Precise positioning method and system for multi-station jig

Abstract

The invention relates to the technical field of precise positioning, and discloses a precise positioning method and system for a multi-station jig, and the method comprises the steps: carrying out the error propagation chain modeling of the real-time position measurement data of each station in a multi-station jig system, and obtaining an inter-station error propagation chain data model; recursive least square estimation is carried out on jig gap change data based on the inter-station error propagation chain data model, and jig gap compensation parameters of all stations are obtained; performing coupled Lyapunov function synchronous convergence analysis on a multi-station error state according to the jig clearance compensation parameter, and generating an inter-station synchronous convergence control instruction; thermal deformation prediction compensation is carried out based on the inter-station synchronous convergence control instruction to obtain accumulative error compensation data, gap parameter changes caused by jig abrasion and temperature changes can be recognized online, and high-precision real-time positioning of a multi-station jig system is achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of precision positioning, and in particular to a precision positioning method and system for a multi-station jig. BACKGROUND

[0002] Traditional multi-station jig positioning methods mainly rely on precise jig geometric parameters and stiffness coefficients for error compensation, but in actual production environments, the geometric parameters of the jig are often difficult to obtain accurately, and key parameters such as jig stiffness coefficients and material expansion coefficients will change dynamically due to factors such as wear and temperature changes, resulting in the inability of compensation methods based on fixed parameters to meet high-precision positioning requirements.

[0003] Existing multi-station jig positioning technology usually adopts an independent compensation strategy for each station, ignoring the coupling relationship of error propagation between stations, and cannot guarantee the synchronous convergence of errors in each station, resulting in limited positioning accuracy of the entire system. At the same time, traditional methods mostly use static compensation mode, lack the ability to actively predict and compensate for time-varying disturbance factors such as jig thermal deformation and positioning pin wear, and are prone to the problem of gradually increasing cumulative errors during long-term continuous processing, seriously affecting the positioning stability and reliability of the multi-station system. SUMMARY

[0004] The present application provides a precision positioning method and system for a multi-station jig, which can identify changes in the gap parameters caused by jig wear and temperature changes in real time, and achieve high-precision real-time positioning of the multi-station jig system.

[0005] The present application provides a precision positioning method and system for a multi-station jig, which can identify changes in the gap parameters caused by jig wear and temperature changes in real time, and achieve high-precision real-time positioning of the multi-station jig system.

[0006] In a first implementation manner of the first aspect, the real-time position measurement data of each station in the multi-station jig system is modeled to obtain an error propagation chain data model between stations, including: ​​​​A three-dimensional coordinate system is established based on spatial position data of each station in the multi-station fixture system, and spatial position relationship data between stations is generated based on the three-dimensional coordinate system, which is described by a homogeneous coordinate transformation matrix; Error propagation relationship modeling is performed based on the spatial position relationship data between stations to obtain a mathematical model of error propagation between stations containing accumulated error of previous stations and local error of a current station; Six-dimensional vector construction processing is performed on translational error components and rotational error components of each station according to the mathematical model of error propagation between stations to obtain a six-dimensional error state vector containing X, Y and Z translational error components and rotational error components around X, Y and Z axes; Based on the six-dimensional error state vector, time-varying factor analysis of fixture wear and thermal deformation is performed on the mathematical model of error propagation between stations to obtain a data model of error propagation chain between stations.

[0007] In combination with the first aspect, in a second implementation manner of the first aspect of the present application, the error propagation relationship modeling based on the spatial position relationship data between stations to obtain a mathematical model of error propagation between stations containing accumulated error of previous stations and local error of a current station comprises: Error propagation relationship between the i-th station and the i-1-th station is analyzed based on the spatial position relationship data between stations to obtain an initial mathematical model of error propagation taking accumulated positioning error vector of the i-th station as a dependent variable and accumulated error of previous stations and local error of a current station as independent variables; Error propagation coefficient calculation is performed based on the initial mathematical model of error propagation to obtain an error propagation matrix between stations describing error propagation law from the i-1-th station to the i-th station; Linear superposition operation is performed on accumulated error vector of previous stations and local error vector of a current station based on the error propagation matrix between stations to obtain accumulated error data containing contribution amount of accumulated error of previous stations and contribution amount of local error of a current station; Error propagation coefficient dynamic update is performed on the initial mathematical model of error propagation based on the accumulated error data to obtain a mathematical model of error propagation between stations.

[0008] In combination with the first aspect, in a third implementation manner of the first aspect of the present application, the fixture gap change data is recursively least square estimated based on the data model of error propagation chain between stations to obtain fixture gap compensation parameters of each station, which comprises: State observation is performed on fixture gap change data based on the data model of error propagation chain between stations to obtain a state observation equation containing a measurement error vector, an observation matrix and a to-be-estimated fixture gap parameter vector; The Kalman gain matrix is obtained by performing Kalman gain calculation on the covariance matrix according to the state observation equation, and the updated covariance matrix is obtained by performing recursive update operation on the covariance matrix based on the Kalman gain matrix; The jig gap compensation parameters of each station are obtained by performing jig gap parameter analysis on the updated covariance matrix.

[0009] In a fourth implementation manner of the first aspect, the jig gap compensation parameters of each station are obtained by performing jig gap parameter analysis on the updated covariance matrix. A tracking forgetting factor of a jig gap time-varying characteristic is calculated based on the updated covariance matrix. The historical data weight distribution matrix is obtained by performing weight distribution on historical jig gap data according to the tracking forgetting factor. The jig gap parameter recursive update equation containing the parameter value of the previous period and the correction amount of the current period is obtained by performing recursive update on the current period jig gap parameter based on the historical data weight distribution matrix. The jig gap compensation parameters of each station are obtained by performing gap change factor analysis based on the jig gap parameter recursive update equation.

[0010] In a fifth implementation manner of the first aspect, the coupled Lyapunov function synchronization convergence analysis on the multi-station error state is performed based on the jig gap compensation parameters to generate the inter-station synchronization convergence control instruction, and the coupled Lyapunov function synchronization convergence analysis on the multi-station error state is performed based on the jig gap compensation parameters to generate the inter-station synchronization convergence control instruction. The inter-station error synchronization convergence criterion containing the synchronization convergence threshold is created by performing error synchronization convergence analysis on the multi-station error state based on the jig gap compensation parameters. The coupled Lyapunov function containing the station weight coefficient and the positive definite weighted matrix is constructed according to the inter-station error synchronization convergence criterion. The synchronization convergence control law equation containing the local feedback gain matrix and the inter-station coupling coefficient is designed based on the coupled Lyapunov function. The inter-station synchronization convergence control instruction is generated by performing coupling coefficient adjustment on the inter-station error difference value according to the synchronization convergence control law equation.

[0011] In a sixth implementation manner of the first aspect, the inter-station synchronization convergence control instruction is generated by performing coupling coefficient adjustment on the inter-station error difference value according to the synchronization convergence control law equation. The inter-station error difference value data containing the absolute error difference value between the i-th station and the adjacent station is obtained by performing difference calculation on the error state of each station based on the synchronization convergence control law equation. The preset synchronization deviation threshold is judged to be exceeded according to the inter-station error difference data, and a coupling coefficient adjustment trigger condition for triggering coupling coefficient adjustment is obtained; The inter-station coupling coefficient is automatically enhanced and adjusted based on the coupling coefficient adjustment trigger condition, and an adjusted inter-station coupling coefficient is obtained. Synchronization convergence time is calculated based on the adjusted inter-station coupling coefficient, and an inter-station synchronization convergence control instruction is generated.

[0012] In a seventh implementation manner of the first aspect, the heat deformation prediction compensation based on the inter-station synchronization convergence control instruction comprises: A jig heat deformation prediction model containing an equivalent thermal expansion coefficient, a jig initial size and a temperature change amount is established based on the inter-station synchronization convergence control instruction. An adaptive parameter update equation containing a learning rate, a heat deformation prediction error and a cost function gradient is constructed according to the jig heat deformation prediction model. The heat deformation parameters are updated in a sliding window based on the adaptive parameter update equation, real-time updated heat deformation compensation parameters are obtained, and cumulative error prediction compensation is performed on the real-time updated heat deformation compensation parameters to obtain cumulative error compensation data.

[0013] In an eighth implementation manner of the first aspect, the cumulative error prediction compensation performed on the real-time updated heat deformation compensation parameters comprises: A cumulative error prediction model containing a prediction model parameter matrix, a state transition matrix and a control input matrix is constructed based on the real-time updated heat deformation compensation parameters. The next period error state is predicted according to the cumulative error prediction model, and next period prediction error state data containing a current error state and a control input amount are obtained. The real-time measurement data are Kalman filter corrected based on the next period prediction error state data, and corrected error state data are obtained. The optimal control amount is calculated based on the corrected error state data, and cumulative error compensation data are obtained.

[0014] The second aspect of the present application provides a precision positioning system of a multi-station jig, which comprises: A modeling module is configured to model real-time position measurement data of each station in a multi-station jig system to obtain an inter-station error propagation chain data model. an estimation module configured to perform recursive least square estimation on the jig gap variation data based on the inter-station error propagation chain data model to obtain jig gap compensation parameters of each station; an analysis module configured to perform coupled Lyapunov function synchronous convergence analysis on the multi-station error state according to the jig gap compensation parameters to generate inter-station synchronous convergence control instructions; a compensation module configured to perform thermal deformation prediction compensation based on the inter-station synchronous convergence control instructions to obtain cumulative error compensation data.

[0015] Compared with the prior art, the present application has the following beneficial effects: by constructing an inter-station error propagation mathematical model containing the cumulative error of the previous station and the local error of the current station, the propagation law of the error in the multi-station system is accurately described, the technical defects of the traditional method of ignoring the inter-station error coupling relationship are overcome, the recursive least square estimation algorithm combined with the forgetting factor mechanism is used to identify the gap parameter variation caused by jig wear, temperature change and the like, the dependence on the accurate jig stiffness coefficient and the material expansion coefficient is eliminated, and the adaptive ability and robustness of parameter estimation are significantly improved. By designing a synchronous convergence control law based on the coupled Lyapunov function, it is ensured that the positioning errors of all stations can be synchronized to converge to the preset threshold within a limited compensation period, and the technical problem that the traditional independent convergence method of each station cannot guarantee the overall performance of the system is solved. A jig thermal deformation prediction model is established and combined with an adaptive parameter updating mechanism to actively predict and compensate the influence of thermal deformation on positioning accuracy, which has better compensation effect and timeliness than the passive compensation method. A three-level transformation structure of the global coordinate system-station coordinate system-local compensation coordinate system is established to realize dynamic real-time updating of the coordinate transformation matrix, ensure that no geometric distortion is generated in the compensation process, and meet the real-time requirements of high-precision machining. The present application has higher control precision and stronger anti-interference ability than single feedback control, and realizes high-precision real-time positioning of the multi-station jig system. BRIEF DESCRIPTION OF DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and those skilled in the art can obtain other drawings according to these drawings without creative labor.

[0017] The structure, proportion, size and the like shown in the drawings of the specification are only used to cooperate with the content disclosed in the specification, to be understood and read by those skilled in the art, and do not have technical significance to limit the conditions that the application can be implemented. Any modification of the structure, change of the proportion relationship or adjustment of the size, without affecting the effect that the application can produce and the purpose that the application can achieve, should still fall within the scope covered by the disclosed technology.

[0018] Figure 1 is a flowchart of a precision positioning method of a multi-station jig provided by an embodiment of the application; Figure 2 is a structural schematic block diagram of a precision positioning system of a multi-station jig provided by an embodiment of the application. DETAILED DESCRIPTION

[0019] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are some of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the application.

[0020] The flowchart shown in the drawings is only an example and does not necessarily include all the contents and operations / steps, nor does it necessarily execute in the order described. For example, some operations / steps can be decomposed, combined or partially combined, so the actual execution order may be changed according to the actual situation.

[0021] It should also be understood that the terms used in this specification of the application are only for the purpose of describing specific embodiments and are not intended to limit the application. As used in the specification and the appended claims of the application, the singular forms "a", "an" and "the" are intended to include the plural forms unless the context clearly indicates otherwise.

[0022] It should be further understood that the term "and / or" used in the specification and the appended claims of the application means any combination of one or more of the associated listed items and all possible combinations, and includes these combinations. Please refer to Figure 1 One embodiment of the precision positioning method of a multi-station jig in the embodiments of the application includes: Step 100, error propagation chain modeling is performed on real-time position measurement data of each station in a multi-station jig system to obtain error propagation chain data model between stations; It can be understood that the execution subject of the present application can be a precision positioning system of a multi-station jig, and can also be a terminal or a server, and the specific implementation is not limited herein. The embodiments of the present application take the server as an example for description.

[0023] Specifically, based on the actual geometric structure and spatial configuration of the entire multi-station jig system, a three-dimensional space coordinate system is established, in which each station is regarded as an independent coordinate origin, and the relative position relationship between each station and other stations is described in the coordinate system. The spatial position transformation relationship between each station is represented by a homogeneous coordinate transformation matrix, which can comprehensively describe the translation and rotation of the coordinate points of any station in the global coordinate system, forming a set of data structures describing the geometric configuration of the multi-station system. Based on the spatial position relationship data formed by the above homogeneous transformation matrix, an error propagation relationship model is established, which represents the total positioning error of a station as a comprehensive error expression form composed of the local error of the station itself and the error of the previous station propagated through space. In the mathematical processing process of the above error relationship model, the error of each station is expressed as a six-dimensional vector, i.e. a six-dimensional error state vector containing three translation error components and three rotation error components, wherein the translation error components include linear displacement deviations in X, Y and Z directions, and the rotation error components describe angular deviations around X, Y and Z axes. Based on the six-dimensional error state vector, the jig wear and thermal deformation time-varying factor analysis of the error propagation mathematical model between stations is carried out. By introducing dynamic parameters of time-varying error influence quantities such as jig surface contact gap change function and thermal expansion increment function, the model is dynamically enhanced on the original structure, so that each segment of the error propagation chain not only transmits the error of the previous station, but also updates the error increment of the current station caused by external disturbance in real time, thereby obtaining an error propagation chain data model between stations with time sequence dynamics, high precision and strong update ability.

[0024] Based on the geometric relative relationship between each station in the multi-station fixture system, the error propagation path between the i-th station and its previous i-1-th station is analyzed. In this analysis, according to the three-dimensional coordinate system and the homogeneous coordinate transformation matrix that have been constructed, the spatial mapping relationship between the two stations is mathematically expanded, and then it is clear how the error is gradually transmitted through the structural connection between the stations. Based on this mapping relationship, an initial error propagation mathematical model is constructed, which takes the cumulative positioning error vector of the i-th station as the dependent variable, and the cumulative error of the i-1-th station and the local error of the i-th station as the independent variables, forming a typical linear transformation function expression, thereby establishing the structural channel of error conduction from the previous station to the current station in mathematical form. On the basis of the initial model constructed, the propagation coefficient used to describe the error transmission strength and direction characteristics is quantitatively solved, that is, the error propagation coefficient between the stations is modeled and operated, and the error propagation matrix that accurately describes how the i-1-th station error acts on the i-th station is obtained. The error propagation matrix has a 6x6 structure, which is used to map the six-dimensional error state of the previous station to the corresponding error state of the current station, while preserving the spatial coupling characteristics, so that the linkage relationship between the translation error and the rotation error can be expressed. Through the construction of the matrix, the attenuation, amplification or direction change of the error amount between the stations is accurately described, and a standardized error transmission mechanism is provided for the system. On the basis of obtaining the error propagation matrix, the cumulative error vector of the i-1-th station and the local error vector of the i-th station are input into the propagation model, and linear superposition calculation is performed to obtain the complete cumulative error data of the i-th station. In order to cope with the change of error propagation law caused by wear, temperature change or external force disturbance of the fixture system in the long-term running process, the propagation coefficient in the initial error propagation model is dynamically adjusted. The adjustment process relies on the real-time measurement data collected by the system, and by establishing the error residual between the actual observation value and the theoretical propagation model, and combining the recursive estimation or least squares optimization method, each element in the propagation matrix is modified in real time, thereby forming an online dynamic updating mechanism for the error propagation coefficient. The error propagation mathematical model between the stations is obtained.

[0025] Step 200, based on the fixture gap change data between the stations, the fixture gap compensation parameters of each station are obtained by recursive least squares estimation. Specifically, a state observation mechanism for dynamically tracking the gap variation behavior of the jig is constructed based on the error propagation chain data model as the core structure. In actual operation, the current station error observation results are collected from high-precision sensors in each compensation period of the system, and the observation data is input as a measurement error vector. At the same time, according to the coupling structure relationship between the stations in the error propagation chain model and the spatial response mode of the jig gap to the error formation, the corresponding observation matrix is constructed to express the mapping relationship between the current error state and the jig gap parameters. The unknown jig gap variation parameters in the system are constructed as an estimated parameter vector, so that the entire state observation system can clearly describe the causal response between the error and the parameters in the data structure. On this basis, the estimation process relies on a recursive least squares estimation method, which introduces a covariance matrix to measure the estimation uncertainty and adaptively adjusts the estimation weight of the current state through the Kalman gain mechanism. Moreover, the system introduces the Kalman gain matrix as the core adjustment factor, and the change of its value determines the influence degree of the current measurement data on the estimation update. When the jig gap changes dramatically, the value of the gain matrix will be automatically amplified, thereby enhancing the influence of new observations on parameter estimation and quickly responding to gap changes. Conversely, when the system is in a stable state, the gain converges to reduce, enhancing the weight of the historical estimation results, ensuring the continuity and robustness of the estimation results in the steady state. In each period, the covariance matrix is recursively adjusted with the observation information update, thereby dynamically correcting the estimation variance and ensuring the stability and rapid response capability of the estimation process in continuous operation in multiple periods. To enhance the adaptability of the system in long-term operation, a forgetting factor mechanism is introduced in the state estimation, and the value of the forgetting factor is set to be between 0.95 and 0.99. This parameter is used to control the retention degree of historical observation data in the estimation update, and the value closer to 1 represents that the system gives higher weight to historical data, which is more suitable for stable system modeling. When the jig has periodic wear, frequent heating or environmental disturbance, appropriately reducing the forgetting factor can improve the sensitivity of the system to new data changes, so that the parameter estimation can respond more quickly to abnormal trends. Therefore, this method has high adaptability and can continuously track the gap changes caused by thermal expansion and contraction, wear and loosening, or structural aging, and dynamically adjust the estimation results. After processing by the recursive least squares estimation method described above, a set of latest jig gap compensation parameters is output for each station.

[0026] By monitoring the rate of change of the internal elements of the covariance matrix, the tracking forgetting factor of the time-varying characteristics of the tool gap is calculated. The factor is a parameter weight decay coefficient dynamically adjusted by the system according to the current state change intensity, and its value range is controlled between 0.95 and 0.99. A larger tracking forgetting factor indicates that the system judges that the current gap change is small, so it gives higher trust to the historical data. When the covariance changes dramatically, the system automatically reduces the forgetting factor, thereby speeding up the adaptation speed to new data. Based on the tracking forgetting factor, the tool gap data recorded in the past period is dynamically weighted and reconstructed, and the historical data weight distribution matrix is generated in the form of exponential weight distribution. This matrix takes time as the horizontal axis and data reliability as the vertical axis, and assigns each historical data a corresponding influence coefficient to form an important structural information matrix reflecting the evolution history of the tool gap. On this basis, the historical data weight distribution matrix and the measurement results of the current period are jointly analyzed to form a recursive updating mechanism of the tool gap parameters, that is, to build the current period parameter value as the synthesis result of the last period estimated value and the current period correction amount. The recursive updating equation makes the system not need to rebuild the complete model every period, but to fine-tune and correct on the basis of the existing estimated value, thereby reducing the computational complexity and improving the stability and real-time performance of the model in the high-frequency update scenario. Based on the change trajectory provided by the recursive updating equation of the tool gap parameters, the gap change factor analysis is performed to identify the typical gap evolution law of each station in the structure, environment and operation state. By analyzing the correction amount, change direction and change rate in the updated parameter sequence, it is determined whether there is a continuous wear trend, enhanced temperature sensitivity or intermittent installation deviation in a station, and the tool gap compensation parameters of each station are obtained.

[0027] Step 300, according to the tool gap compensation parameters, the multi-station error state is coupled with Lyapunov function synchronous convergence analysis, and synchronization convergence control instructions between stations are generated. Specifically, based on the tool gap compensation parameters, the error state vectors of all stations in the current cycle are jointly analyzed, and a set of synchronization convergence judgment mechanism is constructed for the dynamic coupling of multi-node state. The core of this mechanism is to solve whether the error state of each station after local compensation can be converged to the precision control interval allowed by the system as a whole. Therefore, the concept of synchronization convergence threshold is introduced in the error evaluation level, and a unified standard is set to judge the error modulus value of all stations. When the errors of all stations are less than the threshold, it is considered that the system has reached a state of synchronization convergence. According to the error synchronization convergence criterion, a coupled Lyapunov function is constructed, which contains the station weight coefficient and the positive definite weighted matrix. This function regards the error state of all stations as the coupled system state variable, and establishes a kind of energy function that can reflect the global stability of the system by weighted sum of squares of each station error. In this structure, the error vector of each station is multiplied by the corresponding weight and positive definite weighted matrix, which ensures that the Lyapunov function has strict positive definiteness for all error dimensions and can distinguish the control priority of different stations in the system, reflecting the influence of error convergence speed on the overall performance. Based on the stability evaluation framework constructed by the Lyapunov function, a specific synchronization convergence control law equation is designed, which consists of two parts corresponding to local error feedback and state coupling between multiple stations. In the local control part, each station adjusts according to its current error vector, and the adjustment strength is determined by the local feedback gain matrix. In the coupling part between stations, the coupling coefficient is introduced to dynamically balance the error difference between different stations, forming a set of linkage adjustment items about error difference. When the error difference between two stations deviates significantly, the system will automatically increase the weight of the coupling coefficient to produce stronger synchronization feedback, so as to restore the state consistency as soon as possible. The overall purpose of this control law is to make all station error trajectories converge to the synchronization threshold interval within a limited time under the premise of ensuring the asymptotic stability of the system. According to the output generated by the synchronization convergence control law equation, real-time evaluation and dynamic adjustment strategy of the error difference between stations are implemented, and finally a set of synchronization convergence control instructions between stations is formed.

[0028] The error state of all stations is calculated in parallel according to the synchronous convergence control law equation in the current control cycle, and the error state difference between each station and its adjacent station is extracted. The difference is processed in the form of absolute value to form a set of error difference data between stations, which specifically describes the error deviation degree of the i-th station and the surrounding stations in the six-dimensional error state space. Since the error difference data truly reflects the error synchronization degree between stations, it is used as the core basis for judgment in the control logic, and the system relies on this set of data for dynamic branch scheduling of subsequent control logic. The error difference data is compared and analyzed with the pre-set synchronization deviation threshold to determine whether the error difference between some station pairs has exceeded the system allowed range in the current cycle. If the system detects that any error difference exceeds the synchronization deviation threshold, the starting condition of the coupling coefficient adjustment is triggered immediately, forming a set of coupling coefficient adjustment trigger conditions for real-time response. On the premise that the trigger condition is met, based on the amplitude and direction of the error difference, the coupling coefficient between the corresponding station pairs is automatically enhanced and adjusted. The enhancement mechanism takes the absolute value of the error difference as the adjustment factor and sets a gain adjustment ratio, so that the coupling coefficient increases faster when the difference is larger, thereby enhancing the effect of the coupling term on the control quantity. According to the current difference level, the coupling coefficient enhancement factor is set, which not only avoids unnecessary over-regulation under small disturbance, but also quickly improves the convergence speed when a large error difference occurs. The adjusted coupling coefficient constitutes a new set of dynamic coupling relationship matrix between stations. Based on the adjusted coupling coefficient matrix, combined with the error state and feedback path in the current cycle, the synchronous convergence time prediction calculation in the next cycle is carried out. This calculation process mainly depends on the current error initial value, coupling strength distribution and convergence target threshold, and by estimating the eigenvalue of the closed-loop system, the upper bound of the theoretical synchronous convergence time is solved, thereby generating a set of synchronization convergence control instructions between stations for the entire system. These control instructions include the error feedback strength, coupling feedback path and dynamic strength adjustment parameters that each station should follow in the next cycle.

[0029] Step 400, based on the inter-station synchronous convergence control instruction, performing thermal deformation prediction compensation to obtain cumulative error compensation data.

[0030] Specifically, the work station error state and the control response information generated in the synchronous convergence control stage are taken as driving data to establish a jig thermal response prediction model coupled with the thermal deformation characteristics. The model takes the equivalent thermal expansion coefficient of the jig material, the initial geometric size in the process design, and the actual detected temperature change in the current cycle as input variables to describe the thermal expansion behavior of the jig structure under the current thermal boundary conditions. By establishing the thermal deformation prediction model, the spatial deformation caused by environmental or process heating is predicted in each cycle, and the potential deformation is converted into a feedforward compensation amount for subsequent coordinate correction. On the basis of the thermal deformation prediction model, an adaptive parameter update equation is constructed, which includes the learning rate, the thermal deformation prediction error, and the cost function gradient, to solve the model deviation problem caused by material batch, environmental nonlinear interference, and structural diversity. The core objective of the equation is to update the key parameters of the model, such as the equivalent thermal expansion coefficient, based on the residual error between the thermal deformation prediction result and the actual error measurement value in each cycle, i.e., the thermal deformation prediction error. The learning rate, as an adjustment coefficient, controls the parameter update speed and the system response sensitivity, while the cost function gradient is used to guide the parameters to gradually converge to the minimum error direction, thereby realizing real-time correction and precision improvement in the thermal response modeling process. The adaptive mechanism has long-term learning ability and can effectively adapt to the nonlinear change trend of the jig behavior in a dynamic variable temperature environment, so that the model always closely fits the real physical process. Based on the adaptive parameter update equation, a sliding window mechanism is enabled to recursively update the thermal deformation parameters in a plurality of compensation cycles. In each sliding window, the window length is dynamically adjusted according to the time interval or the data update frequency to ensure a balance between the reference value of historical data and the sensitive weight of new data. The existence of the sliding window makes the parameter update have the characteristics of timeliness and stability, and prevents the parameter disturbance from being unstable due to individual abnormal measurement data. The thermal deformation compensation parameters generated under the action of the mechanism are the optimal estimation of the jig deformation behavior under the current thermal state. The thermal deformation compensation parameters updated in real time are input into the cumulative error prediction structure, and are coupled with the structure error and gap error compensation amounts output by the error propagation chain model to form the complete cumulative error compensation data of the current cycle through the superposition calculation of the compensation path.

[0031] The real-time updated thermal compensation parameters are taken as inputs to build a complete cumulative error prediction model. The core of the model is to integrate multiple system variables, including a prediction model parameter matrix, a state transition matrix, and a control input matrix, to comprehensively describe the error evolution behavior of the multi-station fixture system under the combined action of thermal deformation interference, structural pose disturbance, and control compensation. Among them, the prediction model parameter matrix is used to describe the response inertia of the system error in the time sequence, the state transition matrix describes the transmission mode of the error state from the current period to the next period, and the control input matrix corresponds to the control action strength and direction exerted by each station compensation execution unit on the system, which together form the basic framework of error dynamic prediction. Based on the above cumulative error prediction model, the error state of the next period is forward deduced, and the error state, compensation control input and thermal deformation influence of the current period are taken as basic variables to obtain the predicted error state data of the next period containing the position and attitude offset trend of each station through iterative calculation. These prediction data not only estimate the natural expansion trend of the system error under the condition of no correction, but also provide a priori reference for the formulation of subsequent error control strategies, which is suitable for high-precision manufacturing scenarios with high sensitivity requirements for micron-level offset. The system introduces a disturbance simulation function at this stage to consider non-ideal factors such as external temperature fluctuations and equipment load changes, making the prediction results more close to the actual operating conditions. The predicted error state is fused and corrected with the real-time measurement data to solve the deviation between the predicted value and the actual observed value. The Kalman filtering mechanism is introduced to dynamically weigh the two, and by fusing the predicted value and the actual measurement value, a set of corrected error state data is output. The Kalman filter can balance the time continuity brought by the prediction model and the instant accuracy reflected by the measurement data, so as to filter out the measurement noise while retaining the error state change trend. Based on the above corrected error state data, optimal control quantity calculation is performed to determine the error compensation amount required to be applied to each station in the current period. The optimal control quantity calculation process considers multiple objective function components, such as error minimization, compensation energy consumption constraint, control action smoothness, etc., and solves the compensation instruction with the most correction efficiency for the current error state through multi-objective function optimization. The generated cumulative error compensation data is input into the coordinate transformation module and the actuator controller in the form of a structure containing translation and rotation, to drive the compensation mechanism to implement spatial correction actions at a high frequency.

[0032] In the embodiment of the present application, by constructing an inter-station error propagation mathematical model containing the accumulated error of the previous station and the local error of the current station, the error propagation law in the multi-station system is accurately described, the technical defects of the traditional method of ignoring the coupling relationship between the inter-station errors are overcome, the recursive least square estimation algorithm combined with the forgetting factor mechanism is adopted, the gap parameter changes caused by the tool wear, temperature changes and the like can be identified online, the dependence on the accurate tool stiffness coefficient and the material expansion coefficient is eliminated, and the adaptive ability and robustness of parameter estimation are significantly improved. By coupling the Lyapunov function to design a synchronous convergence control law, it is ensured that the positioning errors of all stations can be synchronized to converge to the preset threshold within a limited compensation period, and the technical problem that the traditional independent convergence method of each station cannot guarantee the overall performance of the system is solved. A tool thermal deformation prediction model is established and combined with an adaptive parameter updating mechanism, which can actively predict and compensate the influence of thermal deformation on positioning accuracy, and has better compensation effect and timeliness than the passive compensation method. A three-level transformation structure of the global coordinate system-station coordinate system-local compensation coordinate system is established, the dynamic real-time updating of the coordinate transformation matrix is realized, it is ensured that no geometric distortion is generated in the compensation process, and the real-time requirement of high-precision machining is met. The present application has higher control precision and stronger anti-interference ability than the single feedback control, and realizes high-precision real-time positioning of the multi-station tool system.

[0033] In a specific embodiment, the process of step 100 can specifically include the following steps: A three-dimensional coordinate system is established based on the spatial position data of each station in the multi-station tool system, and spatial position relationship data between stations described by a homogeneous coordinate transformation matrix is generated based on the three-dimensional coordinate system; Error propagation relationship modeling is performed based on the spatial position relationship data between stations, and an inter-station error propagation mathematical model containing the accumulated error of the previous station and the local error of the current station is obtained; According to the inter-station error propagation mathematical model, six-dimensional vector construction processing is performed on the translational error components and rotational error components of each station, and a six-dimensional error state vector containing X, Y and Z translational error components and rotational error components around X, Y and Z axes is obtained; Based on the six-dimensional error state vector, time-varying factor analysis of tool wear and thermal deformation is performed on the inter-station error propagation mathematical model, and an inter-station error propagation chain data model is obtained.

[0034] Specifically, a corresponding three-dimensional coordinate system is established for each station as a geometric node, which meets the requirements of uniqueness and reversibility of the station in space, and a global reference system is established with the first station as the origin. Then, the positional relationship of all stations is expressed in local relative coordinates in sequence, thereby realizing the mapping from the local coordinate system to the global coordinate system. In order to maintain the rigor of spatial transformation and the solvability of engineering implementation, a homogeneous coordinate transformation matrix is introduced to describe the position and attitude transformation between stations. This transformation matrix can express the combined operation of translation and rotation, and has the mathematical properties of composability, reversibility and differentiability in the matrix multiplication structure, which is suitable for subsequent complex calculations such as error propagation, feedback control and attitude reconstruction. After establishing the spatial transformation relationship between stations, an error propagation modeling mechanism is introduced on this spatial geometric framework. The total error state of the i-th station is regarded as the combination of the error state of the previous i-1 station and the local error of the current station in space. That is, the error of each station is not only caused by the geometric deviation and assembly error of the station itself, but also affected by the error transmission of the upstream station, so the error transmission has a chain coupling property. In this structure, the error of the previous station is spatially mapped through the homogeneous transformation matrix between stations, and then added to the local error of the current station for superposition processing, forming a step-by-step accumulation process of error. Based on the above propagation mechanism, the error state of each station is standardized modeled, that is, the spatial error of each station is expressed in the form of a six-dimensional error vector, in which the three-dimensional translation error corresponds to the displacement deviation in the X, Y and Z axis directions, and the three-dimensional rotation error corresponds to the attitude deflection around the X, Y and Z axes. Through unified six-dimensional vector expression, the error state of each station can be standardized input into the error propagation chain model, Kalman estimator or control feedback to update the state, analyze the accuracy and correct the path. At the same time, it is convenient for spatial and temporal monitoring of system error convergence behavior. In the manufacturing and assembly environment, the formation of jig error is not only due to the initial structural deviation, but also affected by various time-varying factors such as wear, thermal deformation and material stress relaxation during operation. Therefore, the error propagation model relying only on the initial calibration parameters and geometric structure information is insufficient to support the long-term precision positioning task of the system. Therefore, a dynamic modeling of time-varying error mechanism is introduced to the established six-dimensional error state vector. A wear attenuation function is embedded in the error propagation chain, which establishes a jig local precision degradation model based on system running time, repeated positioning times and positioning stiffness changes, to adjust the statistical properties of the local error of each station in real time. Secondly, a thermal deformation increment module is constructed, which predicts the structural deformation of the current station under the influence of heat based on the equivalent thermal expansion coefficient of the jig material, the current detected temperature change value and the structure size of the station.These time-varying factors participate in the updating process of the error chain in the form of incremental offset terms in the error propagation model, so that the error propagation in each cycle not only transmits the existing deviation state, but also introduces new time-varying error disturbances according to the environment and use state. Through the above steps, the final inter-station error propagation chain data model has the three characteristics of structural integrity, state real-time and control scalability.

[0035] In a specific embodiment, the process of performing step based on the inter-station spatial position relationship data to model the error propagation relationship and obtain an inter-station error propagation mathematical model containing the cumulative error of the previous station and the local error of the current station can specifically include the following steps: Based on the inter-station spatial position relationship data, the error propagation relationship between the i-th station and the i-1-th station is analyzed to obtain an initial error propagation mathematical model with the cumulative positioning error vector of the i-th station as the dependent variable and the cumulative error of the previous station and the local error of the current station as the independent variable; Based on the initial error propagation mathematical model, inter-station error propagation coefficient calculation is performed to obtain an inter-station error propagation matrix describing the error propagation law from the i-1-th station to the i-th station; Based on the inter-station error propagation matrix, linear superposition operation is performed on the cumulative error vector of the previous station and the local error vector of the current station to obtain cumulative error data containing the contribution amount of the cumulative error of the previous station and the contribution amount of the local error of the current station; Based on the cumulative error data, the error propagation coefficient of the initial error propagation mathematical model is dynamically updated to obtain an inter-station error propagation mathematical model.

[0036] Specifically, based on the established spatial coordinate system and relative position data between stations in the multi-station jig system, the geometric transformation structure of the i-th station relative to the i-1-th station in space is extracted by analyzing the homogeneous coordinate transformation relationship, which includes the three-dimensional position translation relationship and the attitude angle rotation relationship, and an error propagation path with spatial mapping characteristics is constructed accordingly. The path is used to describe the geometric relationship between the stations in the ideal state, and plays a basic role in error transformation and gain propagation in the precision positioning scene. Therefore, in the error modeling stage, the actual error state vector of the i-th station is regarded as a composite vector formed by the superposition of the cumulative term introduced by the upstream station error through spatial transformation and the local error term of the i-th station itself, thereby establishing a initial error propagation model in which the error state of the i-th station is the dependent variable, and the error vector of the i-1-th station and the local disturbance of the i-th station are the independent variables. The mapping relationship between error responses is extracted in the initial model framework, that is, the coefficient terms generated in the transmission process from the i-1-th station error state to the i-th station error state are calculated, which reflect the way in which errors propagate in space through rigid body coordinate transformation, non-ideal installation offset, and rotation coupling. These propagation coefficients constitute a station-to-station error propagation matrix that specifically describes how errors spread from previous stations to the current station. The matrix is a mapping matrix between six-dimensional vectors in structure, which not only needs to preserve the direct response relationship between translation amounts, but also needs to capture the projection coupling effect of rotation errors on linear displacement, especially in the process scenario with attitude deviation amplification. Based on the propagation matrix, the cumulative error vector of the previous station and the local error vector of the current station are fused in a linear superposition form to perform cumulative error calculation operation under spatial transformation. In this process, the system maintains the geometric consistency between vectors and completes period alignment under the condition of consistent time step, ensuring that there is no phase shift or time mismatch in error data processing. Through superposition calculation, the projection contribution of the previous station error to the current station and the error disturbance term caused by the structure disturbance of the current station are separated, and the cumulative error data is obtained. Based on the cumulative error data, a dynamic updating mechanism of error propagation coefficients is constructed to solve the precision decay problem of the propagation matrix caused by condition changes during operation. The difference between the actual error state change measured by the system and the output value of the theoretical propagation model is analyzed, and combined with historical prediction errors, current control input and sensor observation residuals, etc., each coefficient in the error propagation matrix is adjusted adaptively to gradually converge to the direction reflecting the real error propagation law. The updating mechanism is constructed by using sliding window structure, exponential weighted historical error average or incremental adjustment based on measurement residual, and the updating rhythm and amplitude are controlled by adjusting the sensitivity coefficient or threshold setting to prevent the system from producing excessive adjustment under noise or accidental error disturbance. The dynamic updated error propagation mathematical model is obtained.

[0037] In one embodiment, the process of performing step 200 can specifically include the following steps: performing state observation on the inter-tool gap variation data based on the inter-station error propagation chain data model to obtain a state observation equation including a measurement error vector, an observation matrix and a tool gap parameter vector to be estimated; performing Kalman gain calculation on the covariance matrix according to the state observation equation to obtain a Kalman gain matrix, and performing recursive update operation on the covariance matrix based on the Kalman gain matrix to obtain an updated covariance matrix; performing tool gap parameter analysis on the updated covariance matrix to obtain tool gap compensation parameters of each station.

[0038] Specifically, a set of observation structures with dynamic perception ability is established based on the error propagation chain data model between stations. The structure takes the error state obtained in the actual measurement process as the observation input, and takes the gap fluctuation behavior generated in the position change process between stations as the inference target. A state observation equation is constructed to describe the functional relationship between the measurement data and the unknown gap parameters. In the observation equation, the measurement error vector represents the positioning error of the station collected in the current compensation period, the observation matrix is used to map the projection weight of the gap parameter on the error state, and the jig gap parameter vector represents the unknown dynamic gap caused by factors such as wear, thermal deformation, and assembly offset between each station. By establishing the state observation equation, the gap state variable that cannot be directly measured is converted into a problem form that depends on the observation data for reverse estimation, thereby forming the mathematical basis for parameter recursive update and accuracy evaluation. In order to realize the continuous tracking and real-time correction of the gap parameters in the observation equation, the covariance propagation mechanism and Kalman gain adjustment strategy are introduced. Through the update step in the state estimation framework, the reliability of the current observation data is quantitatively analyzed and dynamically weighted. According to the observation matrix and the prediction error variance of the current period, combined with the statistical correlation between system error and observation error, the Kalman gain matrix is calculated. The matrix numerically represents the sensitivity of the current measurement data to the system state update, and the larger the value, the more significant the current observation on the estimation result. The existence of the Kalman gain makes the system have adjustability and adaptability when dealing with the contradiction between historical information and current observation, and can quickly adjust the estimation weight to improve the dynamic response ability when the error changes sharply or the observation reliability improves. Then, the calculated Kalman gain matrix is used to recursively update the system covariance matrix, introducing the observation information of the current period into the state uncertainty measurement process, so that the covariance matrix can reflect the estimation confidence interval and the prediction variance convergence trend under the latest state. This recursive update improves the stability of the estimation system and also realizes sensitive modeling of multi-period change behavior, thereby improving the recognition accuracy of the gap evolution of the system under multi-station high-frequency operation conditions. The updated covariance matrix is analyzed for jig gap parameters. Based on the updated covariance information, the gap change trend between stations is statistically analyzed and structurally identified. Specifically, by tracking the convergence speed, change direction, and fluctuation degree of each diagonal element and correlation term in the covariance matrix, the error increment caused by the change of the jig gap in space and time is back calculated. At the same time, combined with the change trajectory of the Kalman gain, the weight evolution of the observation channel is corrected, so that the jig gap parameters obtained by the final estimation not only have numerical convergence, but also have good engineering interpretability and dynamic robustness. The finally output jig gap compensation parameters are distributed and stored in units of each station for real-time calling, which are used to guide the positioning compensation unit to correct the assembly error and dynamic gap behavior of the current station in space.

[0039] In a specific embodiment, the process of performing step of tool gap parameter analysis on the updated covariance matrix to obtain the tool gap compensation parameters of each station can specifically include the following steps: calculating a tracking forgetting factor of time-varying characteristics of the tool gap based on the updated covariance matrix; weighting and distributing historical tool gap data according to the tracking forgetting factor to obtain a historical data weight distribution matrix; recursively updating the tool gap parameters of the current period based on the historical data weight distribution matrix to obtain a tool gap parameter recursive update equation containing the parameter value of the previous period and the correction amount of the current period; performing gap change factor analysis based on the tool gap parameter recursive update equation to obtain the tool gap compensation parameters of each station.

[0040] Specifically, the update covariance matrix is taken as the input data, and the parameter estimation uncertainty and state change trend information contained in the matrix are used to derive a quantitative index reflecting the amplitude of system state variation. In this process, according to the convergence rate, fluctuation amplitude and principal diagonal element change trend of the covariance matrix, an index factor representing the dynamic degree of error is extracted, and combined with historical observation residual or model fitting error information, a tracking forgetting factor suitable for the gap fluctuation characteristics of the system in the current period is calculated. The forgetting factor is a dynamic adjustment coefficient, and its value is set between 0.95 and 0.99. When the system gap state is relatively stable and the error convergence speed is fast, the forgetting factor tends to 1, meaning that the system gives higher weight to historical data. Conversely, if the covariance fluctuates and the state changes dramatically, the forgetting factor value decreases, enhancing the response weight of new observation data, thereby improving the sensitivity and adaptive ability of the system to gap mutations or abnormal fluctuations. Based on the tracking forgetting factor, the historical gauge gap estimation data stored in the data cache structure is reweighted and distributed to construct a historical data weight distribution matrix for time series weighted regression. The matrix forms an exponential decay model with observation time as the vertical axis and sample weight as the horizontal axis, giving smaller weight to data far from the current period and higher weight to estimation data close to the current period. This non-uniform weighting method can effectively deal with the non-stationary behavior of the gauge gap in long-term operation, enabling the system to have the ability to respond quickly to new disturbances while ensuring the reference value of historical trends, avoiding lag or imbalance caused by fixed weight strategy. Based on the above weight matrix, the recursive update of the current period gauge gap parameter is performed. The update mechanism adopts an incremental structure, and the current period estimation value is represented as the sum of the last period estimation value and the current period correction amount, where the correction amount is jointly determined by the current measurement error, weight distribution result and historical estimation bias. Specifically, according to the weighted average strategy, the estimation values in the historical period are superimposed with the decay coefficient as the weight and fused with the current observation correction term to form the parameter recursive update equation, thereby generating a new gap parameter estimation value. The advantage of this recursive structure is that it avoids the computational burden of full reconstruction, while ensuring that the updated parameter value after each period is optimal representative in the current environment. Moreover, the parameter update speed and correction amplitude can be dynamically adjusted with the forgetting factor, so that the model can evolve slowly in stable state and respond quickly in non-stationary fluctuation, thereby realizing the continuous dynamic gap estimation capability in multi-station system. Based on the latest gauge gap parameters obtained after recursive update, gap change factor analysis is performed.The analysis process mainly includes two directions: one is to extract the trend and calculate the acceleration curve of the time series gap estimation results, which is used to identify whether there is a sustained increasing trend of gap caused by repeated mechanical clamping, friction aging or processing heat effect; The second is to analyze the frequency domain of the fluctuation characteristics of the updated parameters, to detect whether there is high-frequency gap jitter behavior, which is associated with environmental vibration, machine structure resonance or aerodynamic disturbance. Through the analysis of the parameter change rate, the first derivative, the second derivative and their responsiveness to the covariance change rate, the stability level of the current jig gap of each station is determined, the future state risk is predicted, and the maintenance warning or compensation amplitude improvement instruction is issued in advance when necessary. Based on these analysis results, the jig gap compensation parameters required by each station are finally extracted.

[0041] In a specific embodiment, the process of performing step 300 can specifically include the following steps: Based on the jig gap compensation parameters, error synchronous convergence analysis of multi-station error state is performed to create a station-to-station error synchronous convergence criterion containing a synchronous convergence threshold; According to the station-to-station error synchronous convergence criterion, a coupled Lyapunov function containing station weight coefficients and positive definite weighting matrix is constructed; Based on the coupled Lyapunov function, a synchronous convergence control law equation containing local feedback gain matrix and station-to-station coupling coefficient is designed; According to the synchronous convergence control law equation, the station-to-station error difference is adjusted by the coupling coefficient to generate a station-to-station synchronous convergence control instruction.

[0042] Specifically, the jig gap compensation parameters are taken as the basis of the system error state correction input to reconstruct the current error state vectors of each station, and the actual effect of the compensation behavior is reflected through these state vectors. In this process, the positioning error vector of each station is extracted from the error state of all stations, and compared with the error state of other stations at the same time to determine whether there is a problem of error non-uniform convergence. Based on this analysis, a unified error convergence target is set, that is, a synchronous convergence threshold is defined to determine whether multiple stations reach similar error levels in the same control cycle. According to the threshold, an error synchronous convergence criterion is established, which is basically whether the difference between the error states of each station is less than the preset threshold in the sense of spatial norm. When the error difference between any pair of stations exceeds the threshold, it is considered that the system has not reached the synchronous convergence target, and the coupling control mechanism needs to be started to enhance the error uniformity. After the establishment of the above error criterion, the dynamic stability analysis stage is entered, and a Lyapunov function with multi-node coupling characteristics is constructed to measure the overall energy level and convergence trend of the multi-station error system. To adapt to the differences in importance and error sensitivity of each station in the actual multi-station system, the Lyapunov function introduces two structural quantities, the station weight coefficient and the positive definite weighting matrix. The station weight coefficient is used to distinguish the priority of key stations and non-key stations in the overall error control, and the positive definite weighting matrix ensures that the Lyapunov function has a strict positive mapping relationship with the error state, that is, the larger the error value, the larger the corresponding function value, and the function takes the global minimum value when the error is zero. After construction, the Lyapunov function can mathematically prove the asymptotic stability of the system error convergence process, and provide a function basis for the feedback mechanism construction of the subsequent control law design. Based on the coupled Lyapunov function, a synchronous convergence control law equation is designed, which includes a local feedback gain matrix and a coupling coefficient between stations. The error state change of each station is decomposed into two parts, one part is caused by the local adjustment action of the current error of the station, and the adjustment strength is determined by the local feedback gain matrix, and the other part is driven by the error difference between the station and all adjacent stations, and a synchronous control channel is formed across the stations by introducing the coupling coefficient between stations. Under this mechanism, if the error difference between two stations is large, the coupling coefficient between them will increase, thereby increasing the influence of the error difference on the control feedback, so that the system converges to a unified state as soon as possible. The control law has global coordination characteristics and local stability guarantee, which can not only guarantee the synchronization of the overall error trajectory of the system, but also avoid the independent oscillation or instability of some stations, and realize the dynamic consistency regulation of the state between stations.On the basis of the control law taking effect, the system calculates the error difference value between each station in real time in each control cycle and compares it with the synchronization convergence criterion. When it is found that the error difference value between a certain group of stations exceeds the set threshold, the system immediately activates the coupling adjustment mechanism, rapidly increases the synchronization control feedback gain on the path by dynamically adjusting the value of the corresponding coupling coefficient, thereby accelerating the convergence speed of the error channel. On the contrary, when the error difference value tends to be stable and is lower than the threshold, the system will automatically reduce the coupling strength to release resources for other control paths, thereby improving the efficiency and flexibility of the overall control system. The dynamic adjustment of the coupling coefficient based on the error difference value realizes a distributed error coordination network, which makes the control process have the characteristics of self-organization, self-balancing and regional concentration, so as to efficiently adapt to the state coordination needs of the multi-station system under complex operating conditions such as structural asymmetry, non-uniform thermal deformation, inconsistent gap fluctuation, etc. All the adjusted coupling coefficients and feedback matrices are used to generate a new cycle of synchronization convergence control instructions, which include the control feedback strength required by each station in the current cycle, the coupling path priority, the error coordination target and the dynamic adjustment strategy, so that the control system can realize the rapid and consistent adjustment of the error state among multiple stations under the conditions of spatial multi-point synchronization constraint and time continuous feedback.

[0043] In a specific embodiment, the execution step of adjusting the coupling coefficient according to the synchronization convergence control law equation to generate the synchronization convergence control instruction between stations can specifically include the following steps: Based on the synchronization convergence control law equation, the error difference value data between the i-th station and the adjacent station error absolute difference value are obtained by calculating the error state of each station. According to the preset synchronization deviation threshold, the coupling coefficient adjustment trigger condition for triggering the coupling coefficient adjustment is obtained by judging whether the error difference value data exceeds the threshold. Based on the coupling coefficient adjustment trigger condition, the adjusted coupling coefficient between the stations is obtained by automatically enhancing the adjustment of the coupling coefficient between the stations. Based on the adjusted coupling coefficient between the stations, the synchronization convergence time is calculated to generate the synchronization convergence control instruction between the stations.

[0044] Specifically, in each cycle of the multi-station jig system, the error state estimation value of the previous cycle and the real-time observation data of the current cycle are called. The error states of each station in the system are compared with each other according to the synchronous convergence control law equation, and the error difference between the i-th station and all adjacent stations is calculated. The difference calculation is based on a six-dimensional error state vector, considering the translational error in three directions and the rotational error in three directions, and the absolute difference is solved in a unified norm system to ensure that the difference measurement standard is consistent and has engineering interpretability. The obtained error difference data between stations is an error matrix indexed by station pairs, each element of which records the error deviation between adjacent stations in the current control cycle. The matrix directly reflects the spatial distribution characteristics of the system synchronization degree and serves as the basis for triggering subsequent coupling adjustment logic. A uniformly set synchronization deviation threshold is introduced as the boundary standard for error coordination state judgment. The threshold is set according to the comprehensive requirements of the system for accuracy, stability, and response speed, and is at the micron error level. The error difference data is checked item by item, and if the difference between a pair of stations exceeds the threshold, it is determined that the synchronization state between the two stations is not qualified, triggering the dynamic adjustment of the coupling control parameters. At this time, the system will mark the difference matrix position of the over-limit station pair with "coupling coefficient adjustment trigger condition", which is represented in the form of a Boolean flag indicating which station pairs must enter the coupling enhancement adjustment channel in the current control cycle. Through the generation of the trigger condition, the local synchronization imbalance problem in the overall error state is accurately located and responded, thereby avoiding the waste of resources and response delay caused by global redundant adjustment. Based on the determined trigger condition, the coupling coefficient is automatically enhanced and adjusted, and by enhancing the coupling control strength of the imbalance path, the error response weight is improved, thereby promoting the state of the high-deviation station pair to converge to the overall average error level of the system faster. In this process, a segmented enhancement strategy is adopted, i.e., multiple gain intervals are set according to the magnitude of the error difference, and different levels of coupling coefficient amplification parameters are applied in each interval, so that the larger the error is, the faster the adjustment is. When the error is slightly over the limit, the system mainly uses flexible adjustment to avoid system oscillation. The enhancement of the coupling coefficient not only reflects the increase in the absolute value, but also can be supplemented by the coupling path increment, i.e., auxiliary coupling edges are dynamically added based on the original coupling topology, so that the system has stronger local coordination ability. Under this mechanism, an updated inter-station coupling coefficient matrix is generated. With the adjusted coupling coefficient matrix as input, the error state of each station and the Lyapunov function structure parameter are combined to predict the synchronization convergence time. In this prediction process, an analytical expression based on linear state stability theory is constructed to calculate the number of control cycles required for the current error initial value to reach the synchronization threshold range under the enhanced coupling structure, obtaining the upper bound of the theoretical synchronization convergence time.The time upper bound is used to determine whether the synchronization control strategy of the current period meets the scheduling requirements or the beat limit requirements. If the maximum tolerance value of the processing beat is exceeded, the system further increases the coupling coefficient or modifies the feedback gain structure to improve the convergence speed. The predictability of the convergence time enables the controller to have a forward-looking adjustment capability, so that it can predict in advance whether the system is likely to have a risk of synchronization delay in the future several periods due to insufficient error coupling ability. On the basis of all the above analyses, a set of structured inter-station synchronization convergence control instructions is generated. The instructions contain three pieces of information: first, the local feedback gain adjustment amount of each station to ensure rapid attenuation of local errors; second, the coupling coefficient adjustment value of all paths that need to be enhanced to perform synchronization feedback reinforcement of the multi-station coupling channel; and third, the predicted convergence time and strategy state of the current period, which are used to be passed to the upper control manager for beat scheduling or abnormal handling preparation.

[0045] In a specific embodiment, the process of performing step 400 can specifically include the following steps: Based on the inter-station synchronization convergence control instructions, a jig thermal deformation prediction model containing an equivalent thermal expansion coefficient, a jig initial size, and a temperature change amount is established; According to the jig thermal deformation prediction model, an adaptive parameter update equation containing a learning rate, a thermal deformation prediction error, and a cost function gradient is constructed; Based on the adaptive parameter update equation, a sliding window update is performed on the thermal deformation parameters to obtain real-time updated thermal deformation compensation parameters, and a cumulative error compensation is performed on the real-time updated thermal deformation compensation parameters to obtain cumulative error compensation data.

[0046] Specifically, on the basis of the system completing error synchronization control, a thermal deformation prediction model for explaining and predicting the thermal induced displacement behavior of the fixture is established according to the distribution, convergence and dynamic response characteristics of the error between stations. The model takes the equivalent thermal expansion coefficient of the fixture material as the core parameter, takes the original geometric size of the fixture as the reference datum, and combines the temperature variation of each station in the current period to form a deformation prediction mechanism. Through the model, the axial expansion or contraction variation of the fixture structure at different station positions under the action of a certain temperature gradient can be directly derived, providing feedforward information source for subsequent error correction. In order to enable the thermal deformation model to have the ability to dynamically adapt to the changes of the real environment, a parameter update equation with adaptive learning ability is constructed. Especially for the thermal expansion coefficient, which is a material thermal response parameter, its value will change slightly but continuously due to the influence of multiple factors such as working condition aging, surface wear and structure stress accumulation in actual application, so it cannot be fixed. Therefore, an adaptive update mechanism containing learning rate, thermal deformation prediction error and cost function gradient is introduced to correct the thermal response parameter in the model in real time. The learning rate controls the parameter update speed, ensuring that the system can respond quickly when the change trend is obvious, and not introducing too much disturbance when the system is stable; the thermal deformation prediction error is composed of the difference between the thermal expansion prediction value output by the model in the current period and the error observation residual; the gradient of the cost function is used to guide the parameter to converge to the direction of minimum error, so as to continuously improve the prediction accuracy. Through the update mechanism, the thermal response model is continuously optimized in the complex environment with severe temperature change or serious heat conduction lag, so that it is more consistent with the actual working condition. In order to prevent the prediction model from overfitting or updating instability caused by short-term abnormal temperature fluctuation or single-point measurement error, a sliding window strategy is adopted to regulate the parameter update process, that is, in each temperature compensation period, a window interval with fixed or dynamically adjusted length is set, only the observation data in the window are updated with weighting, and the data outside the historical window are excluded from the update mechanism. This strategy maintains the memory of the model to the time trend on the one hand, and avoids the interference of historical outdated data on the current state on the other hand, and can balance the response speed and update robustness by adjusting the window length. For example, the window is appropriately shortened to enhance the response ability of the model in high-speed machining conditions, and the window is lengthened to enhance the stability of the system in long-period thermal equilibrium conditions. The thermal expansion parameter after window update will be directly input into the thermal deformation prediction model in the current period to calculate the thermal induced geometric displacement value of the current fixture at each station. The cumulative error prediction compensation of the real-time updated thermal deformation compensation parameter is used to correct the thermal displacement component in the error propagation chain model.In this compensation calculation, the absolute position drift caused by thermal deformation is included in the spatial error state, and its indirect influence on the error propagation path is considered, especially in the multi-station structure, due to the non-uniformity of thermal expansion, a spatial distribution function is introduced in the error state superposition process, and the influence of thermal deformation is differentiated. At the same time, combined with the error state prediction value of the previous period and the control input, the local disturbance change and other factors of the current period, the system recalculates the current error propagation path, applies the thermal compensation term as the feedforward quantity to the control path, and outputs the comprehensive compensation vector containing the temperature compensation term, the positioning correction term and the coupling error feedback term, and forms the cumulative error compensation data.

[0047] In a specific embodiment, the process of performing step cumulative error prediction compensation on the real-time updated thermal deformation compensation parameters to obtain cumulative error compensation data can specifically include the following steps: Based on the real-time updated thermal deformation compensation parameters, a cumulative error prediction model containing a prediction model parameter matrix, a state transition matrix and a control input matrix is constructed; According to the cumulative error prediction model, the next period error state is predicted to obtain the next period prediction error state data containing the current error state and the control input quantity; Based on the next period prediction error state data, Kalman filter correction is performed on the real-time measurement data to obtain corrected error state data; The corrected error state data is subjected to optimal control quantity calculation to obtain cumulative error compensation data.

[0048] Specifically, the real-time updated thermal deformation compensation parameter is input into the system modeling module as a dynamic variable, and a multi-station error evolution prediction structure is constructed based on the thermal deformation compensation parameter. The structure is based on the station space error propagation chain, and the thermal deformation correction amount of each period is modeled jointly with the control input to generate a cumulative error prediction model including a prediction model parameter matrix, a state transition matrix, and a control input matrix. The prediction model parameter matrix is used to capture the dependence of the system error on the previous state, the state transition matrix describes the transmission path and direction of the error evolution over time in the multi-station space system, and the control input matrix reflects the correction effect of the external compensation action on the system error. Especially with the participation of the real-time updated thermal deformation compensation parameter, the prediction model parameter not only reflects the static error propagation relationship, but also has the ability to dynamically respond to changes in environmental temperature and structural nonlinear deformation, so that the error prediction model has the structural conditions for self-adaptive modeling of thermal time-varying factors. Based on the establishment of the above prediction model, the error state measured in the current period is taken as the initial state vector, and the next period error state is calculated forward through the prediction equation, wherein the control input includes jig gap compensation instructions, space coordinate transformation correction amounts, and thermal deformation prediction compensation values and other complex control items. The system weights and fuses these input signals to output a set of prediction results representing the next period error state. The Kalman filtering mechanism is introduced to correct the prediction value. After the actual measurement data is collected, it is fused with the predicted error state, and the Kalman filtering algorithm is used to balance the dynamic trend advantage of the prediction value and the immediate accuracy advantage of the observation value. The residual error between the observation value and the predicted state is fused, and the weight distribution is performed according to the observation covariance and the prediction covariance, and the current error state is updated to the corrected error state data. The optimal control amount is calculated for the corrected error state data. A multi-objective optimization model is constructed to minimize the prediction error residual and the control input cost function, and various trade-off factors are considered, including error offset minimization, control energy consumption constraint, compensation smoothness and response time limitation, to solve the optimal compensation amount in the current period. The optimal control amount includes the selection strategy of the compensation path, and also includes the error correction amplitude and direction applied by each path, finally forming a compensation strategy balanced in accuracy and cost. The system converts the optimal compensation amount into actual control instructions and distributes them to each station execution end to drive the actuators to perform actions such as spatial pose adjustment, thermal deformation compensation feedback, electric control gap adjustment, or micro servo driven displacement compensation, thereby implementing error correction in the physical system and closing the entire control loop.

[0049] The above describes the precision positioning method of the multi-station jig in the embodiment of the application. The precision positioning system of the multi-station jig in the embodiment of the application is described below. Please refer to Figure 2 An embodiment of the precision positioning system of the multi-station jig in the embodiment of the application includes: The modeling module 11 is used for modeling error propagation chain of real-time position measurement data of each station in the multi-station jig system, to obtain a station-to-station error propagation chain data model; The estimation module 12 is used for performing recursive least square estimation on the jig gap variation data based on the station-to-station error propagation chain data model, to obtain jig gap compensation parameters of each station; The analysis module 13 is used for performing coupled Lyapunov function synchronous convergence analysis on the multi-station error state according to the jig gap compensation parameters, to generate a station-to-station synchronous convergence control instruction; The compensation module 14 is used for performing thermal deformation prediction compensation based on the station-to-station synchronous convergence control instruction, to obtain cumulative error compensation data.

[0050] Through the cooperation of the above components, the station-to-station error propagation mathematical model containing the cumulative error of the previous station and the local error of the current station is constructed, the propagation rule of the error in the multi-station system is accurately described, the technical defects of the traditional method of ignoring the error coupling relationship between stations are overcome, the recursive least square estimation algorithm combined with the forgetting factor mechanism is adopted, the gap parameter variation caused by jig wear and temperature change can be identified online, the dependence on the accurate jig stiffness coefficient and the material expansion coefficient is eliminated, and the adaptive ability and robustness of parameter estimation are significantly improved. The synchronous convergence control law is designed by coupling the Lyapunov function, so that the positioning errors of all stations can be synchronized to converge to the preset threshold within a limited compensation period, and the technical problem that the traditional independent convergence method of each station cannot guarantee the overall performance of the system is solved. The jig thermal deformation prediction model is established and combined with the adaptive parameter updating mechanism, which can actively predict and compensate the influence of thermal deformation on positioning accuracy, and has better compensation effect and timeliness than the passive compensation method. The three-level transformation structure of the global coordinate system-station coordinate system-local compensation coordinate system is established, the dynamic real-time updating of the coordinate transformation matrix is realized, the compensation process does not produce geometric distortion, and the real-time requirement of high-precision machining is met. Compared with single feedback control, the present application has higher control precision and stronger anti-interference ability, and realizes high-precision real-time positioning of the multi-station jig system.

[0051] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the above-described system, system and unit can refer to the corresponding process in the foregoing method embodiments, which will not be repeated here.

[0052] The integrated unit, if implemented in the form of a software function unit and sold or used as an independent product, can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application or the entire or part of the technical solutions that essentially contribute to the prior art can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a plurality of instructions for causing an electronic device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in the various embodiments of the present application. The aforementioned storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and various media that can store program codes.

[0053] The above-described embodiments are merely used to illustrate the technical solutions of the present application, rather than limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacements for some of the technical features; and these modifications or replacements do not cause the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A precision positioning method for a multi-station fixture, characterized in that, The method comprises the following steps: error propagation chain modeling of real-time position measurement data of each station in a multi-station jig system, to obtain a station-to-station error propagation chain data model; recursive least square estimation of jig gap change data based on the station-to-station error propagation chain data model, to obtain jig gap compensation parameters of each station; synchronous convergence analysis of multi-station error states according to the jig gap compensation parameters, to generate station-to-station synchronous convergence control instructions; thermal deformation prediction compensation based on the station-to-station synchronous convergence control instructions, to obtain cumulative error compensation data.

2. The precision positioning method of a multi-station jig according to claim 1, wherein, The error propagation chain modeling of real-time position measurement data of each station in a multi-station jig system, to obtain a station-to-station error propagation chain data model, comprises: establishing a three-dimensional coordinate system based on the spatial position data of each station in the multi-station jig system, and generating station-to-station spatial position relationship data described by a homogeneous coordinate transformation matrix based on the three-dimensional coordinate system; error propagation relationship modeling based on the station-to-station spatial position relationship data, to obtain a station-to-station error propagation mathematical model containing the cumulative error of the previous station and the local error of the current station; six-dimensional vector construction processing of the translational error component and the rotational error component of each station according to the station-to-station error propagation mathematical model, to obtain a six-dimensional error state vector containing the X, Y, Z translational error components and the rotational error components around the X, Y, Z axes; station-to-station error propagation chain data modeling based on the six-dimensional error state vector, including jig wear and thermal deformation time-varying factor analysis of the station-to-station error propagation mathematical model.

3. The method of claim 2, wherein, The error propagation relationship modeling based on the station-to-station spatial position relationship data, to obtain a station-to-station error propagation mathematical model containing the cumulative error of the previous station and the local error of the current station, comprises: error propagation relationship analysis between the i-th station and the i-1-th station based on the station-to-station spatial position relationship data, to obtain an initial error propagation mathematical model with the cumulative positioning error vector of the i-th station as the dependent variable, and the cumulative error of the previous station and the local error of the current station as the independent variables; station-to-station error propagation coefficient calculation based on the initial error propagation mathematical model, to obtain a station-to-station error propagation matrix describing the error propagation law from the i-1-th station to the i-th station; linear superposition operation of the cumulative error vector of the previous station and the local error vector of the current station based on the station-to-station error propagation matrix, to obtain cumulative error data containing the contribution of the cumulative error of the previous station and the contribution of the local error of the current station; dynamic update of the error propagation coefficient of the initial error propagation mathematical model based on the cumulative error data, to obtain a station-to-station error propagation mathematical model.

4. The method of claim 1, wherein, The recursive least square estimation of jig gap change data based on the station-to-station error propagation chain data model, to obtain jig gap compensation parameters of each station, comprises: state observation of jig gap change data based on the station-to-station error propagation chain data model, to obtain a state observation equation containing a measurement error vector, an observation matrix, and a jig gap parameter vector to be estimated; According to the state observation equation, Kalman gain calculation is performed on the covariance matrix to obtain a Kalman gain matrix, and recursive update operation is performed on the covariance matrix based on the Kalman gain matrix to obtain an updated covariance matrix; The updated covariance matrix is analyzed to obtain jig gap compensation parameters of each station.

5. The method of claim 4, wherein, The updated covariance matrix is analyzed to obtain jig gap compensation parameters of each station. A tracking forgetting factor of the jig gap time-varying characteristic is calculated based on the updated covariance matrix; According to the tracking forgetting factor, weight distribution is performed on historical jig gap data to obtain a historical data weight distribution matrix; Based on the historical data weight distribution matrix, the current period jig gap parameter is recursively updated to obtain a jig gap parameter recursive update equation containing the previous period parameter value and the current period correction amount; Based on the jig gap parameter recursive update equation, gap change factor analysis is performed to obtain jig gap compensation parameters of each station.

6. The method of claim 1, wherein, The jig gap compensation parameters are used to analyze the synchronization convergence of the multi-station error state, and a synchronization convergence control instruction between stations is generated, including: Based on the jig gap compensation parameters, error synchronization convergence analysis is performed on the multi-station error state to create a synchronization convergence criterion between stations containing a synchronization convergence threshold; According to the error synchronization convergence criterion between stations, a coupled Lyapunov function containing a station weight coefficient and a positive definite weighting matrix is constructed; Based on the coupled Lyapunov function, a synchronization convergence control law equation containing a local feedback gain matrix and a coupling coefficient between stations is designed; According to the synchronization convergence control law equation, the coupling coefficient between stations is adjusted based on the error difference value to generate a synchronization convergence control instruction between stations.

7. The method of claim 6, wherein, The synchronization convergence control law equation is used to adjust the coupling coefficient between stations based on the error difference value to generate a synchronization convergence control instruction between stations, including: Based on the synchronization convergence control law equation, difference calculation is performed on the error state of each station to obtain error difference value data between stations containing the absolute difference value of the i-th station and the adjacent station error; According to the error difference value data between stations, an over-limit judgment is performed on a preset synchronization deviation threshold to obtain a coupling coefficient adjustment trigger condition for triggering coupling coefficient adjustment; Based on the coupling coefficient adjustment trigger condition, the coupling coefficient between stations is automatically enhanced and adjusted to obtain an adjusted coupling coefficient between stations; Based on the adjusted coupling coefficient between stations, synchronization convergence time calculation is performed to generate a synchronization convergence control instruction between stations.

8. The method of claim 1, wherein, Based on the synchronization convergence control instruction between stations, thermal deformation prediction compensation is performed to obtain cumulative error compensation data, including: Based on the synchronization convergence control instruction between stations, a jig thermal deformation prediction model containing an equivalent thermal expansion coefficient, a jig initial size, and a temperature change amount is established; According to the jig thermal deformation prediction model, an adaptive parameter update equation containing a learning rate, a thermal deformation prediction error, and a cost function gradient is constructed; The hot deformation parameters are updated based on the adaptive parameter updating equation to obtain real-time updated hot deformation compensation parameters, and the real-time updated hot deformation compensation parameters are accumulated error prediction compensated to obtain accumulated error compensation data.

9. The method of claim 8, wherein, The real-time updated hot deformation compensation parameters are accumulated error prediction compensated to obtain accumulated error compensation data, including: An accumulated error prediction model including a prediction model parameter matrix, a state transition matrix and a control input matrix is constructed based on the real-time updated hot deformation compensation parameters; A next cycle error state is predicted according to the accumulated error prediction model to obtain next cycle predicted error state data including a current error state and a control input amount; The real-time measurement data are Kalman filter corrected based on the next cycle predicted error state data to obtain corrected error state data; The corrected error state data are optimal control amount calculated to obtain accumulated error compensation data.

10. A precision positioning system for a multi-station fixture, characterized in that, A precision positioning method for a multi-station jig is used to perform the method according to any one of claims 1-9, and the precision positioning system of the multi-station jig comprises: A modeling module is configured to model error propagation chain data of each station in the multi-station jig system based on real-time position measurement data to obtain a station-to-station error propagation chain data model; An estimation module is configured to perform recursive least square estimation on jig gap change data based on the station-to-station error propagation chain data model to obtain jig gap compensation parameters of each station; An analysis module is configured to perform coupled Lyapunov function synchronous convergence analysis on multi-station error states based on the jig gap compensation parameters to generate station-to-station synchronous convergence control instructions; A compensation module is configured to perform hot deformation prediction compensation based on the station-to-station synchronous convergence control instructions to obtain accumulated error compensation data.

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