Parallel positioning platform construction method, system and equipment

Abstract

The invention belongs to the field of space positioning, and particularly discloses a parallel positioning platform construction method, system and equipment, and the method comprises the steps: obtaining the space size of a working environment of a to-be-constructed parallel positioning platform and a material database of parts; establishing an accurate constraint model of the parallel positioning platform; determining constraint conditions of the precise constraint model according to the space size and the material database, and determining an optimization objective function of the precise constraint model; determining an optimal parameter solution set of the parallel positioning platform by using a multi-objective optimization algorithm based on the precise constraint model, the constraint condition and the optimization objective function; the optimal parameter solution set comprises an effective stroke, a coupling diameter, a skewed slot inclination angle and a metal ball diameter of the actuator; and constructing the parallel positioning platform based on the optimal parameter solution set, so that the parallel positioning platform has the maximum working space in the working environment. The working space of the parallel platform can be utilized to the maximum extent, and meanwhile the compactness of the parallel positioning platform is kept.

Description

Technical Field

[0001] The present application relates to the field of spatial positioning, and more specifically, to a method, system, and device for constructing a parallel positioning platform. Background Art

[0002] In the field of biomedical photonics, the position and posture of image detectors such as complementary metal oxide semiconductor (CMOS) and charge-coupled device (CCD) in microscopic optical imaging systems require precise adjustment, which generally relies on full-degree-of-freedom positioning devices.

[0003] A common approach involves serially mounting a linear displacement stage and a rotational stage. By sequentially connecting multiple translation and rotation units, the detector can be adjusted in multiple degrees of freedom. While this approach is structurally simple, geometric errors in the kinematic chain are transmitted and accumulated step by step, significantly reducing positioning accuracy. Furthermore, the repeated axial stacking results in excessive longitudinal dimensions, making it difficult to fit within the confined interior space of an instrument. This makes it difficult to meet the compactness and accuracy requirements of high-precision optical systems.

[0004] Another approach is a six-axis parallel positioning platform based on the traditional Stewart platform. This solution improves positioning accuracy by introducing position sensors and feedback control systems. The six-axis parallel positioning platform uses parallel actuators and linkages, combined with a position feedback system, to precisely control the detector's position and posture. However, the inherent symmetry and linkage layout of the traditional Stewart platform often require full consideration of motion interference between actuators during kinematic calculations. This significantly limits the effective workspace in compact installation scenarios (such as multi-channel simultaneous imaging acquisition in confocal microscopy).

[0005] Therefore, how to increase the working space of the parallel positioning platform while taking into account the compactness of the structure is a technical problem that needs to be solved urgently. Summary of the Invention

[0006] In view of the shortcomings of the existing technology, the purpose of this application is to provide a method, system and equipment for constructing a parallel positioning platform, aiming to increase the working space of the parallel positioning platform while taking into account the compactness of the structure.

[0007] To achieve the above objectives, in a first aspect, the present application provides a method for constructing a parallel positioning platform, comprising: Obtain the space size of the working environment of the parallel positioning platform to be constructed and the material database of the components; Establish an accurate constraint model for the parallel positioning platform; According to the space size and material database, the constraint conditions of the precise constraint model are determined, and the optimization objective function of the precise constraint model is determined; the optimization objective function is used to characterize the translation space volume and rotation space volume of the parallel positioning platform; Based on the precise constraint model, constraint conditions, and optimization objective function, a multi-objective optimization algorithm is used to determine the optimal parameter solution set for the parallel positioning platform. The optimal parameter solution set includes the effective stroke of the actuator, coupling diameter, chute angle, and metal ball diameter. A parallel positioning platform is constructed based on the optimal parameter solution set so that the parallel positioning platform has the largest working space in the working environment.

[0008] Optionally, the constraint condition includes a volume constraint, and the method for determining the volume constraint includes: Determine the maximum height, length, and width of the work environment; Determine the maximum range of motion in the plane direction according to the maximum length and maximum width; Obtain the platform height and the effective stroke of the actuator when the actuator is reset, calculate the symbolic representation of the additional height generated by the effective stroke and the inclination angle of the chute, ensure that the sum of the platform height and the additional height when the actuator is reset is less than the maximum height, obtain the upper limit of the inclination angle of the chute, and determine the upper and lower limits of the coupling radius, which are used as input parameters for the subsequent workspace optimization function.

[0009] Optionally, the constraint condition further includes a rotation resolution constraint, and a method for determining the rotation resolution constraint and the coupling radius includes: The parallel positioning platform's rotational resolution is set according to the working condition requirements, and the set rotational resolution is used as the minimum increment of posture change. The joint displacement increments corresponding to the six actuators of the parallel positioning platform under the minimum increment are calculated; Obtaining the minimum step of the actuator, traversing the value range of the coupling radius within the adjustable interval, gradually decreasing and increasing the coupling radius, and determining whether the displacement increments of the six joints are all greater than or equal to the minimum step of the actuator; The coupling radius corresponding to the minimum step of the actuator is used as the lower limit of the coupling radius. The coupling radius that satisfies the maximum range of the platform is used as the upper limit. The feasible value range of the coupling radius is determined according to the upper and lower limits of the determined coupling radius, and is used as an input parameter of the subsequent workspace optimization function.

[0010] Optionally, the constraint condition further includes a Hertz limit constraint, and a method for determining the Hertz limit constraint includes: Obtain the load, the contact radius between the chute and the metal ball, and the yield limit of the kinematic pair material; The contact pressure between the chute and the metal ball is determined according to the load force and the contact radius, ensuring that the contact pressure does not exceed the yield limit of the material.

[0011] Optionally, determining the optimization objective function of the precise constraint model includes: According to the precise constraint model, an inverse kinematics equation of the parallel positioning platform is obtained; Based on the inverse kinematics equation, a forward kinematics equation of the parallel positioning platform is obtained; According to the kinematics forward equation, the full posture workspace of the parallel positioning platform is obtained; The full-pose workspace is decomposed into a position space and a rotation space, and the convex hull volumes of the position space and the rotation space are solved to obtain an optimization objective function that characterizes the translation space volume and the rotation space volume of the parallel positioning platform.

[0012] Optionally, the method for solving the inverse kinematic equation includes: Obtain the displacement of the parallel positioning platform in the x-axis, y-axis and z-axis directions, and the rotation angles around the x-axis, y-axis and z-axis; the x-axis, y-axis and z-axis are the horizontal direction, vertical direction and height direction of the parallel positioning platform respectively; Construct the inverse kinematic matrix based on the cotangent value of the inclined slot angle, the direction vectors of each actuator, and the coordinates of the metal ball in the moving coordinate system; The kinematic inverse matrix is ​​used to calculate the six joint displacement increments in combination with the platform displacement and rotation angle.

[0013] Optionally, the kinematics forward solution equation is: constructing a vector matrix according to the maximum displacement increments of the six joints; A motion matrix is ​​constructed based on the cotangent value of the inclined groove angle, the direction vectors of each actuator, and the coordinates of the metal ball in the moving coordinate system; Inverting the motion matrix to obtain an inverse matrix of the motion matrix; The full-posture workspace of the parallel positioning platform is obtained by multiplying the inverse matrix with the vector matrix.

[0014] Optionally, it also includes: The velocity constraint of the parallel positioning platform is determined by differentiating the inverse kinematics equation with respect to time, thereby obtaining a Jacobian matrix of the parallel positioning platform; Dividing the Jacobian matrix into blocks to obtain translation velocity blocks and rotation velocity blocks to simplify kinematic calculations and subsequent feedforward control; The kinematic derivation process of the translation velocity block is completely independent of the rotation state of the parallel positioning platform and is separated from the kinematic iterative calculation in a pre-hardcoded manner; the rotation velocity block is replaced by a small-angle approximation of the rotation matrix during the motion control process, or only a separate iterative calculation is performed to update the rotation velocity block.

[0015] In a second aspect, the present application further provides a parallel positioning platform construction system, comprising: A data acquisition module is used to obtain the spatial size of the working environment of the parallel positioning platform to be constructed and the material database of the components; Model building module, used to build accurate constraint model of parallel positioning platform; a target determination module, configured to determine the constraint conditions of the precise constraint model based on the space size and the material database, and to determine an optimization objective function of the precise constraint model; the optimization objective function is used to characterize the translational space volume and the rotational space volume of the parallel positioning platform; a parameter solving module, configured to determine an optimal parameter solution set of the parallel positioning platform using a multi-objective optimization algorithm based on the precise constraint model, the constraint conditions, and the optimization objective function; the optimal parameter solution set includes the effective stroke of the actuator, the coupling diameter, the chute inclination, and the metal ball diameter; The platform construction module is used to construct a parallel positioning platform based on the optimal parameter solution set, so that the parallel positioning platform has a maximum working space in a working environment.

[0016] The present application also provides a parallel positioning platform constructed based on the method described in any one of the above items, characterized in that it includes a top cover and three ball slot mechanisms arranged at the bottom of the top cover; each ball slot mechanism includes a metal ball, an actuator, an inclined slot and a guide rail; the actuator is used to push the inclined slot to move linearly on the guide rail, so that the inclined slot and the metal ball form a kinematic pair through point contact to adjust the position of the top cover.

[0017] In a third aspect, the present application provides an electronic device comprising: at least one memory for storing programs; and at least one processor for executing the programs stored in the memory. When the program stored in the memory is executed, the processor is used to execute the method described in the first aspect or any possible implementation of the first aspect.

[0018] In a fourth aspect, the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method described in the first aspect or any possible implementation of the first aspect.

[0019] In a fifth aspect, the present application provides a computer program product, which, when executed on a processor, enables the processor to execute the method described in the first aspect or any possible implementation of the first aspect.

[0020] It can be understood that the beneficial effects of the second to fifth aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0021] In general, the above technical solutions conceived by this application have the following beneficial effects compared with the existing technologies: (1) This application utilizes a precise constrained kinematic model and a material database. Taking into account the actual space limitations, the maximization of the workspace is directly set as the optimization objective function. The working condition indicators, space limitations, material properties, etc. are converted into strict constraints. By using a multi-objective optimization algorithm, the optimal geometric and physical parameters are searched under multiple constraints, thereby designing a platform structure that can provide maximum working capacity within a given volume. The balance between performance and size is considered from the design source, avoiding the volume expansion caused by the subsequent performance improvement by adding counterweights or complex mechanisms, achieving high precision, and improving the workspace while maintaining the compactness of the structure.

[0022] (2) This application uses the material database and constraint conditions for optimization, which can ensure that the parallel positioning platform achieves optimal parameter matching while meeting the mechanical performance requirements such as strength and stiffness.

[0023] (3) This application automatically solves the optimal parameter solution set through a multi-objective optimization algorithm, reducing the time and cost required and being able to quickly generate a design solution that meets actual needs.

[0024] (4) This application divides the Jacobian matrix into blocks, and the calculation of the translation velocity block is completely independent of the platform's rotation state. Therefore, during the motion control process, there is no need to update the entire Jacobian matrix in real time as in traditional coupled configurations. Instead, only the iterative calculation and update of the rotation-related parts are required. This significantly reduces the complexity and computational burden of kinematic operations, improves the efficiency of the control algorithm, and lays the foundation for subsequent more accurate and faster feedforward control. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Schematic diagram of the installation space for the three-color imaging system and the corresponding parallel positioning platform; Figure 2 Schematic diagram of the overall structure of the parallel positioning platform; Figure 3 Schematic diagram of the relative positions of the unilateral ball-and-groove mechanism and the actuator; Figure 4A schematic diagram of a process for constructing a parallel positioning platform provided in an embodiment of the present application; Figure 5 A top view of the precise constraint model in an embodiment of the present application; Figure 6 This is a front view of the precise constraint model in the embodiment of the present application; Figure 7 A schematic diagram of the functional modules of a parallel positioning platform construction system provided in an embodiment of the present application; Figure 8 It is a structural diagram of an electronic device provided in an embodiment of the present application.

[0026] Throughout the drawings, the same reference numerals are used to denote the same elements or structures, wherein: 101 is the objective lens; 102 is the first dichroic mirror; 103 is the second dichroic mirror; 104 is the third dichroic mirror; 105 is the lens; 106 is the parallel positioning platform installation space; 201 is the top cover; 202 is the metal ball; 203 is the inclined groove; 204 is the base; 205 is the actuator installation position; 301 is the actuator; 302 is the guide rail; 701 is the data acquisition module; 702 is the model building module; 703 is the target determination module; 704 is the parameter solution module; 705 is the platform construction module. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0028] The term "and / or" as used herein describes an association between related objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A exists alone, A and B exist simultaneously, or B exists alone. The symbol " / " as used herein indicates that the related objects are in an "or" relationship, for example, A / B means either A or B.

[0029] The terms "first" and "second" in this specification and claims are used to distinguish different objects rather than to describe a specific order of objects. For example, "first response message" and "second response message" are used to distinguish different response messages rather than to describe a specific order of response messages.

[0030] In the embodiments of this application, words such as "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of this application should not be interpreted as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0031] In the description of the embodiments of the present application, unless otherwise specified, "multiple" means two or more, for example, multiple processing units means two or more processing units, etc.; multiple elements means two or more elements, etc.

[0032] First, some technical terms involved in the embodiments of this application are introduced.

[0033] Working space: The working space of the parallel positioning platform refers to the entire space range that the central reference point of the parallel positioning platform can reach.

[0034] Translation space: The area in three-dimensional space where the robot's end effector can move, describing the robot's translational capabilities on the x, y, and z axes.

[0035] Rotational space: The angular range within which the robot's end effector can rotate, describing the robot's ability to rotate around the x, y, and z axes.

[0036] The embodiments of the present application are described below in conjunction with the drawings in the embodiments of the present application.

[0037] In an exemplary embodiment, Figure 1 As shown, Figure 1 An application scenario of a parallel platform has been proposed. The three detectors of the three-color system need to be aligned. When the upper detector is used as the reference, the detectors on both sides need to be adjusted. At this time, the detectors can be installed on the parallel platform for adjustment.

[0038] The three-color imaging system includes an objective lens 101 , a first dichroic mirror 102 , a second dichroic mirror 103 , a third dichroic mirror 104 , a lens 105 , and two parallel positioning platform installation spaces 106 .

[0039] Specifically, the target 101 is located at the bottom and is the target object of the imaging system. Light is emitted or reflected from here. The first dichroic mirror 102 is located directly above the target 101, receives light from the illumination light path and reflects it to the objective lens to provide excitation light. The second dichroic mirror 103 is located directly above the first deformable reflector 102, receives the signal of the target object and reflects the signal of the corresponding band to the left detector for reception. The third dichroic mirror 104 is located directly above the second dichroic mirror 103, receives the signal of the target object and reflects the signal of the corresponding band to the right detector for reception. The lens 105 is located at the end of the illumination light path and is used to collimate the incident divergent light into parallel light to ensure that subsequent detectors can receive appropriate light. The parallel positioning platform installation space 106 is located directly above the lens 105 and is used to install the parallel positioning platform. The platform can carry the detector and achieve the alignment of the three-color imaging system by precisely adjusting its position and posture. In an exemplary embodiment, as Figure 2 and Figure 3 As shown, the parallel positioning platform includes a top cover 201 and three ball-and-slot mechanisms arranged at the bottom of the top cover 201. Each ball-and-slot mechanism includes a metal ball 202, an actuator 301, an inclined groove 203 and a guide rail 302. The actuator 301 is fixed to the base 204 through the actuator mounting position 205. The top ends of the three metal balls 202 are connected to the top cover 201 through threads. The actuator 301 is used to push the inclined groove 203 to move linearly on the guide rail 302, so that the inclined groove 203 and the metal balls 202 form a kinematic pair through point contact to adjust the position of the top cover 201. A total of six point high-pair contacts on three sides realize complete motion coupling of the top cover 201. When the actuator 301 pushes the inclined groove 203 to move, the motion coupling point of the ball-and-slot mechanism changes, thereby realizing the adjustment of the position of the top cover 201.

[0040] Reference Figure 4 , the present application provides a method for constructing a parallel positioning platform, comprising: S101 obtains the space size of the parallel positioning platform working environment to be constructed and the material database of the parts; In an exemplary embodiment, the spatial size of the working environment of the parallel positioning platform is defined as a rectangular parallelepiped of a×b×c, where a is the maximum length of the working environment, b is the maximum width of the working environment, and c is the maximum height of the working environment.

[0041] S102. Establish a precise constraint model for the parallel positioning platform; like Figure 5 and Figure 6 As shown, the precise constraints of the parallel positioning platform include: the effective stroke L of the actuator, the coupling diameter D coup , chute inclination θ and the diameter of the metal ball D beq .

[0042] S103. Determine the constraint conditions of the precise constraint model based on the space size and the material database, and determine the optimization objective function of the precise constraint model; the optimization objective function is used to characterize the translational space volume and the rotational space volume of the parallel positioning platform; S104. Based on the precise constraint model, the constraint conditions, and the optimization objective function, a multi-objective optimization algorithm is used to determine an optimal parameter solution set for the parallel positioning platform; the optimal parameter solution set includes the effective stroke of the actuator, the coupling diameter, the chute inclination, and the metal ball diameter; S105. Construct a parallel positioning platform based on the optimal parameter solution set, so that the parallel positioning platform has a maximum working space in a working environment.

[0043] Specifically, in step S103, the constraint conditions of the precise constraint model are determined according to the space size and the material database, and the optimization objective function of the precise constraint model is determined. The optimization objective function is used to characterize the translation space volume and rotation space volume of the parallel positioning platform.

[0044] Furthermore, the constraint condition includes a volume constraint, and the method for determining the volume constraint includes: Determine the maximum height, length, and width of the work environment; Determine the maximum range of motion in the plane direction according to the maximum length and maximum width; Obtain the platform height and effective stroke of the actuator when the actuator is reset, determine the sign of the additional height generated by the effective stroke and the chute inclination, ensure that the sum of the platform height and the additional height when the actuator is reset is less than the maximum height, and determine the upper limit of the chute inclination, which is used as an input parameter for the subsequent workspace optimization function; Determine the upper and lower bounds of the coupling radius, which are used as input parameters for subsequent workspace optimization functions.

[0045] Specifically, the volume constraint is shown in the following formula:

[0046] in, is the platform height when the actuator is reset, is the effective stroke of the actuator, is the chute inclination angle, is the maximum height of the working environment, is the maximum length of the working environment, is the maximum width of the working environment, is the coupling diameter.

[0047] Furthermore, the constraint condition further includes a rotation resolution constraint, and the method for determining the rotation resolution constraint and the coupling radius includes: The parallel positioning platform's rotational resolution is set according to the working condition requirements, and the set rotational resolution is used as the minimum increment of posture change. The joint displacement increments corresponding to the six actuators of the parallel positioning platform under the minimum increment are calculated; Obtaining the minimum step of the actuator, traversing the value range of the coupling radius within the adjustable interval, gradually decreasing and increasing the coupling radius, and determining whether the displacement increments of the six joints are all greater than or equal to the minimum step of the actuator; The coupling radius corresponding to the minimum step of the actuator is used as the lower limit of the coupling radius. The coupling radius that satisfies the maximum range of the platform is used as the upper limit. The feasible value range of the coupling radius is determined based on the upper and lower limits of the determined coupling radius, which is used as an input parameter for the subsequent workspace optimization function. Specifically, the rotation resolution constraint is shown in the following formula:

[0048] in, is the minimum step of the actuator, They are the six joint displacement increments of the parallel positioning platform.

[0049] Furthermore, the constraint condition further includes a Hertz limit constraint, and the constraint condition further includes a Hertz limit constraint. The method for determining the Hertz limit constraint includes: Obtain the load, the contact radius between the chute and the metal ball, and the yield limit of the kinematic pair material; The contact pressure between the chute and the metal ball is determined according to the load force and the contact radius, ensuring that the contact pressure does not exceed the yield limit of the material.

[0050] Specifically, the Hertz limit constraint is shown in the following formula:

[0051] in, F For load, is the yield limit of the kinematic pair material, is the contact radius between the chute and the metal ball.

[0052] In step S104, the established model and constraints are utilized, and a multi-objective optimization algorithm, such as a genetic algorithm or particle swarm optimization, is employed to iteratively optimize key parameters such as the actuator's effective stroke, coupling diameter, chute angle, and metal ball diameter. The optimization process requires balancing conflicts between objectives. For example, increasing the workspace may result in a decrease in structural stiffness. Therefore, an algorithm is used to automatically select the optimal parameter solution set, ultimately determining the design with the best overall performance.

[0053] Finally, based on the optimization results, the detailed design of the parallel positioning platform was completed, including specific implementation steps such as actuator selection, ball-slot assembly machining, and metal ball assembly. The resulting platform achieves the maximum workspace within a given space while meeting strength, accuracy, and reliability requirements, making it suitable for high-precision applications such as precision machining and motion simulation.

[0054] Furthermore, the step S103 of determining the optimization objective function of the precise constraint model includes: S131. According to the precise constraint model, the inverse kinematic equation of the parallel positioning platform is obtained; S132. Based on the inverse kinematic equation, a forward kinematic equation of the parallel positioning platform is obtained; S133. According to the kinematic equations, the full posture workspace of the parallel positioning platform is obtained; S134. Decompose the full-posture workspace into position space and rotation space, and solve the convex hull volumes of the position space and the rotation space to obtain an optimization objective function that characterizes the translation space volume and the rotation space volume of the parallel positioning platform.

[0055] Step 131: Obtain the inverse kinematics equation of the parallel positioning platform according to the precise constraint model.

[0056] The method for solving the inverse kinematic equation includes: Obtain the displacement of the parallel positioning platform in the x-axis, y-axis and z-axis directions, and the rotation angles around the x-axis, y-axis and z-axis; the x-axis, y-axis and z-axis are the horizontal direction, vertical direction and height direction of the parallel positioning platform respectively; Construct the inverse kinematic matrix based on the cotangent value of the inclined slot angle, the direction vectors of each actuator, and the coordinates of the metal ball in the moving coordinate system; The kinematic inverse matrix is ​​used to calculate the six joint displacement increments in combination with the platform displacement and rotation angle.

[0057] Specifically, no. j The coordinates of the center of a metal ball in the moving coordinate system It can be expressed as:

[0058] in, j =1,2,3, For the j The center of the metal ball is in the moving coordinate system. x Axis coordinates, For the j The center of the metal ball is in the moving coordinate system. y Axis coordinates.

[0059] use represents the joint parameter vector of the parallel positioning platform, then the inverse kinematics solution formula can be expressed as:

[0060] in, i =1, 2, ..., 6, representing the sequence numbers of the six joint parameter vectors, is the rotation matrix, is the displacement vector of the moving coordinate system relative to the static coordinate system, For the i The direction vector of the actuator axis is in the form of , is the unit vector of the actuator in the z-axis direction.

[0061] Convert the rotation matrix to Euler angles Parameterization, the following nonlinear equations can be established: ; in, is the center coordinate of the moving part of the parallel positioning platform, is the nutation angle, is the precession angle, is the rotation angle.

[0062] Solving the above nonlinear equations can obtain the joint parameter increments required to change from the current posture to the target posture : .

[0063] Further make the posture of the parallel positioning platform P for: ;

[0064] Considering that only fine-tuning is performed when adjusting the camera phase, it is assumed that the Euler angles are all small angles. Under this premise, the quadratic term can be ignored to simplify the rotation matrix parameterized by the Euler angles. 、 、 Indicates that the parallel positioning platform is around x axis,y axis, z The rotation angle of the axis is: .

[0065] The simplified inverse kinematic equation is: ; in, to is the displacement increment of the six joints of the parallel positioning platform, k is the chute inclination φ The cotangent value of , and the direction vectors corresponding to the two actuators on the same side satisfy the following relationship: .

[0066] Step 132: Based on the inverse kinematics equation, a forward kinematics equation of the parallel positioning platform is obtained.

[0067] The process of solving the kinematic equations is: constructing a vector matrix according to the maximum displacement increments of the six joints; A motion matrix is ​​constructed based on the cotangent value of the inclined groove angle, the direction vectors of each actuator, and the coordinates of the metal ball in the moving coordinate system; Inverting the motion matrix to obtain an inverse matrix of the motion matrix; The full-posture workspace of the parallel positioning platform is obtained by multiplying the inverse matrix with the vector matrix.

[0068] Specifically, the inverse kinematics equation is ,at this time is a constant matrix, so the kinematic equation is:

[0069] in, Representation matrix J The inverse matrix of .

[0070] .

[0071] in, to is the displacement increment of the six joints of the parallel positioning platform, k is the cotangent of the chute angle, For the i The direction vector corresponding to each actuator, i =1,2,3,4,5,6, For the j The coordinates of the metal ball in the moving coordinate system are: j =1,2,3, For parallel positioning platform around x The rotation angle of the axis, For parallel positioning platform around y The rotation angle of the axis, For parallel positioning platform z The rotation angle of the axis, x , y , z are the displacements of the parallel positioning platform along the x-axis, y-axis, and z-axis respectively.

[0072] The above formula shows that for any set of joint parameter increments composed of actuators , by left-multiplying the forward kinematics matrix The corresponding parallel platform posture can be obtained P , the solution process is recorded as ,result P Parallel positioning platform for The kinematic solution of: .

[0073] In a specific application example, the direction vectors of the actuator axes on the three sides of the base are Forming an equilateral triangle, three metal balls D beq When the coupling radius of / 2 is uniformly distributed at an angle of 60° below the top cover, the inverse kinematic equation of the parallel positioning platform is: ; in, For the parallel positioning platform i joint parameters.

[0074] Optionally, it also includes: The Jacobian matrix of the platform is obtained by differentiating the inverse kinematic equation with respect to time , and Divide into translation speed blocks and rotation speed blocks , to simplify kinematic operations.

[0075] Therefore, in motion control, there is no need to update and solve in real time , the rotation term can be calculated separately by iteration , thereby simplifying the kinematic calculations and facilitating subsequent feedforward control.

[0076] After differentiating the inverse kinematic equation with respect to time, the velocity constraint of the parallel positioning platform can be obtained. At this time, the Jacobian array is divided into blocks according to the translation and rotation speeds.

[0077] Note that:

[0078] The rotation velocity term of the Jacobian matrix J depends on the approximate assumption that the rotation matrix has a small angle so that Linearization, however, the kinematic derivation of the translation block of the Jacobian matrix is ​​completely independent of the rotation matrix R. Therefore, compared with the fully coupled Stewart platform with displacement and rotational degrees of freedom, the parallel positioning platform configuration described in this application has its three translational degrees of freedom naturally decoupled from the three rotational degrees of freedom. Therefore, there is no need to update and solve in real time during motion control. , the rotation term can be calculated separately by iteration ,This configuration is beneficial to the simplification of the kinematic calculation and ,subsequent feedforward control of the parallel positioning ,platform.

[0079] The kinematic equation can be expressed as: .

[0080] Step 133: Obtain the full-posture workspace of the parallel positioning platform according to the kinematic forward equation.

[0081] For any specific joint vector Perform forward kinematics calculation to obtain the platform pose corresponding to the joint vector P 0, and P 0 can be represented as .

[0082] Since the boundary of the parallel positioning platform's workspace must appear at the limit stroke of the actuator, the kinematics forward solution is solved for the maximum stroke combination of the actuator, that is, the maximum joint space of the platform, to obtain the point set of the workspace boundary. : .

[0083] Step 134 , decompose the full-pose workspace into position space and rotation space, and solve the convex hull volumes of the position space and the rotation space to obtain an optimization objective function that characterizes the translation space volume and the rotation space volume of the parallel positioning platform.

[0084] In an exemplary embodiment, the point set is finally obtained The form is:

[0085] in, n is the number of joint vectors.

[0086] The full posture workspace at this time ,in, is a six-dimensional Cartesian space. For each column of pose vectors, the first three translation degrees of freedom define the position of the platform, and the last three rotation degrees of freedom define the posture of the platform. Therefore, the first three columns and the last three columns are projected into the three-dimensional Cartesian space. , we can get the position space and rotation space The form: ; .

[0087] Step 104: Based on the precise constraint model, the constraint conditions, and the optimization objective function, a multi-objective optimization algorithm is used to determine an optimal parameter solution set for the parallel positioning platform. The optimal parameter solution set includes the effective stroke of the actuator, the coupling diameter, the chute angle, and the metal ball diameter.

[0088] Step 105: construct a parallel positioning platform based on the optimal parameter solution set, so that the parallel positioning platform has a maximum working space in a working environment.

[0089] In a specific application example, components are selected according to an optimal parameter solution set to construct a parallel positioning platform, so that the parallel positioning platform can obtain a maximum working space in a working environment.

[0090] The present application can design a six-degree-of-freedom parallel positioning platform with a high workspace-to-volume ratio under given workspace requirements. The parallel positioning platform is more compact and saves space. Moreover, the kinematic solution of the parallel positioning platform in a mobile pair-point high pair configuration in which each motion branch is a mobile pair does not change with the influence of posture. Therefore, the motion is smooth and there are no singular points. Compared with the previous Stewart platform, it is more suitable for environments with high compactness requirements such as optical imaging systems.

[0091] Reference Figure 7 , the present application also provides a parallel positioning platform construction system, including: The data acquisition module 701 is used to obtain the space size of the working environment of the parallel positioning platform to be constructed and the material database of the components; Model building module 702, used to build an accurate constraint model of the parallel positioning platform; A target determination module 703 is used to determine the constraint conditions of the precise constraint model based on the space size and the material database, and to determine the optimization objective function of the precise constraint model; the optimization objective function is used to characterize the translational space volume and the rotational space volume of the parallel positioning platform; a parameter solving module 704 for determining an optimal parameter solution set of the parallel positioning platform using a multi-objective optimization algorithm based on the precise constraint model, the constraint conditions, and the optimization objective function; the optimal parameter solution set includes the effective stroke of the actuator, the coupling diameter, the chute inclination angle, and the metal ball diameter; The platform construction module 705 is configured to construct a parallel positioning platform based on the optimal parameter solution set, so that the parallel positioning platform has a maximum working space in a working environment.

[0092] The present application also provides a parallel positioning platform constructed based on the method described in any one of the above items, characterized in that it includes a top cover and three ball slot mechanisms arranged at the bottom of the top cover; each ball slot mechanism includes a metal ball, an actuator, an inclined slot and a guide rail; the actuator is used to push the inclined slot to move linearly on the guide rail, so that the inclined slot and the metal ball form a kinematic pair through point contact to adjust the position of the top cover.

[0093] Optionally, the constraint condition includes a volume constraint, and the volume constraint is shown in the following formula:

[0094] in, is the platform height when the actuator is reset, is the effective stroke of the actuator, is the chute inclination angle, is the maximum height of the working environment, is the maximum length of the working environment, is the maximum width of the working environment, is the coupling diameter.

[0095] Optionally, the constraint condition further includes a rotation resolution constraint, and the rotation resolution constraint is shown in the following formula:

[0096] in, is the resolution of the actuator, They are the six joint displacement increments of the parallel positioning platform.

[0097] Optionally, the constraint condition further includes a Hertz limit constraint, and the Hertz limit constraint is shown in the following formula:

[0098] in, F For load, is the yield limit of the kinematic pair material, is the contact radius between the chute and the metal ball.

[0099] Optionally, determining the optimization objective function of the precise constraint model includes: According to the precise constraint model, an inverse kinematics equation of the parallel positioning platform is obtained; Based on the inverse kinematics equation, a forward kinematics equation of the parallel positioning platform is obtained; According to the kinematics forward equation, the full posture workspace of the parallel positioning platform is obtained; The full-pose workspace is decomposed into a position space and a rotation space, and the convex hull volumes of the position space and the rotation space are solved to obtain an optimization objective function that characterizes the translation space volume and the rotation space volume of the parallel positioning platform.

[0100] Optionally, the method for solving the inverse kinematic equation includes: Obtain the displacement of the parallel positioning platform in the x-axis, y-axis and z-axis directions, and the rotation angle around the x-axis, y-axis and z-axis; the x-axis, y-axis and z-axis are the horizontal direction, vertical direction and height direction of the parallel positioning platform respectively Construct the inverse kinematic matrix based on the cotangent value of the inclined slot angle, the direction vectors of each actuator, and the coordinates of the metal ball in the moving coordinate system; The kinematic inverse matrix is ​​used to calculate the six joint displacement increments in combination with the platform displacement and rotation angle.

[0101] Optionally, the kinematics forward solution equation is: constructing a vector matrix according to the maximum displacement increments of the six joints; A motion matrix is ​​constructed based on the cotangent value of the inclined groove angle, the direction vectors of each actuator, and the coordinates of the metal ball in the moving coordinate system; Inverting the motion matrix to obtain an inverse matrix of the motion matrix; The full-posture workspace of the parallel positioning platform is obtained by multiplying the inverse matrix with the vector matrix.

[0102] It is understandable that the detailed functional implementation of each of the above units / modules can be found in the introduction of the aforementioned method embodiment, and will not be repeated here.

[0103] It should be understood that the above-mentioned device is used to execute the method in the above-mentioned embodiment. The implementation principle and technical effect of the corresponding program module in the device are similar to those described in the above-mentioned method. The working process of the device can refer to the corresponding process in the above-mentioned method and will not be repeated here.

[0104] Reference Figure 8Based on the methods in the above embodiments, an embodiment of the present application provides an electronic device, which may include: a processor (Processor) 810, a communication interface (Communications Interface) 820, a memory (Memory) 830, and a communication bus 840. The processor 810, the communication interface 820, and the memory 830 communicate with each other via the communication bus 840. The processor 810 may call logic instructions in the memory 830 to execute the methods in the above embodiments.

[0105] In addition, the logic instructions in the aforementioned memory 830 can be implemented in the form of a software functional unit and, when sold or used as an independent product, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the portion that contributes to the prior art, or the portion of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application.

[0106] Based on the method in the above embodiment, an embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method in the above embodiment.

[0107] Based on the method in the above embodiment, an embodiment of the present application provides a computer program product. When the computer program product runs on a processor, the processor executes the method in the above embodiment.

[0108] It is understood that the processor in the embodiments of the present application may be a central processing unit (CPU), other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA), other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. The general-purpose processor may be a microprocessor or any conventional processor.

[0109] The method steps in the embodiments of the present application can be implemented by hardware or by a processor executing software instructions. The software instructions can be composed of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, mobile hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be an integral part of the processor. The processor and storage medium can be located in an ASIC.

[0110] The above embodiments can be implemented in whole or in part using software, hardware, firmware, or any combination thereof. When implemented using software, they can be implemented in whole or in part in the form of a computer program product. The computer program product comprises one or more computer instructions. When loaded and executed on a computer, the computer program instructions fully or partially produce the processes or functions described in the embodiments of this application. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted via the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible by a computer or a data storage device such as a server or data center that integrates one or more available media. The available medium can be magnetic media (e.g., floppy disk, hard disk, tape), optical media (e.g., DVD), or semiconductor media (e.g., solid-state drive (SSD)).

[0111] It will be understood that the various numerical numbers involved in the embodiments of the present application are merely distinctions for the convenience of description and are not intended to limit the scope of the embodiments of the present application.

[0112] It is easy for those skilled in the art to understand that the above is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the scope of protection of the present application.

Claims

1. A method for constructing a parallel positioning platform, characterized in that: include: Obtain the space size of the working environment of the parallel positioning platform to be constructed and the material database of the components; Establish an accurate constraint model for the parallel positioning platform; Determining the constraint conditions of the precise constraint model and the optimization objective function of the precise constraint model according to the space size and the material database; the optimization objective function is used to characterize the translation space volume and the rotation space volume of the parallel positioning platform; Based on the precise constraint model, the constraint conditions, and the optimization objective function, a multi-objective optimization algorithm is used to determine an optimal parameter solution set of the parallel positioning platform; the optimal parameter solution set includes the effective stroke of the actuator, the coupling diameter, the chute inclination, and the metal ball diameter; A parallel positioning platform is constructed based on the optimal parameter solution set, so that the parallel positioning platform has a maximum working space in a working environment.

2. The method for constructing a parallel positioning platform according to claim 1, wherein: The constraint condition includes a volume constraint, and a method for determining the volume constraint includes: Determine the maximum height, length, and width of the work environment; Determine the maximum range of motion in the plane direction according to the maximum length and maximum width; Obtain the platform height when the actuator is reset and the effective stroke of the actuator, determine the symbolic representation of the additional height generated by the effective stroke and the inclination angle of the chute, ensure that the sum of the platform height and the additional height when the actuator is reset is less than the maximum height, obtain the upper limit of the inclination angle of the chute, and determine the upper and lower limits of the coupling radius, which are used as input parameters for the subsequent workspace optimization function.

3. The method for constructing a parallel positioning platform according to claim 2, wherein: The constraint condition further includes a rotation resolution constraint, and a method for determining the rotation resolution constraint and the coupling radius includes: The parallel positioning platform's rotational resolution is set according to the working condition requirements, and the set rotational resolution is used as the minimum increment of posture change. The joint displacement increments corresponding to the six actuators of the parallel positioning platform under the minimum increment are calculated; Obtaining the minimum step of the actuator, traversing the value range of the coupling radius within the adjustable interval, gradually decreasing and increasing the coupling radius, and determining whether the displacement increments of the six joints are all greater than or equal to the minimum step of the actuator; The coupling radius corresponding to the minimum step of the actuator is used as the lower limit of the coupling radius. The upper limit is the coupling radius that satisfies the maximum range of motion of the platform; The feasible value range of the coupling radius is determined according to the upper and lower limits of the determined coupling radius, and is used as an input parameter of the subsequent workspace optimization function; The constraint condition further includes a Hertz limit constraint, and a method for determining the Hertz limit constraint includes: Obtain the load, the contact radius between the chute and the metal ball, and the yield limit of the kinematic pair material; The contact pressure between the chute and the metal ball is determined according to the load force and the contact radius, ensuring that the contact pressure does not exceed the yield limit of the material.

4. The method for constructing a parallel positioning platform according to claim 1, wherein: Determining the optimization objective function of the precise constraint model includes: According to the precise constraint model, an inverse kinematics equation of the parallel positioning platform is obtained; Based on the inverse kinematics equation, a forward kinematics equation of the parallel positioning platform is obtained; According to the kinematics forward equation, the full posture workspace of the parallel positioning platform is obtained; The full-pose workspace is decomposed into a position space and a rotation space, and the convex hull volumes of the position space and the rotation space are solved to obtain an optimization objective function that characterizes the translation space volume and the rotation space volume of the parallel positioning platform.

5. The method for constructing a parallel positioning platform according to claim 4, wherein: The method for solving the inverse kinematic equation includes: Obtain the displacement of the parallel positioning platform in the x-axis, y-axis and z-axis directions, as well as the rotation angles around the x-axis, y-axis and z-axis; the x-axis, y-axis and z-axis are the horizontal direction, vertical direction and height direction of the parallel positioning platform respectively; Construct the inverse kinematic matrix based on the cotangent value of the inclined slot angle, the direction vectors of each actuator, and the coordinates of the metal ball in the moving coordinate system; The kinematic inverse matrix is ​​used to calculate the six joint displacement increments in combination with the platform displacement and rotation angle.

6. The method for constructing a parallel positioning platform according to claim 5, characterized in that: The kinematic equation is: constructing a vector matrix according to the maximum displacement increments of the six joints; A motion matrix is ​​constructed based on the cotangent value of the inclined groove angle, the direction vectors of each actuator, and the coordinates of the metal ball in the moving coordinate system; Inverting the motion matrix to obtain an inverse matrix of the motion matrix; The full-posture workspace of the parallel positioning platform is obtained by multiplying the inverse matrix with the vector matrix.

7. The method for constructing a parallel positioning platform according to claim 5, characterized in that: Also includes: The velocity constraint of the parallel positioning platform is determined by differentiating the inverse kinematics equation with respect to time, thereby obtaining a Jacobian matrix of the parallel positioning platform; Dividing the Jacobian matrix into blocks to obtain translation velocity blocks and rotation velocity blocks to simplify kinematic calculations and subsequent feedforward control; The kinematic derivation process of the translation velocity block is completely independent of the rotation state of the parallel positioning platform and is separated from the kinematic iterative calculation in a pre-hardcoded manner; the rotation velocity block is replaced by a small-angle approximation of the rotation matrix during the motion control process, or only a separate iterative calculation is performed to update the rotation velocity block.

8. A parallel positioning platform construction system, characterized in that: include: A data acquisition module is used to obtain the spatial size of the working environment of the parallel positioning platform to be constructed and the material database of the components; Model building module, used to build accurate constraint model of parallel positioning platform; a target determination module, configured to determine the constraint conditions of the precise constraint model based on the space size and the material database, and to determine an optimization objective function of the precise constraint model; the optimization objective function is used to characterize the translational space volume and the rotational space volume of the parallel positioning platform; a parameter solving module, configured to determine an optimal parameter solution set of the parallel positioning platform using a multi-objective optimization algorithm based on the precise constraint model, the constraint conditions, and the optimization objective function; the optimal parameter solution set includes the effective stroke of the actuator, the coupling diameter, the chute inclination, and the metal ball diameter; The platform construction module is used to construct a parallel positioning platform based on the optimal parameter solution set, so that the parallel positioning platform has a maximum working space in a working environment.

9. A parallel positioning platform constructed based on the method according to any one of claims 1 to 7, characterized in that: It includes a top cover and three ball slot mechanisms arranged at the bottom of the top cover; each ball slot mechanism includes a metal ball, an actuator, an inclined slot and a guide rail; the actuator is used to push the inclined slot to move linearly on the guide rail, so that the inclined slot and the metal ball form a kinematic pair through point contact to adjust the position of the top cover.

10. An electronic device, characterized in that: include: at least one memory for storing a computer program; At least one processor is used to execute the program stored in the memory. When the program stored in the memory is executed, the processor is used to execute the method according to any one of claims 1 to 7.

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