Kinematics parameter calibration method and system for industrial robot based on parameter separation and multi-objective optimization

Abstract

The application discloses a kind of industrial robot kinematics parameter calibration method and system based on parameter separation and multi-objective optimization, belongs to industrial robot technical field, by linear-nonlinear parameter separation, introduce multi-objective minimax optimization, effectively handle the non-homogeneity problem of pose information, realize the fast, robust, high-precision robot kinematics parameter identification and compensation.Calibration method includes:1, acquisition robot end in multiple measurement poses under position information;2, the kinematics model of robot is established, and the parameter to be identified is divided into linear set and nonlinear set, to reconstruct separable optimization problem;3, based on the position information collected, construct the multi-objective minimax optimization problem with the optimization worst performance index as the target, by iteration solving linear set and nonlinear set, complete the identification of kinematics parameter;4, the optimal kinematics parameter identified finally is compensated to robot controller, and the kinematics model is updated.

Description

Technical Field

[0001] This invention belongs to the field of industrial robot technology, specifically relating to a method and system for calibrating kinematic parameters of industrial robots based on parameter separation and multi-objective optimization. Background Technology

[0002] The absolute positioning accuracy of industrial robots is a key performance indicator for them to complete high-end manufacturing tasks (such as aerospace assembly and automotive welding). Due to manufacturing and assembly errors, the actual kinematic parameters of the robot deviate from the theoretical model, leading to a decrease in its absolute positioning accuracy. Therefore, kinematic parameter calibration is a core step in improving robot performance.

[0003] Existing parameter calibration methods mostly rely on model-based least squares optimization algorithms, but they suffer from the following technical bottlenecks: 1) Initial value sensitivity and convergence issues: Traditional nonlinear optimization algorithms are very sensitive to the initial values ​​of the identification parameters. When the initial value deviation is large, the optimization process is very likely to get stuck in local optima or even fail to converge, leading to calibration failure.

[0004] 2) Homogeneity and Coordinate System Dependency Issues in Pose Representation: The robot's end-effector pose includes both position (3D) and orientation (3D) information. Position error is measured in length (e.g., millimeters), while orientation error is measured in angle (e.g., radians), and these two are not homogeneous. Inappropriate weight settings can distort the optimization objective and affect convergence. Furthermore, the description of orientation heavily depends on the choice of reference coordinate system; different coordinate system establishment strategies will directly lead to different calibration results.

[0005] 3) Insufficient specific calibration capability: Existing methods have poor universality and robustness for different types of robots with different structures, making it difficult to achieve efficient "specific" calibration.

[0006] Therefore, there is an urgent need for a kinematic parameter calibration method that can overcome initial value sensitivity, solve the problem of pose heterogeneity, and has strong robustness. Summary of the Invention

[0007] To overcome the shortcomings of existing technologies, the present invention aims to provide a method and system for calibrating kinematic parameters of industrial robots based on parameter separation and multi-objective optimization. By separating linear and nonlinear parameters, the dependence of the optimization problem on the initial value is reduced. By introducing multi-objective minimax optimization, the non-homogeneity problem of pose information is effectively handled, thereby realizing fast, robust and high-precision identification and compensation of robot kinematic parameters.

[0008] To achieve the above objectives, the present invention may adopt the following specific technical solutions: On the one hand, this invention provides a method for calibrating kinematic parameters of industrial robots based on parameter separation and multi-objective optimization, including the following steps: Step 1: Collect position information of the robot's end effector in multiple measurement poses; Step 2: Establish the kinematic model of the robot and divide the parameters to be identified into linear and nonlinear sets to reconstruct a separable optimization problem; Step 3: Based on the collected location information, construct a multi-objective minimax optimization problem with the goal of optimizing the worst performance index. By iteratively solving the linear set and the nonlinear set, the kinematic parameters are identified. Step 4: Compensate the optimal kinematic parameters finally identified in Step 3 into the robot controller and update the kinematic model.

[0009] Furthermore, the position information in step 1 includes: measuring the three-dimensional coordinates in space of the three target balls fixed to the end of the robot using a laser tracker.

[0010] Furthermore, the specific content of step 2 is as follows: Step 2.1: Establish the MD-H model of the industrial robot; Step 2.2: Analyze the structure of the MD-H model and divide the kinematic parameters to be identified into a linear parameter set θ_L and a nonlinear parameter set θ_NL; Step 2.3: Based on Step 2.2, the original problem of robot kinematic parameter identification is reconstructed into a separable optimization problem, with the objective function expressed as: Minimize: Σ || f(θ_NL) · θ_L - P_measured ||², Here, f(θ_NL) is a matrix function composed of nonlinear parameters, and P_measured is the actual measured end position vector. By separating, the original problem is decomposed into a nonlinear least squares subproblem with respect to linear parameters and a low-dimensional nonlinear least squares subproblem with respect to nonlinear parameters.

[0011] Furthermore, the MD-H model describes each link i of the robot using four parameters: link length. ai Linkage torsion angle αi Linkage offset di Joint angle θi The geometric error of each link includes the deviation values ​​Δ of four parameters. ai Δ αi Δ di Δ θi and robot coordinate system error Δ xb Δ yb Δ zb Δ rxb Δ ryb Δ rzb Together with the tool coordinate system error, all error parameters form a vector. θ .

[0012] Furthermore, for any given set of nonlinear parameters θ_NL, the linear parameter θ_L can be directly obtained by linear least squares, i.e.: θ_L = pinv( f(θ_NL) ) · (P_measured - g(θ_NL)), where pinv is the pseudo-inverse operation.

[0013] Furthermore, the specific content of step 3 is as follows: Step 3.1: Using the measurement data of the three target balls in Step 1, calculate the six-dimensional pose of the robot's end effector; Step 3.2: For each measurement pose, calculate the position error corresponding to the three target balls, and use the position error as three independent performance indicators; Step 3.3: Construct a multi-objective minimax optimization problem that takes into account pose information, mathematically expressed as: Minimize [ max( J_ball1(θ), J_ball2(θ), J_ball3(θ) ) ], where J_balli(θ) is the comprehensive position error of the i-th target ball under all measured poses. The optimization objective is to optimize the worst-performing target ball among the three target balls, i.e., the "worst performance index", thereby equivalently achieving the overall optimization of the six-dimensional pose accuracy of the robot's end effector. Step 3.4: Solve using an iterative optimization strategy: First, fix the initial nominal value of the nonlinear parameter θ_NL and solve for the linear parameter θ_L; then, use the solved linear parameter θ_L to optimize the nonlinear parameter θ_NL in the reduced-dimensional space; iterate repeatedly until the objective function converges.

[0014] On the other hand, the present invention provides an industrial robot kinematic parameter calibration system based on parameter separation and multi-objective optimization, for performing the above-mentioned industrial robot kinematic parameter calibration method based on parameter separation and multi-objective optimization, including: A high-precision measuring device for acquiring pose information of the robot's end effector, including a laser tracker and multiple target balls mounted on the robot's end effector; Data processing unit for executing linear-nonlinear parameter separation modeling and multi-objective minimax optimization algorithms; The parameter compensation interface is used to write the identification results into the robot controller.

[0015] Compared with the prior art, the present invention has the following advantages: 1) High robustness and fast convergence: This invention significantly reduces the dependence of the optimization problem on the initial value of the parameters by separating linear and nonlinear parameters, expands the convergence domain, and enables the objective function to converge quickly to the global optimum or near-global optimum, thereby improving the success rate and efficiency of the identification process.

[0016] 2) Effectively solves the problem of non-homogeneous pose: This invention cleverly transforms the optimization problem of six-dimensional pose accuracy into the optimization of three homogeneous (length units) performance indicators by constructing a multi-objective minimax problem based on the position errors of three target balls. This avoids the difficulty of manually setting position and attitude weight coefficients, making the optimization process more reasonable and the results more accurate.

[0017] 3) Strong versatility and specific calibration capability: This method solves the common problems in robot calibration from the modeling and algorithm level. Therefore, it has good applicability to different types of industrial robots (such as six-axis, SCARA, etc.) and can perform efficient "specific" calibration for different robot structural characteristics.

[0018] 4) Strong engineering applicability: This invention forms a complete solution from high-precision measurement and advanced algorithms to system integration. The developed system can realize automated and high-precision robot performance testing and calibration, and has high engineering application value. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention. Figure 2 This is a schematic diagram of the measurement system used in this embodiment of the invention (including: robot, laser tracker, target ball). Figure 3 This is a schematic diagram of the linear-nonlinear parameter separation optimization process of the present invention; Figure 4 This is a schematic diagram illustrating the multi-objective minimax optimization principle of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0021] Example 1

[0022] like Figure 1 As shown, the industrial robot kinematic parameter calibration method based on parameter separation and multi-objective optimization is characterized by the following steps: (a) Step 1: Collect position information of the robot end effector in multiple measurement poses.

[0023] (1) Set up the measurement system: including hardware configuration and system calibration.

[0024] Hardware components: such as Figure 2 As shown, the measurement system includes an industrial robot body, a robot control cabinet, a laser tracker (such as an API T3 or Leica AT960), a tracker controller, and a custom target ball mounting plate fixed to the robot's end effector. This mounting plate has three target ball mounting holes that are not on the same straight line, forming a rigid "tool coordinate system definition volume".

[0025] Measurement system calibration: Before measurement begins, tool coordinate system calibration is required. This involves controlling the industrial robot to move to multiple different postures, allowing the laser tracker to measure three target spheres, thereby accurately calculating the transformation relationship between the coordinate system formed by these three target spheres and the coordinate system of the industrial robot's end effector flange. This relationship remains constant throughout the calibration process.

[0026] (2) Plan the measurement pose.

[0027] A pose planning strategy that maximizes workspace coverage and joint excitation is adopted. This involves not only uniformly sampling within the industrial robot's workspace (e.g., using a cubic mesh), but also maximizing the range of motion of each joint to fully excite all kinematic errors to be identified.

[0028] The number of measured poses N is usually no less than 100 to ensure that the observation matrix is ​​full rank and to provide sufficient redundant data to suppress random measurement noise.

[0029] This step, through precise measurement system calibration and scientific pose planning, ensures that the raw data used by subsequent algorithms is of high quality and contains sufficient information, laying a solid foundation for high-precision parameter identification.

[0030] (II) Step 2: Establish the kinematic model of the robot and divide the parameters to be identified into linear and nonlinear sets to reconstruct a separable optimization problem, such as... Figure 3 As shown.

[0031] (1) Step 2.1: Establish the MD-H model of the industrial robot.

[0032] The standard MD-H model describes each link i of the robot using four parameters: link length ai Linkage torsion angle α i Linkage offset di Joint angle θi The geometric error of each link includes the deviation values ​​Δ of four parameters. ai Δ αi Δ di Δ θi In addition, it also includes the coordinate system error Δ of the industrial robot. xb Δ yb Δ zb Δ rxb Δ ryb Δ rzb Combine the tool coordinate system error with all error parameters into a vector. θ Its dimensions are typically 1m×1 (m may be greater than 30).

[0033] (2) Step 2.2: Analyze the structure of the MD-H model and divide the kinematic parameters to be identified into a linear parameter set θ_L and a nonlinear parameter set θ_NL.

[0034] In the robot's kinematic model, the position of the end effector, Pend = [x, y, z]T, can be represented as linear with respect to some parameters and nonlinear with respect to others. By decomposing the MD-H model matrix, the robot's forward kinematic equations can be rewritten as: Pend = f(θ_NL)·θL + g(θ_NL), where θL is the set of linear parameters (e.g., deviations in link length ai and torsion angle αi); θ_NL is the set of nonlinear parameters (e.g., deviations in joint zero position θi and offset di); f(θ_NL) is a matrix determined by the nonlinear parameters; and g(θ_NL) is a vector determined by the nonlinear parameters.

[0035] (3) Step 2.3: Based on step 2.2, the original parameter identification problem of robot kinematic parameter identification is minimized: Σ || P_forward(θ) - P_measured ||² and reconstructed into a separable optimization problem. The separable optimization objective function is expressed as: Minimize: Σ || f(θ_NL) · θ_L - P_measured ||², where f(θ_NL) is a matrix function composed of nonlinear parameters and P_measured is the actual measured end position vector. Through separation, the original problem is decomposed into a nonlinear least squares subproblem with respect to linear parameters and a low-dimensional nonlinear least squares subproblem with respect to nonlinear parameters.

[0036] For any given set of nonlinear parameters θ_NL, the linear parameter θ_L can be directly obtained using linear least squares: θ_L = pinv( f(θ_NL) )·(P_measured - g(θ_NL)), where pinv is the pseudo-inverse operation. Thus, the original high-dimensional nonlinear optimization problem is reduced to a low-dimensional nonlinear least squares problem concerning only the set of nonlinear parameters θ_NL.

[0037] This step transforms a complex, initial-value-sensitive nonlinear problem into a hybrid problem involving an "outer loop" optimizing nonlinear parameters and an "inner loop" analytically solving for linear parameters. This significantly reduces the problem's complexity, expands the convergence region, and enables the algorithm to converge quickly and stably even when iterating from theoretical nominal values.

[0038] (III) Step 3: Based on the collected location information, construct a multi-objective minimax optimization problem with the goal of optimizing the worst performance index. Through iterative solutions to linear and nonlinear sets, identify the kinematic parameters, such as... Figure 4 As shown.

[0039] (1) Step 3.1: Calculate the six-dimensional pose of the robot end effector using the measurement data of the three target balls in step 1.

[0040] For the j The measurement pose is determined based on the measurement coordinates P of the three target balls. ball 1 j ,P ball 2 j ,P ball 3 j The position P of the origin (TCP) of the tool coordinate system at the robot's end effector can be calculated at this time. tcpj and attitude matrix R j .

[0041] (2) Step 3.2: For each measurement pose, calculate the position error corresponding to the three target balls respectively, and use the position error as three independent performance indicators.

[0042] Define the comprehensive position error of the k-th target ball across all N poses. For example, using the root mean square error (RMSE): J_k(θ) = sqrt( (1 / N) Σ_{j=1 to N} || P_ball_k^j_predicted(θ) - P_ball_k^j_measured ||² ), where P_ball_k^j_predicted(θ) is the position of the k-th target ball in the j-th pose calculated using the current target parameter θ through a kinematic model.

[0043] (3) Step 3.3: Construct a multi-objective minimax optimization problem considering pose information, with the mathematical expression: Minimize [ max( J_ball1(θ), J_ball2(θ), J_ball3(θ) ) ], where J_balli(θ) is the comprehensive position error of the i-th target ball under all measured poses. The optimization objective aims to optimize the target ball with the worst performance among the three target balls, that is, the "worst performance index", so as to equivalently achieve the overall optimization of the six-dimensional pose accuracy of the robot end.

[0044] (4) Step 3.4: Solve using an iterative optimization strategy: First, fix the initial nominal value of the non-linear parameter θ_NL and solve for the linear parameter θ_L; then use the solved linear parameter θ_L to optimize the non-linear parameter θ_NL in the reduced-dimensional space; iterate in a loop until the objective function converges.

[0045] Combining the parameter separation in S2, the entire solution process is shown in the following pseudocode: Initialize θ_NL = θ_NL_nominal, iteration count t = 0, tolerance ε = 1e-6.

[0046] while (change in objective function > ε) and (t < max_iterations): Fix θ_NL and solve for θ_L through linear least squares, θ_L(t) = pinv( f(θ_NL(t)) ) · (P_measured - g(θ_NL(t))); Fix θ_L(t) and optimize θ_NL in the reduced-dimensional space to solve the minimax problem.

[0047] Solve the following problem using sequential quadratic programming (SQP) or interior point method: Minimize_{θ_NL, γ} γ, s.t. J_1( {θ_L(t), θ_NL} ) ≤ γ, J_2( {θ_L(t), θ_NL} ) ≤ γ, J_3( {θ_L(t), θ_NL} ) ≤ γ, θ_NL(t + 1) = the optimized θ_NL, t’ = t + 1, output the optimal parameter θ opt = {θ_L(t), θ_NL(t)}.

[0048] This step transforms the challenging six-dimensional pose non-homogeneous optimization problem into a balanced optimization of three homogeneous (length units) targets. This ensures an overall improvement in the industrial robot's accuracy across the entire workspace, rather than focusing on optimizing the accuracy of a specific direction or region, thus achieving highly robust specific calibration.

[0049] (iv) Step 4: Compensate the optimal kinematic parameters finally identified in step 3 into the robot controller and update the kinematic model.

[0050] (1) Parameter compensation The identified optimal parameters θ opt (i.e. Δ) ai ,Δ αi The kinematic model is then added to the robot's nominal model parameters (...) to obtain a new, compensated kinematic model. This new kinematic model is then written into the industrial robot controller, replacing its original internal model. Modern robot controllers typically support model updates via specific API interfaces or parameter files.

[0051] To objectively evaluate the calibration effect, a set of validation poses that were not involved in the calibration process must be used. The absolute positioning accuracy of the robot on these validation poses is compared before and after calibration. Key metrics include: maximum error, mean error, and root mean square error (RMSE).

[0052] Example 2

[0053] This embodiment uses a six-degree-of-freedom industrial robot as the calibration object.

[0054] Hardware configuration: An API T3 laser tracker is used as the measuring device, and a custom fixture with three high-precision reflective target balls is installed at the robot's end effector. The robot control cabinet is connected to an industrial computer with the calibration software of this invention installed via Ethernet.

[0055] Execution S1: Control the robot via an industrial computer to move at a constant speed to approximately 100 different measurement poses. These poses should cover the workspace as much as possible and the joint angle combinations should be representative. Pause at each pose and record the three-dimensional coordinates of the three target spheres measured by the laser tracker.

[0056] Step S2: In the calibration software, establish the MD-H model of the six-DOF robot. Identify some parameters such as link length and link twist angle as linear parameter set θ_L, and identify parameters such as link offset and joint zero position as nonlinear parameter set θ_NL. The software automatically completes the problem reconstruction.

[0057] Perform S3: The calibration software reads all measurement data.

[0058] First, the pose of the robot's end effector relative to the base coordinate system is calculated based on the coordinates of the three target balls.

[0059] Then, the nonlinear parameters are initialized to theoretical values, and the iterative optimization loop is entered.

[0060] In each iteration, the linear least squares problem is first solved to obtain θ_L, and then the Levenberg-Marquardt algorithm is used to optimize θ_NL in order to minimize the overall error of the worst target ball.

[0061] The iteration terminates when the change in the objective function is less than a preset threshold (e.g., 1e-6), and the identified parameter θ is output. opt .

[0062] Execute S4: Set θ opt The parameters were written into the robot controller parameter table. Subsequently, the robot was controlled to move to 50 uncalibrated verification poses for accuracy testing. Experimental results show that the maximum absolute positioning error of the robot decreased from 2.1 mm before calibration to 0.35 mm, verifying the effectiveness of this method.

[0063] Example 3

[0064] This embodiment provides an industrial robot kinematic parameter calibration system based on parameter separation and multi-objective optimization, used to execute the industrial robot kinematic parameter calibration method based on parameter separation and multi-objective optimization described in Embodiment 1 or 2. The calibration system includes: A high-precision measuring device for acquiring pose information of the robot's end effector, including a laser tracker and multiple target balls mounted on the robot's end effector; Data processing unit for executing linear-nonlinear parameter separation modeling and multi-objective minimax optimization algorithms; The parameter compensation interface is used to write the identification results into the robot controller.

[0065] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calibrating kinematic parameters of industrial robots based on parameter separation and multi-objective optimization, characterized in that, Includes the following steps: Step 1: Collect position information of the robot's end effector in multiple measurement poses; Step 2: Establish the kinematic model of the robot and divide the parameters to be identified into linear and nonlinear sets to reconstruct a separable optimization problem; Step 3: Based on the collected location information, construct a multi-objective minimax optimization problem with the goal of optimizing the worst performance index. By iteratively solving the linear set and the nonlinear set, the kinematic parameters are identified. Step 4: Compensate the optimal kinematic parameters finally identified in Step 3 into the robot controller and update the kinematic model.

2. The method for calibrating kinematic parameters of an industrial robot based on parameter separation and multi-objective optimization according to claim 1, characterized in that, The position information in step 1 includes: measuring the three-dimensional coordinates in space of three target balls fixed to the end of the robot using a laser tracker.

3. The method for calibrating kinematic parameters of industrial robots based on parameter separation and multi-objective optimization according to claim 2, characterized in that, The specific details of step 2 are as follows: Step 2.1: Establish the MD-H model of the industrial robot; Step 2.2: Analyze the structure of the MD-H model and divide the kinematic parameters to be identified into a linear parameter set θ_L and a nonlinear parameter set θ_NL; Step 2.3: Based on Step 2.2, the original problem of robot kinematic parameter identification is reconstructed into a separable optimization problem, with the objective function expressed as: Minimize: Σ || f(θ_NL) · θ_L - P_measured ||², Here, f(θ_NL) is a matrix function composed of nonlinear parameters, and P_measured is the actual measured end position vector. By separating, the original problem is decomposed into a nonlinear least squares subproblem with respect to linear parameters and a low-dimensional nonlinear least squares subproblem with respect to nonlinear parameters.

4. The method for calibrating kinematic parameters of an industrial robot based on parameter separation and multi-objective optimization according to claim 3, characterized in that, The MD-H model describes each link i of the robot using four parameters: link length. ai Linkage torsion angle αi Linkage offset di Joint angle θi The geometric error of each link includes the deviation values ​​Δ of four parameters. ai Δ αi Δ di Δ θi and robot coordinate system error Δ xb Δ yb Δ zb Δ rxb Δ ryb Δ rzb Together with the tool coordinate system error, all error parameters form a vector. θ .

5. The method for calibrating kinematic parameters of an industrial robot based on parameter separation and multi-objective optimization according to claim 4, characterized in that, For any given set of nonlinear parameters θ_NL, the linear parameter θ_L can be directly obtained by linear least squares, i.e.: θ_L = pinv( f(θ_NL) ) · (P_measured - g(θ_NL)), where pinv is the pseudo-inverse operation.

6. The method for calibrating kinematic parameters of an industrial robot based on parameter separation and multi-objective optimization according to claim 2, characterized in that, The specific details of step 3 are as follows: Step 3.1: Using the measurement data of the three target balls in Step 1, calculate the six-dimensional pose of the robot's end effector; Step 3.2: For each measurement pose, calculate the position error corresponding to the three target balls, and use the position error as three independent performance indicators; Step 3.3: Construct a multi-objective minimax optimization problem that takes into account pose information, mathematically expressed as: Minimize [ max( J_ball1(θ), J_ball2(θ), J_ball3(θ) ) ], where J_balli(θ) is the comprehensive position error of the i-th target ball under all measured poses. The optimization objective is to optimize the worst-performing target ball among the three target balls, i.e., the "worst performance index", thereby equivalently achieving the overall optimization of the six-dimensional pose accuracy of the robot's end effector. Step 3.4: Solve using an iterative optimization strategy: First, fix the initial nominal value of the nonlinear parameter θ_NL and solve for the linear parameter θ_L; then, use the solved linear parameter θ_L to optimize the nonlinear parameter θ_NL in the reduced-dimensional space; iterate repeatedly until the objective function converges.

7. A kinematic parameter calibration system for an industrial robot based on parameter separation and multi-objective optimization, used to execute the kinematic parameter calibration method for an industrial robot based on parameter separation and multi-objective optimization as described in any one of claims 1-6, characterized in that, include: A high-precision measuring device for acquiring pose information of the robot's end effector, including a laser tracker and multiple target balls mounted on the robot's end effector; Data processing unit for performing linear-nonlinear parameter separation modeling and multi-objective minimax optimization algorithms; The parameter compensation interface is used to write the identification results into the robot controller.

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