AGV bracket multi-axis linkage synchronous control system based on adaptive PID

Abstract

The invention relates to the technical field of automatic control, in particular to an AGV (Automatic Guided Vehicle) bracket multi-axis linkage synchronous control system based on self-adaptive PID (Proportion Integration Differentiation), which comprises a displacement analysis module, an error analysis module, a coupling calculation module, a self-adaptive PID module and a control optimization module. According to the method, the directional error amount is constructed by collecting the displacement difference and combining the acceleration and the angular velocity change, so that the error signal forms an analyzable gradient along the structure direction and establishes dynamic association among multiple axes, and the synchronous response of each axis to the attitude change and the load disturbance is enhanced in a differential mode; the control parameters automatically adjust the proportional integral differential weight along with the error correlation degree, the control quantity forms more balanced distribution among multiple axes and is subjected to component correction and weighting processing to obtain the adjustment output better fitting the structure motion characteristic, the multi-axis collaboration is kept stable under the dynamic load, the attitude keeping capability and the track following precision are synchronously improved, and the control precision is improved. And the overall operation reliability is enhanced.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology, and in particular to a multi-axis linkage synchronous control system for AGV carriages based on adaptive PID. Background Technology

[0002] The field of automatic control technology covers the automatic adjustment and coordinated control of physical quantities such as displacement, speed and attitude of mobile equipment and load-bearing mechanisms during operation. Its core aspects include obtaining the real-time status of the bracket and actuators through sensing quantities such as position and torque, adjusting the output of the drive motor according to the set control law, and maintaining the motion consistency among multiple actuators through closed-loop feedback. Overall, it involves multi-axis motion coordination, load change adaptation and the coordinated work of mechanical structure and control system. The traditional AGV carriage multi-axis linkage synchronous control system refers to a control system used in multi-vehicle material handling scenarios to coordinate and adjust multiple motion axes of the AGV carriage. The technical issues addressed include rapid adaptation of carriage structures for multiple vehicle models and synchronous and stable control of multiple axes under load changes. The traditional method usually customizes the carriage frame to a single specification according to the material size of different vehicle models. The carriage is manually adjusted or replaced to meet the adaptation requirements. At the control level, displacement detection devices are set on each drive motor axis to obtain the actual motion amount and form a deviation signal with the preset trajectory. The drive current of each axis is adjusted according to the proportional-integral-derivative control law. At the same time, the speed and displacement difference of each axis are corrected by using a fixed synchronous compensation relationship. When the load changes, the linkage relationship between multiple axes is maintained by relying on pre-tuned parameters. At the structural level, a fixed support frame and mechanical locking parts are usually used in conjunction with an electric servo three-dimensional adjustment mechanism to adjust the height, width and posture of the carriage to adapt to different material sizes.

[0003] Existing technologies rely on fixed frames and manual adjustments to achieve structural matching during multi-vehicle bracket adaptation. The lack of continuous quantitative data on structural response results in insufficient sensitivity to changes in material dimensions during the adaptation process. Multi-axis linkage control relies on single-axis displacement deviation and preset synchronous compensation relationships to establish a coordination mechanism, which fails to reflect the coupling effects of bracket attitude changes and dynamic loads. Error information remains at the level of independent axial correction during inter-axis transmission, weakening the inter-axis correlation. Under load disturbances, the control system experiences response lag and compensation imbalance, affecting trajectory consistency and reducing operational stability. In long-term operation, uneven multi-axis following and accumulated structural offsets are prone to occur, reducing the reliability and control accuracy of continuous operation in multi-vehicle scenarios. Summary of the Invention

[0004] To address the technical problems existing in the prior art, embodiments of the present invention provide a multi-axis linkage synchronous control system for AGV carriages based on adaptive PID. The technical solution is as follows:

[0005] On the one hand, an adaptive PID-based multi-axis linkage synchronous control system for AGV carriages is provided, which includes:

[0006] The displacement analysis module collects data on the displacement of the execution shaft, the acceleration and angular velocity of the bracket, sorts them by time, calculates the displacement difference between adjacent sampling points, analyzes the changes in acceleration and angular velocity and combines them with the displacement difference to generate an error state vector and transmit it to the error analysis module.

[0007] The error analysis module, based on the error state vector, analyzes the error gradient vector group of adjacent time points, and projects the bracket structure direction vector calculated by the preset bracket geometric model to generate directional error components and transmits them to the coupled calculation module.

[0008] The coupling calculation module performs data exchange between multiple execution axes based on the directional error component, extracts the component of this execution axis and performs differential calculation with the components of other execution axes and calculates the correlation degree, analyzes the rate of change of the directional error component and compares it with the correlation degree, generates a coupling difference component and transmits it to the adaptive PID module.

[0009] The adaptive PID module, based on the coupling difference components, calculates the proportional and differential weights for the difference terms exceeding the coupling judgment threshold, analyzes the integral weights for the difference terms below the coupling judgment threshold, merges all weights into an adaptive PID group, and accumulates the displacement differences of multiple execution axes to generate the multi-axis control results of the AGV carriage.

[0010] The control optimization module extracts proportional weights, integral weights, and derivative weights from the AGV carriage multi-axis control results and adaptive PID group to perform component-by-component correction on the AGV carriage multi-axis control results. It then performs weighted synthesis of the correction values ​​and the original control results to generate optimized AGV carriage multi-axis control results.

[0011] As a further embodiment of the present invention, the error state vector includes displacement difference components, acceleration change characteristics, and angular velocity change characteristics; the directional error components include projection error components, structural orientation correlation components, and orientation offset components; the coupling difference components include multi-axis error comparison quantities, multi-axis rate of change ratio quantities, and multi-axis correlation degree difference components; the AGV bracket multi-axis control results include proportional adjustment weights, integral adjustment weights, and derivative adjustment weights; and the optimized AGV bracket multi-axis control results include proportional correction components, integral correction components, and derivative correction components.

[0012] As a further aspect of the present invention, the displacement analysis module includes:

[0013] The data analysis submodule collects and sorts the data of the execution shaft displacement, bracket acceleration and angular velocity by sampling time. It calculates the displacement difference between adjacent sampling points based on the time difference and displacement value of adjacent sampling points, performs a subtraction operation on the displacement difference of each pair of adjacent sampling points, records the displacement difference value according to the calculation result, and generates a displacement difference sequence.

[0014] The attitude disturbance submodule calls the displacement difference sequence and performs differential operation on the acceleration and angular velocity data at the same time. It then filters the data based on the attitude disturbance threshold and merges the filtered acceleration and angular velocity changes into attitude disturbance values ​​to generate an attitude disturbance value sequence.

[0015] The error state submodule performs a sequential concatenation operation on the displacement difference sequence and the attitude disturbance value sequence, arranging the displacement difference and attitude disturbance value at the same time into a single state vector and expanding it in chronological order to generate an error state vector.

[0016] As a further aspect of the present invention, the attitude disturbance threshold is determined by analyzing all the difference values ​​between the acceleration change and the angular velocity change within a set historical time window, calculating the amplitude of the acceleration difference value sequence and the angular velocity difference value sequence according to the time position, merging them into a unified change set, and then extracting the median value after sorting the change set according to the numerical size.

[0017] As a further aspect of the present invention, the error analysis module includes:

[0018] The error difference module performs subtraction on the error terms at adjacent time points based on the error state vector. For each error term sequence, it calculates the difference component with adjacent error values ​​as participating terms and arranges them in chronological order. It identifies and records the corresponding change trends at time points and generates an error difference sequence.

[0019] The gradient vector submodule calls the error difference sequence, performs vector component comparison on multiple error components in the sequence, calculates the rate of change of multiple components based on the same time point and arranges them into a vector group according to the component direction, performs amplitude comparison on the vector group to determine the component change amplitude, and generates an error gradient vector group.

[0020] The component extraction submodule calculates the bracket structure direction vector and performs vector projection based on the error gradient vector group. It then performs inner product operation on the multi-vector components of the gradient vector group and the bracket structure direction vector, records the results, and arranges them into a directional sequence in chronological order to generate directional error components.

[0021] As a further aspect of the present invention, the coupling calculation module includes:

[0022] The inter-axis exchange submodule performs data exchange between multiple execution axes based on the directional error components. It extracts the directional error components of the current execution axis and the other execution axes according to their corresponding axis positions, identifies and records the differences between the directional error components of multiple execution axes, and generates the inter-axis error difference quantity.

[0023] The differential construction submodule calls the inter-axis error difference amount and uses the directional error component of the current execution axis as the comparison benchmark. It performs vector difference for the two types of data and performs subtraction operation on the multi-vector components according to the same index position. It performs amplitude comparison on the subtraction result to determine the differential amplitude and generates the directional differential amplitude.

[0024] The coupling comparison submodule calculates the change of the directional error component between adjacent sampling points based on the directional difference amplitude, performs amplitude comparison with the directional difference amplitude item by item and records the comparison difference, performs weighted calculation on the difference sequence, and generates the coupling difference component.

[0025] As a further aspect of the present invention, the adaptive PID module includes:

[0026] The differential component screening submodule compares the coupled differential components with the coupling judgment threshold, judges the coupled differential components with the coupling judgment threshold, distinguishes the differential components that exceed the coupling judgment threshold from the differential components that do not reach the coupling judgment threshold and adds an identifier, and generates a differential classification sequence.

[0027] The weight generation submodule calls the differential classification sequence to perform proportional and differential weight calculations on data items that exceed the coupling judgment threshold based on the difference between the differential component and the coupling judgment threshold, and to perform integral weight calculations on data items that do not reach the coupling judgment threshold based on the magnitude of the difference component change, thereby obtaining an adaptive PID sequence.

[0028] The weight fusion submodule extracts the proportional weight, integral weight, and derivative weight according to the adaptive PID sequence, performs a product operation with the corresponding error terms in the coupled differential component, and performs a weighted summation of all product results to generate the AGV bracket multi-axis control result.

[0029] As a further aspect of the present invention, the coupling determination threshold is determined by setting a historical sliding window, acquiring all coupling difference components generated by multiple execution axes within the historical sliding window, analyzing them, sorting the difference components by numerical value and determining the median value.

[0030] As a further aspect of the present invention, the control optimization module includes:

[0031] The weight extraction submodule, based on the AGV bracket multi-axis control results and the adaptive PID group, distinguishes the proportional component, integral component and derivative component, extracts the multi-component according to the corresponding weight value in the adaptive PID group, and arranges them in the order of components to generate a proportional integral derivative weight sequence.

[0032] The component correction submodule calls the proportional-integral-derivative weight sequence, performs component-by-component adjustment on the multi-components according to the proportional-integral-derivative weight sequence based on the AGV bracket multi-axis control results, and performs difference calculation to generate a multi-axis correction difference sequence.

[0033] The weighted synthesis submodule performs weighted superposition of the multi-control components and the multi-axis correction difference sequence based on the AGV carriage multi-axis control results, performs sequence reconstruction on the superposition results, and outputs the reconstructed sequence in the order of the execution axes to generate the optimized AGV carriage multi-axis control results.

[0034] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following:

[0035] By collecting displacement differences and combining them with acceleration and angular velocity changes to construct error state variables, the error information is guided to form a quantifiable gradient along the direction of the bracket structure. Then, by strengthening the common response of each axis to attitude changes and load disturbances through differential correlation of error components between multiple axes, the error signals form a dynamic coupling relationship between multiple axes. Based on the coupling sensitivity, the proportional, integral, and derivative weights are adaptively adjusted so that the control quantity achieves distributed balance among multiple axes according to the degree of error correlation. The control results are then subjected to component correction and weighted synthesis to form an adjustment output that better fits the motion characteristics of the bracket structure, improving the coordination consistency between multiple axes and the stability under load changes, and improving the attitude maintenance capability and trajectory following accuracy during operation. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This is a schematic diagram of the system of the present invention;

[0038] Figure 2 This is a schematic diagram of the system framework of the present invention;

[0039] Figure 3 This is a flowchart of the displacement analysis module in this invention;

[0040] Figure 4 This is a flowchart of the error analysis module in this invention;

[0041] Figure 5 This is a flowchart of the coupled calculation module in this invention;

[0042] Figure 6 This is a flowchart of the adaptive PID module in this invention;

[0043] Figure 7 This is a flowchart of the control optimization module in this invention. Detailed Implementation

[0044] The technical solution of the present invention will now be described with reference to the accompanying drawings.

[0045] In embodiments of the present invention, words such as "exemplarily," "for example," etc., are used to indicate that something is an example, illustration, or description. Any embodiment or design described as "exemplary" in the present invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the word "exemplary" is intended to present the concept in a concrete manner. Furthermore, in embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one.

[0046] In the embodiments of this invention, the terms "image" and "picture" may sometimes be used interchangeably. It should be noted that, without emphasizing the distinction between them, they convey the same meaning. Similarly, the terms "of," "corresponding (relevant)," and "corresponding" may sometimes be used interchangeably. It should be noted that, without emphasizing the distinction between them, they convey the same meaning.

[0047] In this embodiment of the invention, sometimes a subscript such as W1 may be written in a non-subscript form such as W1. When the difference is not emphasized, the meaning they express is the same.

[0048] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0049] This invention provides a multi-axis linkage synchronous control system for AGV carriages based on adaptive PID, such as... Figure 1-2 The diagram shown illustrates a multi-axis linkage synchronous control system for AGV carriages based on adaptive PID control. This system includes:

[0050] The displacement analysis module collects data on the displacement of the execution shaft, the acceleration and angular velocity of the bracket, sorts them by time, calculates the displacement difference between adjacent sampling points, analyzes the changes in acceleration and angular velocity and combines them with the displacement difference to generate an error state vector and transmit it to the error analysis module.

[0051] The error analysis module, based on the error state vector, analyzes the error gradient vector group at adjacent time points, and projects the bracket structure direction vector calculated by the preset bracket geometric model to generate directional error components and transmit them to the coupled calculation module.

[0052] The coupling calculation module performs data exchange between multiple execution axes based on the directional error component. It extracts the component of the current execution axis and performs differential calculation with the components of other execution axes, calculates the correlation degree, analyzes the change rate of the directional error component and compares it with the correlation degree, generates the coupling difference component and passes it to the adaptive PID module.

[0053] The adaptive PID module, based on the coupling difference component, calculates the proportional and derivative weights for the difference terms that exceed the coupling judgment threshold, analyzes the integral weights for the difference terms that do not reach the coupling judgment threshold, merges all weights into an adaptive PID group, and accumulates the displacement difference of multiple execution axes to generate the multi-axis control result of the AGV carriage.

[0054] The control optimization module extracts proportional weights, integral weights, and derivative weights from the AGV carriage multi-axis control results and adaptive PID group to perform component-by-component correction on the AGV carriage multi-axis control results. The correction values ​​are then weighted and synthesized with the original control results to generate the optimized AGV carriage multi-axis control results.

[0055] The error state vector includes displacement difference components, acceleration change characteristics, and angular velocity change characteristics. The directional error components include projection error components, structural orientation correlation components, and orientation offset components. The coupling difference components include multi-axis error comparison quantities, multi-axis rate of change ratio quantities, and multi-axis correlation degree difference components. The AGV bracket multi-axis control results include proportional adjustment weights, integral adjustment weights, and derivative adjustment weights. The optimized AGV bracket multi-axis control results include proportional correction components, integral correction components, and derivative correction components.

[0056] Specifically, such as Figure 2 , 3 As shown, the displacement analysis module includes:

[0057] The data analysis submodule collects and sorts the data of the execution shaft displacement, bracket acceleration and angular velocity by sampling time. It calculates the displacement difference between adjacent sampling points based on the time difference and displacement value of adjacent sampling points, performs a subtraction operation on the displacement difference of each pair of adjacent sampling points, records the displacement difference value according to the calculation result, and generates a displacement difference sequence.

[0058] In the operation of a flexible intelligent automated guided vehicle (AGV) for lean automotive manufacturing, the high-precision rotary encoder located on the AGV's drive wheels is activated first. The data acquisition frequency is set to 100 Hz, meaning data is collected every ten milliseconds. The central system stores the collected raw data stream in a high-speed buffer. Each data set includes a sampling timestamp, the real-time displacement value of the actuator axis (in millimeters), the acceleration value of the bracket along the travel direction (in meters per second squared), and the angular velocity value of the bracket around the vertical axis (in radians per second). After completing a full logistics delivery cycle, a quicksort algorithm is used to organize all data packets in the buffer according to their time sequence. The timestamp field of each data packet is read, and the storage addresses are rearranged by comparing the time values ​​of adjacent data packets, ensuring that all data is linearly distributed strictly according to the sampling time from earliest to latest, forming an ordered time-series dataset. After sorting, the displacement difference calculation stage begins. Two adjacent sampling points in the ordered dataset are sequentially locked and defined as the current sampling point and the previous sampling point, respectively. First, the timestamps of two sampling points are read for difference verification, and the result of subtracting the time of the previous sampling point from the time of the current sampling point is calculated. If the time difference is within the tolerance range of the preset sampling period of ten milliseconds (e.g., ±0.1 milliseconds), then the execution axis displacement value of the current sampling point is extracted as the minuend, and the execution axis displacement value of the previous sampling point is extracted as the subtrahend, and the subtraction operation is performed. The value obtained by this operation is the adjacent displacement difference, which physically represents the increase in the travel distance of the AGV within the ten-millisecond sampling period. This subtraction operation is repeated for each pair of adjacent sampling points in the sequence, and the calculated displacement difference values ​​are written into a dedicated storage space according to the corresponding time index order to generate a displacement difference sequence. To intuitively illustrate the data acquisition and processing process, five consecutive sampling points of data from a certain AGV during the linear acceleration phase are selected and listed in Table 1.

[0059] Table 1. AGV Axis Displacement and Dynamic Parameter Acquisition Table

[0060]

[0061] As shown in Table 1, by performing point-by-point differential calculations on the original displacement data, a sequence of adjacent displacement differences reflecting the instantaneous velocity change trend was obtained. For example, at a sampling time of 10.03 seconds, the displacement of the execution axis was 1530.15 mm. Compared to 1515.00 mm at 10.02 seconds, the difference between the two was 15.15 mm. This value was accurately recorded and used as the basic element for generating the displacement difference sequence, providing core positional increment data for subsequent evaluation of the AGV's motion status.

[0062] The attitude disturbance submodule calls the displacement difference sequence and performs differential operations on the acceleration and angular velocity data at the same time. It then filters the data based on the attitude disturbance threshold and merges the filtered acceleration and angular velocity changes into attitude disturbance values, generating an attitude disturbance value sequence.

[0063] The generated displacement difference sequence is used as a time reference index, and the sorted bracket acceleration and angular velocity data are read synchronously. This aims to quantify the degree of attitude change of the AGV under complex workshop conditions. Acceleration and angular velocity readings at the same time point are locked, along with the corresponding readings from the previous time point. During differential calculation, the floating-point unit is called to calculate the absolute value of the difference between the current acceleration and the previous acceleration, i.e., the acceleration change; simultaneously, the absolute value of the difference between the current angular velocity and the previous angular velocity is calculated, i.e., the angular velocity change. Absolute values ​​are used here to capture the amplitude characteristics of the disturbance, ignoring its directional influence. To effectively identify abnormal jitter and eliminate environmental noise, an attitude disturbance threshold is introduced for data filtering. This threshold is based on benchmark tests of the AGV on a standard industrial self-leveling floor. During the test, the AGV ran in a straight line at its rated speed of 1.5 meters per second without load. By continuously collecting 5,000 sets of data, the average background noise of acceleration change was calculated to be 0.02 radians per second, and the background noise of angular velocity change was 0.005 radians per second. Based on the principle of three standard deviations and combined with the engineering safety factor, the acceleration disturbance threshold is set to 0.06, and the angular velocity disturbance threshold is set to 0.015 radians per second. During the screening process, the calculated acceleration change is compared with the acceleration disturbance threshold, and the angular velocity change is compared with the angular velocity disturbance threshold. The judgment logic is as follows: if either change is greater than its corresponding threshold, it is determined that there is an attitude disturbance at the current moment, and the original value of the change at that moment is retained; if both are lower than their corresponding thresholds, it is determined to be normal driving vibration, and the change at that moment is forcibly set to zero. Based on the screened data, a vector merging operation is performed. For each valid sampling moment, a double-precision floating-point array space of size two is allocated. Taking a moment extended in Table 1 as an example, it is set that after 10.05 seconds, affected by the ground cable trough, the acceleration jumps from 0.21 to 0.35, that is, the acceleration change is 0.14, and the angular velocity changes from 0.02 to 0.022, the change is 0.002. At this point, the acceleration change of 0.14 is greater than the threshold of 0.06, and the angular velocity change of 0.002 is less than the threshold of 0.015. The filtered acceleration change of 0.14 is written to the first position of the array, and the zeroed angular velocity change of 0 is written to the second position of the array, thus constructing a two-dimensional attitude perturbation value vector (with values ​​of 0.14 and 0). This process is repeated for all data points in the entire time series to generate an attitude perturbation value sequence consisting of a series of two-dimensional vectors. This sequence accurately eliminates minor vibration disturbances and retains only the dynamic characteristics that have a substantial impact on vehicle stability.

[0064] The error state submodule performs sequential concatenation operations based on the displacement difference sequence and the attitude disturbance value sequence, arranging the displacement difference and attitude disturbance values ​​at the same time into a single state vector and expanding them in chronological order to generate an error state vector;

[0065] The generated displacement difference sequence and the generated attitude disturbance value sequence are read. Since both sequences are sorted based on the same timestamp, a parallel indexing method is used, with the time index as the cursor, to simultaneously extract the displacement difference values ​​and attitude disturbance vectors at the same moment. The purpose of this step is to align the dispersed kinematic parameters (displacement) and dynamic parameters (disturbance) in the time dimension. During the sequential concatenation operation, a new single state vector structure is constructed. This structure is defined as a row vector containing three components. First, the displacement difference value at the current moment is assigned to the first component position of the state vector, which represents the longitudinal motion capability of the AGV in the current sampling period. Next, the first element of the attitude disturbance vector at the same moment (i.e., the filtered acceleration change) is assigned to the second component position of the state vector, representing the stability of the vehicle's translational direction. Finally, the second element of the attitude disturbance vector (i.e., the filtered angular velocity change) is assigned to the third component position of the state vector, representing the stability of the vehicle's rotational direction. Taking a sampling time of 10.05 seconds as an example, the displacement difference calculated in the preceding steps is 15.35 mm, and the attitude disturbance vector corresponding to this moment is set to (0.14, 0). After performing the stitching operation, the generated single state vector contains three values: 15.35, 0.14, and 0. The above stitching operation is performed on all sampling points in chronological order, and the generated single state vectors are stored row by row into the error state matrix to complete the expansion of the time dimension and generate a complete error state vector. In order to evaluate the physical meaning of this state vector, a comprehensive error reference range is set. This reference range is set according to the standard operating parameters of the AGV under full load conditions, where the normal range of the displacement difference component is set to 14.8 mm to 15.2 mm (corresponding to the travel within 10 milliseconds at a standard speed of 1.5 m / s), the normal range of the acceleration disturbance component is 0 to 0.06, and the normal range of the angular velocity disturbance component is 0 to 0.015. The generated vector (15.35, 0.14, 0) was compared item by item with the baseline interval: the displacement difference of 15.35 mm exceeded the upper limit of 15.2 mm, indicating that the vehicle speed was slightly too high; the acceleration disturbance of 0.14 exceeded the upper limit of 0.06, indicating a significant translational impact; the angular velocity disturbance of 0 was within the normal range. This comparison result shows that at 10.05 seconds, the AGV was in an unstable state of overspeeding and longitudinal impact. By generating an error state vector containing multi-dimensional physical characteristics, the motion health of the AGV at a specific moment can be completely reproduced within a single data structure, providing accurate numerical basis for subsequent deviation compensation control.

[0066] Specifically, such as Figure 2 , 4 As shown, the error analysis module includes:

[0067] The error difference module, based on the error state vector, performs subtraction on error terms at adjacent time points. For each error term sequence, it calculates the difference component with adjacent error values ​​as participating terms and arranges them in chronological order. It identifies and records the corresponding change trends at time points and generates an error difference sequence.

[0068] Based on the error state vector, a sliding window with time as the axis is first established, covering the current time point and the immediately preceding time point. Using the error state vector calculated in the previous step at 10.05 seconds as a baseline, the vector value is (15.35, 0.14, 0). As the clock advances to 10.06 seconds, the latest state data is read from the corresponding address in the data acquisition buffer. At 10.06 seconds, the AGV control performs a minor correction: the axis displacement difference decreases to 15.25 mm, the bracket acceleration disturbance decreases to 0.10, and the angular velocity disturbance increases slightly to 0.005, generating the error state vector at 10.06 seconds (15.25, 0.10, 0.005). Subsequently, the floating-point unit is called to perform a vector subtraction operation. This operation is not a simple numerical subtraction, but rather a difference calculation performed on the corresponding components in the vector. First, the displacement difference component is selected. Subtracting 15.35 mm from 10.05 mm at 10.06 seconds (15.25 mm) yields -0.10 mm, reflecting the convergence trend of the displacement error. Next, the acceleration disturbance component is selected. 0.10 - 0.14 = -0.04, indicating that the translational impact is weakening. Finally, the angular velocity disturbance component is selected. 0.005 - 0 = 0.005, showing a slight increase in the rotational trend. The differences obtained from these three calculations are arranged in the original vector order to construct the error difference vector (-0.10, -0.04, 0.005) for this time interval. The above subtraction operation is repeated for all adjacent time points in the error state sequence, and the error difference vector generated by each operation is stored in an independent data block according to the timestamp order to generate the error difference sequence. To visually demonstrate the numerical changes in this process, the calculation results of five consecutive sets of data from 10.05 seconds to 10.09 seconds are listed in Table 2.

[0069] Table 2 Results of Error State Vector Difference Operation

[0070]

[0071] As shown in Table 2, the dynamic changes of various error parameters are clearly recorded through point-by-point differencing. The advantage of this method is that by calculating the error difference between adjacent time points, not only is the absolute magnitude of the error determined, but the rate and direction (positive or negative sign) of error change are also quantified. This allows identification of whether the error is in the divergence or convergence phase, providing direct data support for subsequent gradient analysis. The calculation results show that the displacement difference remains negative within the interval of 10.05 to 10.09 seconds, indicating that the AGV's overspeed condition is being gradually corrected, and the correction force remains stable.

[0072] The gradient vector submodule calls the error difference sequence, performs vector component comparison on multiple error components in the sequence, calculates the rate of change of multiple components based on the same time point, arranges them into a vector group according to the component direction, performs amplitude comparison on the vector group to determine the component change amplitude, and generates an error gradient vector group.

[0073] The error difference sequence is invoked, and the standard sampling time interval set by the clock is read. This interval has been confirmed as 10 milliseconds, or 0.01 seconds, in the previous steps. The core task is to convert the discrete difference values ​​into gradient physical quantities that reflect the degree of change. For each error difference vector, division operations are performed on the displacement difference value, acceleration difference value, and angular velocity difference value. Taking the data at 10.06 seconds as an example, the displacement difference value -0.10 in Table 2 is read, and divided by the sampling interval 0.01 to obtain a displacement error gradient of -10; the acceleration difference value -0.04 / 0.01=-4 is read to obtain an acceleration error gradient of -4; the angular velocity difference value 0.005 / 0.01=0.5 is read to obtain an angular velocity error gradient of 0.5. After completing the ratio calculation, these three gradient values ​​are rearranged according to the original component directions to construct the error gradient vector (-10, -4, 0.5). Next, an amplitude comparison operation is performed to determine the severity of the overall error change. The square root operation instruction is invoked to calculate the Euclidean norm of each component in the gradient vector. The specific calculation process is as follows: first, -10 squared equals 100, -4 squared equals 16, and 0.5 squared equals 0.25; then, these three squares are added together to obtain 116.25; finally, the square root of this sum is taken to obtain a value approximately equal to 10.78, which is the magnitude of the error gradient vector, representing the overall magnitude of the state change at the current moment. To assess whether this magnitude is within a controllable range, a gradient magnitude safety threshold is set. This threshold is obtained through statistical analysis of AGV emergency stop test data. In the full-load emergency stop experiment, the maximum gradient magnitude was monitored to be 25 without cargo tipping over. Based on this, a safety threshold of 20 is set. The calculated magnitude of 10.78 is compared with the threshold of 20. Since 10.78 is less than 20, the current rate of change is determined to be within a safe and controllable range. The results show that although the AGV is undergoing rapid error correction (displacement gradient reaches -10), the overall dynamic changes are stable, and no violent oscillations that could potentially damage the mechanical structure occur. Through this process, an error gradient vector set containing both directional and amplitude information is generated, accurately characterizing the derivative features of the AGV's operating state.

[0074] The component extraction submodule calculates the bracket structure direction vector and performs vector projection based on the error gradient vector group. It performs inner product operation on the multi-vector components of the gradient vector group and the bracket structure direction vector and records them. The components are arranged in chronological order as a directional sequence to generate directional error components.

[0075] Based on the generated error gradient vector set, the AGV mechanical structure parameter table stored in the read-only memory is read to obtain the mounting angle and force axis direction of the bracket relative to the chassis. In the current flexible manufacturing scenario, to accommodate lateral material gripping, the bracket is set to deflect 10 degrees relative to the direction of travel. The direction vector of the bracket structure is calculated accordingly. This vector is a unit vector with the x-coordinate being the cosine of the 10-degree angle, the y-coordinate being the sine of the 10-degree angle, and the vertical coordinate being 0 (for horizontal operation). By looking up tables or calculations, the cosine of 10 degrees is approximately 0.985, and the sine of 10 degrees is approximately 0.174. Therefore, the direction vector of the bracket structure is determined to be (0.985, 0.174, 0). Subsequently, the generated error gradient vector set is called to perform vector projection operations. Taking the gradient vector (-10, -4, 0.5) at time 10.06 as an example, this vector is used to perform a dot product (inner product) operation with the direction vector of the bracket structure. The specific steps of the calculation are as follows: First, calculate the product of the first component of the gradient vector -10 and the first component of the structural vector 0.985, the result is -9.85; second, calculate the product of the second component of the gradient vector -4 and the second component of the structural vector 0.174, the result is -0.696; finally, calculate the product of the third component of the gradient vector 0.5 and the third component of the structural vector 0, the result is 0. Add the above three product results together, i.e., (-9.85) + (-0.696) + 0 = -10.546. This value is the directional error component, which physically represents the projection intensity of the error change on the main force axis of the bracket. Perform this projection operation on all gradient vectors in the sequence in chronological order, and store the calculation results in the directional sequence sequentially. Set the axial stress change threshold of the bracket structure to 15. Compare the absolute value of the calculation result 10.546 with the threshold 15, the result shows that it does not exceed the threshold. The results show that, despite the existence of error correction actions, the rate of stress change generated by these actions in the key force direction of the bracket is within a safe range and will not cause displacement or damage to the precision automotive parts on the bracket. This achieves a deep integration analysis of error data and mechanical structure characteristics.

[0076] Specifically, such as Figure 2 , 5 As shown, the coupled computation module includes:

[0077] The inter-axis exchange submodule, based on the directional error component, performs data exchange between multiple execution axes. It extracts the directional error component of the current execution axis and the directional error components of the other execution axes according to the axis sequence position, identifies and records the differences between the directional error components of multiple execution axes, and generates the inter-axis error difference quantity.

[0078] Based on the generated directional error components, in flexible manufacturing scenarios, AGVs are typically equipped with two-wheel differential drive or four-wheel omnidirectional drive, with each drive wheel considered an independent axle. First, data synchronization commands are sent to the servo drivers of each axle via the internal high-speed CAN bus (Controller Area Network) to ensure that the data of all axes is locked within the same clock cycle. The generated directional error component of this axle (set as the left front drive wheel) is the core data, and the directional error components of the right front drive wheel (and other axles) at the same timestamp are retrieved synchronously. A data exchange buffer is established, pairing the data of this axle with the data of the other axles according to their axis numbers. Taking 10.06 seconds as an example, the directional error component value of this axle is read from memory as -10.546 (unit: dimensionless projected intensity value). Simultaneously, the directional error component transmitted from the right front drive wheel at the same time point is received. Assuming the right front wheel is traveling on a ground area with slightly different friction coefficients, its force feedback is smaller, and the directional error component processed by the same algorithm is -5.200. Data extraction and difference identification operations are then performed, and the two values ​​are placed into the calculation unit. During the calculation, a numerical subtraction operation is performed, that is, the directional error component of this execution axis is subtracted from the directional error components of the other execution axes. The calculation process is: -10.546 - (-5.200) = -10.546 + 5.200 = -5.346. This value is defined as the inter-axle error difference, and its physical meaning lies in quantifying the asymmetric error impact experienced by the left and right drive wheels at the same moment. This exchange and calculation process is continuously executed according to the time series, and the results are recorded in the database. To clearly show the comparison of inter-axle data, data from 10.05 seconds to 10.09 seconds are selected and listed in Table 3.

[0079] Table 3. Directional Error Components and Differences of Biaxial Actuators

[0080]

[0081] As shown in Table 3, the lateral comparison of inter-axle data can capture the off-center loading trend during vehicle operation in real time. For example, at 10.06 seconds, the absolute value of the difference reaches 5.346, indicating that the left wheel system bears a significantly greater error correction pressure than the right side. This often indicates that the vehicle body is experiencing some degree of roll or unilateral slippage risk, providing key asymmetric feature inputs for subsequent differential construction.

[0082] The differential construction submodule calls the inter-axis error difference and uses the directional error component of the current execution axis as the comparison benchmark. It performs vector difference for the two types of data and performs subtraction operation on the multi-vector components according to the same index position. It performs amplitude comparison on the subtraction result to determine the differential amplitude and generates the directional differential amplitude.

[0083] The generated inter-axis error difference sequence is invoked, and the directional error component sequence of the current execution axis is simultaneously locked as a comparison benchmark. The core task is to further isolate the pure deviation component and eliminate common-mode interference through a quadratic difference operation. Using the time index as a pointer, the inter-axis error difference of -5.346 at 10.06 seconds is extracted, along with the directional error component of the current execution axis as the benchmark, -10.546. A difference operation vector containing the above two values ​​is constructed, and the subtraction operation of the components within the vector is performed. Specifically, the inter-axis error difference is used as the minuend, and the directional error component of the current execution axis is used as the subtrahend. The operation logic is described as: -5.346 - (-10.546) = -5.346 + 10.546, and the calculated result is approximately 5.200. This calculation step is essentially restoring the deviation contribution of the off-axis (right wheel) relative to the zero point (sign inverted), but mathematically, it represents the relative distance between the current axis and the inter-axis difference. Subsequently, an amplitude comparison operation was performed on the subtraction result to determine the magnitude of the differential amplitude, ignoring its directionality. The absolute value function was called, and the absolute value of 5.200 was taken, resulting in 5.200. This value was marked as the directional differential amplitude. To verify the reasonableness of this amplitude and prevent data overflow, a differential amplitude warning baseline value was set. This baseline value was set based on the stress value corresponding to the maximum permissible speed difference of the dual-shaft drive. In laboratory bench testing, when the speed difference between the left and right wheels reached 10% of the rated value, the corresponding differential amplitude was measured to be 15.0. Therefore, 15.0 was set as the warning baseline value. The calculated 5.200 was compared with the baseline value 15.0. Since 5.200 is less than 15.0, the current differential amplitude was determined to be within the normal operating range. This result indicates that although there is an error difference between the left and right wheels, this difference, compared to the error level of the shaft itself, has not yet resulted in an uncontrolled situation with excessive dispersion. The calculated directional difference amplitude of 5.200 is stored in the sequence in chronological order. This data reflects the uniformity of the internal error distribution of the multiaxis. The smaller the value, the better the consistency, and the larger the value, the stronger the internal antagonism.

[0084] The coupling comparison submodule calculates the change of the directional error component between adjacent sampling points based on the directional difference amplitude, performs amplitude comparison with the directional difference amplitude item by item and records the comparison difference, performs weighted calculation on the difference sequence, and generates the coupling difference component.

[0085] Based on the directional difference amplitude, the directional error component sequence of this execution axis is first invoked to calculate the rate of change. The component value at the current time 10.06 seconds (-10.546) and the component value at the previous sampling time 10.05 seconds (see Table 3, -9.500) are read. The sampling period is read as 0.01 seconds. The rate of change calculation is performed: first, the change is calculated, i.e., the current value -10.546 - (-9.500) = -1.046; then, this change is divided by the time interval 0.01 seconds to calculate the directional error component change rate of -104.6. This index physically represents the burst rate of error energy in the time dimension. Next, the directional difference amplitude 5.200 generated in the previous step is invoked and compared with the absolute value of the rate of change. The absolute value of the rate of change, 104.6, is calculated, and then the directional difference amplitude 5.200 is subtracted, resulting in a comparison difference of 99.4. This difference reveals the degree of disparity between dynamic shocks (rate of change) and static differences (difference magnitude). Finally, a weighted calculation is performed on this difference sequence to generate the coupled difference component. The weights are set based on the dynamic response characteristic curve. During low-speed, stable operation, more attention is paid to static differences, resulting in lower weights; during high-speed or drastic changes, more attention is paid to dynamic shocks, resulting in higher weights. A dynamic weighting function based on a rate of change threshold is preset. The baseline threshold for the rate of change is set to 50.0. Since the absolute value of the currently calculated rate of change, 104.6, is greater than 50.0, it is determined to be in the high dynamic range, and a high weight coefficient of 0.6 is automatically matched; if it is less than 50.0, a low weight coefficient of 0.3 is matched. Multiplying the comparison difference value of 99.4 by the weight coefficient 0.6, i.e., 99.4 * 0.6 = 59.64, is the final generated coupled difference component. The results show that at 10.06 seconds, the vehicle not only faces significant inter-axle differences but also experiences extremely rapid error growth (reflected by a rate of change of -104.6), and this dynamic growth dominates (with a significantly positive coupling value). This coupling difference component will be directly transmitted to the AGV's motion controller as a feedforward compensation signal, strongly suppressing impending vehicle attitude instability and realizing a closed-loop logic from data analysis to control decision-making.

[0086] Specifically, such as Figure 2 , 6 As shown, the adaptive PID module includes:

[0087] The differential component screening submodule compares the coupled differential components with the coupling judgment threshold, judges the coupled differential components with the coupling judgment threshold, distinguishes the differential components that exceed the coupling judgment threshold from the differential components that do not reach the coupling judgment threshold and adds a label, and generates a differential classification sequence.

[0088] Based on the generated coupling difference component sequence, the latest coupling difference component value stored in the cache is first read. According to the calculation results above, the coupling difference component of the left front drive wheel at 10.06 seconds is 59.64. Simultaneously, the coupling difference component data of the right front drive wheel at the same time is retrieved. To establish a complete control group, the coupling difference component of the right front wheel is calculated to be 10.44 using the same algorithm logic. This value is relatively small because the ground environment where the right front wheel is located is relatively flat, and its inter-axle difference contribution is small. At this point, two key values ​​are temporarily stored in memory: 59.64 for the left axle and 10.44 for the right axle. A coupling judgment threshold is then introduced for determination. This threshold is set based on the linear response range test of the AGV servo drive. In the frequency response test for the AGV under full load conditions, when the coupling strength of the input signal exceeds 40.0, the current response of the servo motor shows a nonlinear saturation trend, leading to a significant increase in control overshoot. Based on this experimental data, to ensure the linear stability of the control, the coupling judgment threshold is strictly set to 40.0. The comparison instruction is invoked, first comparing the left-axis coupling differential component 59.64 with the threshold 40.0. Since 59.64 is greater than 40.0, the result is "threshold exceeded". A high-sensitivity dynamic identifier (e.g., binary code 01) is then written to the header of the data packet, indicating that the axis is currently in a rapidly changing, unstable state, requiring a highly responsive control strategy. Next, the right-axis coupling differential component 10.44 is compared with the threshold 40.0. Since 10.44 is less than 40.0, the result is "threshold not reached". A low-sensitivity static identifier (e.g., binary code 10) is written to the data packet, indicating that the axis is in a relatively stable, fine-tuning state, suitable for a control strategy that eliminates steady-state errors. This logic is repeated for all axes, generating a differential classification sequence containing the axis number, coupling value, and status identifier. The advantage of this classification process is that it digitally isolates actuators in different dynamic states, preventing the "one-size-fits-all" application of a single control parameter across multiple axes, and laying the logical foundation for subsequent hierarchical adaptive control.

[0089] The weight generation submodule calls the differential classification sequence. For data items that exceed the coupling judgment threshold, it performs proportional and differential weight calculation based on the difference between the differential component and the coupling judgment threshold. For data items that do not reach the coupling judgment threshold, it performs integral weight calculation based on the change amplitude of the differential component, thus obtaining an adaptive PID sequence.

[0090] Based on the state identifiers in the differential classification sequence, different weight calculation paths are activated. For left front axis data identified as "exceeding the threshold," a proportional-derivative (PD)-dominated weight calculation procedure is executed. First, the overshoot is calculated by subtracting the coupling decision threshold of 40.0 from the left axis coupling difference component of 59.64, resulting in a difference of 19.64. The preset proportional baseline value is 1.5, and the proportional gain coefficient is 0.02; the preset derivative baseline value is 0.5, and the derivative gain coefficient is 0.01. A weighting operation is performed: the difference of 19.64 is multiplied by the proportional gain coefficient of 0.02, resulting in an increment of 0.3928, which is then added to the proportional baseline value of 1.5 to calculate the adaptive proportional weight of 1.8928. Similarly, the difference of 19.64 is multiplied by the derivative gain coefficient of 0.01, resulting in an increment of 0.1964, which is then added to the derivative baseline value of 0.5 to calculate the adaptive derivative weight of 0.6964. At this point, to prevent response lag caused by integral saturation, the integral weight is forcibly reset to 0. This set of parameters (1.8928, 0, 0.6964) constitutes the high-dynamic PID control vector for the left axis. For the right front axis data marked as "not reaching the threshold," the integral (I)-dominated weight calculation program is activated. The current coupling differential component of the right axis (10.44) and the value of the previous sampling time (set to 10.00) are read, and the differential component change amplitude is calculated to be 0.44. The preset integral reference value is 0.8, and the integral sensitivity coefficient is 0.5. The change amplitude of 0.44 is multiplied by the integral sensitivity coefficient of 0.5 to obtain an increment of 0.22, which is then added to the integral reference value of 0.8 to calculate the adaptive integral weight of 1.02. At this point, the proportional weight and derivative weight maintain their default steady-state values ​​of 1.0 and 0.2, respectively. This set of parameters (1.0, 1.02, 0.2) constitutes the steady-state PID control vector for the right axis. The calculated parameters for each axis are sequentially packaged to generate an adaptive PID sequence. Table 4 is provided to clearly illustrate the parameter generation results under different conditions.

[0091] Table 4 Adaptive PID Weight Generation Parameter Table

[0092]

[0093] As shown in Table 4, differentiated control parameters were dynamically generated based on real-time operating conditions. The high proportional term (1.893) and derivative term (0.696) on the left axis ensured rapid suppression of severe disturbances, while the high integral term (1.020) on the right axis focused on eliminating small steady-state deviations. This data-driven adaptive parameter generation mechanism effectively solved the technical challenge of traditional fixed PID parameters failing to balance speed and stability.

[0094] The weight fusion submodule extracts the proportional weight, integral weight and derivative weight according to the adaptive PID sequence, performs a product operation with the corresponding error term in the coupled differential component, and performs a weighted summation of all product results to generate the AGV bracket multi-axis control result.

[0095] Based on the generated adaptive PID sequence, the final control quantity synthesis stage begins. To avoid positive feedback instability caused by single-axis speed, the "synchronization reference value" for multiple axes is first calculated. The displacement difference components of the left front axle (15.25 mm) and the right front axle (7.50 mm) are extracted, and their average value (15.25 + 7.50) / 2 = 11.375 mm is calculated and set as the current synchronization target displacement. Subsequently, the "synchronization error term" for each axis is calculated. For the left front axle, its synchronization error is "synchronization reference value - actual displacement", i.e., 11.375 − 15.25 = −3.875 mm (a negative value indicates that the axis is overspeeding and needs to decelerate). For the right front axle, its synchronization error is 11.375 − 7.50 = +3.875 mm (a positive value indicates that the axis is lagging and needs to accelerate). Next, PID weighted calculation is performed: taking the left front axle as an example, the adaptive PID parameters (1.8928, 0, 0.6964) are extracted. The first step, proportional (P) stage: multiply the synchronization error -3.875 by the proportional weight 1.8928, i.e., −3.875×1.8928≈−7.33; the second step, integral (I) stage: the weight is 0, and the result is 0; the third step, derivative (D) stage: extract the displacement change gradient (assuming a gradient of -2.0 due to deceleration), multiply it by the derivative weight 0.6964, i.e., −2.0×0.6964=−1.39. The final synthesized left-axis control compensation is: −7.33+0+(−1.39)=−8.72. This negative compensation is superimposed on the basic drive command, which will effectively suppress the overspeed trend of the left axis. Taking the right front axle as an example, the PID parameters are extracted as (1.0, 1.02, 0.2). The proportional component: the synchronization error of +3.875 is multiplied by the weight 1.0, resulting in +3.875. The integral component: assuming a historical cumulative synchronization error of +5.0 (constant lag), it is multiplied by the weight 1.02, resulting in 5.0 × 1.02 = 5.10. The differential component: the displacement gradient (assumed to be +1.0) is multiplied by the weight 0.2, resulting in 0.2. The final synthesized right-axis control compensation is: 3.875 + 5.10 + 0.2 = +9.175. This positive compensation will significantly increase the right-axis speed. Finally, the calculated left-axis compensation (-8.72) and right-axis compensation (+9.175) are output in the order of the axes being executed. This result demonstrates that by introducing a synchronization reference, the states of the left-axis being "too fast" and the right-axis being "too slow" are correctly identified, and forced synchronization of the fast and slow axes is achieved through opposite positive and negative compensation signals, completely avoiding the instability risk caused by positive feedback.

[0096] Specifically, such as Figure 2 , 7 As shown, the control optimization module includes:

[0097] The weight extraction submodule, based on the AGV bracket multi-axis control results and adaptive PID group, distinguishes the proportional, integral and derivative components, extracts the multi-components according to the corresponding weight values ​​in the adaptive PID group, and arranges them in the order of components to generate a proportional-integral-derivative weight sequence.

[0098] Based on the generated multi-axis control results of the AGV carriage, the latest calculated values ​​in the buffer are first read: the control result for the left front axle is -8.72 (negative values ​​represent suppression / deceleration commands), and the control result for the right front axle is +9.175 (positive values ​​represent compensation / acceleration commands). Then, the corresponding adaptive PID group parameters are synchronously retrieved: (1.8928, 0, 0.6964) for the left axis and (1.0, 1.02, 0.2) for the right axis. The core task is to map the total control quantity back to specific PID weight dimensions to evaluate the actual contribution of each component under the current load. First, a reference physical quantity is set—the rated output torque command value of the drive motor, calibrated to 50.0 N·m. This reference value is used to perform a normalization extraction ratio calculation on the current control result (using the absolute value to calculate the amplitude percentage). For the left front axle, |−8.72| / 50.0=0.1744, meaning the "left axle load efficiency coefficient" is 0.1744. For the right front axle, calculate |+9.175| / 50.0=0.1835, meaning the "right axle load efficiency coefficient" is 0.1835. Next, extract the weighted components based on the above coefficients: Left axle (high-sensitivity dynamic group): Proportional component extraction value: 1.8928×0.1744≈0.3301; Differential component extraction value: 0.6964×0.1744≈0.1215; Integral component is 0. Right axle (steady-state holding group): Proportional component extraction value: 1.0×0.1835=0.1835; Integral component extraction value: 1.02×0.1835≈0.1872; Differential component extraction value: 0.2×0.1835≈0.0367. Arrange the above values ​​in "left-axis PID, right-axis PID" order to generate a proportional-integral-derivative weighted sequence: (0.3301, 0, 0.1215, 0.1835, 0.1872, 0.0367). This sequence is not a simple parameter replication, but reflects the actual physical weighted contribution of each PID parameter under the current specific control output intensity, providing a quantitative basis for subsequent fine-tuning of the motor's nonlinear characteristics.

[0099] The component correction submodule calls the proportional-integral-derivative weight sequence, performs component-by-component adjustment on multiple components according to the proportional-integral-derivative weight sequence based on the AGV bracket multi-axis control results, and performs difference calculation to generate a multi-axis correction difference sequence.

[0100] The generated proportional-integral-derivative weighted sequence is invoked, and a "reverse heat loss compensation model" is introduced. The logic of this model is that heating of the motor coil causes a decrease in the torque constant (experimentally measured attenuation rate of 5%, coefficient 0.05). To maintain the target torque, an additional compensation signal must be actively output. Compensation values ​​are calculated for each non-zero component in the sequence. The calculation principle is: based on the sign direction of the original control command, a gain compensation value in the same direction is generated. For the left front axle (current command is negative), a negative compensation value needs to be generated to enhance the negative torque: left axle proportional compensation value: 0.3301 × 0.05 × (−1) = −0.0165; left axle derivative compensation value: 0.1215 × 0.05 × (−1) = −0.0061. For the right front axle (current command is positive), positive compensation values ​​need to be generated to enhance the positive torque: right axle proportional compensation value: 0.1835 × 0.05 × (+1) = +0.0092; right axle integral compensation value: 0.1872 × 0.05 × (+1) = +0.0094; right axle differential compensation value: 0.0367 × 0.05 × (+1) = +0.0018. The calculated compensation values ​​are arranged in their original order to generate a multi-axis correction difference sequence. Table 5 illustrates this process.

[0101] Table 5. Results of PID Weight Component Correction and Difference Calculation

[0102]

[0103] As shown in Table 5, negative compensation was generated on the left axis and positive compensation was generated on the right axis, indicating that the control strength is being enhanced in both directions to offset the power loss caused by thermal decay.

[0104] The weighted synthesis submodule performs weighted superposition of the multi-control components and the multi-axis correction difference sequence based on the AGV carriage multi-axis control results, and performs sequence reconstruction on the superposition result. The reconstructed sequence is output according to the execution axis order to generate the optimized AGV carriage multi-axis control results.

[0105] First, the original AGV carriage multi-axis control results (left axis -8.72, right axis +9.175) and the generated multi-axis correction difference sequence are read. To map the small weighted compensation values ​​to the final torque command, a "compensation gain weighting factor" is introduced and set to 10.0. First, the left front axis data is processed: compensation value accumulation is performed: (−0.0165) + (−0.0061) = −0.0226. Weighted synthesis is performed: the original value is added to (total compensation value multiplied by the weighting factor). Calculation formula: −8.72 + (−0.0226 × 10.0) = −8.72 − 0.226 = −8.946. Result analysis: The absolute value of the left axis command increased from 8.72 to 8.946, which means that a larger torque was applied in the negative direction, effectively compensating for thermal decay and ensuring the execution force of deceleration / suppression actions. Next, the right front axle data is processed: Compensation value accumulation is performed: 0.0092 + 0.0094 + 0.0018 = +0.0204. Weighted synthesis is then performed: +9.175 + (0.0204 × 10.0) = 9.175 + 0.204 = 9.379. Result analysis shows that the right axle command increased from 9.175 to 9.379, improving the driving force in the positive direction and ensuring the accuracy of the acceleration / compensation action. Finally, sequence reconstruction is performed on these two values, outputting the optimized control sequence (-8.946, 9.379) according to the format required by the AGV's underlying driver. This result demonstrates that, after processing by the optimization module, the directionality of the command was successfully identified, and "reverse thermal compensation" conforming to physical characteristics was implemented, preventing insufficient actual output torque due to motor overheating, thereby achieving high-precision multi-axis synchronous control.

[0106] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A multi-axis linkage synchronous control system for AGV carriages based on adaptive PID, characterized in that, The system includes: The displacement analysis module collects data on the displacement of the execution shaft, the acceleration and angular velocity of the bracket, sorts them by time, calculates the displacement difference between adjacent sampling points, analyzes the changes in acceleration and angular velocity and combines them with the displacement difference to generate an error state vector and transmit it to the error analysis module. The error analysis module, based on the error state vector, analyzes the error gradient vector group of adjacent time points, and projects the bracket structure direction vector calculated by the preset bracket geometric model to generate directional error components and transmits them to the coupled calculation module. The coupling calculation module performs data exchange between multiple execution axes based on the directional error component, extracts the component of this execution axis and performs differential calculation with the components of other execution axes and calculates the correlation degree, analyzes the rate of change of the directional error component and compares it with the correlation degree, generates a coupling difference component and transmits it to the adaptive PID module. The adaptive PID module, based on the coupling difference components, calculates the proportional and differential weights for the differences exceeding the coupling judgment threshold, analyzes the integral weights for the difference terms below the coupling judgment threshold, merges all weights into an adaptive PID group, and accumulates the displacement differences of multiple execution axes to generate the multi-axis control results of the AGV carriage.

2. The AGV bracket multi-axis linkage synchronous control system based on adaptive PID according to claim 1, characterized in that, The error state vector includes displacement difference components, acceleration change characteristics, and angular velocity change characteristics. The directional error components include projection error components, structural orientation correlation components, and orientation offset components. The coupling difference components include multi-axis error comparison quantities, multi-axis rate of change ratio quantities, and multi-axis correlation degree difference components. The AGV bracket multi-axis control results include proportional adjustment weights, integral adjustment weights, and derivative adjustment weights.

3. The AGV bracket multi-axis linkage synchronous control system based on adaptive PID according to claim 1, characterized in that, The displacement analysis module includes: The data analysis submodule collects and sorts the data of the execution shaft displacement, bracket acceleration and angular velocity by sampling time. It calculates the displacement difference between adjacent sampling points based on the time difference and displacement value of adjacent sampling points, performs a subtraction operation on the displacement difference of each pair of adjacent sampling points, records the displacement difference value according to the calculation result, and generates a displacement difference sequence. The attitude disturbance submodule calls the displacement difference sequence and performs differential operation on the acceleration and angular velocity data at the same time. It then filters the data based on the attitude disturbance threshold and merges the filtered acceleration and angular velocity changes into attitude disturbance values ​​to generate an attitude disturbance value sequence. The error state submodule performs a sequential concatenation operation on the displacement difference sequence and the attitude disturbance value sequence, arranging the displacement difference and attitude disturbance value at the same time into a single state vector and expanding it in chronological order to generate an error state vector.

4. The AGV bracket multi-axis linkage synchronous control system based on adaptive PID according to claim 3, characterized in that, The attitude disturbance threshold is determined by analyzing all the difference values ​​between the acceleration change and the angular velocity change within a set historical time window. The amplitude of the acceleration difference value sequence and the angular velocity difference value sequence are calculated according to the time position and merged into a unified change value set. The change value set is then sorted by numerical value and the median value is extracted.

5. The AGV bracket multi-axis linkage synchronous control system based on adaptive PID according to claim 1, characterized in that, The error analysis module includes: The error difference module performs subtraction on the error terms at adjacent time points based on the error state vector. For each error term sequence, it calculates the difference component with adjacent error values ​​as participating terms and arranges them in chronological order. It identifies and records the corresponding change trends at time points and generates an error difference sequence. The gradient vector submodule calls the error difference sequence, performs vector component comparison on multiple error components in the sequence, calculates the rate of change of multiple components based on the same time point and arranges them into a vector group according to the component direction, performs amplitude comparison on the vector group to determine the component change amplitude, and generates an error gradient vector group. The component extraction submodule calculates the bracket structure direction vector and performs vector projection based on the error gradient vector group. It then performs inner product operation on the multi-vector components of the gradient vector group and the bracket structure direction vector, records the results, and arranges them into a directional sequence in chronological order to generate directional error components.

6. The AGV bracket multi-axis linkage synchronous control system based on adaptive PID according to claim 1, characterized in that, The coupling calculation module includes: The inter-axis exchange submodule performs data exchange between multiple execution axes based on the directional error components. It extracts the directional error components of the current execution axis and the other execution axes according to their corresponding axis positions, identifies and records the differences between the directional error components of multiple execution axes, and generates the inter-axis error difference quantity. The differential construction submodule calls the inter-axis error difference amount and uses the directional error component of the current execution axis as the comparison benchmark. It performs vector difference for the two types of data and performs subtraction operation on the multi-vector components according to the same index position. It performs amplitude comparison on the subtraction result to determine the differential amplitude and generates the directional differential amplitude. The coupling comparison submodule calculates the change of the directional error component between adjacent sampling points based on the directional difference amplitude, performs amplitude comparison with the directional difference amplitude item by item and records the comparison difference, performs weighted calculation on the difference sequence, and generates the coupling difference component.

7. The AGV bracket multi-axis linkage synchronous control system based on adaptive PID according to claim 1, characterized in that, The adaptive PID module includes: The differential component screening submodule compares the coupled differential components with the coupling judgment threshold, judges the coupled differential components with the coupling judgment threshold, distinguishes the differential components that exceed the coupling judgment threshold from the differential components that do not reach the coupling judgment threshold and adds an identifier, and generates a differential classification sequence. The weight generation submodule calls the differential classification sequence to perform proportional and differential weight calculations on data items that exceed the coupling judgment threshold based on the difference between the differential component and the coupling judgment threshold, and to perform integral weight calculations on data items that do not reach the coupling judgment threshold based on the magnitude of the difference component change, thereby obtaining an adaptive PID sequence. The weight fusion submodule extracts the proportional weight, integral weight, and derivative weight according to the adaptive PID sequence, performs a product operation with the corresponding error terms in the coupled differential component, and performs a weighted summation of all product results to generate the AGV bracket multi-axis control result.

8. The AGV bracket multi-axis linkage synchronous control system based on adaptive PID according to claim 7, characterized in that, The coupling determination threshold is determined by setting a historical sliding window, acquiring all coupling difference components generated by multiple execution axes within the historical sliding window, analyzing them, sorting the difference components by numerical value, and analyzing the median value.

9. The AGV bracket multi-axis linkage synchronous control system based on adaptive PID according to claim 1, characterized in that, The system also includes: The control optimization module extracts proportional weights, integral weights, and derivative weights from the AGV carriage multi-axis control results and the adaptive PID group to perform component-by-component correction on the AGV carriage multi-axis control results, and performs weighted synthesis on the correction values ​​and the original control results to generate optimized AGV carriage multi-axis control results. The optimized AGV carriage multi-axis control results include proportional correction components, integral correction components, and derivative correction components.

10. The AGV bracket multi-axis linkage synchronous control system based on adaptive PID according to claim 1, characterized in that, The control optimization module includes: The weight extraction submodule, based on the AGV bracket multi-axis control results and the adaptive PID group, distinguishes the proportional component, integral component and derivative component, extracts the multi-component according to the corresponding weight value in the adaptive PID group, and arranges them in the order of components to generate a proportional integral derivative weight sequence. The component correction submodule calls the proportional-integral-derivative weight sequence, performs component-by-component adjustment on the multi-components according to the proportional-integral-derivative weight sequence based on the AGV bracket multi-axis control results, and performs difference calculation to generate a multi-axis correction difference sequence. The weighted synthesis submodule performs weighted superposition of the multi-control components and the multi-axis correction difference sequence based on the AGV carriage multi-axis control results, performs sequence reconstruction on the superposition results, and outputs the reconstructed sequence in the order of the execution axes to generate the optimized AGV carriage multi-axis control results.

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