Optimal base station configuration generation method and system for multilateral measurement field of laser tracker

Abstract

The invention provides an optimal base station configuration generation method and system for a multilateral measurement field of a laser tracker. The method comprises the following steps: S1, configuring a measurement point arrangement scheme; s2, configuring a spatial geometry relationship, and generating an initial configuration pool; s3, carrying out observability verification on the series configuration of the initial configuration pool according to the parameters of the laser tracker, and forming a candidate configuration pool by the configuration passing the verification; s4, calculating the geometric deployment index value of each configuration in the candidate configuration pool, selecting the configuration with the minimum GDI value as the optimal configuration, and performing multilateral measurement in combination with the measurement point arrangement scheme; and S5, carrying out measuring point coordinate calculation on the multilateral measurement data, and analyzing the measuring point deviation cause facing the test requirement. According to the invention, the optimal base station configuration can be generated in a targeted manner for different measurement scenes and test requirements for multilateral measurement, the influence of laser interference ranging errors on data post-processing is reduced, and the operation precision and robustness of a multilateral measurement system are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of three-dimensional coordinate measurement, and in particular to a method and system for generating an optimal base station configuration of a laser tracker multi-lateral measurement field. BACKGROUND

[0002] Laser tracker multi-lateral measurement technology plays an increasingly important role in engineering fields such as aerospace, advanced manufacturing, and precision assembly due to its advantages of large space, high precision, and high efficiency. This technology, through the cooperative work of multiple base stations, constructs a large-scale, high-space three-dimensional coordinate measurement field, and has the ability to accurately measure and reconstruct the precision status of large complex components and manufacturing equipment. With the continuous improvement of modern industry's requirements for ultra-large size workpiece measurement precision and on-site adaptability, laser tracker multi-lateral measurement systems have become one of the key supporting technologies for ensuring the quality of high-end equipment manufacturing, realizing digital detection and process optimization, and their application scope is continuously expanding to intelligent manufacturing, robot calibration, large equipment and component assembly, and other high-precision spatial positioning scenarios.

[0003] In the construction process of a laser tracker multi-lateral measurement system, the spatial layout planning of base stations is a key link that determines the overall measurement performance. The rational configuration of base station positions not only directly affects the accuracy and stability of spatial coordinate calculation, but also relates to the adaptability of the measurement system to complex site environments and the feasibility of engineering implementation. In practical applications, base station deployment needs to consider multiple factors such as the geometric configuration of the measurement space, the completeness of the target area coverage, and error suppression. Unreasonable base station configuration can easily lead to uneven distribution of measurement accuracy, significant error amplification, and even the appearance of measurement blind areas, which seriously affects the reliability and consistency of spatial coordinate calculation results. Therefore, how to establish a scientific base station optimization configuration method according to specific measurement task requirements, generate a layout scheme that takes into account accuracy, robustness, and engineering applicability, has become a key proposition for the systematic development of laser tracker multi-lateral measurement technology, and has important practical significance for improving the overall efficiency of large-scale industrial site measurement.

[0004] Chinese patent document CN116976193A discloses a method for planning the optimal measurement station of a laser tracker. This method uses the GJK collision detection algorithm to judge the accessibility of the station's light path based on the three-dimensional model of the measured object and the measurement point data, then constructs a station planning function, and uses an improved hybrid grey wolf algorithm to calculate the optimal measurement station of the laser tracker. However, the measurement station planning function constructed by this method takes minimizing the number of measurement stations as the objective function and takes light path accessibility as the optimization condition, which has insufficient consideration of the relationship between base station configuration and measurement data uncertainty. SUMMARY

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for generating optimal base station configurations for a multi-sided measurement field of a laser tracker.

[0006] A method for generating optimal base station configuration for a multi-sided measurement field of a laser tracker, provided by the present invention, includes: Step S1: Configure the measurement point layout scheme based on the measurement scenario and testing requirements; Step S2: Generate an initial configuration pool based on the relationship between the optimal calculation conditions and the spatial geometry of the multi-sided measurement field base station configuration. Step S3: Perform observability verification on the series of configurations in the initial configuration pool based on the laser tracker parameters, and form a candidate configuration pool from the configurations that pass the verification. Step S4: Calculate the geometric deployment index value of each configuration in the candidate configuration pool, select the configuration with the smallest GDI value as the optimal configuration, and perform multilateral measurement in combination with the measurement point layout scheme.

[0007] Preferred options also include: Step S5: Calculate the coordinates of the measurement points in the multilateral measurement data, analyze the causes of measurement point deviations in line with testing requirements, and output the analysis results.

[0008] The preferred set of measurement points designed for specific measurement scenarios and testing requirements is as follows: In the reference coordinate system (R-CS), it is denoted as .

[0009] Preferably, the initial configuration pool construction process includes: Generate a candidate base station location pool based on Hammersley sequences. Subsequently, the generation of each configuration within the initial configuration pool adopts a construction method from planar to spatial representation. The process of building the group configuration is as follows: Build a configuration plane, from Three numbers were selected from the list. The locations of the laser tracker base stations were used to form a temporary three-point combination. When three interconnecting segments When the following geometric relationship is satisfied:

[0010] Depend on The geometric plane constructed by the three points is determined to be an approximately isosceles right triangle, with an approximation degree of [missing information]. ; This is a preset tolerance parameter for controlling the degree of approximation; Perform fine-tuning of the planar site locations, listing the base station locations corresponding to the right-angle vertices. The first position, at this time the combination of three points in the plane is denoted as , record , as a reference length , the position of the acute vertex is updated to by the following formula:

[0011] wherein, , ; at this time, the planar figure constructed by the updated base station combination forms an isosceles right triangle in theory; Construct the configuration space geometry; based on the generated three-point combination and its corresponding reference length , the fourth tracking station position is calculated by the following formula:

[0012] The signed calculation results in the above formula are recorded as and respectively, and finally a four-point combination is constructed, which forms a positive right space tetrahedron in theory: ; After traversing all station combinations in the candidate base station position pool and performing the above calculation process, the generated initial configuration pool is recorded as .

[0013] Preferably, the observability verification process includes: determination ; Verify the feasibility of the configuration implemented by the measured machine tool, i.e. the reachability of the last two tracking instrument base station positions and , which is simplified to the evaluation of the following formula:

[0014] wherein, is the reachable range; Perform observability determination on the preset measurement point , which needs to traverse the four base station positions contained in to ensure that the preset measurement point can be observed at all times during the station transfer and the measurement process; define the direction vector from the tracking instrument base station to the preset measurement point as , which is consistent with the direction of the laser beam; combine the corresponding of the four base station positions .​Afterwards, the average direction vector is calculated by the following formula The center axis vector of the cone

[0015] The cone angle of the cone is half of the minimum observation range required by the configuration The observability determination for the measurement point is described as the evaluation of the following formula:

[0016] Wherein, , is the nominal observation range, is the preset scale factor; All configurations in the initial configuration pool that pass the observability determination in this stage collectively constitute the candidate configuration pool .

[0017] Preferably, the screening process of the optimal configuration screening includes: Calculate the geometric deployment index value of each configuration in the candidate configuration pool ; The base station configuration relative to any preset measurement point establishes a measurement residual equation set according to the distance formula between two points as follows:

[0018] Wherein, represents the actual measured value of the distance between and ; Linearize the above formula, and the coordinate value of the measurement point is obtained through the best unbiased estimate of its linearized form, and at this time the calculation deviation of is represented as:

[0019] Wherein, is the Jacobian matrix of the unknown variable , is the measurement noise covariance matrix; define the unit vector from the tracker base station pointing to the measurement point as:

[0020] Wherein, ,​​​​ ; Depend on Composition, specifically expressed as:

[0021] in, Measurement noise covariance matrix Depending on the instrument measurement uncertainty, the relationship is expressed as follows:

[0022] in, and This is an inherent parameter for the instrument's measurement uncertainty, provided by the manufacturer. Measurement noise is modeled as a normal distribution. , The expression is as follows:

[0023] Unknown quantities caused by distance measurement noise The deviation, whose covariance matrix estimate is calculated by the following formula:

[0024] Then configure For measuring points The weighted geometric precision factor is defined as:

[0025] in, Represents the trace of a matrix; Computational Configuration For the measurement point set Define the WGDOP values ​​of all measurement points within the system. The geometric deployment metrics are:

[0026] This index value is oriented towards the scenario of solving the coordinates of the measurement points, reflecting the configuration. With measurement point set The average amplification effect of the spatial geometric relationship formed by each measuring point on non-uniform measurement noise; Optimal configuration By selecting from the candidate configuration pool The configuration with the smallest GDI value is selected to determine the optimal configuration.

[0027] An optimal base station configuration generation system for a multi-sided measurement field of a laser tracker, provided by the present invention, includes: Module M1: Configures the measurement point layout scheme based on the measurement scenario and testing requirements; Module M2: Generates an initial configuration pool based on the relationship between optimal computational conditions and the spatial geometry of the multi-sided measurement field base station configuration. Module M3: Performs observability verification on a series of configurations in the initial configuration pool based on the laser tracker parameters, and constructs a candidate configuration pool from the verified configurations. Module M4: Calculates the geometric deployment index value of each configuration in the candidate configuration pool, selects the configuration with the smallest GDI value as the optimal configuration, and performs multilateral measurements in conjunction with the measurement point layout scheme.

[0028] Preferred options also include: Module M5: Calculates the coordinates of measurement points in multi-dimensional measurement data, analyzes the causes of measurement point deviations for testing requirements, and outputs the analysis results.

[0029] The preferred set of measurement points designed for specific measurement scenarios and testing requirements is as follows: In the reference coordinate system (R-CS), it is denoted as .

[0030] Preferably, the initial configuration pool construction process includes: Generate a candidate base station location pool based on Hammersley sequences. Subsequently, the generation of each configuration within the initial configuration pool adopts a construction method from planar to spatial representation. The process of building the group configuration is as follows: Build a configuration plane, from Three numbers were selected from the list. The locations of the laser tracker base stations were used to form a temporary three-point combination. When three interconnecting segments When the following geometric relationship is satisfied:

[0031] Depend on The geometric plane constructed by the three points is determined to be an approximately isosceles right triangle, with an approximation degree of [missing information]. ; This is a preset tolerance parameter for controlling the degree of approximation; Perform fine-tuning of the planar site locations, listing the base station locations corresponding to the right-angle vertices. The first position, at this time the combination of three points in the plane is denoted as ,remember ,by Reference datum length The acute angle vertex is expressed by the following formula. Location updated to :

[0032] in, , At this time, the updated base station combination The constructed planar figure theoretically forms an isosceles right triangle; Construct configuration space geometry; based on the generated three-point combination and its corresponding reference length The location of the fourth tracking station is calculated using the following formula. :

[0033] The calculation results with positive and negative signs in the above formula are respectively denoted as: and Ultimately, this constructs a four-point combination that theoretically forms a right-angled spatial tetrahedron: ; Traverse the candidate base station location pool After combining all sites and performing the above calculation process, the generated initial configuration pool is denoted as . .

[0034] Preferred, observability verification processes include: determination ; Verify the configuration of the machine tool under test The feasibility, namely the location of the last two tracker base stations. and The accessibility can be simplified to an evaluation of the following formula:

[0035] in, Within reach; Set up measurement points The observability determination requires traversing... The locations of the four base stations included ensure the preset measurement points. It can be observed at all stations and the light is continuous during the measurement process; defined from the tracker base station Pointing to the preset measurement point The direction vector is The vector direction is consistent with the laser beam direction; the locations of the four base stations are merged. corresponding Then, the average direction vector is calculated using the following formula. As a cone bag Central axis vector:

[0036] in, cone bag The cone apex angle is configured Half of the minimum required observation range; configuration For the observation point The observability determination is described as the evaluation of the following formula:

[0037] Wherein, , is the nominal observation range, is the preset scale factor; Initial configuration pool All configurations determined by the current phase of observability determination in the initial configuration pool constitute the candidate configuration pool .

[0038] Preferably, the screening process of the optimal configuration screening includes: Calculate the geometric deployment index value of each configuration in the candidate configuration pool Base station configuration Relative to any preset observation point According to the distance formula between two points, the measurement residual equation set is established as follows:

[0039] Wherein, represents The measured value of the distance between ; Linearize the above formula, and the coordinate value of the observation point is obtained by the best unbiased estimate of its linearized form, and at this time The calculation deviation of

[0040] Wherein, is The Jacobian matrix of the unknown variable , is the measurement noise covariance matrix; define the unit vector from the tracker base station Pointing to the observation point :

[0041] Wherein, , ; Composed of , the specific expression is:

[0042] Wherein, ; the measurement noise covariance matrix Depends on the instrument measurement uncertainty, and the relationship is represented as:​

[0043] wherein, with is the instrument measurement uncertainty inherent parameter given by the manufacturer. Considering the measurement noise is modeled as normal distribution , is expressed as:

[0044] The distance measurement noise causes the unknown bias, whose covariance matrix estimate is calculated by:

[0045] Then the configuration for the measurement point is defined as:

[0046] wherein, denotes the trace of a matrix; The configuration for the measurement point set is defined as: The geometric deployment indicator of the configuration is defined as:

[0047] The indicator value is oriented to the context of coordinate solution of the measurement point, and reflects the average amplification effect of the spatial geometric relationship between the configuration and each measurement point in the measurement point set to the non-uniform measurement noise; The optimal configuration is determined by selecting the configuration with the minimum GDI value from the candidate configuration pool .

[0048] Compared with the prior art, the present application has the beneficial effects as follows: 1. The optimal base station configuration generation method proposed in the present application can generate optimal base station configurations for different measurement scenarios and test requirements for multi-lateral measurement, reduce the influence of laser interference distance measurement error on data post-processing, and improve the precision and robustness of the multi-lateral measurement system operation.

[0049] 2. The present application comprehensively considers different measurement scenarios and test requirements, and generates optimal base station configurations for different engineering application scenarios.

[0050] 3. This invention ensures the superiority of the configuration in spatial geometry and its feasibility in engineering practice by constructing an initial configuration pool based on optimal computational conditions and verifying its observability.

[0051] 4. This invention introduces the Geometric Deployment Indicator (GDI) as the final selection criterion for configuration, making the screening process clear and easy to automate. Attached Figure Description

[0052] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a schematic diagram of a polygonal measurement system applicable to turntable calibration according to an embodiment of the present invention.

[0053] Figure 2 This is a schematic diagram of the multilateral measurement field measurement scheme involved in the embodiment of the present invention.

[0054] Figure 3 This is a schematic diagram of the optimal configuration involved in the embodiments of the present invention.

[0055] Figure 4 This is a comparative configuration diagram involving an embodiment of the present invention.

[0056] Figure 5 This is a diagram showing the results of the analysis of the accuracy of the measurement point coordinate calculation and the extended uncertainty involved in the embodiments of the present invention.

[0057] Figure 6 This is a flowchart of the method of the present invention. Detailed Implementation

[0058] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0059] like Figure 6 As shown, a method for generating the optimal base station configuration for a multi-sided measurement field of a laser tracker includes the following steps: Step 1: Measurement Point Layout Design. Using the multi-sided measurement field of the laser tracker as the basic measurement method, a measurement point layout design is carried out based on the measurement scenario and testing requirements.

[0060] Step 2: Initial Configuration Pool Generation. Based on the relationship between optimal computational conditions and the spatial geometry of the multi-sided measurement field base station configuration, a series of base station configurations with optimal computational conditions are generated to construct the initial configuration pool.

[0061] Step 3: Observability verification. Perform observability verification on the series of configurations in the initial configuration pool according to the laser tracker parameters, and the configurations passing the verification form the candidate configuration pool.

[0062] Step 4: Optimal configuration screening and execution. Calculate the geometric deployment index (GDI) value of each configuration in the candidate configuration pool, select the configuration with the minimum GDI value as the optimal configuration, and execute multi-lateration combined with the measurement point arrangement scheme.

[0063] Step 5: Post-processing of multi-lateration field data. Measurement point coordinate solution, measurement point deviation cause analysis facing test requirements.

[0064] Among them, the measurement point set designed for specific measurement scenarios and test requirements is , denoted as in the reference coordinate system (R-CS).

[0065] Each configuration in the initial configuration pool is a four-point combination that forms a right rectangular tetrahedron in space, and this spatial geometry has been mathematically proven to have optimal calculation conditions.

[0066] The construction process of the initial configuration pool is as follows: Generate candidate base station position pool based on Hammersley sequence After that, the generation of each configuration in the initial configuration pool uses a construction method from plane to space, taking the construction process of the first configuration as an example.

[0067] First, construct the configuration plane. Select three laser tracker base station positions numbered from to form a temporary three-point combination . When the three interconnected line segments satisfy the following geometric relationships:

[0068] The geometric plane constructed from the three points can be determined as an approximately isosceles right triangle, with an approximation degree of , which facilitates subsequent adjustment operations. is a pre-set tolerance parameter for controlling the approximation degree.

[0069] Then, fine-tune the plane site positions. Place the base station positions corresponding to the right-angle vertices in the first place of , and the plane three-point combination is denoted as . Denote , and take as the reference reference length . Update the position of the acute-angle vertex to :

[0070] in, , At this point, the updated base station combination... The constructed planar figure theoretically forms an isosceles right triangle, and this plane can serve as the constituent plane of a regular right tetrahedron in space.

[0071] Finally, the configuration space geometry is constructed. This is based on the generated three-point combination. and its corresponding reference length The location of the fourth tracking station can be calculated using the following formula. :

[0072] The calculation results with positive and negative signs in the above formula are respectively denoted as: and Ultimately, a four-point combination that theoretically forms a right-angled spatial tetrahedron is constructed. .

[0073] Traverse the candidate base station location pool After combining all sites and performing the above calculation process, the generated initial configuration pool is denoted as . .

[0074] The observability determination process for base station configuration is as follows: by Taking the judgment process as an example, firstly, the configuration of the machine tool under test is verified. The feasibility, namely the location of the last two tracker base stations. and The reachability of these two locations is calculated by an algorithm in the previous stage, rather than directly from the candidate base station location pool. Since the selection is limited and may fall outside the reachable range, this step can be simplified to evaluating the following formula:

[0075] in, Within reach.

[0076] Then, the preset measurement points were set. The observability determination requires traversing... The locations of the four base stations included ensure the preset measurement points. It can be observed at all stations and the light is continuous during the measurement process. (Definition from tracker base station) Pointing to the preset measurement point The direction vector is The vector direction is consistent with the laser beam direction. The locations of the four base stations are merged. Corresponding Afterwards, the average direction vector can be calculated by the following formula As the central axis vector of the cone :

[0077] Wherein, The cone vertex angle of the cone is half of the minimum observation range required by the configuration . The observability determination for the measurement point can be described as the evaluation of the following formula:

[0078] Wherein, , is the nominal observation range, is the preset scale factor.

[0079] All configurations in the initial configuration pool that pass the observability determination in this stage collectively constitute the candidate configuration pool .

[0080] The screening process of the optimal configuration screening is as follows: Calculate the geometric deployment index (GDI) value of each configuration in the candidate configuration pool , for example. The base station configuration relative to any preset measurement point can be established according to the distance formula between two points to establish a measurement residual equation group as follows: Wherein,

[0081] represents the actual measured value of the distance between and . Linearize the above formula, and the coordinate value of the measurement point is obtained through the best unbiased estimate of its linearized form, at which time the calculation deviation of is represented as: Wherein,

[0082] is the Jacobian matrix of for the unknown variable , is the measurement noise covariance matrix. Define the unit vector from the tracker base station pointing to the measurement point as:

[0083] ​​wherein, , . may be composed of , and the specific expression is:

[0084] wherein, . The measurement noise covariance matrix depends on the instrument measurement uncertainty, and the relationship is expressed as:

[0085] wherein, and is the instrument measurement uncertainty inherent parameter given by the manufacturer. Considering that the measurement noise is modeled as a normal distribution , can be expressed as:

[0086] The distance measurement noise causes the unknown quantity deviation, and its covariance matrix estimate value can be calculated by the following formula:

[0087] Then configure for the measurement point The weighted geometric dilution of precision (WGDOP) is defined as:

[0088] wherein, denotes the trace of the matrix.

[0089] Calculate the configuration The WGDOP value for all measurement points in the measurement point set , the geometric deployment index (GDI) of the configuration is defined as:

[0090] The index value is oriented towards the context of measurement point coordinate solution, and reflects the average amplification effect of the spatial geometric relationship between the configuration and each measurement point in the measurement point set to the non-uniform measurement noise.

[0091] Finally, the optimal configuration is determined by selecting the configuration with the smallest GDI value from the candidate configuration pool .

[0092] Combined with the optimal configuration and the preset measurement point set , complete the measurement scheme design, perform laser tracker multi-angle measurement based on the measurement scheme, and collect distance measurement data.

[0093] The laser tracker multi-angle measurement data can be directly used for solving the coordinates of the measurement points. For different measurement scenes and test requirements, the coordinate deviations of the measurement points have different causes, which can be further identified and analyzed.

[0094] Embodiment 1 The embodiment discloses a method for generating an optimal base station configuration of a laser tracker multi-angle measurement field. The implementation object is a rotary table of a five-axis machining center. The measurement scene and test requirement are the measurement and identification of the geometric error of the rotary axis of the multi-axis machine tool. The working space of the five-axis machining center is , and the coordinates of the nominal rotation center of the rotary table in the machine tool mechanical coordinate system are .

[0095] The multi-angle measurement system arranged for the rotary table is shown in Figure 1 .

[0096] The specific implementation process is as follows: Step 1: Measurement point arrangement scheme design.

[0097] The measurement points of the multi-angle measurement system are arranged for the rotary table error measurement of the multi-axis machining center. During the execution of the built multi-angle measurement system, the tracker body is installed on the rotary table to map the rotation motion of the measured rotary table; the reflector is installed at the end of the main shaft as the base station side. According to the data volume requirement of subsequent error identification, at least three coordinate deviation information of the measurement points need to be obtained at each command angle of the rotary table, which respectively correspond to the three installation positions of the laser tracker body on the rotary table. The included angle between the three installation positions and the rotation center is approximately 120 degrees, and the rotation radii are , the measurement point set is , and in the reference coordinate system (R-CS), it is , as shown in Figure 2 . The subsequent three steps aim to generate the base station configuration shown in Figure 2 , including .

[0098] Step 2: Initial configuration pool generation.

[0099] S2.1 Generate candidate base station position pool First, based on the Hammersley sequence generation principle (dimension 3, number 300), generate the candidate base station position pool according to the nominal working space of the machine tool.

[0100] S2.2 Construct initial configuration Construct the first When configuring groups, the configuration plane is built first. From Three numbers were selected from the list. The locations of the laser tracker base stations were used to form a temporary three-point combination. When three interconnecting segments When the following geometric relationship is satisfied:

[0101] Depend on The geometric plane constructed by the three points can be determined as an approximately isosceles right triangle, with an approximation degree of... This facilitates subsequent adjustments. This is a preset tolerance parameter for controlling the degree of approximation.

[0102] Then, fine-tuning of the site locations was performed. The locations of the base stations corresponding to the right-angle vertices were listed in... The first position, at this time the combination of three points in the plane is denoted as .remember ,by Reference datum length The acute angle vertex is expressed by the following formula. Location updated to :

[0103] in, , At this point, the updated base station combination... The constructed planar figure theoretically forms an isosceles right triangle, and this plane can serve as the constituent plane of a regular right tetrahedron in space.

[0104] Finally, the configuration space geometry is constructed. This is based on the generated three-point combination. and its corresponding reference length The location of the fourth tracking station can be calculated using the following formula. :

[0105] The calculation results with positive and negative signs in the above formula are respectively denoted as: and Ultimately, a four-point combination that theoretically forms a right-angled spatial tetrahedron is constructed. .

[0106] Traverse the candidate base station location pool After combining all sites and repeating the S2.2 calculation process described above, the resulting initial configuration pool is denoted as... .

[0107] Step 3: Configure observability verification.

[0108] When the determination is made, the feasibility of the configuration of the machine tool to be measured is first verified, i.e. the accessibility of the last two tracking station base station positions . These two positions are calculated by an algorithm in the previous stage, rather than being selected directly from the pool of candidate base station positions , and thus can be beyond the accessible range (the nominal working space of the machine tool). This step can be simplified to an evaluation of the following formula:

[0109] wherein, is the accessible range.

[0110] Subsequently, the observability determination of the preset measurement point is made, which needs to traverse the four base station positions contained in to ensure that the preset measurement point can be observed when switching stations and that the light is constantly measured during the measurement process. The direction vector from the tracking station base station to the preset measurement point is defined as , which is consistent with the direction of the laser beam. After merging the corresponding of the four base station positions , the average direction vector can be calculated as the central axis vector of the cone :

[0111] wherein, . The cone top angle of the cone is half of the minimum observation range required for the configuration . The observability determination of the configuration for the measurement point can be described as an evaluation of the following formula:

[0112] wherein, , is the nominal observation range, is the preset proportion factor.

[0113] All configurations in the initial configuration pool that pass the observability determination in this stage collectively constitute the candidate configuration pool .

[0114] Step 4: Optimal configuration screening and execution.

[0115] The candidate configuration pool The geometry deployment index (GDI) value of each configuration is taken as an example. The base station configuration is taken as an example. The measurement residual equation set can be established according to the distance formula between two points as follows:

[0116] wherein, represents the actual measured distance between the two points.The linearization of the above formula is performed, and the coordinate value of the measurement point is obtained through the best unbiased estimate of the linearization form, and the calculation deviation of is represented as:

[0117] wherein, is the Jacobian matrix of the unknown variable , is the measurement noise covariance matrix. The unit vector from the tracker base station to the measurement point is defined as:

[0118] wherein, , . can be composed of , and the specific expression is:

[0119] wherein, . The measurement noise covariance matrix depends on the instrument measurement uncertainty, and the relationship is represented as:

[0120] wherein, and are inherent parameters of the instrument measurement uncertainty, which are given by the manufacturer. Considering that the measurement noise is modeled as a normal distribution , can be expressed as:

[0121] The distance measurement noise causes the deviation of the unknown variable , and the covariance matrix estimate value can be calculated by the following formula:

[0122] Therefore, the configuration is aimed at the measurement point​​ The weighted geometric precision factor (WGDOP) is defined as follows:

[0123] in, Represents the trace of a matrix.

[0124] Computational Configuration For the measurement point set Define the WGDOP values ​​of all measurement points within the system. The Geometric Deployment Indicator (GDI) is:

[0125] This index value is oriented towards the scenario of solving the coordinates of the measurement points, reflecting the configuration. With measurement point set The spatial geometric relationship formed by the measurement points within the measurement area has an average amplification effect on non-uniform measurement noise.

[0126] Ultimately, the optimal configuration By selecting from the candidate configuration pool The configuration with the smallest GDI value is selected to determine the optimal configuration. Includes four base station locations and a multilateral measurement scheme, such as Figure 3 As shown, subsequent multilateral measurements will be performed according to this scheme.

[0127] Step 5: Post-processing of multilateral measurement field data.

[0128] The Levenberg-Marquardt algorithm is used to solve for the coordinates of the measurement points. To reflect the optimal configuration... The superiority of the configurations was demonstrated by selecting three sets of comparison configurations. Figure 4 As shown. 1000 Monte Carlo simulations were run to compare the coordinate calculation accuracy and robustness of the four configurations. Measurement noise was measured using a normal distribution. Modeling, Figure 2 Two-thirds of the measurement points shown are used for measurement system calibration, and the other one-third are used for accuracy and robustness verification.

[0129] Simulation analysis results are as follows Figure 5 As shown, the optimal configuration can be observed. and Significant differences exist in both computational accuracy and robustness. The mean absolute error (MAE) calculated in the three directions reaches More than 4 times; the other two random configurations The MAE values ​​are respectively 1.7 times and 2.3 times. At the same measurement noise level, showed the lowest average expanded uncertainty (EU), with an average of 0.26 μm in three directions, only for random configuration 52.92%, 38.08% and 23.72% of the corresponding values.

[0130] In the embodiment, the above configuration screening and subsequent calculation and analysis process can be performed by computer program instructions related hardware. The program can be stored in a computer readable storage medium, including but not limited to a magnetic disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM).

[0131] The screening strategy provided by the application is practical, and the best base station configuration finally screened can support high stability and high precision point coordinate calculation; the application does not change the existing multi-lateral measurement field architecture, does not need to introduce third-party equipment or standard parts, and has the advantages of high implementation efficiency, good universality for the same industrial measurement problem, and strong expansibility.

[0132] The application also provides a laser tracker multi-lateral measurement field optimal base station configuration generation system, which can be realized by executing the process steps of the laser tracker multi-lateral measurement field optimal base station configuration generation method, that is, the laser tracker multi-lateral measurement field optimal base station configuration generation method can be understood as the preferred embodiment of the laser tracker multi-lateral measurement field optimal base station configuration generation system by those skilled in the art.

[0133] Specifically, a laser tracker multi-lateral measurement field optimal base station configuration generation system comprises: Module M1: configuring a point arrangement scheme based on a measurement scene and a test requirement; Module M2: generating an initial configuration pool based on the relationship between optimal calculation conditions and the spatial geometry of the multi-lateral measurement field base station configuration; Module M3: performing observability verification on a series of configurations of the initial configuration pool according to laser tracker parameters, and constructing a candidate configuration pool with the configurations that pass the verification; Module M4: calculating the geometric deployment index value of each configuration in the candidate configuration pool, selecting the configuration with the smallest GDI value as the optimal configuration, and performing multi-lateral measurement in combination with the point arrangement scheme.

[0134] Further comprising: Module M5: performing point coordinate calculation on multi-lateral measurement data, analyzing the causes of point deviation facing the test requirement, and outputting the analysis results.

[0135] The point set designed for a specific measurement scene and test requirement is , denoted as in a reference coordinate system (R-CS).

[0136] The initial configuration pool construction process includes: Generate a candidate base station location pool based on Hammersley sequences. Subsequently, the generation of each configuration within the initial configuration pool adopts a construction method from planar to spatial representation. The process of building the group configuration is as follows: Build a configuration plane, from Three numbers were selected from the list. The locations of the laser tracker base stations were used to form a temporary three-point combination. When three interconnecting segments When the following geometric relationship is satisfied:

[0137] Depend on The geometric plane constructed by the three points is determined to be an approximately isosceles right triangle, with an approximation degree of [missing information]. ; This is a preset tolerance parameter for controlling the degree of approximation; Perform fine-tuning of the planar site locations, listing the base station locations corresponding to the right-angle vertices. The first position, at this time the combination of three points in the plane is denoted as ,remember ,by Reference datum length The acute angle vertex is expressed by the following formula. Location updated to :

[0138] in, , At this time, the updated base station combination The constructed planar figure theoretically forms an isosceles right triangle; Construct configuration space geometry; based on the generated three-point combination and its corresponding reference length The location of the fourth tracking station is calculated using the following formula. :

[0139] The calculation results with positive and negative signs in the above formula are respectively denoted as: and Ultimately, this constructs a four-point combination that theoretically forms a right-angled spatial tetrahedron: ; Traverse the candidate base station location pool After combining all sites and performing the above calculation process, the generated initial configuration pool is denoted as . .

[0140] The process of observability verification includes: determination ; verify the feasibility of the implementation configuration of the machine tool, i.e. the accessibility of the last two tracking instrument base station positions , which is simplified as the evaluation of the following formula:

[0141] wherein, is the accessible range; conduct the observability determination of the preset measurement point , which needs to traverse the four base station positions contained in to ensure that the preset measurement point can be observed and the light is constantly measured during the switching station; define the direction vector from the tracking instrument base station to the preset measurement point as , which is consistent with the direction of the laser beam; after merging the corresponding of the four base station positions , calculate the average direction vector as the central axis vector of the cone :

[0142] wherein, ; the cone top angle of the cone is half of the minimum observation range required by the configuration ; the observability determination of the configuration for the measurement point is described as the evaluation of the following formula:

[0143] wherein, , is the nominal observation range, is a preset proportion factor; all configurations in the initial configuration pool that pass the observability determination in this stage jointly constitute the candidate configuration pool .

[0144] The screening process of the optimal configuration screening includes: calculate the geometric deployment index value of each configuration in the candidate configuration pool ; the base station configuration relative to any preset measurement point ​​The measurement residual equations are established according to the distance formula between two points as follows:

[0145] wherein, represents the measured value of the distance between the two points; The linearization of the above formula is performed, and the coordinate values of the measuring points are obtained through the best unbiased estimation of the linearization form, and at this time the calculation bias of is represented as:

[0146] wherein, is the Jacobian matrix of the unknown variables , and is the measurement noise covariance matrix; the unit vector from the tracking instrument base station to the measuring point is defined as:

[0147] wherein, , is composed of , and the specific expression is:

[0148] wherein, ; the measurement noise covariance matrix depends on the instrument measurement uncertainty, and the relationship is represented as:

[0149] wherein, and are the instrument measurement uncertainty inherent parameters given by the manufacturer. Considering that the measurement noise is modeled as a normal distribution , , the expression is:

[0150] The distance measurement noise causes the bias of the unknown quantity , and the covariance matrix estimation value is calculated through the following formula:

[0151] Then the configuration of the weighted geometric precision factor for the measuring point is defined as: ​​​

[0152] wherein, denotes the trace of a matrix; configuration for the set of survey points WGDOP values of all survey points in the set, define the configuration The geometric deployment index of the configuration is:

[0153] The index value is oriented to the context of survey point coordinate solution, reflecting the configuration and the spatial geometric relationship formed by each survey point in the set The average amplification effect of non-uniform measurement noise; optimal configuration The configuration with the minimum GDI value is selected from the candidate configuration pool to determine.

[0154] Those skilled in the art know that in addition to implementing the system provided by the present application and each device, module, unit thereof in a pure computer readable program code manner, the same function can be achieved by logically programming the method steps in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers and embedded microcontrollers. Therefore, the system provided by the present application and each device, module, unit thereof can be considered as a hardware component, and the devices, modules, units included therein for achieving various functions can also be considered as structures within the hardware component; the devices, modules, units for achieving various functions can also be considered as both software modules for achieving methods and structures within the hardware component.

[0155] The specific embodiments of the present application are described above. It should be understood that the present application is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essential content of the present application. In the case of no conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A method for generating optimal base station configuration in a polygonal measurement field of a laser tracker, characterized in that, include: Step S1: Configure the measurement point layout scheme based on the measurement scenario and testing requirements; Step S2: Generate an initial configuration pool based on the relationship between the optimal calculation conditions and the spatial geometry of the multi-sided measurement field base station configuration. Step S3: Perform observability verification on the series of configurations in the initial configuration pool based on the laser tracker parameters, and form a candidate configuration pool from the configurations that pass the verification. Step S4: Calculate the geometric deployment index value of each configuration in the candidate configuration pool, select the configuration with the smallest GDI value as the optimal configuration, and perform multilateral measurement in combination with the measurement point layout scheme.

2. The method for generating the optimal base station configuration for a multi-sided measurement field of a laser tracker according to claim 1, characterized in that, Also includes: Step S5: Calculate the coordinates of the measurement points in the multilateral measurement data, analyze the causes of measurement point deviations in line with testing requirements, and output the analysis results.

3. The method for generating the optimal base station configuration for a multi-sided measurement field of a laser tracker according to claim 1, characterized in that, The set of measurement points designed for specific measurement scenarios and testing requirements is In the reference coordinate system R-CS, it is denoted as .

4. The method for generating the optimal base station configuration for a multi-sided measurement field of a laser tracker according to claim 1, characterized in that, The initial configuration pool construction process includes: Generate a candidate base station location pool based on Hammersley sequences. Subsequently, the generation of each configuration within the initial configuration pool adopts a construction method from planar to spatial representation. The process of building group configurations is as follows: Build a configuration plane, from Three numbers were selected from the list. The locations of the laser tracker base stations were used to form a temporary three-point combination. When three interconnecting segments When the following geometric relationship is satisfied: Depend on The geometric plane constructed by the three points is determined to be an approximately isosceles right triangle, with an approximation degree of [missing information]. ; This is a preset tolerance parameter for controlling the degree of approximation; Perform fine-tuning of the planar site locations, listing the base station locations corresponding to the right-angle vertices. The first position, at this time the combination of three points in the plane is denoted as ,remember ,by Reference datum length The acute angle vertex is expressed by the following formula. Location updated to : in, , At this time, the updated base station combination The constructed planar figure theoretically forms an isosceles right triangle; Construct configuration space geometry; based on the generated three-point combination and its corresponding reference length The location of the fourth tracking station is calculated using the following formula. : The calculation results with positive and negative signs in the above formula are respectively denoted as: and Ultimately, this constructs a four-point combination that theoretically forms a right-angled spatial tetrahedron: ； Traverse the candidate base station location pool After combining all sites and performing the above calculation process, the generated initial configuration pool is denoted as . .

5. The method for generating the optimal base station configuration for a multi-sided measurement field of a laser tracker according to claim 1, characterized in that, The process of observability verification includes: judgement ; Verify the configuration of the machine tool under test The feasibility, namely the location of the last two tracker base stations. and The accessibility can be simplified to an evaluation of the following formula: in, Within reach; Set up measurement points The observability determination requires traversing... The locations of the four base stations included ensure the preset measurement points. It can be observed at all stations and the light is continuous during the measurement process; defined from the tracker base station Pointing to the preset measurement point The direction vector is The vector direction is consistent with the laser beam direction; the locations of the four base stations are merged. corresponding Then, the average direction vector is calculated using the following formula. As a cone bag Central axis vector: in, cone bag The cone apex angle is configured Half of the minimum required observation range; configuration For measuring points The observability criterion is described as an evaluation of the following formula: in, , For nominal observation range, This is a preset scaling factor; Initial configuration pool All configurations that pass the observability determination in this stage constitute the candidate configuration pool. .

6. The method for generating the optimal base station configuration for a multi-sided measurement field of a laser tracker according to claim 1, characterized in that, The optimal configuration selection process includes: Calculate the candidate configuration pool Geometric deployment metric values ​​for each configuration; Base station configuration Relative to any preset measuring point Based on the formula for the distance between two points, the following set of measurement residual equations is established: in, express and Measured distance between them; Linearize the above equation, measuring points The coordinate values ​​are obtained through the best unbiased estimate of their linearized form, at which point... The calculation deviation is expressed as: in, yes For unknown variables Jacobian matrix, To measure the noise covariance matrix; define the noise covariance matrix from the tracker base station. Pointing to the measuring point The unit vector is: in, , ; Depend on Composition, specifically expressed as: in, Measurement noise covariance matrix Depending on the instrument measurement uncertainty, the relationship is expressed as: in, and The inherent parameters of the instrument measurement uncertainty are defined; the measurement noise is modeled as a normal distribution. , The expression is as follows: Unknown quantities caused by distance measurement noise The deviation, whose covariance matrix estimate is calculated by the following formula: Then configure For measuring points The weighted geometric precision factor is defined as: in, Represents the trace of a matrix; Computational Configuration For the measurement point set Define the WGDOP values ​​of all measurement points within the system. The geometric deployment metrics are: This index value is oriented towards the scenario of solving the coordinates of the measurement points, reflecting the configuration. With measurement point set The average amplification effect of the spatial geometric relationship formed by each measuring point on non-uniform measurement noise; Optimal configuration By selecting from the candidate configuration pool The configuration with the smallest GDI value is selected to determine the optimal configuration.

7. An optimal base station configuration generation system for a multi-sided measurement field of a laser tracker, characterized in that, include: Module M1: Configures the measurement point layout scheme based on the measurement scenario and testing requirements; Module M2: Generates an initial configuration pool based on the relationship between optimal computational conditions and the spatial geometry of the multi-sided measurement field base station configuration. Module M3: Performs observability verification on a series of configurations in the initial configuration pool based on the laser tracker parameters, and constructs a candidate configuration pool from the verified configurations. Module M4: Calculates the geometric deployment index value of each configuration in the candidate configuration pool, selects the configuration with the smallest GDI value as the optimal configuration, and performs multilateral measurements in conjunction with the measurement point layout scheme.

8. The optimal base station configuration generation system for a multi-sided measurement field of a laser tracker according to claim 7, characterized in that, Also includes: Module M5: Calculates the coordinates of measurement points in multi-dimensional measurement data, analyzes the causes of measurement point deviations for testing requirements, and outputs the analysis results.

9. The optimal base station configuration generation system for a multi-sided measurement field of a laser tracker according to claim 7, characterized in that, The set of measurement points designed for specific measurement scenarios and testing requirements is In the reference coordinate system R-CS, it is denoted as .

10. The optimal base station configuration generation system for a multi-sided measurement field of a laser tracker according to claim 7, characterized in that, The initial configuration pool construction process includes: Generate a candidate base station location pool based on Hammersley sequences. Subsequently, the generation of each configuration within the initial configuration pool adopts a construction method from planar to spatial representation. The process of building group configurations is as follows: Build a configuration plane, from Three numbers were selected from the list. The locations of the laser tracker base stations were used to form a temporary three-point combination. When three interconnecting segments When the following geometric relationship is satisfied: Depend on The geometric plane constructed by the three points is determined to be an approximately isosceles right triangle, with an approximation degree of [missing information]. ; This is a preset tolerance parameter for controlling the degree of approximation; Perform fine-tuning of the planar site locations, listing the base station locations corresponding to the right-angle vertices. The first position, at this time the combination of three points in the plane is denoted as ,remember ,by Reference datum length The acute angle vertex is expressed by the following formula. Location updated to : in, , At this time, the updated base station combination The constructed planar figure theoretically forms an isosceles right triangle; Construct configuration space geometry; based on the generated three-point combination and its corresponding reference length The location of the fourth tracking station is calculated using the following formula. : The calculation results with positive and negative signs in the above formula are respectively denoted as: and Ultimately, this constructs a four-point combination that theoretically forms a right-angled spatial tetrahedron: ； Traverse the candidate base station location pool After combining all sites and performing the above calculation process, the generated initial configuration pool is denoted as . .

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