A robot body parameter self-calibration method based on sphere center distance constraint

Abstract

The application relates to the technical field of robot calibration, in particular to a robot body parameter self-calibration method based on a ball center distance constraint, which comprises the following steps: a calibration error model based on a ball center distance constraint is established; a calibration equation of robot body parameter error and distance error is obtained; a constraint ball plate used for calibration is designed to obtain measurement data and establish a constraint equation; an LM algorithm is used for parameter identification of the constraint equation to obtain a robot body parameter compensation value; and the robot body parameter compensation value is compensated to a robot kinematics model for simulation verification. The method can realize simple and efficient calibration of the robot body parameter by means of a self-made calibration ball plate, does not need to rely on external high-price measuring equipment, and can achieve the purpose of improving the absolute positioning accuracy of the robot.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of robot calibration, and particularly relates to a robot body parameter self-calibration method based on a spherical center distance constraint. BACKGROUND

[0002] When a robot is programmed offline, a theoretical model is generally used for calculation and an actual model is used for action; deviations exist in the process of robot body manufacturing, installation and the like, so that the theoretical model and the actual model are mismatched, and then the absolute positioning accuracy of the robot is not high. Through calibration technology, the body parameter error of the actual model of the robot is obtained, and the theoretical model is compensated, so that the error caused by the model inconsistency can be eliminated.

[0003] The existing calibration with the aid of external equipment (such as a laser tracker) has good calibration accuracy, but there are problems such as high equipment purchase and maintenance cost, and strict equipment transportation conditions.

[0004] Therefore, it is very necessary to develop a self-calibration scheme without the aid of external measuring equipment and with certain guaranteed calibration accuracy. SUMMARY

[0005] The present application aims to overcome the problems of the prior art, and provides a robot body parameter self-calibration method based on a spherical center distance constraint, so as to solve the problem that the robot body parameter calibration needs the aid of external measuring equipment and then brings a high calibration threshold.

[0006] The above object is achieved by the following technical scheme:

[0007] A robot body parameter self-calibration method based on a spherical center distance constraint comprises the following steps:

[0008] Step (1) establishing a calibration error model based on a spherical center distance constraint, obtaining a calibration equation of the robot body parameter error and the distance error;

[0009] Step (2) designing a constraint ball plate for calibration to obtain measurement data, and establishing a constraint equation;

[0010] Step (3) using an LM algorithm to perform parameter identification on the constraint equation in step (2), and obtaining a robot body parameter compensation value;

[0011] Step (4) compensating the robot body parameter compensation value in step (3) to a robot kinematics model, and performing simulation verification.

[0012] Further, the step (1) is specifically:

[0013] The robot end position quantity obtained from the robot forward kinematics model is set as x, x is a function of robot body parameters, and the total differential expression of the end position error is obtained by taking partial derivatives of x with respect to each parameter:

[0014]

[0015] In the formula, Δx represents the difference between the theoretical position and the actual position of the robot; Δθ i represents the robot zero position error; Δα i represents the robot twist angle error; Δa i represents the robot rod length error; Δd i represents the robot offset error; and Δβ2 represents the deviation of the 2nd and 3rd axes of the robot.

[0016] A calibration ball plate with a known ball center distance is used as a measuring tool, and the ball center distance is set as Dr; a robot with a dial gauge at the end contacts the spherical surface to obtain fitting points, and the ball center calculated by the theoretical model of the robot is fitted, and then the theoretical ball center distance is calculated, which is set as Dc, so that:

[0017] Dr-Dc=|ΔS1-ΔS2| (2)

[0018] In the formula, ΔS1 is the position error vector of the robot at the ball center 1; and ΔS2 is the position error vector of the robot at the ball center 2.

[0019] ΔS1=J1(Δθ i , Δα i , Δa i , Δd i , Δβ2) (3)

[0020] ΔS2=J2(Δθ i , Δα i , Δa i , Δd i , Δβ2) (4)

[0021] Both can be established by formula (1) formula with each body parameter of the robot, formula (3), formula (4) is substituted into formula (2) to obtain the calibration equation of the robot body parameter error and the distance error:

[0022] Dr-Dc=J(Δθ i , Δα i , Δa i , Δd i , Δβ2) (5).

[0023] Further, the robot body parameters include rod length, offset, zero position, and twist angle.

[0024] Further, the design for the constraint ball plate in step (2) comprises an equilateral triangle-shaped carrier plate, three corners of the carrier plate are respectively provided with ball bodies of the same specification, each ball body is connected with the carrier plate perpendicularly through a stand column; a universal angle support is arranged at the bottom of the carrier plate, and the top of the universal angle support is connected with the center point of the carrier plate.

[0025] Further, the constraint equation in step (2) is in the form of Ax=b.

[0026] Further, the step (3) specifically comprises:

[0027] Step (3.1) gives an algorithm iteration initial value x0, a step size lower limit S, an iteration number upper limit k, an error lower limit err and a step size validity judgment rou;

[0028] Step (3.2) calculates an iteration step size s and judges whether the step size s is less than S, if yes, the iteration is ended, otherwise, the next step is entered;

[0029] Step (3.3) updates x using the calculated step size, wherein x=x+s;

[0030] Step (3.4) substitutes the updated x into the objective function to observe whether the calculation error is less than the last calculation error, if yes, the updated x is used to enter the next iteration; otherwise, the current iteration is invalid, and the damping term needs to be updated to recalculate the step size s;

[0031] Step (3.5) stops the iteration when the calculation error is less than the given error lower limit err or the step size s is less than S, and the algorithm is ended.

[0032] Further, the step (4) is specifically: a new end point position is obtained by recalculating the robot forward kinematics with a compensation parameter, a new ball center is obtained by fitting the new point position, and then a ball center distance after parameter compensation is obtained; whether the ball center distance after compensation converges to the real value of the ball center distance is compared to realize the accuracy of the identification result.

[0033] Beneficial effects

[0034] The robot body parameter self-calibration method based on ball center distance constraint provided by the application can realize simple and efficient calibration of the robot body parameter by means of the self-made calibration ball plate, without the help of external high-price measuring equipment, and the purpose of improving the absolute positioning accuracy of the robot can be achieved. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 The flow chart of the robot body parameter self-calibration method based on ball center distance constraint is provided in the application.

[0036] Figure 2Distance error and position error relationship diagram in a robot body parameter self-calibration method based on sphere center distance constraint according to the application;

[0037] Figure 3 Calibration sphere plate structure schematic diagram in a robot body parameter self-calibration method based on sphere center distance constraint according to the application;

[0038] Figure 4 LM algorithm flowchart in a robot body parameter self-calibration method based on sphere center distance constraint according to the application;

[0039] Figure 5 Comparison folded line diagram before and after sphere center distance compensation in a robot body parameter self-calibration method based on sphere center distance constraint according to the application. DETAILED DESCRIPTION

[0040] The application will be described in further detail below with reference to the drawings and embodiments. The described embodiments are only some of the embodiments of the application, rather than all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the application.

[0041] As shown in the drawings, Figure 1 A robot body parameter self-calibration method based on sphere center distance constraint, comprising the following steps:

[0042] Step (1) establishing a calibration error model based on sphere center distance constraint, obtaining a calibration equation of robot body parameter error and distance error;

[0043] Step (2) designing a constraint sphere plate for calibration to obtain measurement data, and establishing a constraint equation;

[0044] Step (3) using an LM algorithm to perform parameter identification on the constraint equation in step (2), and obtaining a robot body parameter compensation value;

[0045] Step (4) compensating the robot body parameter compensation value in step (3) to a robot kinematics model, and performing simulation verification.

[0046] The step (1) in the embodiment is specifically:

[0047] The robot end position quantity obtained from the robot forward kinematics model is set as x, x is a function of robot body parameters (the robot body parameters include rod length, bias, zero position and torsion angle), and the total differential expression of the end position error is obtained by taking partial derivatives of x with respect to each parameter:

[0048]

[0049] where Δx represents the difference between the theoretical position and the actual position of the robot; Δθ i represents the zero position error of the robot; Δα i represents the twist angle error of the robot; Δa i represents the rod length error of the robot; Δd i represents the offset error of the robot; Δβ2represents the axis deviation of the 2nd and 3rd axes of the robot;

[0050] The relationship between the distance error and the position error can be simply illustrated as shown in the accompanying drawings. Figure 2

[0051] where P1 is the theoretical position point of the robot at position 1, P1' is the actual position point of the robot at position 1, P2 is the theoretical position point of the robot at position 2, and P2' is the actual position point of the robot at position 2. When the distance between P1 and P2 is large enough, the vector is considered to be parallel to the vector , and the vector is the position error of the robot at position 1, and the vector is the position error of the robot at position 2. The vector is translated to the position shown in the drawing , and thus , and the distance error of the robot at positions 1 and 2 is the vector , and the vector Thus, according to the vector relationship above, the distance error of the robot at the two positions is equal to the modulus of the difference between the position error vectors of the robot at the two positions.

[0052] A calibration sphere plate with a known sphere center distance is used as a measuring tool, and the sphere center distance is set as Dr. A robot with a dial gauge at the end contacts the spherical surface to obtain fitting points, and a sphere center calculated by a robot theoretical model is fitted from the fitting points, and a theoretical sphere center distance is calculated and set as Dc, and thus

[0053] Dr-Dc=|ΔS1-ΔS2| (2)

[0054] where ΔS1is the position error vector of the robot at the sphere center 1, and ΔS2is the position error vector of the robot at the sphere center 2.

[0055] ΔS1=J1(Δθ i , Δα i , Δa i , Δd i , Δβ2) (3)

[0056] ΔS2=J2(Δθ​i , Δα i , Δa i , Δd i , Δβ2) (4)

[0057] Both can be established by formula (1) formula with the body parameters of the robot, formula (3), formula (4) into formula (2) to get the robot body parameters and distance error calibration equation:

[0058] Dr-Dc=J(Δθ i , Δα i , Δa i , Δd i , Δβ2) (5).

[0059] As Figure 3 shown, the embodiment step (2) described in the design for calibration of the constraint ball plate, the constraint ball plate includes an equilateral triangle shaped carrier plate 1, the three corners of the carrier plate 1 are respectively provided with the same size of the ball 2, each of the ball 2 is connected with the carrier plate 1 perpendicularly through the column 3; the bottom of the carrier plate 1 is provided with a universal angle bracket (not marked in the figure), the top of the universal bracket is connected with the center point of the carrier plate, which is convenient for the space adjustment of the carrier plate 1.

[0060] The calibration ball plate design meets the following conditions:

[0061] ① The ball center distance design value of the ball plate is 300 mm, and the actual value of the ball center distance needs to be accurately obtained by using a three coordinate measuring machine.

[0062] ② The attitude of the ball plate is variable to facilitate obtaining the spatial distance constraint of different attitudes.

[0063] ③ The ball plate is reliable and the spatial position is adjustable.

[0064] Among them, the constraint equation is like Ax=b, and how to solve the equation is the category of parameter identification. It is commonly used to solve the equation by least square method, and the solution of x=(A T A) -1 A T b equation, however, each column of the coefficient matrix A of the constraint equation established has a certain linear correlation, and the condition number of the matrix A is not ideal, and the solution obtained by using the least square method is not reliable.

[0065] And using iterative solution method can monitor the iterative results of each step in real time, and prevent the problem of non-convergence of the solution caused by the ill-conditioned coefficient matrix.

[0066] The step (3) in the embodiment is specifically: the LM iterative algorithm adds a damping term in the iteration process, which can be regarded as a combination of the steepest descent method and the Newton method. When the iteration result is far from the true value, the LM can be regarded as the steepest descent method: the iteration is slow but ensures convergence; when the iteration result is close to the true value, the LM can be regarded as the Newton method: the iteration is fast. Specifically, the following steps are included:

[0067] Step (3.1) gives the initial value x0 of the algorithm iteration, the lower limit of the step size S, the upper limit of the iteration times k, the lower limit of the error err, and the step size validity judgment rou;

[0068] Step (3.2) calculates the iteration step size s and judges whether the step size s < S is true, if true, the iteration is ended, otherwise the next step is entered;

[0069] Step (3.3) updates x using the calculated step size, wherein x = x + s;

[0070] Step (3.4) substitutes the updated x into the objective function to observe whether the calculation error < the last calculation error is true, if true, the updated x is used to enter the next iteration; otherwise, the current iteration is invalid, and the damping term needs to be updated to recalculate the step size s;

[0071] Step (3.5) stops the iteration when the calculation error is less than the given error lower limit err or the step size s < S, and the algorithm is ended.

[0072] The step (4) in the embodiment is specifically: a new end point position is obtained by recalculating the robot forward kinematics with the compensation parameter, a new ball center is obtained by fitting the new point position, and then a ball center distance after parameter compensation is obtained. Whether the ball center distance after compensation converges to the true value of the ball center distance is compared to realize the accuracy of the identification result.

[0073] The embodiment realizes simple and efficient calibration of the robot body parameters by means of the calibration ball plate.

[0074] The simulation experiment design and verification results are as follows:

[0075] 1. Simulation experiment design: simulate the robot calibration process, and specify the model in the robot controller as the theoretical value of the robot body parameters, while the actual robot body has certain errors.

[0076] During simulation, these errors are taken as known quantities, and the constraint balls on the ball plate are marked as ball 1, ball 2, and ball 3. The true value of the ball center distance between ball 1 and ball 2 is L = 299.9952 mm, the true value of the ball center distance between ball 1 and ball 3 is L = 299.7996 mm, and the true value of the ball center distance between ball 2 and ball 3 is L = 299.7827 mm.

[0077] In the simulation environment, the ball plate is placed in the robot workspace, 8 collection points are constructed on each spherical surface, the pose of the collection points constructed on the spherical surface is given to the simulation model (the body compensation parameters are known) to calculate the inverse kinematics of the robot, the joint angle combination obtained is given to the forward kinematics of the theoretical model of the robot in the controller (without compensation value), then the end pose of the point constructed on the spherical surface under the theoretical model can be obtained, the least square method is used to fit the theoretical end position of the ball surface collection points to obtain the theoretical ball center, and then the theoretical ball center distance is obtained.

[0078] The constraint equation of the ball center distance difference and the robot body parameter error amount can be obtained through formula (1) and formula (2), the LM identification algorithm is used to solve the body error amount and then obtain the robot body compensation parameters, the compensation parameters are given to the theoretical model of the controller, the ball center distance is recalculated, and whether the ball center distance after compensation converges to the vicinity of the real value of the ball center distance is observed.

[0079] 2. Simulation verification result: 10 groups of values are given for every two ball center distances during simulation, and the ball center distance values before and after compensation of the 10 groups are compared as shown in the table. Figure 5 It can be observed from the table that the ball center distance after compensation obviously converges to the vicinity of the real value of the ball center distance, and the body calibration result based on the ball center distance constraint is verified to be effective.

[0080] The above only describes the embodiments of the present application and is not used to limit the present application, any modification, equivalent replacement, improvement, etc. made by those skilled in the art within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A robot body parameter self-calibration method based on a sphere center distance constraint, characterized in that, The application relates to a robot body parameter calibration method, which comprises the following steps: Step (1) establishing a calibration error model based on a spherical center distance constraint to obtain a calibration equation of robot body parameter error and distance error; Step (2) designing a constraint ball plate for calibration to obtain measurement data and establishing a constraint equation; Step (3) using an LM algorithm to perform parameter identification on the constraint equation in step (2) to obtain a robot body parameter compensation value; Step (4) compensating the robot body parameter compensation value in step (3) to a robot kinematics model for simulation verification. The step (1) is specifically as follows: The robot end position quantity obtained from the robot forward kinematics model is set as x, and x is a function of the robot body parameters. The total differential expression of the end position error is obtained by taking the partial derivative of x with respect to each parameter as: (1) wherein, represents the difference between the theoretical position and the actual position of the robot; represents the zero error of the robot; represents the twist angle error of the robot; represents the rod length error of the robot; represents the bias error of the robot; represents the deviation of the 2, 3 axis of the robot; Using a calibration sphere plate with known center distance as a measuring tool, the center distance is set as Dr; using a robot with a dial gauge at the end to contact the spherical surface to obtain fitting points, and the center of the sphere calculated by the theoretical model of the robot is fitted, and then the theoretical center distance is calculated, which is set as Dc, then: (2) wherein is the position error vector of the robot at the sphere center 1; is the position error vector of the robot at the sphere center 2; ， Both can be established by formula (1) formula with the robot each body parameter, formula (3), formula (4) into formula (2) get robot body parameter error and distance error calibration equation: .

2. The robot body parameter self-calibration method based on the sphere center distance constraint according to claim 1, wherein, The robot body parameters include rod length, bias, zero position and torsion angle.

3. The robot body parameter self-calibration method based on the sphere center distance constraint of claim 1, wherein, The constraint ball plate for calibration in step (2) comprises an equilateral triangular carrier plate, identical spherical bodies are arranged at three corners of the carrier plate, each spherical body is vertically connected with the carrier plate through a stand column, a universal angle support is arranged at the bottom of the carrier plate, and the top of the universal angle support is connected with the center point of the carrier plate.

4. The robot body parameter self-calibration method based on the sphere center distance constraint of claim 1, wherein, The constraint equation in step (2) is Ax=b.

5. The robot body parameter self-calibration method based on the sphere center distance constraint of claim 1, wherein, The step (3) specifically comprises the following steps: Step (3.1) giving an algorithm iteration initial value x0, a step length lower limit S, an iteration number upper limit k, an error lower limit err and a step length validity judgment rou; Step (3.2) calculating an iteration step length s and judging whether the step length s is less than the step length lower limit S, if yes, the iteration is ended, otherwise, the next step is entered; Step (3.3) updating x by using the calculated step length, wherein x = x + s; Step (3.4) substituting the updated x into a target function to observe whether the current calculation error is less than the last calculation error, if yes, the updated x is used for the next iteration; otherwise, the current iteration is invalid, and the damping term needs to be updated to recalculate the step length s; Step (3.5) stopping the iteration when the calculation error is less than the given error lower limit err or the step length s is less than the step length lower limit S, and the algorithm is ended.

6. The robot body parameter self-calibration method based on the sphere center distance constraint of claim 1, wherein, The step (4) is specifically as follows: a new end point position is obtained by recalculating the robot forward kinematics with the compensation parameter, a new spherical center is obtained by fitting the new point position, then a compensated spherical center distance is obtained, and whether the compensated spherical center distance converges to the real value of the spherical center distance is compared to realize verification of the accuracy of the identification result.

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