Digital twinning-based 3-PSS pneumatic parallel robot virtual-real mapping control method

Abstract

The invention discloses a 3-PSS pneumatic parallel robot virtual-real mapping control method based on digital twinning, and belongs to the technical field of industrial robot control and digital twinning. The method comprises the following steps: constructing a three-layer digital twin system which comprises a physical space, a virtual space and an application service layer; a finite time tracking differentiator is designed at a virtual end for smoothing a reference trajectory, a finite time expansion state observer is designed for estimating friction and coupling disturbance, and an integral sliding mode controller is designed for compensating disturbance and controlling output; a virtual-real error mapping controller is designed at an entity end to realize rapid and accurate tracking of an expected position; proving the stability of the system by adopting a Lyapunov method; the problem that the control precision of the 3-PSS pneumatic parallel robot is reduced due to the influence of pneumatic nonlinearity, external disturbance and model inconsistency under complex working conditions is solved, and finally it is guaranteed that the 3-PSS pneumatic parallel robot based on digital twinning can achieve high-precision and quick-response space position trajectory tracking.

Description

Technical Field

[0001] This invention belongs to the field of industrial robot control and digital twin technology, and particularly relates to a virtual-real mapping control method for a 3PSS pneumatic parallel robot based on digital twin. Background Technology

[0002] Pneumatic actuators, due to their simple structure, high output force, and good compliance, have been widely used in industrial intelligent manufacturing scenarios such as grasping operations, packaging and sorting, medical assistance, and precision assembly. In applications involving multi-actuator collaborative operation, parallel robot structures, with their advantages of high rigidity, strong load-bearing capacity, and fast dynamic response, are widely used for high-speed, high-precision motion control tasks. Among them, the 3-PSS pneumatic parallel robot can achieve spatial translational motion at the end effector through multi-branch collaborative drive, showing promising application prospects in trajectory tracking and precision operation. Therefore, its motion control performance has become a key factor restricting the system's application effectiveness. However, due to the inherent physical characteristics of pneumatic systems, the 3-PSS pneumatic parallel robot still faces many difficulties in high-precision trajectory tracking control. On the one hand, the compressibility of gas, the nonlinear characteristics of servo valves, and friction factors cause the system dynamics to exhibit strong nonlinearity and parameter uncertainty; on the other hand, the coupling effect and external disturbances between multiple drive branches inevitably lead to the accumulation of displacement tracking errors, thereby reducing control accuracy. Existing control methods often rely on relatively accurate model parameters and a large number of repeated experimental parameter tuning processes. This not only requires high hardware performance, but also has a long development cycle and high experimental costs, making it difficult to achieve rapid deployment and stable control under complex working conditions.

[0003] Digital twin technology, by constructing a virtual model highly consistent with the physical object in terms of structural characteristics, motion laws, and dynamic behavior, enables information mapping and co-evolution between physical and digital systems, providing a new technical approach for the modeling, analysis, and control of complex aerodynamic systems. With the help of the digital twin framework, control algorithm design, parameter optimization, and performance evaluation can be completed in virtual space, thereby reducing repetitive experiments on the physical system, improving system development efficiency, and reducing experimental risks. However, for 3-PSS pneumatic parallel robots, how to effectively suppress the impact of aerodynamic nonlinearity, coupling disturbances, and model mismatch on control performance within the digital twin framework, and achieve high-precision motion consistency between the virtual and physical systems, still lacks a systematic and effective solution.

[0004] This invention proposes a virtual-real mapping control method for a 3-PSS pneumatic parallel robot based on digital twins. By constructing a three-layer digital twin system and establishing a dynamic model of the parallel robot, a finite-time tracking differentiator, a finite-time extended state observer, and an integral sliding mode controller are introduced into the virtual space to achieve fast and accurate tracking of the desired displacement trajectory. Simultaneously, by designing a virtual-real mapping control mechanism, the virtual operation results are effectively transferred to the physical system, suppressing tracking errors caused by model inconsistencies, disturbances, and communication factors. This method fully leverages the advantages of digital twin technology in virtual verification and control optimization, providing an effective approach to improve the trajectory tracking accuracy and system robustness of 3-PSS pneumatic parallel robots under complex working conditions. Summary of the Invention

[0005] The purpose of this invention is to provide a virtual-real mapping control method for a 3-PSS pneumatic parallel robot based on digital twins, so as to solve the problem of insufficient control accuracy caused by model inconsistency and disturbance in the prior art.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A digital twin-based control method for 3-PSS pneumatic parallel robots using virtual-real mapping includes the following steps:

[0008] Step 1: Construct a digital twin model of the 3-PSS pneumatic parallel robot: Based on the structural parameters, motion constraints and drive form of the physical 3-PSS pneumatic parallel robot, construct a virtual 3-PSS pneumatic parallel mechanism model in the digital simulation environment that is consistent with the physical system in terms of structure and motion characteristics, and establish a three-layer digital twin system including the physical entity layer, the digital twin virtual layer and the information interaction layer.

[0009] Step 2, establish the dynamic system model of the 3-PSS pneumatic parallel robot: Based on the dynamic modeling method of parallel robots, establish the dynamic relationship model between the end displacement of the 3-PSS pneumatic parallel robot and the driving input, which is used to describe the motion characteristics of the system under the action of control input and disturbance.

[0010] Step 3, Design a finite-time tracking differentiator: For the desired end displacement trajectory, design a finite-time tracking differentiator to smooth the reference displacement signal and obtain its finite-time converged differential signal, providing a continuous and differentiable reference input for subsequent controller design;

[0011] Step 4, Design a finite-time extended state observer: Based on the dynamic model, construct a finite-time extended state observer to uniformly model the model uncertainty, external disturbances and unmodeled dynamics in the system and realize online estimation within a finite time.

[0012] Step 5, Design an integral sliding mode controller: Construct an integral sliding mode surface based on the end displacement tracking error and its integral term, and combine it with the disturbance estimation results of the finite-time extended state observer to design a control law to achieve finite-time stable tracking of the virtual model's end displacement to the desired displacement trajectory;

[0013] Step 6, design the virtual-real mapping controller: send the end displacement data and corresponding control quantities obtained from the digital twin virtual model to the physical entity layer through serial communication, and based on the deviation between the virtual end displacement and the physical end displacement, map and correct the control input of the physical system to realize the transfer of virtual motion results to the physical system.

[0014] Step 7: Perform stability analysis: Use the Lyapunov method to test the convergence of the finite-time extended state observer, integral sliding mode controller, and virtual-real mapping controller.

[0015] Furthermore, step 1 specifically includes the following:

[0016] Step 1.1, Geometric Modeling and Assembly: Based on the structural parameters of the Physical 3-PSS pneumatic parallel robot, a fully assembled 3D model is established, including an equilateral triangular base, three rodless cylinders and their sliding modules, connecting arms, ball joints and end effectors, to ensure that the virtual model and the physical entity are completely consistent in geometric structure.

[0017] Step 1.2, Physical Attribute Configuration: Assign physical attributes to the virtual model, including the mass, center of mass position, moment of inertia of each component, as well as the stroke limit of the rodless cylinder and the force-displacement characteristics of the proportional control valve, to ensure that the virtual system is consistent with the physical system in terms of dynamic behavior;

[0018] Step 1.3, Sensor and Actuator Modeling: Integrate a virtual encoder in the virtual environment to simulate a displacement sensor; integrate a proportional valve model to simulate the input-output characteristics of a pneumatic actuator; establish an end effector pose measurement module to acquire the position and attitude information of the virtual end effector in real time;

[0019] Step 1.4: Construct a three-layer digital twin system architecture and configure virtual and physical data interfaces: Establish a three-layer digital twin system consisting of a physical entity layer, a digital twin virtual layer, and an information interaction layer, and configure real-time data interfaces to achieve virtual and physical interaction.

[0020] Furthermore, step 1.4 specifically includes the following:

[0021] Step 1.4.1: Establish a digital twin system consisting of a physical entity layer, a digital twin virtual layer, and an information interaction layer; whereby...

[0022] The physical entity layer includes: a 3-PSS pneumatic parallel robot, an industrial computer, an analog output card, a data acquisition card, a proportional directional control valve, and a displacement sensor;

[0023] The digital twin virtual layer includes: a virtual robot model built in a digital simulation platform, integrating control algorithms, an observer module, and a kinematics solution module;

[0024] The information interaction layer realizes bidirectional data communication between the physical layer and the virtual layer through the RS232 serial port, including status feedback, control command transmission and virtual-physical synchronization signal;

[0025] Step 1.4.2: Deploy the communication protocol in the industrial control computer to achieve the following data interaction:

[0026] Transmission from the virtual layer to the physical entity layer: Real-time displacement of three rodless cylinders

[0027] Transmission from the virtual layer to the physical entity layer: control voltage and compensation control quantity

[0028] The information interaction layer enables real-time calculation and feedback of virtual and real displacement errors.

[0029] Furthermore, step 2 specifically includes the following:

[0030] Regarding the first ( Considering the rodless cylinder dynamics of a single drive chain:

[0031]

[0032] in, For piston and load mass, For the piston's acceleration, It is a nonlinear frictional force. It is the acceleration due to gravity. For the effective area of ​​the piston, It is a two-chamber air pressure, Define the cylinder mounting angle; to facilitate controller design, transform the model into a state-space form and define the state variables. , Friction, gravity components, and model uncertainties are combined into a lumped disturbance. ,get:

[0033]

[0034] in, For lumped disturbance terms, For virtual system control gain, To control the input; for a three-degree-of-freedom parallel system, define the system state vector and the control input vector:

[0035]

[0036]

[0037]

[0038] The overall system model is as follows:

[0039]

[0040] in, It includes friction, cross-coupling terms, and unmodeled dynamics.

[0041] Furthermore, the design of the finite-time tracking differentiator in step 3 is as follows:

[0042] Given the desired displacement command Design the following differentiator for each channel:

[0043]

[0044] in, yes Smooth tracking signal, It is its differential signal; It is the tracking displacement error. It is the tracking speed error; ; Adjustable gain; Let be the power coefficient; by selecting appropriate parameters, such that... This can prove the tracking error system:

[0045]

[0046] It is stable over a finite time, meaning it exists over a finite time. This makes for ,have ,in It is any small positive number.

[0047] Furthermore, the design of the finite-time extended state observer in step 4 is as follows:

[0048] Will Considered an expansion state ,Right now And let its derivative be... Bounded, that is The extended system is:

[0049]

[0050] Design the following finite-time extended state observer:

[0051]

[0052] in, They are The estimated value; This represents the displacement estimation error; For observer gain; Power; ;

[0053] Define observation error , The error dynamics are:

[0054]

[0055] To prove the stability of the designed finite-time extended state observer, an auxiliary vector is constructed. Choose the Lyapunov function ,in It is a positive definite symmetric matrix; for By differentiating and substituting into error dynamics, we can derive the following:

[0056]

[0057] in It is a positive definite matrix. express The smallest eigenvalue, It is related to the observer gain The relevant adjustable parameters; when Sometimes, ;

[0058] Then, by constructing suitable parameters, it can be proven that positive constants exist. This makes it possible to achieve the goal within a limited time. Within this region, the observation error converges to the following bounded region:

[0059]

[0060] in, This is the Herwitz matrix; thus, it shows that the estimation errors of displacement, velocity, and disturbance are uniformly and eventually bounded over a finite time.

[0061] Furthermore, the design of the integral sliding mode controller in step 5 is as follows:

[0062] Smooth reference signal provided by finite-time TD and the perturbation estimates provided by ESO An integral sliding mode controller is designed to achieve high-precision and robust tracking of the desired trajectory by the virtual model;

[0063] Reduce the displacement tracking error of the virtual system With speed tracking error They are respectively:

[0064]

[0065]

[0066] Design an integral sliding surface:

[0067]

[0068] in, These are adjustable parameters; It is a nonlinear saturation function used to suppress flutter;

[0069] Design the sliding mode arrival law:

[0070]

[0071] Thus, the control input can be derived:

[0072]

[0073] When the parameters satisfy:

[0074] UnionPay Merchant Services Co., Ltd.

[0075] Sliding surface It converges to a bounded region within a finite time:

[0076]

[0077] in, This is the upper bound of the disturbance estimation error. The boundary layer thickness is a saturation function.

[0078] Furthermore, the design of the virtual-real mapping controller in step 6 is as follows:

[0079] Let the physical entity displacement be The virtual system displacement is Then the virtual and real displacement error Error between real and virtual speeds They are respectively:

[0080]

[0081] The virtual-to-real mapping sliding surface is constructed as follows:

[0082]

[0083] in, These are adjustable parameters;

[0084] Based on the sliding mode arrival law:

[0085]

[0086] Obtain the compensation control voltage:

[0087]

[0088] The final control input for the physical entity is:

[0089]

[0090] in, This is the scaling factor. For virtual system control gain, For physical system control gain.

[0091] Compared with the prior art, the present invention has the following beneficial technical effects:

[0092] 1. This invention constructs a digital twin virtual model in a digital simulation environment that is consistent with the physical 3-PSS pneumatic parallel robot in terms of structural parameters and motion constraints. The trajectory tracking control task is preferentially completed in the virtual space, and the virtual operation results are mapped to the physical system. This method avoids the measurement error problems introduced by traditional geometric modeling or external sensing methods when model parameters are inaccurate or environmental conditions change, thus improving the stability and robustness of displacement acquisition.

[0093] 2. This invention treats the aerodynamic nonlinearity, branch coupling effect and friction generated during the motion of the 3-PSS pneumatic parallel robot as equivalent disturbances. A finite-time extended state observer is introduced at the virtual end to estimate the above disturbances online and compensate for them in the integral sliding mode controller, which effectively reduces the impact of disturbances on trajectory tracking accuracy.

[0094] 3. This invention introduces a virtual-real mapping control mechanism to migrate the control quantities and displacement data generated by the virtual terminal within one operating cycle to the physical system. Based on the virtual-real displacement deviation, the physical control input is corrected, thereby achieving motion consistency between the virtual and physical systems without the need to construct complex real-time feedback channels. This method has a clear structure, low engineering implementation difficulty, and the stability and effectiveness of the designed finite-time extended state observer, integral sliding mode controller, and virtual-real mapping control strategy are verified by Lyapunov stability analysis. Attached Figure Description

[0095] Figure 1 This is a schematic diagram of the virtual-real mapping control method for a 3-PSS pneumatic parallel robot based on digital twins according to the present invention.

[0096] Figure 2 This is a schematic diagram of the design process of the present invention;

[0097] Figure 3 A schematic diagram of a virtual 3-PSS pneumatic parallel robot;

[0098] Figure 4 This is a schematic diagram of the step trajectory tracking of the 3-PSS pneumatic parallel robot based on digital twin according to the present invention.

[0099] Figure 5 This is a schematic diagram of the square trajectory tracking of the 3-PSS pneumatic parallel robot based on digital twin according to the present invention;

[0100] Figure 6 A schematic diagram of perturbation estimation for a finite-time extended state observer;

[0101] Figure 7 A schematic diagram showing the comparison between the reference displacement, the displacement tracked by the tracking differentiator, the actual displacement, and the displacement estimated by the observer. Detailed Implementation

[0102] To make the objectives of this invention clearer and the technical solutions more explicit, this invention will be described in detail with reference to the following accompanying drawings and specific embodiments.

[0103] Figure 1 The diagram shown illustrates the control method of this invention, demonstrating the virtual-real mapping control method for a 3-PSS pneumatic parallel robot based on digital twins.

[0104] The following is combined with Figure 1-7 The control method described in this invention is described in detail, but is not intended to limit the invention.

[0105] See Figure 2 This embodiment provides a virtual-real mapping control method for a 3-PSS pneumatic parallel robot based on digital twins, including the following steps:

[0106] Step 1: Construct a digital twin model of the 3-PSS pneumatic parallel robot: Based on the structural parameters, motion constraints and drive form of the physical 3-PSS pneumatic parallel robot, construct a virtual 3-PSS pneumatic parallel mechanism model in the digital simulation environment that is consistent with the physical system in terms of structure and motion characteristics, and establish a three-layer digital twin system including the physical entity layer, the digital twin virtual layer and the information interaction layer.

[0107] Step 2, establish the dynamic system model of the 3-PSS pneumatic parallel robot: Based on the dynamic modeling method of parallel robots, establish the dynamic relationship model between the end displacement of the 3-PSS pneumatic parallel robot and the driving input, which is used to describe the motion characteristics of the system under the action of control input and disturbance.

[0108] Step 3, Design a finite-time tracking differentiator: For the desired end displacement trajectory, design a finite-time tracking differentiator to smooth the reference displacement signal and obtain its finite-time converged differential signal, providing a continuous and differentiable reference input for subsequent controller design;

[0109] Step 4, Design a finite-time extended state observer: Based on the dynamic model, construct a finite-time extended state observer to uniformly model the model uncertainty, external disturbances and unmodeled dynamics in the system and realize online estimation within a finite time.

[0110] Step 5, Design an integral sliding mode controller: Construct an integral sliding mode surface based on the end displacement tracking error and its integral term, and combine it with the disturbance estimation results of the finite-time extended state observer to design a control law to achieve finite-time stable tracking of the virtual model's end displacement to the desired displacement trajectory;

[0111] Step 6, design the virtual-real mapping controller: send the end displacement data and corresponding control quantities obtained from the digital twin virtual model to the physical entity layer through serial communication, and based on the deviation between the virtual end displacement and the physical end displacement, map and correct the control input of the physical system to realize the transfer of virtual motion results to the physical system.

[0112] Step 7: Perform stability analysis: Use the Lyapunov method to test the convergence of the finite-time extended state observer, integral sliding mode controller, and virtual-real mapping controller.

[0113] As a specific implementation of this embodiment, step 1 specifically includes the following:

[0114] Step 1.1, Geometric Modeling and Assembly

[0115] like Figure 3 As shown, in 3D modeling software such as SolidWorks, based on the structural parameters of the physical 3-PSS pneumatic parallel robot, a fully assembled 3D model is established, including an equilateral triangular base, three rodless cylinders and their sliding modules, connecting arms, ball joints and end effectors, to ensure that the virtual model and the physical entity are completely consistent in geometric structure.

[0116] Step 1.2, Physical Attribute Configuration

[0117] Assign physical properties to the virtual model, including the mass, center of mass position, and moment of inertia of each component, as well as the stroke limit of the rodless cylinder and the force-displacement characteristics of the proportional control valve, to ensure that the virtual system is consistent with the physical system in terms of dynamic behavior;

[0118] Step 1.3, Sensor and Actuator Modeling

[0119] A virtual encoder is integrated into the virtual environment to simulate a displacement sensor; a proportional valve model is integrated to simulate the input-output characteristics of a pneumatic actuator; and an end effector pose measurement module is established to acquire the position and attitude information of the virtual end effector in real time.

[0120] Step 1.4: Construct a three-tier digital twin system architecture and configure virtual and physical data interfaces.

[0121] Establish a three-layer digital twin system consisting of a physical entity layer, a digital twin virtual layer, and an information interaction layer, and configure a real-time data interface to achieve virtual-physical interaction.

[0122] 1) Establish a digital twin system consisting of a physical entity layer, a digital twin virtual layer, and an information interaction layer;

[0123] ①The physical entity layer includes: 3-PSS pneumatic parallel robot, industrial computer, analog output card (ADLINKPCI-6208V), data acquisition card (ADLINKPCI-1784U), proportional directional control valve (FestoMPYE-5-1 / 8-LF-010-B) and displacement sensor (SMCML2B32-450);

[0124] ② The digital twin virtual layer includes: a virtual robot model built in a digital simulation platform, integrating control algorithms, observer modules, and kinematics solution modules;

[0125] ③ The information interaction layer realizes bidirectional data communication between the physical layer and the virtual layer through the RS232 serial port, including status feedback, control command transmission and virtual-physical synchronization signals;

[0126] 2) Deploy a communication protocol in the industrial control computer to achieve the following data interaction:

[0127] ①Transmission from the virtual layer to the physical entity layer: Real-time displacement of three rodless cylinders

[0128] ②Transmission from the virtual layer to the physical entity layer: control voltage and compensation control quantity

[0129] ③ The information interaction layer enables real-time calculation and feedback of virtual and real displacement errors;

[0130] As a specific implementation of this embodiment, step 2 specifically includes the following:

[0131] To achieve high-performance control, a mathematical model reflecting the inherent dynamic characteristics of the system needs to be established. For the first... ( Considering the rodless cylinder dynamics of a single drive chain:

[0132]

[0133] in, For piston and load mass, For the piston's acceleration, It is a nonlinear frictional force. It is the acceleration due to gravity. For the effective area of ​​the piston, It is a two-chamber air pressure, Define the cylinder mounting angle; to facilitate controller design, transform the model into a state-space form and define the state variables. (Displacement) (Velocity) combines friction, gravity components, and model uncertainties into a lumped disturbance. We can obtain:

[0134]

[0135] in, For lumped disturbance terms, For virtual system control gain, To control the input; for a three-degree-of-freedom parallel system, define the system state vector and the control input vector:

[0136]

[0137] The overall system model is as follows:

[0138]

[0139] in It includes friction, cross-coupling terms, and unmodeled dynamics.

[0140] As a specific implementation of this embodiment, step 3 specifically includes the following:

[0141] To provide the controller with a smooth and continuously differentiable reference signal, and to avoid noise amplification caused by direct differentiation of step or discontinuous desired trajectories, a finite-time tracking differentiator is designed.

[0142] Given the desired displacement command Design the following differentiator for each channel:

[0143]

[0144] in, yes Smooth tracking signal, It is its differential signal; It is the tracking displacement error. It is the tracking speed error; ; Adjustable gain; The coefficient is the power factor; by selecting b 11 = b 12 = b 13 = 1.4, b 21 = b 22 = b 23 = 6, b 31 = b 32 = b 33 = 5, τ1 = 0.6, τ2 = 0.8, it can be proven that the tracking error system is:

[0145]

[0146] It is stable over a finite time, meaning it exists over a finite time. This makes for ,have ,in It is any small positive number.

[0147] As a specific implementation of this embodiment, step 4 specifically includes the following:

[0148] To estimate and compensate for the total system disturbance in real time Design a finite-time extended state observer; Considered an expansion state ,Right now And let its derivative be... Bounded, that is The extended system is:

[0149]

[0150] Design a time-limited ESO as follows:

[0151]

[0152] in, They are The estimated value; This represents the displacement estimation error; For observer gain; Power; ;

[0153] Define observation error , The error dynamics are:

[0154]

[0155] To prove the stability of the designed finite-time extended state observer, an auxiliary vector is constructed. Candidate Lyapunov functions were selected. ,in It is a positive definite symmetric matrix that satisfies:

[0156]

[0157] calculate :

[0158]

[0159] Substituting into the error dynamic equation (4.3), we get:

[0160]

[0161] in:

[0162]

[0163] right By differentiating and substituting into error dynamics, we can derive the following:

[0164]

[0165] make ,but:

[0166]

[0167] because It is a Hurwitz matrix, and there exists a symmetric positive definite matrix. satisfy:

[0168]

[0169] Substituting, we get:

[0170]

[0171] Using the Cauchy-Schwarz inequality:

[0172]

[0173] therefore:

[0174]

[0175] To specifically demonstrate the auxiliary vector Consider the convergence region and corresponding convergence time, with two cases:

[0176] Scenario 1: When At that time, among them

[0177] at this time ,have:

[0178]

[0179] Substitute (4.12):

[0180]

[0181] Select parameters such that:

[0182]

[0183] in Then it exists satisfy:

[0184]

[0185] According to the finite-time stability lemma, the convergence time... satisfy:

[0186]

[0187] Scenario 2: When hour

[0188] at this time Consideration area:

[0189]

[0190] We can obtain:

[0191]

[0192] Convergence time satisfy:

[0193]

[0194] Total convergence time:

[0195]

[0196] Q.E.D.

[0197] As a specific implementation of this embodiment, step 5 specifically includes the following:

[0198] Smooth reference signal provided by finite-time TD and the perturbation estimates provided by ESO An integral sliding mode controller is designed to achieve high-precision and robust tracking of the desired trajectory by the virtual model.

[0199] Reduce the displacement tracking error of the virtual system With speed tracking error They are respectively:

[0200]

[0201] Design a sliding surface that incorporates error integrals:

[0202]

[0203] in, These are adjustable parameters; It is a nonlinear saturation function, defined as:

[0204]

[0205] Design a sliding mode control law based on the power-approaching law:

[0206]

[0207] in, , , ; This is a saturation function used to eliminate flutter:

[0208]

[0209] Combine equations (5.2), (5.3) and system model (2.2), and use the disturbance estimate. By performing feedforward compensation, the control law can be derived:

[0210]

[0211] To prove the stability of the designed integral sliding mode controller, a Lyapunov function is selected. Differentiating it and substituting the control law (5.4) into it, we get:

[0212]

[0213] in The perturbation estimation error has been proven to be bounded by ESO. Let... .

[0214] To specifically demonstrate the convergence region and corresponding convergence time of the designed integral sliding surface, consider the following two cases:

[0215] Scenario 1: When hour, ,but: By selecting a sufficiently large , can make To ensure that the system state reaches the boundary layer within a finite time. Convergence time :

[0216]

[0217] Scenario 2: When hour, Substituting the values, we can prove that there exist parameter choices that make... The time remains negative constant within the boundary layer; upper bound of convergence time:

[0218]

[0219] in:

[0220]

[0221] Total convergence time:

[0222]

[0223] In summary, sliding surface In a limited time Converging inward to the following bounded region:

[0224]

[0225] in This is the upper bound of the disturbance estimation error. The boundary layer thickness is a saturation function; furthermore, from the definition of the sliding surface, the displacement tracking error is... and speed tracking error It is also consistent and ultimately bounded.

[0226] As a specific implementation of this embodiment, step 6 specifically includes the following:

[0227] To eliminate motion deviations between the virtual system and physical entities caused by model mismatch and environmental differences, and to achieve true virtual-real synchronization, a virtual-real mapping controller is designed.

[0228] Let the physical entity displacement be The virtual system displacement is Then the virtual and real displacement error Error between real and virtual speeds They are respectively:

[0229]

[0230] A simplified dynamic model of a physical entity can be described as follows:

[0231]

[0232] in For physical system control gain; for physical entity final control input By virtual control quantity and mapping compensation amount synthesis:

[0233]

[0234] in For gain matching; substituting (6.3) into (6.2) and subtracting from the virtual model (2.2), we obtain the virtual-real error dynamics:

[0235]

[0236] Drawing on the sliding mode control concept from step five, design the sliding surface for this system:

[0237]

[0238] Design convergence law:

[0239]

[0240] Combining error dynamics (6.4) and utilizing ESO to... Based on the estimation, the virtual-real mapping compensation control law is derived:

[0241]

[0242] The stability analysis of this controller is completely similar to the analysis process of the integral sliding mode controller in step five. (Selection) It can be proven that when the parameters satisfy Under the same conditions, sliding surface It can converge to a bounded region within a finite time, thus ensuring the accuracy of virtual and real displacement errors. and speed error The consistent eventual boundedness enables high-precision tracking of the motion of physical entities on virtual models.

[0243] The present invention will now be described in conjunction with specific embodiments:

[0244] To verify the effectiveness of the proposed digital twin-based virtual-real mapping control method for 3-PSS pneumatic parallel robots, experimental verification is presented, demonstrating that the digital twin-based virtual-real mapping control method for 3-PSS pneumatic parallel robots is effective, as detailed below:

[0245] Example 1: Fixed-point position tracking experiment

[0246] To verify the basic performance of the digital twin system and the virtual-real mapping control strategy, a fixed-point tracking experiment was first conducted. The robot's initial position was set as a point in the workspace. mm (with the center of the base as the origin of the coordinate system), the target position is mm; this motion corresponds to a step displacement of 300 mm in space by the end effector.

[0247] Figure 4 The experimental results of step tracking are shown. The dotted line in the figure represents the desired displacement trajectory. The dashed line represents the tracking displacement generated by the integral sliding mode controller at the virtual end in the method of this invention. The solid line represents the final tracking displacement of the physical entity after being controlled by the virtual-real mapping. .

[0248] from Figure 4 It is evident that the method proposed in this embodiment has a fast response speed and small overshoot; the trajectories of the virtual end and the physical end highly overlap, indicating that the virtual-physical mapping controller effectively achieves synchronization.

[0249] Example 2: Square Trajectory Tracking Experiment

[0250] To further verify the system's tracking performance and virtual-real synchronization capability under continuous complex trajectories, a square trajectory tracking experiment was conducted. The desired trajectory was described by the following parametric equations:

[0251]

[0252] This trajectory causes the end effector to move along a square path in the XY plane while slowly rising along the Z-axis.

[0253] Figure 5 The experimental results of square trajectory tracking are shown. In the figure, the dotted line represents the desired trajectory, and the dashed line represents the tracking trajectory of the virtual terminal using the method of this invention. The solid line represents the tracking trajectory of the physical entity. It can be clearly seen that the tracking trajectory of the method in this embodiment closely matches the expected trajectory, and the trajectories of the virtual end and the physical end almost completely overlap, demonstrating the effectiveness of the virtual-physical mapping control of the 3-PSS pneumatic parallel robot based on digital twins.

[0254] Example 3: Observer Performance Verification

[0255] The performance of the finite-time extended state observer (ESO) is crucial to the robustness of the entire control system. Figure 6This demonstrates the total disturbance experienced by the ESO on the three rodless cylinders in a square trajectory tracking experiment. Estimated curves (including friction and cross-coupling) It can be seen that ESO can quickly and smoothly estimate time-varying disturbances, providing accurate information for the feedforward compensation of the controller.

[0256] Figure 7 Further comparison was made of the reference displacement in the step response. (Dotted line) Signal after TD smoothing (Solid line) Actual displacement (Dashed line) and the displacement estimated by ESO (Dotted line). The image shows, right It achieves smooth tracking without overshoot, and This allows for accurate estimation of the system's actual displacement. The curves of the three parameters perfectly coincide in the steady state phase, verifying the effectiveness of the finite-time tracking differentiator and the finite-time extended state observer design.

[0257] in conclusion:

[0258] The fixed-point and continuous trajectory tracking experiments demonstrated in this invention show that the proposed digital twin-based virtual-real mapping control method can significantly improve the trajectory tracking accuracy and response speed of the 3-PSS pneumatic parallel robot. The finite-time ESO effectively estimates and compensates for system disturbances, the integral sliding mode controller ensures high-performance tracking of the virtual end, and the virtual-real mapping controller successfully synchronizes the excellent control performance of the virtual end to the physical entity, achieving high-precision motion control with "virtual-real consistency." This method provides an effective and engineering-feasible solution for high-performance control of pneumatic parallel robots.

[0259] Based on the disclosure and teachings of the foregoing specification, those skilled in the art can make changes and modifications to the above embodiments. Therefore, the present invention is not limited to the specific embodiments described above, and any obvious improvements, substitutions, or modifications made by those skilled in the art based on the present invention are within the scope of protection of the present invention.

Claims

1. A virtual-real mapping control method for a 3-PSS pneumatic parallel robot based on digital twins, characterized in that, Includes the following steps: Step 1: Construct a digital twin model of the 3-PSS pneumatic parallel robot: Based on the structural parameters, motion constraints and drive form of the physical 3-PSS pneumatic parallel robot, construct a virtual 3-PSS pneumatic parallel mechanism model in the digital simulation environment that is consistent with the physical system in terms of structure and motion characteristics, and establish a three-layer digital twin system including the physical entity layer, the digital twin virtual layer and the information interaction layer. Step 2, establish the dynamic system model of the 3-PSS pneumatic parallel robot: Based on the dynamic modeling method of parallel robots, establish the dynamic relationship model between the end displacement of the 3-PSS pneumatic parallel robot and the driving input, which is used to describe the motion characteristics of the system under the action of control input and disturbance. Step 3, Design a finite-time tracking differentiator: For the desired end displacement trajectory, design a finite-time tracking differentiator to smooth the reference displacement signal and obtain its finite-time converged differential signal, providing a continuous and differentiable reference input for subsequent controller design; Step 4, Design a finite-time extended state observer: Based on the dynamic model, construct a finite-time extended state observer to uniformly model the model uncertainty, external disturbances and unmodeled dynamics in the system and realize online estimation within a finite time. Step 5, Design an integral sliding mode controller: Construct an integral sliding mode surface based on the end displacement tracking error and its integral term, and combine it with the disturbance estimation results of the finite-time extended state observer to design a control law to achieve finite-time stable tracking of the virtual model's end displacement to the desired displacement trajectory; Step 6, design the virtual-real mapping controller: send the end displacement data and corresponding control quantities obtained from the digital twin virtual model to the physical entity layer through serial communication, and based on the deviation between the virtual end displacement and the physical end displacement, map and correct the control input of the physical system to realize the transfer of virtual motion results to the physical system. Step 7: Perform stability analysis: Use the Lyapunov method to test the convergence of the finite-time extended state observer, integral sliding mode controller, and virtual-real mapping controller.

2. The virtual-real mapping control method for a 3-PSS pneumatic parallel robot based on digital twins according to claim 1, characterized in that, Step 1 specifically includes the following: Step 1.1, Geometric Modeling and Assembly: Based on the structural parameters of the Physical 3-PSS pneumatic parallel robot, a fully assembled 3D model is established, including an equilateral triangular base, three rodless cylinders and their sliding modules, connecting arms, ball joints and end effectors, to ensure that the virtual model and the physical entity are completely consistent in geometric structure. Step 1.2, Physical Attribute Configuration: Assign physical attributes to the virtual model, including the mass, center of mass position, moment of inertia of each component, as well as the stroke limit of the rodless cylinder and the force-displacement characteristics of the proportional control valve, to ensure that the virtual system is consistent with the physical system in terms of dynamic behavior; Step 1.3, Sensor and Actuator Modeling: Integrate a virtual encoder in the virtual environment to simulate a displacement sensor; integrate a proportional valve model to simulate the input-output characteristics of a pneumatic actuator; establish an end effector pose measurement module to acquire the position and attitude information of the virtual end effector in real time; Step 1.4: Construct a three-layer digital twin system architecture and configure virtual and physical data interfaces: Establish a three-layer digital twin system consisting of a physical entity layer, a digital twin virtual layer, and an information interaction layer, and configure real-time data interfaces to achieve virtual and physical interaction.

3. The virtual-real mapping control method for a 3-PSS pneumatic parallel robot based on digital twins according to claim 2, characterized in that, Step 1.4 specifically includes the following: Step 1.4.1: Establish a digital twin system consisting of a physical entity layer, a digital twin virtual layer, and an information interaction layer; among which, The physical entity layer includes: a 3-PSS pneumatic parallel robot, an industrial computer, an analog output card, a data acquisition card, a proportional directional control valve, and a displacement sensor; The digital twin virtual layer includes: a virtual robot model built in a digital simulation platform, integrating control algorithms, an observer module, and a kinematics solution module; The information interaction layer realizes bidirectional data communication between the physical layer and the virtual layer through the RS232 serial port, including status feedback, control command transmission and virtual-physical synchronization signal; Step 1.4.2: Deploy the communication protocol in the industrial control computer to achieve the following data interaction: Transmitting from the virtual layer to the physical entity layer: the real-time displacement of three rodless cylinders; Transmission from the virtual layer to the physical entity layer: control voltage and compensation control quantity; The information interaction layer enables real-time calculation and feedback of virtual and real displacement errors.

4. The virtual-real mapping control method for a 3-PSS pneumatic parallel robot based on digital twins according to claim 3, characterized in that, Step 2 specifically includes the following: Regarding the first ( Considering the rodless cylinder dynamics of a single drive chain: in, For piston and load mass, For the piston's acceleration, It is a nonlinear frictional force. It is the acceleration due to gravity. For the effective area of ​​the piston, It is a two-chamber air pressure, Define the cylinder mounting angle; to facilitate controller design, transform the model into a state-space form and define the state variables. , Friction, gravity components, and model uncertainties are combined into a lumped disturbance. ,get: in, For lumped disturbance terms, For virtual system control gain, To control the input; for a three-degree-of-freedom parallel system, define the system state vector and the control input vector: The overall system model is as follows: in, It includes friction, cross-coupling terms, and unmodeled dynamics.

5. The virtual-real mapping control method for a 3-PSS pneumatic parallel robot based on digital twins according to claim 4, characterized in that, The design of the finite-time tracking differentiator in step 3 is as follows: Given the desired displacement command Design the following differentiator for each channel: in, yes Smooth tracking signal, It is its differential signal; It is the tracking displacement error. It is the tracking speed error; ; Adjustable gain; Let be the power coefficient; by selecting appropriate parameters, such that... This can prove the tracking error system: It is stable over a finite time, meaning it exists over a finite time. This makes for ,have ,in It is any small positive number.

6. The virtual-real mapping control method for a 3-PSS pneumatic parallel robot based on digital twins according to claim 5, characterized in that, The design of the finite-time extended state observer in step 4 is as follows: Will Considered an expansion state ,Right now And let its derivative be... Bounded, that is The extended system is: Design the following finite-time extended state observer: in, They are The estimated value; This represents the displacement estimation error; For observer gain; Power; ; Define observation error , The error dynamics are: To prove the stability of the designed finite-time extended state observer, an auxiliary vector is constructed. Candidate Lyapunov functions are selected. ,in It is a positive definite symmetric matrix; for By differentiating and substituting into error dynamics, we can derive the following: in It is a positive definite matrix. express The smallest eigenvalue, It is related to the observer gain The relevant adjustable parameters; when Sometimes, ; Then, by constructing suitable parameters, it can be proven that positive constants exist. This makes it possible to achieve the goal within a limited time. Within this region, the observation error converges to the following bounded region: in, This is the Herwitz matrix; thus, it shows that the estimation errors of displacement, velocity, and disturbance are uniformly and eventually bounded over a finite time.

7. The virtual-real mapping control method for a 3-PSS pneumatic parallel robot based on digital twins according to claim 6, characterized in that, The design of the integral sliding mode controller in step 5 is as follows: Reduce the displacement tracking error of the virtual system With speed tracking error They are respectively: Design an integral sliding surface: in, These are adjustable parameters; It is a nonlinear saturation function used to suppress flutter; Design the sliding mode arrival law: Thus, the control input can be derived: When the parameters satisfy: Sliding surface It converges to a bounded region within a finite time: in, This is the upper bound of the disturbance estimation error. The boundary layer thickness is a saturation function.

8. The virtual-real mapping control method for a 3-PSS pneumatic parallel robot based on digital twins according to claim 7, characterized in that, The design of the virtual-real mapping controller in step 6 is as follows: Let the physical entity displacement be The virtual system displacement is Then the virtual and real displacement error Error between real and virtual speeds They are respectively: The virtual-to-real mapping sliding surface is constructed as follows: in, These are adjustable parameters; Based on the sliding mode arrival law: Obtain the compensation control voltage: The final control input for the physical entity is: in, This is the scaling factor. For virtual system control gain, For physical system control gain.

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