Cooperative control method and device for high-precision coordinated motion system

Abstract

The invention discloses a cooperative control method for a high-precision cooperative motion system, and the method comprises the steps: obtaining an expected trajectory of a main execution unit, and converting the expected trajectory into prediction sub-trajectories corresponding to a plurality of auxiliary execution units; calculating a local tracking error and a synchronization error according to the predicted sub-trajectory and the actual trajectory of the auxiliary execution unit; calculating a corresponding estimation error through a predictive disturbance observer; local tracking control corresponding to each auxiliary execution unit is obtained through calculation; constructing a self-adaptive cross coupler and performing coupling compensation calculation based on the synchronization error to obtain self-adaptive cross coupling control; and based on adaptive cross-coupling control and local tracking control, generating a total control input, and verifying the generated total control input by using a Lyapunov function. The invention further provides a cooperative control device. The method provided by the invention has the advantages of fast dynamic response, low buffeting, high-precision synchronization and time delay robustness, occupies less computing resources, and is suitable for various edge devices.

Description

Technical Field

[0001] This invention belongs to the field of nonlinear robust control and multi-actuator cooperative control technology, and particularly relates to a cooperative control method and device for high-precision coordinated motion systems. Background Technology

[0002] In collaborative motion scenarios such as multi-axis CNC, dual-drive gantry platforms, parallel robots, and tendon-driven fingers, cross-coupled control (CCC) has long relied on allocating contour / synchronization errors. However, fixed-gain CCC based on PID control struggles to balance high-frequency tracking and high-precision synchronization under strong nonlinearity and frictional / elastic coupling. Sliding mode control (SMC) is robust to uncertainties but prone to chattering; traditional disturbance observers can mitigate gain switching, but performance degrades significantly with communication / execution delays. Delay compensation methods such as MPC / Smith are either highly sensitive to the model or computationally expensive, hindering high-speed real-time control and embedded deployment. These issues are particularly prominent in compliant / variable stiffness systems and biomimetic tendon systems, posing a significant challenge to high-precision collaborative control.

[0003] Patent document CN120995406A discloses a laser operation process control system based on multi-element fusion, including a multi-element perception and fusion module, an intelligent decision-making module, a multi-actuator collaborative control module, a system overall control and human-machine interaction module, and a self-learning and optimization module. By integrating multiple sensors to collect geometric topography, temperature field, plasma characteristics, and environmental data of the operation area in real time, a "fusion situation information map" is generated through feature extraction and fusion. Combined with a high-fidelity digital twin model, forward prediction is performed to predict the topography evolution, thermodynamic behavior, and potential defects of the processing area. Based on the prediction results, the laser, motion mechanism, and auxiliary gas unit are synchronously controlled through a high-speed industrial network to realize multi-actuator collaborative operation, coordinate task scheduling, status monitoring, and human-machine interaction. By comparing actual data with prediction results, the model parameters and decision-making strategies are continuously optimized.

[0004] Patent document CN121246568A discloses a multi-motor cooperative drive and torque distribution method and system. The method includes: real-time acquisition of motor speed, current, battery SOC, and vehicle driving condition data; preprocessing the acquired multi-source data to eliminate noise interference and extract signal features; establishing a torque demand model based on vehicle driving condition classification and calculating the target torque of the vehicle; constructing a torque distribution model with integrated driving condition weights, and dynamically allocating the torque of each motor by combining motor efficiency characteristics, battery SOC status, and road resistance through an improved particle swarm optimization algorithm; real-time monitoring of motor status during driving, and recording the torque distribution data into a database after the vehicle has finished driving, and optimizing the torque demand model and torque distribution model parameters. Summary of the Invention

[0005] The purpose of this invention is to provide a collaborative control method and device for high-precision coordinated motion systems. This method has fast dynamic response, low jitter, high-precision synchronization and time delay robustness, and low computational resource consumption, making it adaptable to various edge devices.

[0006] To achieve the first objective of this invention, the following technical solution is provided: a cooperative control method for a high-precision coordinated motion system, wherein the high-precision coordinated motion system includes a main execution unit and multiple auxiliary execution units, as well as a predictive disturbance observer and a fast terminal sliding mode controller, and the cooperative control method includes the following steps: The desired trajectory of the main execution unit is obtained, and the desired trajectory is converted into predicted sub-trajectories corresponding to multiple auxiliary execution units through a second-order continuously differentiable function; Based on the predicted sub-trajectory and the actual trajectory of the auxiliary execution unit, the corresponding local tracking error is calculated, and all local tracking errors are averaged to obtain the corresponding synchronization error. The generalized disturbance of the predictive disturbance observer is defined based on the disturbance factors, and the difference between the feedforward prediction estimate output by the predictive disturbance observer and the generalized disturbance is calculated to obtain the corresponding estimation error. Based on the local tracking error, a sliding surface is constructed on the corresponding auxiliary execution unit by a fast terminal sliding mode controller, and the local tracking control corresponding to each auxiliary execution unit is calculated based on the sliding surface and the feedforward prediction estimate output by the predictive disturbance observer. An adaptive cross-coupler is constructed and coupling compensation calculation is performed based on synchronization error to obtain adaptive cross-coupling control; Based on adaptive cross-coupling control and local tracking control, the total control input is generated and verified using the Lyapunov function.

[0007] Specifically, the expression for the second-order continuously differentiable function is as follows: ; in, Represents the desired trajectory. Indicates the first i Predicted sub-trajectories of each auxiliary execution unit.

[0008] Specifically, the expression for the local tracking error is as follows: ; in, Indicates the first i The actual trajectory of each auxiliary execution unit Indicates the first i Predicted sub-trajectories of each auxiliary execution unit For the first iLocal tracking error of each auxiliary execution unit , and They are respectively , and The rate of change.

[0009] Specifically, the average calculation process for the synchronization error is as follows: ; in, Indicates the first i Local tracking error of each auxiliary execution unit This represents the average local tracking error of n auxiliary execution units.

[0010] Specifically, the interference factors include actuator lag, communication delay, unmodeled dynamics, and external disturbances.

[0011] Specifically, the expression for the local tracking control is as follows: ; in, express The second derivative, Indicates sliding mode gain. Indicates the first i Sliding surfaces of auxiliary execution units Indicates a boundary layer. This indicates the estimation error.

[0012] Specifically, the expression for the sliding surface is as follows: ; in, express rate of change, , Indicates the first i The constants of each auxiliary execution unit in the fast terminal sliding mode controller Indicates the first i Local tracking error of each auxiliary execution unit Represents a symbolic function.

[0013] Specifically, the expression for the adaptive cross-coupler is as follows: ; in Indicates the first i The constant term of each auxiliary execution unit in the adaptive cross-coupler Indicates the first i Adaptive control gain of each auxiliary execution unit Indicates the firsti The base gain of each auxiliary execution unit This indicates synchronization error.

[0014] Specifically, the expression for the predictive disturbance observer is as follows: ; in, This indicates feedforward prediction estimation. Indicates the internal state. Indicates the observer gain. Indicates the first i The actual trajectory of each auxiliary execution unit This indicates the main control input.

[0015] To achieve the second objective of this invention, the following technical solution is provided: a cooperative control device for executing the steps of the above-described cooperative control method for high-precision coordinated motion systems, comprising: The geometric mapping module generates predicted sub-trajectories for each auxiliary execution unit based on the expected trajectory of the main execution unit. The error construction module generates corresponding local tracking errors and synchronization errors based on the predicted sub-trajectory and the actual trajectory of the auxiliary execution unit. Predictive perturbation observers are used to generate corresponding feedforward prediction estimates in real time; A fast terminal sliding mode controller is used to generate local tracking control; An adaptive cross-coupler is used to generate adaptive cross-coupled control.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention proposes a predictive observation-enhanced fast terminal sliding mode cooperative control architecture for high-precision cooperative motion systems. It predicts and feeds forward to compensate for generalized disturbances such as communication delay, actuator hysteresis, friction, and external loads. Simultaneously, it utilizes fast terminal sliding mode to achieve finite-time convergence of errors and reduces switching gain under disturbance compensation to suppress chattering. Furthermore, it employs an adaptive cross-coupling mechanism to adjust coupling gain online based on synchronization errors to rapidly reduce synchronization deviations and residual oscillations between multiple actuators. Therefore, this invention can significantly improve trajectory tracking accuracy, synchronization consistency, and stability under complex nonlinear and strongly disturbed environments, improve overshoot and settling time under abrupt changes such as step jumps, and maintain good real-time performance and engineering feasibility without requiring computationally expensive online optimization. It is applicable to various coordinated motion systems requiring high-precision and robust cooperative control. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the cooperative control method for high-precision coordinated motion systems provided in this embodiment; Figure 2 The trajectory tracking response, tracking error, and synchronization error of the auxiliary system under the action of the three controllers provided in this embodiment are described. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0019] like Figure 1 As shown in this embodiment, a cooperative control method for a high-precision coordinated motion system includes the following steps: The high-precision coordinated motion system includes a main execution unit and multiple auxiliary execution units, as well as a predictive disturbance observer and a fast termination sliding mode controller. The cooperative control method includes the following steps: The desired trajectory of the main execution unit is obtained, and the desired trajectory is converted into predicted sub-trajectories corresponding to multiple auxiliary execution units through a second-order continuously differentiable function; Based on the predicted sub-trajectory and the actual trajectory of the auxiliary execution unit, the corresponding local tracking error is calculated, and all local tracking errors are averaged to obtain the corresponding synchronization error. The generalized disturbance of the predictive disturbance observer is defined based on the disturbance factors, and the difference between the feedforward prediction estimate output by the predictive disturbance observer and the generalized disturbance is calculated to obtain the corresponding estimation error. Based on the local tracking error, a sliding surface is constructed on the corresponding auxiliary execution unit by a fast terminal sliding mode controller, and the local tracking control corresponding to each auxiliary execution unit is calculated based on the sliding surface and the feedforward prediction estimate output by the predictive disturbance observer. An adaptive cross-coupler is constructed and coupling compensation calculation is performed based on synchronization error to obtain adaptive cross-coupling control; Based on adaptive cross-coupling control and local tracking control, the total control input is generated and verified using the Lyapunov function.

[0020] More specifically, in this embodiment, the dynamic equations of the auxiliary system are expressed as follows: .

[0021] in The total control input is used for local tracking control. and adaptive cross-coupling control It consists of two parts: .

[0022] The aforementioned predictive disturbance observer adopts the following structure: And in the implementation, the measurement noise is passed through A trade-off setting is made with the bandwidth limit to balance fast convergence and noise robustness.

[0023] Parameters of adaptive cross-coupler It can be tuned in sections according to the mission phase (high-speed straight section, low-speed / curved section, impact and disturbance section) to balance synchronization, stability and overshoot suppression under different conditions.

[0024] The main execution unit and multiple auxiliary execution units satisfy the following relationship: This ensures kinematic consistency between master and slave and reduces the impact caused by mapping discontinuities.

[0025] The Lyapunov stability proof process in this embodiment is as follows: The Lyapunov function is selected as follows: in right Differentiation yields: definition ,but definition Estimation is performed using Young's inequality: The final result is: choose Then it exists Make: when hour, Therefore ,but: when hour, Therefore ,but: because ,but , Multiply both sides simultaneously have to Therefore Therefore: right Differentiating, we get: There exists a constant Make: Therefore: right Differentiating, we get: According to Young's inequality, we have: like Then it exists Make: Therefore: final: According to Young's inequality: Therefore: in, .definition ,but: According to Lyapunov stability theory, when hour, It must be less than 0. Therefore, the system is uniformly and eventually bounded, and all system errors and disturbance estimation errors will converge to a single point. Within the bounded domain determined by the origin.

[0026] This embodiment also provides a cooperative control device for executing the steps of the cooperative control method for high-precision coordinated motion systems provided in the above embodiments, including: The geometric mapping module generates predicted sub-trajectories for each auxiliary execution unit based on the expected trajectory of the main execution unit. The error construction module generates corresponding local tracking errors and synchronization errors based on the predicted sub-trajectory and the actual trajectory of the auxiliary execution unit. Predictive perturbation observers are used to generate corresponding feedforward prediction estimates in real time; A fast terminal sliding mode controller is used to generate local tracking control; An adaptive cross-coupler is used to generate adaptive cross-coupled control.

[0027] To better illustrate the technical effects of the method provided in this embodiment, the following actual demonstration process is provided.

[0028] A sinusoidal signal was selected as the target trajectory to test the tracking performance and robustness of the controller, and compared with PID-CC and SMC-CC controllers.

[0029] The expression for a sinusoidal signal is: The mapping functions for the two auxiliary motors are taken as follows: .

[0030] The response of the three controllers to the trajectory tracking of the sinusoidal signal is as follows: Figure 2 As shown in (a) above, the trajectory tracking error is as follows: Figure 2As shown in (b) of the diagram. All three controllers can achieve basic tracking of the target trajectory changing at high frequencies, and the trajectory tracking curves basically match the target trajectory. However, there are significant differences in tracking accuracy and dynamic response performance. It can also be observed that the maximum trajectory tracking error occurs near the peak of the sinusoidal trajectory, because at this time the main and auxiliary motors are switching directions of motion, and the combined effect of system inertia and external disturbances affects the instantaneous response capability of the controllers. The peak values ​​of the trajectory response curves of the PID-CC and SMC-CC controllers deviate somewhat from the peak value of the sinusoidal trajectory, indicating that the PID-CC and SMC-CC controllers cannot quickly adjust to track the target, and their adjustment capability in the fast dynamic response phase is limited. The deviation is particularly significant for the PID-CC controller. In contrast, the SMC-CC controller improves the dynamic response characteristics to some extent, but still has slight steady-state errors and chattering issues. The predictive disturbance observer and fast terminal sliding mode design in the P-DO-FTSMSC controller not only significantly improve the dynamic response speed and synchronous tracking capability of the system, but also effectively suppress the error accumulation caused by high-frequency disturbances. Its trajectory tracking curve almost completely overlaps with the target trajectory, with minimal error fluctuation, exhibiting superior tracking accuracy and robustness. It also demonstrates excellent dynamic performance and control stability in high-frequency trajectory tracking tasks.

[0031] Synchronization errors of the three controllers are as follows Figure 2 As shown in (c) of the diagram. From... Figure 2 As shown in (c), the PID-CC, SMC-CC and P-DO-FTSMSC controllers all exhibited oscillations of varying degrees at startup, with the PID-CC controller exhibiting the largest oscillation amplitude and the P-DO-FTSMSC controller exhibiting the smallest oscillation amplitude.

[0032] Furthermore, the synchronization error of the PID-CC controller exhibited large and continuous oscillations, indicating that the PID-CC controller is unable to effectively control the auxiliary system when faced with system nonlinearity and strong disturbances.

[0033] In contrast, the SMC-CC and P-DOFTSMSC controllers exhibit faster decay of transient oscillations in the initial stage, subsequently maintaining small-amplitude high-frequency oscillations near zero, demonstrating better dynamic stability and disturbance rejection performance. Furthermore, because the P-DOFTSMSC controller integrates an adaptive cross-coupling mechanism, it can dynamically adjust the coupling gain based on the real-time errors between auxiliary systems, thereby achieving more precise cooperative control.

[0034] PID-CC and SMC-CC controllers, using only fixed coupling coefficients, cannot adaptively adjust to changes in system state, resulting in an inability to maintain stable cooperative following relationships at different motion stages. Under the combined effect of an adaptive coupling strategy and a predictive disturbance observer, the P-DO-FTSMSC controller not only significantly reduces the oscillation amplitude of synchronization errors but also accelerates error convergence, enabling the system to quickly enter a stable state. This further verifies its superior synchronization control performance under complex dynamic conditions.

[0035] To more intuitively describe the trajectory tracking performance of the three controllers, evaluation metrics for tracking error and synchronization error, including MAE (Mean Absolute Error) and RMSE (Root Mean Square Error), were calculated. The calculation results are shown in Table 1. The results show that during the control process of Slave I, compared with the PID-CC controller, the MAE of the SMC-CC and P-DO-FTSMSC controllers were reduced by 83.09% and 85.94%, respectively, and the RMSE was reduced by 61.19% and 76.70%, respectively. During the control process of Slave II, compared with the PID-CC controller, the MAE of the SMC-CC and P-DO-FTSMSC controllers were reduced by 82.92% and 84.25%, respectively, and the RMSE was reduced by 67.46% and 79.48%, respectively. This indicates that sliding mode control and its improved methods can significantly suppress error accumulation and improve system response accuracy in high-frequency trajectory tracking. Regarding synchronization error, compared with the PID-CC controller, the MAE of the SMC-CC and P-DO-FTSMSC controllers were reduced by 84.91% and 87.64%, respectively, and the RMSE was reduced by 65.85% and 84.39%, respectively. Among them, the P-DO-FTSMSC controller had the lowest error indicators and the best overall performance.

[0036] This is mainly due to the adaptive cross-coupling mechanism and predictive disturbance observer integrated in the controller, which enables it to dynamically adjust the coupling gain according to the real-time state between the main and auxiliary systems, achieving higher precision in coordination compensation and disturbance suppression, thereby maintaining more stable synchronization performance under complex dynamic conditions.

[0037] Furthermore, the terms "upper," "lower," "inner," "outer," "front," and "rear" are used for descriptive purposes only and should not be construed as indicating or implying relative importance. Unless otherwise specifically stated, the relative steps, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention.

[0038] Of course, the above description is only a specific embodiment of the present invention and is not intended to limit the scope of the present invention. All equivalent changes or modifications made to the structure, features and principles described in the claims of the present invention should be included in the scope of the claims of the present invention.

[0039] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered 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 cooperative control method for high-precision coordinated motion systems, characterized in that, The high-precision coordinated motion system includes a main execution unit and multiple auxiliary execution units, as well as a predictive disturbance observer and a fast termination sliding mode controller. The cooperative control method includes the following steps: The desired trajectory of the main execution unit is obtained, and the desired trajectory is converted into predicted sub-trajectories corresponding to multiple auxiliary execution units through a second-order continuously differentiable function; Based on the predicted sub-trajectory and the actual trajectory of the auxiliary execution unit, the corresponding local tracking error is calculated, and all local tracking errors are averaged to obtain the corresponding synchronization error. The generalized disturbance of the predictive disturbance observer is defined based on the disturbance factors, and the difference between the feedforward prediction estimate output by the predictive disturbance observer and the generalized disturbance is calculated to obtain the corresponding estimation error. Based on the local tracking error, a sliding surface is constructed on the corresponding auxiliary execution unit by a fast terminal sliding mode controller, and the local tracking control corresponding to each auxiliary execution unit is calculated based on the sliding surface and the feedforward prediction estimate output by the predictive disturbance observer. An adaptive cross-coupler is constructed and coupling compensation calculation is performed based on synchronization error to obtain adaptive cross-coupling control; Based on adaptive cross-coupling control and local tracking control, the total control input is generated and verified using the Lyapunov function.

2. The cooperative control method for high-precision coordinated motion systems according to claim 1, characterized in that, The expression for the second-order continuously differentiable function is as follows: ； in, Represents the desired trajectory. Indicates the first i Predicted sub-trajectories of each auxiliary execution unit.

3. The cooperative control method for high-precision coordinated motion systems according to claim 1, characterized in that, The expression for the local tracking error is as follows: ； in, Indicates the first i The actual trajectory of each auxiliary execution unit Indicates the first i Predicted sub-trajectories of each auxiliary execution unit For the first i Local tracking error of each auxiliary execution unit , and They are respectively , and The rate of change.

4. The cooperative control method for high-precision coordinated motion systems according to claim 1, characterized in that, The average calculation process for the synchronization error is as follows: ； in, Indicates the first i Local tracking error of each auxiliary execution unit This represents the average local tracking error of n auxiliary execution units.

5. The cooperative control method for high-precision coordinated motion systems according to claim 1, characterized in that, The interference factors include actuator lag, communication delay, unmodeled dynamics, and external disturbances.

6. The cooperative control method for high-precision coordinated motion systems according to claim 1, characterized in that, The expression for the local tracking control is as follows: ； in, express The second derivative, Indicates sliding mode gain. Indicates the first i Sliding surfaces of auxiliary execution units Indicates a boundary layer. This indicates the estimation error.

7. The cooperative control method for high-precision coordinated motion systems according to claim 1 or 6, characterized in that, The expression for the sliding surface is as follows: ； in, express rate of change, , Indicates the first i The constants of each auxiliary execution unit in the fast terminal sliding mode controller Indicates the first i Local tracking error of each auxiliary execution unit Represents a symbolic function.

8. The cooperative control method for high-precision coordinated motion systems according to claim 1, characterized in that, The expression for the adaptive cross-coupler is as follows: ； in Indicates the first i The constant term of each auxiliary execution unit in the adaptive cross-coupler Indicates the first i Adaptive control gain of each auxiliary execution unit Indicates the first i The base gain of each auxiliary execution unit This indicates synchronization error.

9. The cooperative control method for high-precision coordinated motion systems according to claim 1, characterized in that, The expression for the predictive disturbance observer is as follows: ； in, This indicates feedforward prediction estimation. Indicates the internal state. Indicates the observer gain. Indicates the first i The actual trajectory of each auxiliary execution unit This indicates the main control input.

10. A cooperative control device, characterized in that, The steps for performing the cooperative control method for a high-precision coordinated motion system as described in any one of claims 1 to 8 include: The geometric mapping module generates predicted sub-trajectories for each auxiliary execution unit based on the expected trajectory of the main execution unit. The error construction module generates corresponding local tracking errors and synchronization errors based on the predicted sub-trajectory and the actual trajectory of the auxiliary execution unit. Predictive perturbation observers are used to generate corresponding feedforward prediction estimates in real time; A fast terminal sliding mode controller is used to generate local tracking control; An adaptive cross-coupler is used to generate adaptive cross-coupled control.

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