Series robot calibration algorithm based on exponential product

Abstract

The invention discloses a series robot calibration algorithm based on an index product, and the algorithm comprises the following steps: A1, building an index product motion model according to a robot joint axis and coordinate points on the axis through an index product modeling method, a2, differentiating the positions of the robot hand-eye, the kinematics and the calibration object relative to the robot base coordinate system to obtain a hand-eye, kinematics and calibration object position error model based on an exponential product; b1, obtaining an initial value of a robot system hand-eye matrix # imgabs0 # and an initial value of a calibration object relative to the position Bp of a robot base through a closed solution method based on a Kronecker product; b2, taking the difference between the predicted value and the measured value of the base position of the calibration object under the robot base as a target function; and B3, establishing an optimization algorithm by taking the hand-eye, kinematics and calibration object position parameters of the robot as to-be-optimized parameters, and carrying out iterative optimization calculation on the hand-eye, kinematics and calibration object position parameters of the robot by using a Newton iteration method.

Description

Technical Field

[0001] The present invention relates to geometric parameter calibration of a serial robot, and more specifically, to a calibration algorithm for geometric parameters of a serial robot. Background Art

[0002] Robot geometry calibration is an effective method to improve robot positioning accuracy and is widely used in various robot applications, such as mechanical manufacturing, parts assembly, construction, and medical surgery. The robot's geometry parameters include the robot's joint kinematic parameters, the position of the robot from the measuring sensor, and the position of the tool relative to the robot. Robot geometry calibration is the process of identifying accurate geometry parameters by measuring robot joint angles, sensor measurements, and other data.

[0003] Robot geometric parameter calibration includes several processes: measurement, modeling, identification, and compensation. Measurement refers to the process of controlling the robot to move within the measurement range of the measurement sensor to obtain the robot joint angle and sensor measurement data; modeling refers to the establishment of a mapping relationship between the measurement value and the geometric parameters to be identified for the robot system; identification is the process of calculating the geometric parameters using the values ​​obtained in the measurement process; compensation is the process of compensating the geometric parameters obtained by identification with the nominal geometric parameters.

[0004] At present, for the calibration of geometric parameters of serial robots, there is an algorithm based on the improved DH model, Euler angle and translation vector modeling. The scenario of this algorithm is to use a visual sensor installed at the end of the robot as a sensor and four standard balls installed on a fixed workbench as tools. This algorithm establishes the posture between the robot and the tool and the posture between the robot and the sensor through Euler angles and translation vectors. The established error identification model satisfies the minimum, continuity and completeness. The above algorithm can be found in the literature "C.Yu, and J.Xi, "Simultaneous and on-line calibration of a robot-based inspectioning system," Robotics and Computer-Integrated Manufacturing, vol. 49, pp. 349-360, 2018.".

[0005] The above-mentioned serial robot geometric parameter calibration algorithm satisfies the minimum, continuity and completeness. However, the algorithm has the following disadvantages:

[0006] 1. The positions between the four standard balls installed on the fixed workbench need to be calibrated in advance with a laser tracker; the laser tracker is a precision measuring device with high cost and time-consuming installation, which increases the cost and inconvenience of the calibration process;

[0007] 2. Use improved DH parameters and Euler angles for modeling; improved DH parameters can avoid the singularity problem of classic DH parameters when two adjacent joints are parallel, but it is necessary to introduce different parameters to replace the original parameters when two adjacent joints are parallel, and the DH model needs to establish a coordinate system at each joint, which is complicated; Euler angles are used to represent the posture between the robot and the sensor and between the robot and the tool. Euler angles have singular conditions. When the posture to be identified is near these singular conditions, it may cause the calibration algorithm identification matrix to be singular, resulting in the algorithm not converging. Summary of the invention

[0008] In order to solve the deficiencies in the prior art, the main purpose of the present invention is to provide a serial robot calibration algorithm based on exponential product, which can realize a more convenient and quick calibration process.

[0009] In order to achieve the above main purpose, the present invention discloses a serial robot calibration algorithm based on exponential product, which comprises the following steps:

[0010] A. Establish the robot hand-eye, kinematics and calibration object position error models based on exponential product. Compared with the DH model, the exponential product model does not need to establish a coordinate system at each joint, nor does it need to introduce different parameters when adjacent joints are parallel, and the steps are simple.

[0011] A1. According to the robot joint axis and the coordinate points on the axis, the robot exponential product motion model is established according to the exponential product modeling method, and the complete robot kinematic model is established by considering the robot hand-eye and the calibration object relative to the robot base coordinate system:

[0012]

[0013] In the formula B p is the position of the calibration object in the robot base coordinate system {B}, ξ i (i=1,…,m) is the joint rotation corresponding to the i-th joint of the robot, m is the number of joints of the robot, is the homogeneous transformation matrix of the sensor coordinate system {S} relative to the robot base coordinate system {B} when all joints of the robot are at zero position, S p is the position of the calibration object under {S}, θ i (i=1,…,m) represents the rotation angle of the robot’s i-th joint, and ^ represents the cross product operation;

[0014] A2. Differentiate the robot's hand-eye, kinematics, and calibration object positions relative to the robot's base coordinate system to obtain the robot's hand-eye, kinematics, and calibration object position error models based on exponential products;

[0015] Jx = b (2)

[0016]

[0017] Where b represents the residual, x represents the error of the hand-eye, kinematics, and calibration object relative to the robot base coordinate system, and J represents the Jacobian matrix mapping x to b; I 3×3 is a third-order unit matrix, F is a coefficient matrix containing the positive kinematics information of each level of the robot, which is used to identify the error of each joint rotation, G is a coefficient matrix for eliminating redundant parameters of rotation / translation joints, and H is a coefficient matrix for reasonably selecting error parameters;

[0018] B. Design calibration algorithm;

[0019] B1. Obtain the hand-eye matrix of the robot system through the closed solution method based on Kronecker product and the position of the calibration object relative to the robot base B The initial value of p;

[0020] B2, the difference between the predicted value and the measured value of the base position of the calibration object under the robot base is used as the objective function, that is, the residual b in formula (2);

[0021] B3. Establish an optimization algorithm using the robot's hand-eye, kinematics and calibration object position parameters as the parameters to be optimized, and use the Newton iteration method to iteratively optimize and calculate the robot's hand-eye, kinematics and calibration object position parameters.

[0022] In step B3, the algorithm flow is as follows:

[0023]

[0024]

[0025] In the algorithm is the nominal homogeneous transformation matrix of {S} relative to {B} when all joints of the robot are at zero position, is the nominal rotation of each joint of the robot, is the nominal hand-eye matrix, B p n is the nominal position of the calibration object under {B}, is the rotation matrix from {B} to {S} after the robot's forward kinematics calculation, The translation vector from {B} to {S} after the forward kinematics calculation of the robot.

[0026] According to a specific embodiment of the present invention, it further includes step C: selecting error parameters, arbitrarily selecting 6 parameters in two mutually perpendicular joints to determine the base coordinate system. The error model established in step A has redundant parameters. Taking advantage of the fact that the robot base coordinate system can be arbitrarily set, 6 parameters in two mutually perpendicular joints can be arbitrarily selected to determine the base coordinate system, thereby removing 6 redundant parameters and meeting the requirements of the minimal calibration model. Adjusting the matrix H in the calibration model can achieve the elimination of redundant parameters. After eliminating the 6 redundant parameters, only one calibration object is needed to provide position information to calibrate the hand-eye, kinematics and calibration object position parameters in the model, avoiding the use of multiple calibration objects to provide posture information, so that there is no need to use a laser tracker to determine the position between the calibration objects, which greatly simplifies the calibration process.

[0027] According to a specific embodiment of the present invention, in step C, if the first two joints of the robot are perpendicular to each other, the base coordinate system is determined by using the first two joints of the robot. If the first two joints of the robot are perpendicular to each other, the base coordinate system can be determined by using the first two joints of the robot, so that the robot base coordinate system can be determined by using the first and second joint structural parameters of the robot, which is convenient for solving the inverse kinematics after the robot is calibrated, and can avoid large changes in the robot urdf model, thereby ensuring the accuracy of the robot model in the simulation environment, and at the same time, the structural parameters can be used to determine the posture relationship between the robot base coordinate systems in the multi-robot task scenario.

[0028] The present invention has the following beneficial effects:

[0029] 1. Compared with the prior art, the geometric parameter calibration algorithm of the serial robot proposed in the present invention only requires one calibration object, does not need to use multiple standard balls, and does not need to use a laser tracker to measure the relative positions between the calibration balls in advance, which can greatly simplify the calibration process and reduce the calibration cost;

[0030] 2. Using exponential product for kinematic modeling can avoid using DH kinematic modeling. It is not necessary to establish a coordinate system at each joint, which can simplify the modeling process of the calibration algorithm.

[0031] 3. Using the first two joints of the robot to determine the base coordinate system of the robot can ensure that the robot's kinematic model will not change significantly compared with the original kinematic model, which is convenient for solving inverse kinematics and can ensure the accuracy of the robot model in the simulation environment;

[0032] 4. Use the first two joints of the robot to determine the base coordinate system of the robot. In the robot task scenario, the structural parameters can be used to determine the posture relationship between the robot base coordinate system.

[0033] In order to more clearly illustrate the purpose, technical solutions and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is a schematic diagram of the equipment used in Example 1 and the corresponding functions;

[0035] Figure 2 This is a schematic diagram of the calibration process of the serial robot in Example 1. DETAILED DESCRIPTION

[0036] In the following description, many specific details are explained in conjunction with the embodiments to facilitate a full understanding of the present invention. However, it should be understood that the following embodiments and detailed descriptions are only for illustrative purposes and do not limit the scope of protection of the present invention.

[0037] Example 1

[0038] This embodiment provides a serial robot calibration algorithm based on exponential product, which includes the following steps:

[0039] A. Establish robot hand-eye, kinematics and calibration object position error models based on exponential product;

[0040] A1. According to the robot joint axis and the coordinate points on the axis, the robot exponential product motion model is established according to the exponential product modeling method, and the complete robot kinematic model is established by considering the robot hand-eye and the calibration object relative to the robot base coordinate system:

[0041]

[0042] In the formula B p is the position of the calibration object in the robot base coordinate system {B}, ξ i (i=1,…,m) is the joint rotation corresponding to the i-th joint of the robot, m is the number of joints of the robot, is the homogeneous transformation matrix of the sensor coordinate system {S} relative to the robot base coordinate system {B} when all joints of the robot are at zero position, S p is the position of the calibration object under {S}, θ i (i=1,…,m) represents the rotation angle of the robot’s i-th joint, and ^ represents the cross product operation;

[0043] A2. Differentiate the robot's hand-eye, kinematics, and calibration object positions relative to the robot's base coordinate system to obtain the robot's hand-eye, kinematics, and calibration object position error models based on exponential products;

[0044] Jx = b (2)

[0045]

[0046] Where b represents the residual, x represents the error of the hand-eye, kinematics, and calibration object relative to the robot base coordinate system, and J represents the Jacobian matrix mapping x to b; I 3×3 is a third-order unit matrix, F is a coefficient matrix containing the positive kinematics information of each level of the robot, which is used to identify the error of each joint rotation, G is a coefficient matrix for eliminating redundant parameters of rotation / translation joints, and H is a coefficient matrix for reasonably selecting error parameters;

[0047] B. Design calibration algorithm;

[0048] B1. Obtain the hand-eye matrix of the robot system through the closed solution method based on Kronecker product and the position of the calibration object relative to the robot base B The initial value of p;

[0049] B2, the difference between the predicted value and the measured value of the base position of the calibration object under the robot base is used as the objective function, that is, the residual b in formula (2);

[0050] B3. Establish an optimization algorithm using the robot's hand-eye, kinematics and calibration object position parameters as the parameters to be optimized, and use the Newton iteration method to iteratively optimize and calculate the robot's hand-eye, kinematics and calibration object position parameters;

[0051] C. Select error parameters and arbitrarily select 6 parameters from two mutually perpendicular joints to determine the base coordinate system. If the first two joints of the robot are mutually perpendicular, the first two joints of the robot are used to determine the base coordinate system.

[0052] This embodiment provides an experimental process and results of geometric parameters of a serial robot system.

[0053] The equipment used in this embodiment includes: a UniversalRobot UR5 serial robot 1, a line laser sensor 2 installed at the end of the UniversalRobot UR5 serial robot 1 as a sensor, a standard ball 3 fixedly installed as a calibration object, and a host computer 4, such as Figure 1 The host computer 4 sends a trajectory command to the Universal Robot UR5 serial robot 1, and the Universal Robot UR5 serial robot 1 feeds back a joint angle signal to the host computer; the host computer 4 sends a map acquisition command to the line laser sensor 2, and the line laser sensor 2 feeds back point cloud data to the host computer 4.

[0054] First, confirm the nominal kinematic parameters of the robot. The robot used in this embodiment is UR5, and its nominal kinematic parameters are shown in Table 1:

[0055] Table 1 Nominal kinematic parameters of UR5 robot

[0056]

[0057] Next, start calibration. The calibration process is as follows Figure 2 shown.

[0058] First, the robot is controlled to drive the sensor to measure the position of the calibration object in different postures, and the robot's posture and the measured position of the calibration object are recorded. The information obtained is used to calculate the initial value of the hand-eye using a closed solution based on the Kronecker product. and the initial position of the calibration object relative to {B} B p n .

[0059] Then, the robot's joints are controlled to measure the position of the calibration object at different angles, and the robot's joint angles and the measured position of the calibration object are recorded.

[0060] Finally, using the recorded information, and B p n The robot's hand-eye, kinematic and calibration object position parameters are iteratively calculated using a robot geometric error model based on exponential product.

[0061] Although the present invention has been described above through embodiments, the above embodiments are only used to exemplarily describe the feasible implementation schemes of the present invention, and are not used to limit the protection scope of the present invention. Any equivalent substitutions or changes made by those skilled in the art in accordance with the present invention should also be covered by the protection scope defined by the claims of the present invention.

Claims

1. A serial robot calibration algorithm based on exponential product, characterized in that: The steps include: A. Establish robot hand-eye, kinematics and calibration object position error models based on exponential product; A1. According to the robot joint axis and the coordinate points on the axis, the robot exponential product motion model is established according to the exponential product modeling method, and the complete robot kinematic model is established by considering the robot hand-eye and the calibration object relative to the robot base coordinate system: In the formula B p is the position of the calibration object in the robot base coordinate system {B}, ξ i (i=1,…,m) is the joint rotation corresponding to the i-th joint of the robot, m is the number of joints of the robot, is the homogeneous transformation matrix of the sensor coordinate system {S} relative to the robot base coordinate system {B} when all joints of the robot are at zero position, S p is the position of the calibration object under {S}, θ i (i=1,…,m) represents the rotation angle of the robot’s i-th joint, and ^ represents the cross product operation; A2. Differentiate the robot's hand-eye, kinematics, and calibration object positions relative to the robot's base coordinate system to obtain the robot's hand-eye, kinematics, and calibration object position error models based on exponential products; Jx = b (2) Where b represents the residual, x represents the error of the hand-eye, kinematics, and calibration object relative to the robot base coordinate system, and J represents the Jacobian matrix mapping x to b; I 3×3 is a third-order unit matrix, F is a coefficient matrix containing the positive kinematics information of each level of the robot, which is used to identify the error of each joint rotation, G is a coefficient matrix for eliminating redundant parameters of rotation / translation joints, and H is a coefficient matrix for reasonably selecting error parameters; B. Design calibration algorithm; B1. Obtain the hand-eye matrix of the robot system through the closed solution method based on Kronecker product and the position of the calibration object relative to the robot base B The initial value of p; B2, the difference between the predicted value and the measured value of the base position of the calibration object under the robot base is used as the objective function, that is, the residual b in formula (2); B3. Establish an optimization algorithm using the robot's hand-eye, kinematics and calibration object position parameters as the parameters to be optimized, and use the Newton iteration method to iteratively optimize and calculate the robot's hand-eye, kinematics and calibration object position parameters.

2. The serial robot calibration algorithm based on exponential product according to claim 1, characterized in that: The method further comprises step C: selecting error parameters, and arbitrarily selecting 6 parameters of two mutually perpendicular joints to determine the base coordinate system.

3. The serial robot calibration algorithm based on exponential product according to claim 2 is characterized in that: In step C, if the first two joints of the robot are perpendicular to each other, the base coordinate system is determined using the first two joints of the robot.

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