Five-axis hybrid robot error parameter calibration method based on ball bar instrument

Abstract

The invention relates to the technical field of robot control, in particular to a five-axis hybrid robot error parameter calibration method based on a ball-bar instrument, which measures pose errors existing in a working space caused by various factors such as self structure errors and measurement errors of a robot by adopting equipment such as the high-precision ball-bar instrument and a circular grating. And the error is mapped to an error model of the five-axis hybrid robot, so that real structural parameters of the five-axis hybrid robot are obtained to compensate a kinematic model, and then the robot is controlled according to a new kinematic model, so that the kinematic error of the tail end of the robot is reduced.

Description

Technical Field

[0001] The present invention relates to the field of robot control technology, and specifically relates to a ballbar-based five-axis hybrid robot error parameter calibration method. Background Art

[0002] The motion accuracy and positioning accuracy of parallel robots are their important performance indicators. Among the main factors affecting the accuracy of parallel robots, the geometric parameter error of the connecting rod has a much greater impact on the accuracy of the end of the parallel robot than the flexible deformation error of the connecting rod and the flexible deformation error of the joint. The impact caused by the geometric parameter error accounts for about 80%; almost 95% of parallel robots can reduce their position and direction positioning errors through calibration technology. At present, the positioning accuracy of parallel robots on the market is only at the millimeter level. It is necessary to improve the motion and positioning accuracy of the end of the robot arm through kinematic calibration and error compensation technology to expand its application field. In recent years, with the explosive application of parallel robotic arms in domestic automated production lines and the continuous advancement of the "machine replacement project", the importance of kinematic calibration and error compensation of parallel robots has become increasingly prominent.

[0003] The kinematic calibration of parallel robots includes specially designed measurement methods and corresponding parameter identification models and identification algorithms. Although it is a common method to use a laser tracker to measure the three-dimensional position error of the end of the robot arm for kinematic calibration, its wide application is limited by factors such as complex operation mode and high price. Although kinematic calibration can also be performed using a ballbar, the current market only calibrates the kinematic error parameters of three-axis parallel robots, and there is no kinematic error parameter calibration for hybrid five-axis. In addition, due to the mechanical structure limitations of the five-axis hybrid robot, it cannot be calibrated using a laser measuring instrument after installation, so a ballbar is needed to calibrate it. Summary of the invention

[0004] In view of the deficiencies in the prior art, the object of the present invention is to provide a method for calibrating error parameters of a five-axis hybrid robot based on a ballbar.

[0005] To achieve the above object, the present invention provides the following technical solution: a method for calibrating error parameters of a five-axis hybrid robot based on a ballbar, the steps of which are:

[0006] (1) Based on the existing five-axis hybrid parallel robot model, the kinematics are derived using the closed-loop vector method, and then the ballbar error compensation model of the robot is established based on the differential motion equation;

[0007] (2) Set a circular trajectory R located on the XY plane of the robot workspace coordinate system i , the center of the circle is O i, the rod length is L, the angle between the ballbar rod and the horizontal plane, the feasibility of the trajectory is verified through the robot simulation model, and then the calibration experiment is carried out;

[0008] (3) Write a motion control program for the robot based on the given motion trajectory and operation method on the robot control software, use the program to drive the robot to move and verify that its motion trajectory is consistent with the original motion trajectory, and write a MATLAB data processing program to process the data generated by the experiment;

[0009] (4) Install the circular grating and ballbar in the designated workspace and at the end of the robot and connect the devices to the PC via USB. Start and debug the corresponding application of the instrument. After zeroing the instrument, prepare to start the experiment:

[0010] (5) Start the robot and execute the programmed program to make the end effector rotate along trajectory R for one circle. Read the joint drive value Q corresponding to each motion point when the end of the parallel robot makes circular motion again. i The motion state of the robot end is monitored in real time, and the ballbar measurement value L(j,i) and the rotation angle of the ballbar corresponding to each point on the Jth trajectory are recorded.

[0011] (6) Complete the circular trajectory L j After the measurement, adjust the angle between the ballbar and the horizontal plane to γ j+1 , set a circular trajectory R located on the XY plane of the spatial coordinate system j+1 , whose center is O j+1 , the rod length radius is L j+1 , repeat the above experiment;

[0012] (7) Read the saved experimental data in MATLAB software and process the data, including: first, according to the forward motion equation of the parallel robot, substitute the joint drive value corresponding to the trajectory to calculate the theoretical spatial position of the end of the parallel robot and the spatial position of the end of the ballbar, respectively S(j,i) and S o (j,i); the theoretical spatial position of the end of the parallel robot and the theoretical spatial position of the end of the ballbar are subtracted and divided by the theoretical rod length to obtain the unit vector η(j,i) of the ballbar. Finally, the actual joint angle value measured by the circular grating is matched with the timestamp of the ballbar.

[0013] 8) On the basis of step (7), according to the error mapping model established in MTATLAB, the end roundness error ΔL(j,i) measured by the ballbar is brought into the five-axis hybrid error mapping model to identify the actual structural parameters of the five-axis parallel robot. Then, the structural parameters in the theoretical model are replaced, and a new parallel robot inverse solution is established to describe the workspace of the end of the five-axis parallel robot, so as to achieve compensation of the parallel robot motion error. The corrected model is substituted into the experiment, and the above steps are repeated to verify the accuracy and effectiveness of the identified parameters.

[0014] In some of the embodiments, the error compensation model in step (1) includes an XY plane error compensation model, a YZ plane error compensation model, and an XZ plane error compensation model.

[0015] In some of the embodiments, in step (2), the set circular trajectory is the bottom surface contour of a cone with the ballbar as the generatrix, and the size of the cone apex angle is adjusted according to the change of the angle γ between the ballbar rod and the horizontal plane, and spatial measurement is achieved by continuously adjusting the angle γ.

[0016] In some of the embodiments, in step (5), the continuous motion of the robot in space is discretized, and its overall infinite points are equivalently represented by points that can be quickly processed by finite calculations; and multi-plane detection breaks the limitation of the nominal length of the ballbar itself, and realizes the detection of any plane and any size of circular surface within a certain area.

[0017] In some of the embodiments, in step (7), the error compensation is expressed by separating the error into components in the three directions of X, Y, and Z in the spatial coordinate system XYZ, and dividing the error compensation into plane XY, plane XZ, and plane YZ; finally, these compensation parameters are integrated by mathematical methods and compensated into the robot model.

[0018] Compared with the prior art, the present invention has the following beneficial effects:

[0019] 1. The ballbar error parameter mapping model of the five-axis hybrid robot proposed in the present invention can effectively model the ballbar error parameters of the hybrid robot and ensure the least square solution of the error parameters, which not only improves the calibration accuracy of the hybrid robot, but also enhances its stability and repeatability in continuous or repeated operations. In addition, the least squares iteration strategy with a regularization term is adopted to further reduce the phenomenon of model overfitting, making the error parameters of the hybrid robot more accurate after calibration, and greatly improving the reliability of the model;

[0020] 2. The ballbar error parameter modeling of the present invention is mainly achieved by establishing a comprehensive error parameter mapping model and model, which combines the kinematic error mapping model of the serial mobile platform and the parallel mobile platform. The accuracy of the identification model is optimized by the first-order perturbation principle and iterative calculation, thereby improving the error parameter identification accuracy of the five-axis hybrid robot. After the kinematic parameter identification, it is ensured that the five-axis robot can maintain a better high-precision standard during operation;

[0021] 3. The application of a new calibration method for a five-axis hybrid robot based on a ballbar enables the system to calibrate the ballbar kinematic parameters even in a complex structural environment. This control strategy reduces the debugging and maintenance costs of robot error calibration due to the ballbar's high measurement efficiency and simplified calibration steps. The robot can maintain high motion accuracy during use, reducing the need for frequent maintenance and recalibration, and reducing the operating cost of the system.

[0022] Details of one or more embodiments of the present application are presented in the following drawings and descriptions to make other features, purposes and advantages of the present application more concise and easy to understand. The present application is fully described and understood through the embodiments of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a motion trajectory diagram of the structure experiment of the embodiment of the present invention;

[0024] Figure 2 It is a schematic diagram of the parallel modules of the embodiment structure of the present invention;

[0025] Figure 3 This is an overall schematic diagram of a five-axis hybrid robot according to an embodiment of the present invention;

[0026] Figure 4 It is the overall flow chart of the present invention.

[0027] In the figure: 1. Workbench; 2. Circular grating angle measurement device; 3. Ballbar; 4. Three-axis parallel module. DETAILED DESCRIPTION

[0028] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0029] See also Figure 1-4 The present invention provides a technical solution: a method for calibrating error parameters of a five-axis hybrid robot based on a ballbar, the steps of which are as follows:

[0030] (1) Based on the existing five-axis hybrid parallel robot model, the kinematics are derived using the closed-loop vector method, and then the ballbar error compensation model of the robot is established based on the differential motion equation;

[0031] (2) Set a circular trajectory R located on the XY plane of the robot workspace coordinate system i , the center of the circle is O i , the rod length is L, the angle between the ballbar rod and the horizontal plane, the feasibility of the trajectory is verified through the robot simulation model, and then the calibration experiment is carried out;

[0032] (3) Write a motion control program for the robot based on the given motion trajectory and operation method on the robot control software, use the program to drive the robot to move and verify that its motion trajectory is consistent with the original motion trajectory, and write a MATLAB data processing program to process the data generated by the experiment;

[0033] (4) Install the circular grating and ballbar in the designated workspace and at the end of the robot and connect the devices to the PC via USB. Start and debug the corresponding application of the instrument. After zeroing the instrument, prepare to start the experiment:

[0034] (5) Start the robot and execute the programmed program to make the end effector rotate along trajectory R for one circle. Read the joint drive value Q corresponding to each motion point when the end of the parallel robot makes circular motion again. i The motion state of the robot end is monitored in real time, and the ballbar measurement value L(j,i) and the rotation angle of the ballbar corresponding to each point on the Jth trajectory are recorded.

[0035] (6) Complete the circular trajectory L j After the measurement, adjust the angle between the ballbar and the horizontal plane to γ j+1 , set a circular trajectory R located on the XY plane of the spatial coordinate system j+1 , whose center is O j+1 , the rod length radius is L j+1 , repeat the above experiment, such as Figure 1 As shown;

[0036] (7) Read the saved experimental data in MATLAB software and process the data, including: first, according to the forward motion equation of the parallel robot, substitute the joint drive value corresponding to the trajectory to calculate the theoretical spatial position of the end of the parallel robot and the spatial position of the end of the ballbar, respectively S(j,i) and S o(j,i); the theoretical spatial position of the end of the parallel robot and the theoretical spatial position of the end of the ballbar are subtracted and divided by the theoretical rod length to obtain the unit vector η(j,i) of the ballbar. Finally, the actual joint angle value measured by the circular grating is matched with the timestamp of the ballbar.

[0037] 8) On the basis of step (7), according to the error mapping model established in MTATLAB, the end roundness error ΔL(j,i) measured by the ballbar is brought into the five-axis hybrid error mapping model to identify the actual structural parameters of the five-axis parallel robot. Then, the structural parameters in the theoretical model are replaced, and a new parallel robot inverse solution is established to describe the workspace of the end of the five-axis parallel robot, so as to achieve compensation of the parallel robot motion error. The corrected model is substituted into the experiment, and the above steps are repeated to verify the accuracy and effectiveness of the identified parameters.

[0038] The error compensation model in step (1) includes an XY plane error compensation model, a YZ plane error compensation model, and an XZ plane error compensation model.

[0039] In step (2), the set circular trajectory is the bottom profile of a cone with the ballbar as the generatrix. The size of the cone apex angle is adjusted according to the change of the angle γ between the ballbar rod and the horizontal plane. The spatial measurement is achieved by continuously adjusting the angle γ.

[0040] In step (5), the continuous motion of the robot in space is discretized, and its overall infinite points are equivalently represented by points that can be quickly processed by finite calculations; and multi-plane detection breaks the limitation of the nominal length of the ballbar itself, and realizes the detection of any plane and any size of circular surface within a certain area.

[0041] In step (7), the error compensation is expressed by separating the error into components in the three directions of X, Y, and Z in the spatial coordinate system XYZ, and dividing the error compensation into planes XY, XZ, and YZ; finally, these compensation parameters are integrated through mathematical methods and compensated into the robot model.

[0042] Through this technical solution, in actual application, the following steps are included:

[0043] (1) Derivation and simulation of tool motion chain error mapping model

[0044] 1) The tool kinematic chain of the present invention is mainly composed of a 2PRU-PUR parallel mechanism. The projection diagram of the fixed Cartesian coordinate system is established in the parallel mechanism. Figure 2As shown, the X axis is collinear with C1C2, the Y axis is along the direction of O1C3, the Z axis satisfies the right-hand rule, the origin of the moving coordinate system o-xyz is the midpoint of o, the X axis is collinear with B1B2, the Y axis is along the direction of oB3, the Z axis satisfies the right-hand rule, and the coordinate system of the tool tip is defined as o t -xyz.

[0045] Calculate the joint drive value Q of the parallel robot according to the closed-loop vector method i =[Q1,Q2,Q3] and the error source, and also obtain the parallel fixed coordinate system O t -Convert the joint drive value under XYZ to the real-time pose P of the center of the moving platform Ot =[X0,Y0,Z0,α x ,β y ], due to the particularity of the mechanism, in the case of theoretical parameters, Y0 = 0, the inverse kinematics expression is as follows:

[0046]

[0047] Based on the differential method, the mapping relationship between the parallel mechanism posture error and the structural parameter error is derived. This mapping relationship can be obtained by taking the total differential on both sides of the inverse kinematics equation, which is specifically expressed as follows:

[0048]

[0049] Where: [δx ci ,δy ci ],[δx bi ,δy bi ],δl i They are fixed platform installation error, moving platform installation position error, and rod length error. j (j=1,2,3) is the mapping relationship between the posture error and the end degree of freedom error, which is specifically expressed as follows:

[0050]

[0051] The above formula is organized into a matrix form to obtain the mapping between the moving platform origin position error and the kinematic error parameters:

[0052]

[0053] Where δx c ,δx b ,δl,δq satisfy the following relationship:

[0054]

[0055] So far, the mapping relationship between the parallel mechanism moving platform origin position error and structural parameter error is obtained:

[0056]

[0057] Where: J ik,p1 ,J ik,p2 ,J ik,p They are the attitude Jacobian, the structural parameter error Jacobian, and the mapping Jacobian of the end attitude error and structural parameter error of the parallel mechanism.

[0058] 2) Based on the established dynamic platform error model, the tool end error model needs to be established.

[0059] like Figure 2 As shown, firstly, the relationship between the tool end point position P and the moving platform posture is:

[0060]

[0061] Among them, the actual position vector of the tool end point P in the fixed coordinate system is P = (P x ,P y ,P z ) T , the coordinates of the center of mass of the moving platform l c =(0,0,l c ) represents the theoretical size of the tool.

[0062] Combining the relationship between the end platform posture and the tool, a first-order linear perturbation is performed on both sides, and the following is obtained:

[0063]

[0064] in is the position error of the moving platform, is the tool end position error, ΔΩ is the tool end posture error, Δl c =(δd1,δd2,δd3) T Refers to the error term of the tool end point in the moving coordinate system.

[0065] in This is equivalent to solving the angular velocity of the moving platform.

[0066] Further sorting can be obtained:

[0067]

[0068] So far, the mapping relationship between the structural parameter error and the end position error is obtained, which is expressed as follows:

[0069] δp ik =J ik δr ik

[0070] in The Jacobian matrix representing the mapping between position error and structure error, Represents the mapping Jacobian matrix between position error and structure error,.

[0071] (2) Derivation and simulation of five-axis hybrid error mapping model

[0072] On the basis of establishing the terminal error mapping model of the three-axis parallel module error mapping model, a series workbench is also needed to establish a complete five-axis hybrid terminal error parameter mapping model, and finally a simulation experiment of structural parameter identification can be carried out. The three-dimensional model of the five-axis hybrid robot is as follows: Figure 3 shown.

[0073] First, the inverse kinematics of the five-axis hybrid robot is derived. In general, during machining, the programmed tool path trajectory represents the tool tip point O of the workpiece motion chain. t -xyz relative to the end of the workpiece kinematic chain O w -The relative position of xyz can be expressed as:

[0074] w P t =P t -P w

[0075] According to the above formula, the ideal inverse kinematic expression of the tool tip position of the five-axis hybrid robot relative to the workpiece can be written as:

[0076]

[0077] Where (X, Y, Z, α, β) is the input position of the tool end relative to the workpiece system. It is the five-axis drive value.

[0078] Then the error mapping model of the workpiece kinematic chain is established.

[0079] like Figure 3 As shown, the base coordinate system of the workbench is O-x1y1z1, and the moving coordinate system of the workbench is O w -xyz, where the vector representation of the workbench in the base coordinate system is as follows:

[0080]

[0081] Where (beta, gamma) are the rotation angles around the x-axis and y-axis of the base coordinate system, respectively, and q x is the moving value of the serial platform.

[0082] The first-order perturbation of the above equation yields:

[0083]

[0084] So far, the mapping relationship between the structural parameter error and the end position error is obtained, which is expressed as follows:

[0085] δp w =J w δr w

[0086] When the five-axis hybrid robot moves along the tool path, the workpiece coordinate system must be determined first. o The error is caused by the combined influence of the end error of the three-axis parallel module and the worktable movement error. When the ballbar is moved in a circle around the fixed point, after the workpiece coordinate system is determined, the moving point r on the ballbar j,k Only the error at the end of the parallel module has an effect, while the fixed point r s Only affected by the workbench movement error.

[0087] Based on the above principle, we can s and moving point r j,k The error modeling is carried out separately to obtain the five-axis hybrid kinematic error model.

[0088] At a known δp ik =J ik δr ik Based on this, add the worktable movement error δp w =J w δr w , which is expressed as follows:

[0089]

[0090]

[0091] So far, the error terminal mapping model of the five-axis hybrid robot has been obtained.

[0092] (3) Ballbar error mapping model establishment and simulation

[0093] The position vector of the ballbar fixed point under Oxyz is r s , the position vector r of the parallel mechanism tool end point P in the k=1,2,…,n configuration in the j=1,2,…,m arc trajectory segment j,k , which is expressed as follows:

[0094]

[0095] In the formula, l j,k and They are respectively represented as the length of the ballbar and the unit vector pointing from point S to point P. The above formula is perturbed in the first order and expressed as follows:

[0096]

[0097] Dot product on both sides of the equation because And where δr i,k =δp i,k ,

[0098] A s =[J ik,d 0 3×3 ], so it is expressed as follows

[0099]

[0100] j=1,2,…,mk=1,2,…,n

[0101] In the initial configuration, it is known that θ=J0δr ik , and in order to eliminate the rigid body displacement, the above formulas are combined to construct 6+m×n constraint equations, which are simplified into matrix form as follows:

[0102]

[0103] Where Δl is the roundness error matrix measured when the ballbar is working, and H is the total error parameter identification matrix of the ballbar, as shown below:

[0104]

[0105] In the formula, H m The ballbar error parameter identification matrix corresponding to the mth circular trajectory is expressed as follows:

[0106]

[0107] So far, the ballbar error parameter mapping model of the five-axis hybrid robot is obtained, and the formula is as follows:

[0108]

[0109] In the formula, δΩ ik =[δl], J ik =[H].

[0110] The application of a new calibration method for a five-axis hybrid robot based on a ballbar enables the system to calibrate the ballbar kinematic parameters even in a complex structural environment. This control strategy reduces the debugging and maintenance costs of robot error calibration due to the ballbar's efficient measurement and simplified calibration steps. The robot can maintain high motion accuracy during use, reduce frequent maintenance and recalibration requirements, and reduce the operating cost of the system.

[0111] The above embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

[0112] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for calibrating error parameters of a five-axis hybrid robot based on a ballbar, characterized in that: The steps are: (1) Based on the existing five-axis hybrid parallel robot model, the kinematics are derived using the closed-loop vector method, and then the ballbar error compensation model of the robot is established based on the differential motion equation; (2) Set a circular trajectory R located on the XY plane of the robot workspace coordinate system i , the center of the circle is O i , the rod length is L, the angle between the ballbar rod and the horizontal plane, the feasibility of the trajectory is verified through the robot simulation model, and then the calibration experiment is carried out; (3) Write a motion control program for the robot based on the given motion trajectory and operation method on the robot control software, use the program to drive the robot to move and verify that its motion trajectory is consistent with the original motion trajectory, and write a MATLAB data processing program to process the data generated by the experiment; (4) Install the circular grating and ballbar in the designated workspace and at the end of the robot and connect the devices to the PC via USB. Start and debug the corresponding application of the instrument. After zeroing the instrument, prepare to start the experiment: (5) Start the robot and execute the programmed program to make the end effector rotate along trajectory R for one circle. Read the joint drive value Q corresponding to each motion point when the end of the parallel robot makes circular motion again. i The motion state of the robot end is monitored in real time, and the ballbar measurement value L(j,i) and the rotation angle of the ballbar corresponding to each point on the Jth trajectory are recorded. (6) Complete the circular trajectory L j After the measurement, adjust the angle between the ballbar and the horizontal plane to γ j+1 , set a circular trajectory R located on the XY plane of the spatial coordinate system j+1 , whose center is O j+1 , the rod length radius is L j+1 , repeat the above experiment; (7) Read the saved experimental data in MATLAB software and process the data, including: first, according to the forward motion equation of the parallel robot, substitute the joint drive value corresponding to the trajectory to calculate the theoretical spatial position of the end of the parallel robot and the spatial position of the end of the ballbar, respectively S(j,i) and S o (j,i); the theoretical spatial position of the end of the parallel robot and the theoretical spatial position of the end of the ballbar are subtracted and divided by the theoretical rod length to obtain the unit vector η(j,i) of the ballbar. Finally, the actual joint angle value measured by the circular grating is matched with the timestamp of the ballbar. 8) On the basis of step (7), according to the error mapping model established in MTATLAB, the end roundness error ΔL(j,i) measured by the ballbar is brought into the five-axis hybrid error mapping model to identify the actual structural parameters of the five-axis parallel robot. Then, the structural parameters in the theoretical model are replaced, and a new parallel robot inverse solution is established to describe the workspace of the end of the five-axis parallel robot, so as to achieve compensation of the parallel robot motion error. The corrected model is substituted into the experiment, and the above steps are repeated to verify the accuracy and effectiveness of the identified parameters.

2. The error parameter calibration method of a five-axis hybrid robot based on a ballbar according to claim 1, characterized in that: The error compensation model in step (1) includes an XY plane error compensation model, a YZ plane error compensation model, and an XZ plane error compensation model.

3. The error parameter calibration method of a five-axis hybrid robot based on a ballbar according to claim 1, characterized in that: In step (2), the set circular trajectory is the bottom profile of a cone with the ballbar as the generatrix. The size of the cone apex angle is adjusted according to the change of the angle γ between the ballbar rod and the horizontal plane. The spatial measurement is achieved by continuously adjusting the angle γ.

4. The error parameter calibration method of a five-axis hybrid robot based on a ballbar according to claim 1, characterized in that: In step (5), the continuous motion of the robot in space is discretized, and its overall infinite points are equivalently represented by points that can be quickly processed by finite calculations; and multi-plane detection breaks the limitation of the nominal length of the ballbar itself, and realizes the detection of any plane and any size of circular surface within a certain area.

5. The error parameter calibration method of a five-axis hybrid robot based on a ballbar according to claim 1, characterized in that: In step (7), the error compensation is expressed by separating the error into components in the three directions of X, Y, and Z in the spatial coordinate system XYZ, and dividing the error compensation into planes XY, XZ, and YZ; finally, these compensation parameters are integrated through mathematical methods and compensated into the robot model.

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