Passive derivative linear motion error compensation method for electric cylinder of six-degree-of-freedom electric platform

Abstract

The invention relates to a passive derivative linear motion error compensation method for electric cylinders of a six-degree-of-freedom electric platform, and the method comprises the steps: building a kinematics inverse solution equation of six-degree-of-freedom mechanical environment simulation equipment, and obtaining the motion telescoping amount of six electric cylinders; establishing a motion equation of a six-degree-of-freedom mechanical environment simulation equipment branch chain; the rotating angle of the cylinder rod of the electric cylinder relative to the cylinder barrel is calculated through the variable quantity of the vector included angle between the cylinder rod fixing end of the upper hooke joint assembly and the cylinder barrel fixing end of the lower hooke joint assembly; calculating an error caused by passive derivative linear motion of the electric cylinder according to a motion equation of a six-degree-of-freedom mechanical environment simulation equipment branch chain; and correcting the elongation amount of the electric cylinder obtained by the kinematics inverse solution as the error amount to obtain the corrected control elongation amount of the electric cylinder. Therefore, the position and attitude precision of the six-degree-of-freedom mechanical environment simulation equipment for spaceflight inertial navigation product performance test and semi-physical simulation test can meet the technical index requirements.

Description

Technical Field

[0001] This invention belongs to the technical field of six-degree-of-freedom mechanical environment simulation equipment, and relates to a method for compensating for the error of passively derived linear motion of an electric cylinder on a six-degree-of-freedom electric platform. Background Technology

[0002] The six-degree-of-freedom (DOF) mechanical environment simulation equipment for aerospace inertial navigation product performance testing and hardware-in-the-loop (HIL) simulation experiments employs a 6-UCU type high-precision six-DOF parallel mechanism driven by electric cylinders. Through the coordinated extension, retraction, and rotation of the six electric cylinders, combined with the two-DOF follower rotation of the upper and lower Hooke hinge components, the upper platform achieves six-DOF motion in three-dimensional space: longitudinal, lateral, vertical, roll, pitch, and yaw. This provides a near-realistic mechanical simulation environment for inertial navigation product performance testing and HIL simulation. Because the electric cylinders achieve linear motion of the cylinder rod through a helical pair, and there is a helical relationship between its linear and rotational motions, the passive rotation of the cylinder rod relative to the cylinder barrel leads to a passively derived linear motion of the cylinder rod, causing corresponding errors that affect the actual position and attitude accuracy of the six-DOF mechanical environment simulation equipment.

[0003] Existing 6-UCU six-degree-of-freedom mechanical environment simulation equipment for performance testing and hardware-in-the-loop simulation of low-to-medium precision aerospace inertial navigation products typically treats errors caused by the passively derived linear motion of electric cylinders as system errors and does not compensate for them as long as the accuracy meets technical requirements. However, for six-degree-of-freedom mechanical environment simulation equipment for performance testing and hardware-in-the-loop simulation of high-precision aerospace inertial navigation products, one existing method is to add a rotational degree of freedom around the electric cylinder axis to the electric cylinder with an internal anti-rotation mechanism. This makes the axial extension and rotational motion of the electric cylinder lever independent of its rotational motion, fundamentally eliminating the derived linear motion. This method increases the cost of the electric cylinder and the complexity of the system. Another method is to add a high-precision linear displacement sensor to the outside of the electric cylinder and use the feedback signal from the displacement sensor to achieve closed-loop position control of the electric cylinder. This method requires an additional high-precision displacement sensor and additional acquisition channels in the motion control computer, similarly increasing the development cost and complexity of the system. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose a method for compensating for the error of passively derived linear motion of electric cylinders in a six-degree-of-freedom electric platform. This method compensates for the error caused by the passively derived linear motion of electric cylinders during the movement of a six-degree-of-freedom mechanical environment simulation device, so that the position and attitude accuracy of the six-degree-of-freedom mechanical environment simulation device used for performance testing of aerospace inertial navigation products and hardware-in-the-loop simulation experiments meets the technical requirements.

[0005] The solution to the technical problem of this invention is: a method for compensating for the error of passively derived linear motion of a six-degree-of-freedom electric platform electric cylinder, comprising the following steps: Establish the coordinate system of the six-degree-of-freedom mechanical environment simulation device, including the inertial coordinate system and the volume coordinate system, and then establish the inverse kinematic equation of the six-degree-of-freedom mechanical environment simulation device to obtain the motion extension and contraction of the six electric cylinders; Establish the motion equations of the six-degree-of-freedom mechanical environment simulation equipment branch: Construct a single-branch closed-loop drive system of electric cylinder + servo motor + encoder + driver, and on this basis, establish the motion equations between the linear displacement output of the electric cylinder rod and the rotation angle input of the servo motor. An equation for the rotation angle between the cylinder rod and cylinder barrel of the electric cylinder is constructed in the inertial coordinate system: the rotation angle of the cylinder rod relative to the cylinder barrel is calculated by the change in the vector angle between the fixed end of the upper Hooke hinge assembly and the fixed end of the lower Hooke hinge assembly. , i =1~6; Based on the relative rotation angle , i =1~6, combined with the motion equations of the branches of the six-degree-of-freedom mechanical environment simulation equipment, the error caused by the passively derived linear motion of the electric cylinder is calculated. ; Will The elongation of the electric cylinder obtained from the inverse kinematics solution is corrected as an error quantity to obtain the corrected control elongation of the electric cylinder.

[0006] Furthermore, the coordinate system for establishing the six-degree-of-freedom mechanical environment simulation device is specifically as follows: Establish an inertial coordinate system at the center of the plane of the lower Hooke's hinge assembly. g}: O g - X g Y g Z g Establish a body coordinate system at the center of the plane of the upper Hooke hinge assembly. p}:O p - X p Y p Z p The rotation center coordinates of the upper and lower Hooke hinge components are respectively A i , B i , i =1~6; The rotation center of the upper Hooke hinge assembly is in the body coordinate system { pThe coordinates under} are represented as follows: a i p =[ a ix p , a iy p , a iz p ] T , i =1,…,6, the rotation center of the lower Hooke's hinge assembly is in the inertial coordinate system { g The coordinates under} are represented as follows: b i =[ b ix , b iy , b iz ] T , i =1,…,6; use t =[ x , y , z ] T This represents the coordinate vector of the origin of the volume coordinate system in the inertial coordinate system. ω This represents the angular velocity vector of the upper platform.

[0007] Furthermore, the inverse kinematic equations for establishing the six-degree-of-freedom mechanical environment simulation device are specifically as follows: Length vector of 6 electric cylinders , i =1~6 represents ,in R Let be the rotation transformation matrix, representing the coordinate transformation from the inertial coordinate system to the volume coordinate system; using Z ψ - Y θ - X φ The order of transformation, R The expression is:

[0008] in ψ , θ , φ To show the attitude of going to the platform q t The three Euler angles are called yaw, pitch, and roll, respectively. c represents cosine, s represents sinine; assuming the length of the electric cylinder is... L i ,i =1,2,…,6, then Therefore, the extension and retraction of the electric cylinder is ,in Let the initial length of the electric cylinder be the value of the six-degree-of-freedom mechanical environment simulation device when it is in the zero-position; and assume the generalized coordinates of the platform on the six-degree-of-freedom mechanical environment simulation device. q It is known that the extension and retraction of the six electric cylinders can be calculated using the above formulas.

[0009] Furthermore, the equations of motion for the branches of the six-degree-of-freedom mechanical environment simulation device are established as follows: Assume the rotation angle of the servo motor is β Using the principle of the lead screw and nut, the linear motion of the electric cylinder can be expressed as: ,in P n is the lead of the electric cylinder lead screw. If the lead screw turns right, n is 2; if the lead screw turns left, n is 1.

[0010] Furthermore, the calculated rotation angle of the electric cylinder rod relative to the cylinder barrel... Specifically: In the inertial coordinate system { g Under}, using vectors k i , j i This represents the unit direction vector of the two axes of the upper Hooke's hinge assembly. m i , n i This represents the unit direction vector of the two axes of the lower Hooke hinge assembly. The change in the rotation angle between the cylinder rod and the cylinder barrel is represented by this vector. k i and m i The change in the included angle is used to represent the vector; j i Represented as ,in Let be the unit vector of the connection axis between the upper Hooke hinge assembly and the upper platform in the body coordinate system; according to the structural form of the two-degree-of-freedom Hooke hinge, we have , , , Then the vector k i , i =1,2,…,6 and m i , i =1,2,…,6 is represented as: , , i=1,2,…,6; therefore, k i and m i The size of the spatial angle is expressed as: , i =1,2,…,6; The formula obtained from the above is... Modify the initial vector between 0° and 180°. The default positive direction is the angle calculated when the upper platform is at the working zero position. Normalize to the range of 0° to 90° using the following method:

[0011] Let counterclockwise rotation of the cylinder rod relative to the cylinder barrel be defined as positive. Then, the relative rotation angle is expressed as... , i =1,2,…,6; where When the platform on the six-degree-of-freedom mechanical environment simulation device is in the working zero position, the vector... k i and m i The initial included angle; l z It is a unit vector. l z =(0, 0, 1).

[0012] Furthermore, the error caused by the passively derived linear motion of the electric cylinder is calculated. As shown below: , i =1~6.

[0013] Furthermore, based on the error It can also obtain the position and attitude errors of the platform on the six-degree-of-freedom mechanical environment simulation device caused by the passive derivative motion of the electric cylinder: ,in It is the Jacobian matrix that represents the changes in position and attitude of the upper platform due to the change in the length of the electric cylinder.

[0014] A computer-readable storage medium storing a computer program, wherein when executed by a processor, the computer program implements the steps of the passive derived linear motion error compensation method for the electric cylinder of the six-degree-of-freedom electric platform.

[0015] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the passive derived linear motion error compensation method for the electric cylinder of the six-degree-of-freedom electric platform.

[0016] A computer program product includes a computer program that, when executed by a processor, implements the steps of the passive derived linear motion error compensation method for the electric cylinder of the six-degree-of-freedom electric platform.

[0017] The advantages of this invention compared to the prior art are: (1) The present invention compensates for the error caused by the passive linear motion of the electric cylinder. Compared with other applications that ignore this error, it significantly improves the position and attitude accuracy of the six-degree-of-freedom mechanical environment simulation equipment used for performance testing of aerospace inertial navigation products and hardware-in-the-loop simulation test.

[0018] (2) Compared with adding a rotational degree of freedom around the axis of the electric cylinder to the electric cylinder with an internal anti-rotation mechanism to meet the six degrees of freedom of the upper platform in space for the degree of freedom of a single motion chain, the present invention is easier to implement, less difficult to implement in engineering, requires lower hardware costs, and is easier to apply in engineering practice.

[0019] (3) Compared to adding a high-precision linear displacement sensor to the outside of the electric cylinder and using the feedback signal of the displacement sensor to achieve closed-loop control of the electric cylinder position, this invention, while fully ensuring the position and attitude accuracy of the six-degree-of-freedom mechanical environment simulation device, has the advantages of being easier to implement, requiring lower hardware costs, and being easier to apply in practical engineering. This method is also applicable to other 6-UCU type six-degree-of-freedom motion platforms driven by electric cylinders and is suitable for widespread application. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the platform components of the six-degree-of-freedom mechanical environment simulation device of the present invention; Figure 2 This is a coordinate schematic diagram of the six-degree-of-freedom mechanical environment simulation device of the present invention; Figure 3 This is a block diagram illustrating the control principle of the six-degree-of-freedom mechanical environment simulation device system of the present invention; Figure 4 This is a vector diagram showing the structural components of the electric cylinder and the upper and lower Hooke hinge components of the present invention. Figure 5 This is a block diagram illustrating the principle of the passive linear motion error compensation algorithm for the electric cylinder of the present invention. Detailed Implementation

[0021] This invention aims to propose a method for compensating for the passive derived linear motion error of the electric cylinder in a 6-UCU type six-degree-of-freedom electric motion platform. By mathematically modeling the derived linear motion caused by the passive rotation of the electric cylinder rod relative to the cylinder barrel during the motion of a six-degree-of-freedom mechanical environment simulation device used in aerospace inertial navigation product performance testing and hardware-in-the-loop simulation experiments, and calculating and analyzing this error model, a method for compensating for the passive derived linear motion error of the electric cylinder is proposed. This method is implemented through motion control software, which compensates for the error in real time during platform motion, thereby eliminating the error and improving the actual position and attitude accuracy of the six-degree-of-freedom electric motion platform. This method is also applicable to other 6-UCU type six-degree-of-freedom motion platforms driven by electric cylinders.

[0022] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0023] Example 1 like Figure 1 As shown, in this embodiment, the six-degree-of-freedom mechanical environment simulation equipment for aerospace inertial navigation product performance testing and hardware-in-the-loop simulation experiment adopts a 6-UCU type high-precision six-degree-of-freedom parallel mechanism driven by electric cylinders. The six electric cylinders 3 are driven by servo motor 4. Under the control of motion control algorithm, the six electric cylinders perform coordinated extension and rotation movements. Combined with the two-degree-of-freedom follow-rotation of the upper Hooke hinge assembly 2 and the lower Hooke hinge assembly 5, the upper platform 1 realizes six-degree-of-freedom movements of longitudinal translation, lateral translation, lifting and lowering, as well as roll, pitch and yaw in three-dimensional space, providing a near-realistic mechanical simulation environment for inertial navigation product performance testing and hardware-in-the-loop simulation.

[0024] The present invention proposes a method for compensating for the passively derived linear motion error of a six-degree-of-freedom electric platform electric cylinder, comprising the following steps: S1. Establish the coordinate system of the six-degree-of-freedom mechanical environment simulation device, including the inertial coordinate system and the volume coordinate system, and then establish the inverse kinematic equation of the six-degree-of-freedom mechanical environment simulation device to obtain the motion extension and contraction of the six electric cylinders.

[0025] like Figure 2 As shown, the rotation centers of the Hooke's hinge assembly and the lower Hooke's hinge assembly on the six-degree-of-freedom mechanical environment simulation device are located at radii of... r a and r b On the circumference. Establish an inertial coordinate system at the center of the plane of the lower Hooke's hinge assembly. g}: O g - X g Y g Z gEstablish a body coordinate system at the center of the plane of the upper Hooke hinge assembly. p}:O p - X p Y p Z p The coordinates of the rotation centers of the upper and lower Hooke hinge components are respectively... A i , B i ( i =1~6). The rotation center of the upper Hooke hinge assembly is in the body coordinate system { p The coordinates under} are represented as follows: a i p =[ a ix p , a iy p , a iz p ] T , i =1,…,6, the rotation center of the lower Hooke's hinge assembly is in the inertial coordinate system { g The coordinates under} are represented as follows: b i =[ b ix , b iy , b iz ] T , i =1,…,6. Use t =[ x , y , z ] T This represents the coordinate vector of the origin of the volume coordinate system in the inertial coordinate system. ω This represents the angular velocity vector of the upper platform.

[0026] Based on spatial vector relationships, the length vectors of the six electric cylinders... ( i =1~6) can be represented as ,in R Let be the rotation transformation matrix, representing the coordinate transformation from the inertial coordinate system to the volume coordinate system. (Using...) Z ψ - Y θ - X φ The order of transformation, therefore RThe expression is:

[0027] in ψ , θ , φ To show the attitude of going to the platform q t The three Euler angles are called yaw, pitch, and roll. c represents cosine, and s represents sinine. Assume the length of the electric cylinder is... L i ( i =1,2,…,6), then Therefore, the extension and retraction of the electric cylinder is ,in Let this be the initial length of the electric cylinder when the six-degree-of-freedom mechanical environment simulation device is in its zero-position. Therefore, assume the generalized coordinates of the platform on the six-degree-of-freedom mechanical environment simulation device. q It is known that the extension and retraction of the six electric cylinders can be calculated using the above formulas. Based on this, the electric cylinders can be controlled by a servo motor to perform reciprocating linear motion, so that the upper platform can move according to the trajectory given by the control command.

[0028] S2. Establish the motion equations of the six-degree-of-freedom mechanical environment simulation equipment branch: Construct a single-branch closed-loop drive system of electric cylinder + servo motor + encoder + driver, and on this basis, establish the motion equations between the linear displacement output of the electric cylinder rod and the rotation angle input of the servo motor.

[0029] The six-degree-of-freedom mechanical environment simulation device has six branches, such as Figure 3 As shown, a single branch consists of an electric cylinder, a servo motor, an angle encoder, and a driver. The motion control card in the six-degree-of-freedom mechanical environment simulation device receives instructions from the motion control computer, controlling the driver to drive the servo motor. The servo motor outputs corresponding torque and speed, which in turn drives the electric cylinder to achieve the corresponding linear reciprocating motion. Simultaneously, the angle encoder installed on the servo motor collects and feeds back the servo motor's rotation angle and speed information in real time, realizing closed-loop control of a single branch. Therefore, the motion equation between the linear displacement output of the electric cylinder rod and the rotation of the servo motor can be established. Assume the rotation angle of the servo motor is... β Using the principle of lead screw and nut, the linear motion of the electric cylinder can be expressed as: ,in P n is the lead of the electric cylinder lead screw. If the lead screw turns right, n is 2; if the lead screw turns left, n is 1.

[0030] S3. Construct the equation for the rotation angle between the electric cylinder rod and the cylinder barrel in the inertial coordinate system: Calculate the rotation angle of the electric cylinder rod relative to the cylinder barrel by measuring the change in the vector angle between the fixed end of the upper Hooke hinge assembly and the fixed end of the lower Hooke hinge assembly. , i =1~6.

[0031] like Figure 4 As shown, in the inertial coordinate system { g Under}, using vectors k i , j i This represents the unit direction vector of the two axes of the upper Hooke's hinge assembly. m i , n i This represents the unit direction vector of the two axes of the lower Hooke's hinge assembly. The change in the rotation angle between the cylinder rod and the cylinder barrel can be represented by this vector. k i and m i The change in the included angle is used to represent the vector. j i It can be represented as ,in Let be the unit vector of the connection axis between the upper Hooke's hinge assembly and the upper platform in the body coordinate system. Based on the structural form of a two-degree-of-freedom Hooke's hinge, we have... , , , Then the vector k i , i =1,2,…,6 and m i , i =1,2,…,6 can be represented as: , , i =1,2,…,6; therefore, k i and m i The size of the spatial angle can be expressed as: , i =1,2,…,6; The formula is obtained from this. Modify the initial vector between 0° and 180°. The default positive direction is the angle calculated when the upper platform is at the working zero position. Normalization to the range of 0° to 90° is achieved using the following method:

[0032] Let counterclockwise rotation of the cylinder rod relative to the cylinder barrel be defined as positive. Then, the relative rotation angle can be expressed as: , i =1,2,…,6; where When the platform on the six-degree-of-freedom mechanical environment simulation device is in the working zero position, the vector... k i and m i The initial included angle; l z It is a unit vector. l z =(0, 0, 1).

[0033] S4. Based on the relative rotation angle , i =1~6, combined with the motion equations of the branches of the six-degree-of-freedom mechanical environment simulation equipment, the error caused by the passively derived linear motion of the electric cylinder is calculated. .

[0034] The extension and retraction changes of each electric cylinder caused by passive derivative motion can be expressed as: , i =1~6, then the position and attitude errors of the platform on the six-degree-of-freedom mechanical environment simulation device caused by the passive derived motion of the electric cylinder can be expressed as: ,in It is the Jacobian matrix that represents the changes in position and attitude of the upper platform due to the change in the length of the electric cylinder.

[0035] S5, will The elongation of the electric cylinder obtained from the inverse kinematics solution is corrected as an error quantity to obtain the corrected control elongation of the electric cylinder.

[0036] Based on the above principles, a method for compensating for passive linear motion errors of electric cylinders was developed using software. Figure 5 The principle block diagram of the compensation method is shown below, and its specific implementation is as follows: First, by q i =(i=1, 2, … , 6) to calculate the relative rotation angle change in real time. And the resulting additional elongation of the electric cylinder. Then, As an error quantity, the elongation of the electric cylinder obtained from the inverse kinematics solution By making corrections, the controlled elongation of the electric cylinder can be obtained. This invention utilizes a graphical programming language to develop software that implements the error compensation method. A software module for the error compensation method is developed and embedded into the real-time motion control system software of the six-degree-of-freedom mechanical environment simulation device. The single-branch motion control of the six-degree-of-freedom mechanical environment simulation device compensates for the error, ensuring that the position and attitude accuracy of the six-degree-of-freedom mechanical environment simulation device used for inertial device testing meets the technical specifications.

[0037] This application provides a computer-readable storage medium storing computer instructions that, when executed on a computer, cause the computer to perform... Figure 5 The method described.

[0038] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage and optical storage) containing computer-usable program code.

[0039] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0040] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0041] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0042] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

[0043] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for compensating for the error of passively derived linear motion of an electric cylinder on a six-degree-of-freedom electric platform, characterized in that: Includes the following steps: Establish the coordinate system of the six-degree-of-freedom mechanical environment simulation device, including the inertial coordinate system and the volume coordinate system, and then establish the inverse kinematic equation of the six-degree-of-freedom mechanical environment simulation device to obtain the motion extension and contraction of the six electric cylinders; Establish the motion equations of the six-degree-of-freedom mechanical environment simulation equipment branch: Construct a single-branch closed-loop drive system of electric cylinder + servo motor + encoder + driver, and on this basis, establish the motion equations between the linear displacement output of the electric cylinder rod and the rotation angle input of the servo motor. An equation for the rotation angle between the cylinder rod and cylinder barrel of the electric cylinder is constructed in the inertial coordinate system: the rotation angle of the cylinder rod relative to the cylinder barrel is calculated by the change in the vector angle between the fixed end of the upper Hooke hinge assembly and the fixed end of the lower Hooke hinge assembly. , i =1~6; Based on the relative rotation angle , i =1~6, combined with the motion equations of the branches of the six-degree-of-freedom mechanical environment simulation equipment, the error caused by the passively derived linear motion of the electric cylinder is calculated. ; Will The elongation of the electric cylinder obtained from the inverse kinematics solution is corrected as an error quantity to obtain the corrected control elongation of the electric cylinder.

2. The method for compensating for the passively derived linear motion error of a six-degree-of-freedom electric platform electric cylinder according to claim 1, characterized in that, The coordinate system for establishing the six-degree-of-freedom mechanical environment simulation device is specifically as follows: Establish an inertial coordinate system at the center of the plane of the lower Hooke's hinge assembly. g }: O g - X g Y g Z g Establish a body coordinate system at the center of the plane of the upper Hooke hinge assembly. p }:O p - X p Y p Z p The rotation center coordinates of the upper and lower Hooke hinge components are respectively A i , B i , i =1~6; The rotation center of the upper Hooke hinge assembly is in the body coordinate system { p The coordinates under} are represented as follows: a i p =[ a ix p , a iy p , a iz p ] T , i =1,…,6, the rotation center of the lower Hooke's hinge assembly is in the inertial coordinate system { g The coordinates under} are represented as follows: b i =[ b ix , b iy , b iz ] T , i =1,…,6; use t =[ x , y , z ] T This represents the coordinate vector of the origin of the volume coordinate system in the inertial coordinate system. ω This represents the angular velocity vector of the upper platform.

3. The method for compensating for the passively derived linear motion error of a six-degree-of-freedom electric platform electric cylinder according to claim 2, characterized in that, The inverse kinematic equations for establishing the six-degree-of-freedom mechanical environment simulation device are as follows: Length vector of 6 electric cylinders , i =1~6 represents ,in R Let be the rotation transformation matrix, representing the coordinate transformation from the inertial coordinate system to the volume coordinate system; using Z ψ - Y θ - X φ The order of transformation, R The expression is: in ψ , θ , φ To show the attitude of going to the platform q t The three Euler angles are called yaw, pitch, and roll, respectively. c represents cosine, s represents sinine; assuming the length of the electric cylinder is... L i , i =1,2,…,6, then Therefore, the extension and retraction of the electric cylinder is ,in Let the initial length of the electric cylinder be the value of the six-degree-of-freedom mechanical environment simulation device when it is in the zero-position; and assume the generalized coordinates of the platform on the six-degree-of-freedom mechanical environment simulation device. q It is known that the extension and retraction of the six electric cylinders can be calculated using the above formulas.

4. The method for compensating for the passively derived linear motion error of a six-degree-of-freedom electric platform electric cylinder according to claim 3, characterized in that, The equations of motion for the branches of the six-degree-of-freedom mechanical environment simulation device are established as follows: Assume the rotation angle of the servo motor is β Using the principle of the lead screw and nut, the linear motion of the electric cylinder can be expressed as: ,in P n is the lead of the electric cylinder lead screw. If the lead screw turns right, n is 2; if the lead screw turns left, n is 1.

5. The method for compensating for the passively derived linear motion error of a six-degree-of-freedom electric platform electric cylinder according to claim 4, characterized in that, The calculated rotation angle of the electric cylinder rod relative to the cylinder barrel is... Specifically: In the inertial coordinate system { g Under}, using vectors k i , j i This represents the unit direction vector of the two axes of the upper Hooke's hinge assembly. m i , n i This represents the unit direction vector of the two axes of the lower Hooke hinge assembly. The change in the rotation angle between the cylinder rod and the cylinder barrel is represented by this vector. k i and m i The change in the included angle is used to represent this; vector j i Represented as ,in Let be the unit vector of the connection axis between the upper Hooke hinge assembly and the upper platform in the body coordinate system; according to the structural form of the two-degree-of-freedom Hooke hinge, we have , , , Then the vector k i , i =1,2,…,6 and m i , i =1,2,…,6 is represented as: 、 ， i =1,2,…,6； therefore, k i and m i The size of the spatial angle is expressed as: ， i =1,2,…,6； The formula obtained from the above is... Modify the initial vector between 0° and 180°. The default positive direction is the angle calculated when the upper platform is at the working zero position. Normalize to the range of 0° to 90° using the following method: Let counterclockwise rotation of the cylinder rod relative to the cylinder barrel be defined as positive. Then, the relative rotation angle is expressed as... , i =1,2,…,6; where When the platform on the six-degree-of-freedom mechanical environment simulation device is in the working zero position, the vector... k i and m i The initial included angle; l z It is a unit vector. l z =(0, 0, 1).

6. The method for compensating for the passively derived linear motion error of a six-degree-of-freedom electric platform electric cylinder according to claim 5, characterized in that, The error caused by the passive linear motion of the electric cylinder is calculated. As shown below: ， i =1~6。 7. The method for compensating for the passively derived linear motion error of a six-degree-of-freedom electric platform electric cylinder according to claim 6, characterized in that, According to error It can also obtain the position and attitude errors of the platform on the six-degree-of-freedom mechanical environment simulation device caused by the passive derivative motion of the electric cylinder: ,in It is the Jacobian matrix that represents the changes in position and attitude of the upper platform due to the change in the length of the electric cylinder.

8. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 7.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 7.

Images