A method for giving structural error in simulation of kinematic calibration of parallel mechanism

Abstract

This invention discloses a method for determining the structural error during kinematic calibration simulation of a parallel mechanism, applicable to the calibration of industrial parallel robots. The method involves establishing structural constraint equations for the parallel mechanism to determine independent variables in the structural parameters; combining the structural constraint equations and independent variable values ​​to calculate the values ​​of non-independent variables in the structural parameters; calculating the motion of each prismatic joint under ideal structural parameter conditions with a given target pose, establishing the correlation between pose parameters and motion; given an initial structural error value, calculating the structural error value conforming to geometric constraints using constraint equations and nonlinear least squares method, and calculating the norm of the residuals. If the residuals meet the requirements, the structural error for kinematic calibration simulation of the parallel mechanism can be generated; if the residual value does not meet the requirements, the generated structural error is used as input, and a new structural error value is generated again using constraint equations and nonlinear least squares method, and the residual calculation is repeated until the residual value meets the requirements, thus generating a structural error that meets the requirements and accurately verifying the structural error identification accuracy of the error model.

Description

Technical Field

[0001] This invention relates to the field of high-precision operation of parallel robots, and in particular to a method for determining structural errors during kinematic calibration simulation of parallel mechanisms. Background Technology

[0002] Parallel robots used in high-precision operations require calibration for operational accuracy before application. Calibration is generally performed using kinematic calibration methods. During kinematic calibration, the accuracy of the established error model needs to be analyzed, i.e., kinematic calibration simulation is conducted. In kinematic calibration simulation, the structural error of the parallel mechanism is first given, then the error model is used to identify the structural error, and the given structural error is compared with the identified structural error. The difference between the two is analyzed to determine the identification accuracy of the error model.

[0003] The structural errors of parallel mechanisms are coupled, and the given error must conform to geometric constraints. Structural errors that do not conform to geometric constraints will lead to a decrease in the identification accuracy of the error model, affecting its practical application. Therefore, it is necessary to propose a method for giving structural errors during kinematic calibration simulation of parallel mechanisms to accurately verify the structural error identification accuracy of the error model. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a method for specifying structural errors during kinematic calibration simulation of parallel mechanisms. This method can accurately specify structural errors that conform to the geometric constraints of parallel mechanisms, thus truly reflecting the accuracy of structural error identification in the error model.

[0005] The proposed technical solution of this invention is as follows: Establish the structural constraint equations of the parallel mechanism to determine the independent variables in the structural parameters; combine the structural constraint equations and the independent variable values ​​to calculate the non-independent variable values ​​in the structural parameters; under ideal structural parameter conditions, calculate the motion of each moving joint when given a target pose, and establish the correlation between pose parameters and motion; given an initial structural error value, calculate the structural error value that conforms to the geometric constraint relationship through the constraint equations and the nonlinear least squares method, and calculate the norm of the residual. If the residual meets the requirements, the structural error during the kinematic calibration simulation of the parallel mechanism can be generated; if the residual value does not meet the requirements, the generated structural error is used as input, and a new structural error value is generated again through the constraint equations and the nonlinear least squares method, and the residual calculation is repeated until the residual value meets the requirements, i.e., a structural error that meets the requirements is generated.

[0006] The beneficial effect of this invention is that, during the kinematic calibration of parallel mechanisms, it can accurately reflect the structural error identification accuracy of the error model established by the kinematic calibration, thereby improving the reliability of the calibration. (1) Ensure that the structural error identification results are stable and have good repeatability, avoid calibration failure caused by random errors, and avoid deviations in subsequent work due to fluctuations in calibration results; (2) Ensure that the identification results are closer to the actual structural error values, reduce the deviation between the identified values ​​and the actual values, provide accurate data for error compensation, and avoid ineffective compensation; (3) Provide technical support for subsequent motion control and precision optimization, reduce equipment trajectory deviation caused by unreliable calibration, improve the stability of parallel mechanism operation, and extend equipment service life. Attached Figure Description

[0007] (1) Figure 1 A schematic diagram illustrating the method for providing structural errors during kinematic calibration simulation of parallel mechanisms.

[0008] (2) Figure 2 This is a schematic diagram of a parallel mechanism. Detailed Implementation

[0009] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0010] like Figures 1-2 As shown:

[0011] A method for specifying structural errors during kinematic calibration simulation of parallel mechanisms, comprising the following steps:

[0012] (1) Establish the structural constraint equations of the parallel mechanism and determine the combination of independent variables in the structural parameters;

[0013] (2) Combining the structural constraint equations, use the combination of independent variables in the structural parameters to represent the combination of non-independent variables in the structural parameters;

[0014] (3) Under ideal structural parameters, calculate the motion of each prismatic joint when the target pose is given, and establish the relationship between pose parameters and motion.

[0015] (4) Given the initial structural error combination e 0. By using constraint equations and nonlinear least squares method, a combination of structural errors that conforms to geometric constraints is fitted and optimized. e 1. Calculate the norm of the residuals;

[0016] (5) If the residuals meet the requirements, the structural errors for kinematic calibration simulation of the parallel mechanism can be generated; if the residuals do not meet the requirements, the generated structural errors will be combined. e 1 is used as input, and through constraint equations and nonlinear least squares method, a new combination of structural errors is generated iteratively again. e 2…… e nThe residual calculation is repeated until the residual value meets the requirements, thus generating a structural error combination that meets the requirements. e n .

[0017] Figure 2 In the symbol, a variable containing 'S' represents a ball joint, and a variable containing 'S' represents a ball joint. X p , Y p , Z p The variable represents the shift joint. O b -x b y b z b Represents the global coordinate system. O t - x t y t z t This indicates the coordinate system of the moving platform.

[0018] Details are as follows:

[0019] (1) Figure 2 The parallel mechanism in the diagram has 3 degrees of freedom. Analysis shows that there are 3 pose parameters (along the global coordinate system). z b Axis translation, about the global coordinate system x b Axis rotation, around the global coordinate system y b (Axis rotation) can be arbitrarily specified in the workspace. Furthermore, other pose parameters (along the global coordinate system) can be calculated from existing pose parameters. x b Axis translation, along the global coordinate system y b Axis translation, about the global coordinate system z b (axis rotation), determine all pose parameters () x , y , z , α , β , γ The structural constraint equations of the parallel mechanism are established through the spatial vector chain, as shown in equation (1):

[0020] (1)

[0021] In equation (1), This represents the z-axis movement of locator 1 in the global coordinate system. , , , , , , , The definition is similar. The actual direction vector of locator 1 is represented by the following method:

[0022] (2)

[0023] In equation (2), This represents the position error of the origin of the coordinate system of locator 2 relative to the global coordinate system in the x-direction. , Definition and similar; This represents the position error of ball joint point 2 relative to the coordinate system of the moving platform in the x-direction. , Definition and Similarly; 900 indicates that the initial Z-axis displacement of each positioner is 900mm; , , , Definition and Similarly. The symbol "||" indicates taking the modulus.

[0024] In equation (1), This indicates the position of the ball joint point corresponding to positioner 1 in the coordinate system of the moving platform, and its value is:

[0025] (3)

[0026] In equation (3), Represents the ideal position of the ball joint point 1 in the coordinate system of the moving platform. x To coordinates, , Definition and Similarly; the symbol "T" indicates transpose. , , Definition and similar.

[0027] In equation (1), This represents the coordinates of the center point of the moving platform in the global coordinate system. ,in, This indicates that the origin of the moving platform coordinate system is in the global coordinate system. x To coordinates, , Definition and similar.

[0028] In equation (1), This represents the attitude transformation matrix of the moving platform relative to the global coordinate system, following the first revolution around the global coordinate system. x b Axis, after orbiting the global coordinate system y b Axis, and finally around the global coordinate system z b The method for calculating the rotation of the shaft is as follows:

[0029] (4)

[0030] In equation (1), Value ,in, Indicates locator 1 z Towards the ideal value of the motion of the moving pair, This represents the error value of the z-axis locator pair motion. , , , Definition and similar. , , , The displacement of the moving pair is the ideal value.

[0031] In equation (1), This represents the coordinates of the origin of the locator's coordinate system relative to the global coordinate system, and its calculation method is the same as... Similarly, add the error value for each direction to the initial coordinates in each direction. , , Definition and similar.

[0032] Equation (1) is the structural constraint equation for the parallel mechanism. Figure 2 For the parallel mechanism shown, the combination of independent variables in its structural parameters is as follows: , , , , , , , , , , , , , , , , , , , , , , , , , , , , .

[0033] (2) Combining the structural constraint equations, use combinations of independent variables in the structural parameters to represent combinations of non-independent variables in the structural parameters. For Figure 2 For the parallel mechanism shown, the combination of non-independent variables is: , , , , The calculation method is shown in equation (2).

[0034] (3) Under ideal structural parameter conditions, calculate the motion of each prismatic joint when the target pose is given, and establish the correlation between pose parameters and motion. For Figure 2 For the parallel mechanism shown, the pose parameters x , y , z , α , β , γ With exercise volume , , , , The relationship between them can be represented as:

[0035] (5)

[0036] In equation (5), i Indicates the locator number, i =1,2,3,4. , , .

[0037] (4) Given the initial structural error combination e 0. By using constraint equations and nonlinear least squares method, a combination of structural errors that conforms to geometric constraints is fitted and optimized. e 1. And calculate the norm of the residual. In MATLAB software, use the lsqnonlin function (nonlinear least squares method), combined with the pose parameters and motion quantities calculated by equation (5), and equation (1), given the initial structural error combination e0 (e.g., [1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0]), optimize the structural error combination that meets the constraint relationship of equation (1). e 1. Calculate the norm of the residuals.

[0038] (5) If the residuals meet the requirements, the structural errors for kinematic calibration simulation of the parallel mechanism can be generated; if the residuals do not meet the requirements, the generated structural errors will be combined. e 1 is used as input, and through constraint equations and nonlinear least squares method, a new combination of structural errors is generated iteratively again. e 2…… e n The residual calculation is repeated until the residual value meets the requirements, thus generating a structural error combination that meets the requirements. e n .

[0039] The parts not covered in this invention are the same as or can be implemented using existing technologies.

[0040] For those skilled in the art, various modifications and improvements can be made without departing from the concept of this invention, and these all fall within the scope of protection of this invention.

Claims

1. A method for determining structural errors during kinematic calibration simulation of parallel mechanisms, characterized by: Establish the structural constraint equations of the parallel mechanism and determine the independent variables in the structural parameters; combine the structural constraint equations and the values ​​of independent variables to calculate the values ​​of non-independent variables in the structural parameters; under ideal structural parameter conditions, calculate the motion of each prismatic joint when given a target pose, and establish the correlation between pose parameters and motion; given an initial structural error value, calculate the structural error value that meets the geometric constraint relationship through constraint equations and nonlinear least squares method, and calculate the norm of the residuals. If the residuals meet the requirements, the structural error for kinematic calibration simulation of the parallel mechanism can be generated. If the residual value does not meet the requirements, the generated structural error is used as input, and a new structural error value is generated again through constraint equations and nonlinear least squares method. The residual calculation is repeated until the residual value meets the requirements, that is, a structural error that meets the requirements is generated.

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