P g To the direction vector Z of the i-th joint axis 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 ;

[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 component force vector F Gi , and then we can get the gravitational moment M on joint i Gi =±||F Gi ||·||L i ||.

[0169] In the above embodiment, when measuring the measurement configuration {θ1,…,θ k} j Under this condition, the joint k in the measurement configuration {θ1,…,θ k} j The pose error vector E at j ,include:

[0170] In the measurement configuration {θ1,…,θ k} j The actual pose P of joint k is measured by the pose 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 {θ1,…,θ k} j Calculate the nominal pose vector p of joint k k(j) ;

[0172] The actual pose P ka(j) and joint k nominal pose vector p k(j) Subtract and get the joint k in the measurement configuration {θ1,…,θ k} j The pose error vector E at j .

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

[0174]

[0175] in:

[0176]

[0177] Where 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 mapping the gravity torque of the i-th joint to the pose error of the k-th joint at the end; M 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: 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 joint elastic coefficients, including:

[0180] Define Δu as the first identification result Δu (0) , multiply it by weight w and then add it to u (0) Add up 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 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 iterative 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) The final identification results 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 and classified 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, 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) Used as the nominal MDH parameters of the robot arm to solve the inverse kinematics;

[0186] Subtract λ from the joint i angle command obtained by inverse solution i(q) M Gi , to obtain the final angle command of all joints after compensation; wherein M Gi is the gravity torque of joint i at the inverse solution, and λ i(q) is the identification result of the joint elastic coefficient in the qth identification.

[0187] The system provided by the embodiment is used for executing the above-mentioned method embodiments, and the specific process and detailed content are referred to the above-mentioned embodiments, which will not be repeated here.

[0188] The performance of the calibration method based on the rigid-flexible coupling model and the iterative identification provided by the present application and the typical MDH calibration method is compared through simulation.

[0189] (1) The nominal values of the MDH parameters of the hyper-redundant robot arm are assumed to be shown in Table 1, the MDH parameter error values and the joint elastic coefficient values are shown in Table 2, the initial value of the iteration weight is w=1, the threshold value is ε=0.02, and the w is multiplied by a coefficient 0.1 for reduction when the iteration diverges each time.

[0190] Table 2 MDH parameter error and joint elastic coefficient of hyper-redundant robot arm

[0191]

[0192] (2) The measurement configuration {θ1,…,θ 12} j (j=1,2,…,60) is selected according to the specific embodiment.

[0193] (3) The E used by the MDH calibration method is simulated to generate. Each element of the required pose error E j =[Δx j ,Δy j ,Δz j ,Δα j ,Δβ j ,Δγ j ] T is obtained by the following formula:

[0194]

[0195] In the formula, 0 T 12a is obtained by the following formula at the measurement configuration {θ1,…,θ 12} j :

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

[0197] where, (i-1)a T ia denotes the actual i T (i-1) affected by Δu i . Replacing {α i ,a i ,θ i ,d i} in equation (2) with {α i +δα i ,a i +δa i ,θ i +δθ i ,d i +δd i} gives (i-1)a T ia . In equation (31) 0 T 12 is obtained from equation (1) at i = 12 and measurement configurations {θ1,…,θ 12} j generated in the detailed description at 60 measurement configurations, i.e., E j is established. To distinguish from E used in this invention, E is denoted as E MDH here.

[0198] (4) Simulate to generate E used in the new calibration method (i.e., this invention). Similar to step (3) above, 0 T 12a is still obtained from equation (31) at measurement configurations {θ1,…,θ 12} j . The difference is that in equation (31) (i-1)a T ia denotes the actual i T i affected by both Δu (i-1) and λ i . Specifically, replacing {α i ,a i ,θ i ,d i} in equation (2) with {α i +δα i ,a i +δa i ,θ i +δθ i ,d i +δdi} where δθ i is the assumed δθ i is the calculated λ i M Gi is the sum of the elements of the vector M Gi is the gravity torque experienced by joint i at the measured configuration {θ1,…,θ 12} j at step 11 of the detailed description. The E 0 T 12 is the same as the T 0 T 12 generated by the detailed description at the 60 measured configurations. Combining the E j vector E.

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

[0200] E MDH = J MDH Δu MDH (32)

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

[0202] (6) According to the formula Δu = J + E and the iterative identification Δu MDH of the detailed description, Δu MDH is replaced by Δu (0) , that is, Δu (q) .

[0203] (7) The oth element (o represents the serial number of the error parameter in the Δu vector, and the serial numbers o of the elements δa1, δa1, …, δd MDH of Δu (0) , Δu (q) and Δu MDH are 1, 2, …, 48 in turn, and the serial numbers o of the elements δa1, δa1, …, λ 12 of Δu (0) , Δu (q) and Δu 12The identification accuracy of u (o) is denoted by δu ca (o) and calculated by the following formula:

[0204]

[0205] where Δu MDH (o) is the identification result corresponding to the assumed value Δu (0) (o), Δu (q) (o), and Δu MDH (o), respectively. Figure 7

[0206] (8) 1000 measurement points are randomly generated in the robot motion space, and the distribution is shown in Figure 8 . Then, the identification results of Δu (0) , Δu (q) , and Δu re are compensated, respectively, and the absolute positioning residuals E of the 12th joint of the robot after MDH calibration, the first step of the new method iteration calibration, and the complete iteration of the new method calibration are calculated at the testth measurement point (test = 1, 2, …, 1000), respectively, according to the following formula:

[0207]

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

[0209] (9) The positioning error of the uncalibrated robot at the measurement point test is obtained by step (4) and formula (34) as a control group for the above three groups of residuals. Where Δx test , Δy test , and Δz test in formula (34) are the corresponding components of E obtained in step (4). The statistical results of the control group are shown in Figure 9 .

[0210] (10) The parameter identification accuracy δu(o) of each parameter identified by each iteration of the new method is calculated by formula (34) respectively, and the results are shown in Figure 10

[0211] (11) The positioning residual of the kth joint of the robot arm at the above 1000 measurement points is calculated by formula (34) after compensating the identification result of each iteration in the new method of the application respectively, and the results are shown in Figure 11

[0212] Result analysis: As shown in Figure 7 The parameter identification accuracy of the application is significantly better than that of the MDH method. Figure 9 It is shown that the MDH method, the single calibration of the application and the iterative calibration of the application can effectively reduce the residual error. Among them, the single calibration of the application obtains a smaller variance and a smaller median residual error 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 application obtains the smallest residual error, which significantly improves the calibration accuracy compared with the other two. Figure 10 It is shown that with the increase of the number of iterations, the identification accuracy of each parameter shows an overall improvement trend and finally tends to be stable. Figure 11 It is shown that the absolute positioning residual of the robot arm gradually decreases with the increase of the number of iterations and finally tends to be stable. The overall result shows that the application improves the model integrity and more truly represents the rigid and flexible coupling characteristics of the robot arm. Moreover, the application overcomes the problem of increased linearization error caused by improving the model integrity through the iterative identification algorithm, ensures the parameter identification accuracy, and realizes the unity of calibration integrity and accuracy.

[0213] ​​In an embodiment of the present application, a computing device, which can be a terminal, can include a processor, a communications interface, a memory, a display screen and an input device. The processor, the communications interface and the memory can communicate with each other through a communication bus. The processor is configured to provide computing and control capabilities. The memory includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The computer program is executed by the processor to implement the method of any of the above embodiments. The internal memory provides an environment for running the operating system and the computer program in the non-volatile storage medium. The communications interface is configured to communicate with external terminals in a wired or wireless manner. The wireless manner can be achieved through WIFI, a management network, NFC (Near Field Communication) or other technologies. The display screen can be a liquid crystal display screen or an electronic ink display screen. The input device can be a touch layer overlaid on the display screen, or a key, a trackball or a touchpad arranged on the housing of the computing device, or an external keyboard, a touchpad or a mouse, etc. The processor can invoke the logical instructions in the memory.

[0214] In addition, the logical instructions in the memory described above can be implemented in the form of a software functional unit and sold or used as a standalone product, which can be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the present application, in essence, or the parts that contribute to the prior art, or parts of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present application. The aforementioned storage medium includes a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and various media that can store program codes.

[0215] In an embodiment of the present application, a computer program product is provided, which includes a computer program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions that, when executed by a computer, enable the computer to perform the methods provided by the various embodiments described above.

[0216] In an embodiment of the present application, a non-transitory computer-readable storage medium is provided, which stores server instructions. The computer instructions enable a computer to perform the methods provided by the various embodiments described above.

[0217] The computer readable storage medium provided by the above embodiment has similar implementation principles and technical effects to the method embodiment, and thus will not be described here.

[0218] The present application is described with reference to flowcharts and / or block diagrams according to the methods, devices (systems), and computer program products of the embodiments. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to produce a machine, so that the instructions executed by the computer or other programmable data processing devices generate a device that implements the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 an apparatus that implements the functions specified in one or more flows or blocks.

[0219] These computer program instructions can also be stored in a computer readable memory that can direct the computer or other programmable data processing devices to work in a specific manner, so that the instructions stored in the computer readable memory produce a manufactured product that includes instruction devices, which implement the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 an apparatus that implements the functions specified in one or more flows or blocks.

[0220] These computer program instructions can also be loaded into a computer or other programmable data processing device, so that a series of operation steps are performed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide a process for implementing the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 an apparatus that implements the functions specified in one or more flows or blocks.

[0221] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

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 hyper-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 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 pose error vector E is Δu at the jth measurement configuration. j The mapping Jacobian matrix, based on 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 manipulator calibration method according to claim 1, wherein: 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 the sensor and the bracket; Determine the common center of gravity P g To the direction vector Z of the i-th joint axis 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 component force vector F Gi , and then we can get the gravitational moment M on joint i Gi =±||F Gi ||·||L i ||.

3. The flexible hyper-redundant manipulator calibration method according to claim 1, wherein: In the measurement configuration {θ1,…,θ k } j Under this condition, 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 pose P of joint k is measured by the pose 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 joint k nominal pose vector p k(j) Subtract and get the joint k in the measurement configuration {θ1,…,θ k } j The pose error vector E at j .

4. The flexible hyper-redundant manipulator calibration method according to claim 1, wherein: J j The pose error vector E is Δu at the jth measurement configuration. j The mapping Jacobian matrix, based on J k 、 and M G The constructed mapping Jacobian matrix includes: in: Where 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 mapping the gravity torque of the i-th joint to the pose error of the k-th joint at the end; M G is the gravitational moment M acting on all joints Gi The diagonal matrix formed.

5. The flexible hyper-redundant manipulator calibration method according to claim 1, wherein: Transform E=JΔu to obtain Δu, which is: Δu=J + E, J + is the generalized inverse matrix of J.

6. The flexible hyper-redundant manipulator calibration method according to claim 1, wherein: The Δu obtained by solving E = JΔu is defined as the first identification result. The 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 weight w and then add it to u (0) Add up 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 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 iterative 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) The final identification results of MDH parameters and joint elastic coefficients.

7. The flexible hyper-redundant manipulator calibration method according to claim 1, wherein: The final identification results of the MDH parameters and joint elastic coefficients are used 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, 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) Used as the nominal MDH parameters of the robot arm to solve the inverse kinematics; Subtract λ from the joint i angle 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 hyper-redundant robotic arm calibration system, characterized in that: include: The first processing module establishes the nominal forward kinematics model of the redundant manipulator based on the MDH criterion 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 hyper-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 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 pose error vector E is Δu at the jth measurement configuration. j The mapping Jacobian matrix, based on 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, and obtains the final identification results of the MDH parameters and joint elastic coefficients. The final identification results of the MDH parameters and joint elastic coefficients are used to perform step-by-step classification compensation on the MDH parameter errors and joint elastic coefficients to obtain the final compensated rotation angle instructions of all joints.

9. A computer-readable storage medium storing one or more programs, characterized in that: The one or more programs include instructions that, 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 according to claims 1 to 7.

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