Hydraulic mechanical arm modeling and optimizing method based on digital twinning technology

Abstract

The invention discloses a hydraulic mechanical arm modeling and optimizing method based on a digital twinning technology, which comprises the following steps: based on geometric performance parameters of a hydraulic mechanical arm, establishing a corresponding virtual geometric morphology model through modeling software; establishing a corresponding kinematics attribute model based on the position and attitude data of each joint of the hydraulic mechanical arm; optimizing the kinematics attribute model by using an Adam optimization method to obtain an optimized attribute model; constructing a dynamic simulation model of the hydraulic system according to the working state data of each component in the hydraulic system; integrating the virtual geometric morphology model, the optimized attribute model and the dynamic simulation model to obtain a digital twinborn model of the hydraulic mechanical arm; and operating state data of the hydraulic mechanical arm are collected in real time, and the state of the digital twin model is updated based on the operating state data. According to the method, the modeling precision of the hydraulic mechanical arm is effectively improved.

Description

Technical Field

[0001] The present invention relates to the field of robotic arm control technology, and more particularly to a hydraulic robotic arm modeling and optimization method based on digital twin technology. Background Art

[0002] With the rapid development of industrial automation, industrial robots are widely used in manufacturing, aerospace, logistics, and other fields, playing a vital role in production and handling. Compared to electrically driven robots, hydraulic robots offer higher load capacity and superior precision. However, due to their long-term operation in complex and changing environments, subject to large load fluctuations, hydraulic robots are susceptible to external interference and often face the risk of component failure and performance degradation. Therefore, improving stability and diagnostic capabilities has become a pressing issue.

[0003] However, improving the stability of hydraulic robots and diagnosing faults requires interdisciplinary and integrated technologies, and traditional design optimization consumes significant resources. Digital twin technology, with its unique advantages, offers a completely new approach to robot design, control, and optimization. By constructing virtual replicas of physical equipment and synchronizing data between the physical and digital worlds in real time, combined with the massive amount of structured and unstructured data generated during the twin simulation process, digital twin technology enables equipment status monitoring, predictive maintenance, and intelligent optimization. Applying digital twin technology to the design of hydraulic robots not only enables comprehensive monitoring and precise modeling of the robot's status, but also simulates the robot's operating process through virtual models, identifying potential faults in advance, optimizing control strategies, and improving the hydraulic robot's performance and efficiency.

[0004] Therefore, how to model hydraulic robots based on digital twin technology to help ensure the stable and reliable operation of hydraulic robots and have certain fault diagnosis and prediction capabilities is an urgent problem that technical personnel in this field need to solve. Summary of the Invention

[0005] In view of the above problems, the present invention provides a hydraulic robotic arm modeling and optimization method based on digital twin technology to at least solve some of the technical problems mentioned in the above background technology.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] An embodiment of the present invention provides a hydraulic mechanical arm modeling and optimization method based on digital twin technology, comprising:

[0008] Based on the geometric performance parameters of the hydraulic manipulator, a corresponding virtual geometric model is established through modeling software;

[0009] Based on the joint position and posture data of the hydraulic manipulator, a corresponding kinematic attribute model is established;

[0010] Optimizing the kinematic attribute model using the Adam optimization method to obtain an optimized attribute model;

[0011] Constructing a dynamic simulation model of the hydraulic system based on the working status data of each component in the hydraulic system;

[0012] Integrating the virtual geometric model, the optimized property model, and the dynamic simulation model to obtain a digital twin model of the hydraulic robotic arm;

[0013] The operating status data of the hydraulic mechanical arm is collected in real time, and the status of the digital twin model is updated based on the operating status data.

[0014] Furthermore, the established virtual geometric model is lightweighted;

[0015] The lightweight processing includes: reducing the number of polygons and vertices of the virtual geometric model, simplifying the geometric structure and optimizing the surface smoothness.

[0016] Furthermore, the kinematic attribute model includes a twin attribute model based on forward kinematics and a twin attribute model based on inverse kinematics.

[0017] Furthermore, the improved DH parameter method is used to establish the twin attribute model based on forward kinematics;

[0018] For multiple links in a hydraulic manipulator, the improved DH parameters of the i-th link include: the rotation angle of the i-1th link, the length of the i-1th link, the offset of the i-th link, and the joint angle corresponding to the i-th link;

[0019] Among them, the i-th connecting rod and the i-1-th connecting rod are two adjacent connecting rods.

[0020] Furthermore, the improved DH parameter method is used to establish the twin attribute model based on forward kinematics, specifically including:

[0021] Based on the improved DH parameters of the i-th link, a transformation matrix is ​​established for the coordinate system of the i-th link relative to the coordinate system of the i-1-th link. The transformation matrices between each two links are multiplied in sequence to obtain the twin property model equation based on forward kinematics.

[0022] Wherein, the transformation matrix is ​​expressed as:

[0023]

[0024] Among them, αi-1 represents the rotation angle of the i-1th connecting rod; a i-1 represents the length of the i-1th connecting rod; d i represents the offset of the i-th connecting rod; θ i represents the joint angle corresponding to the i-th link; Represents the total transformation matrix from the coordinate system of the i-th link to the coordinate system of the i-1-th link; and There are 4 steps in the whole transformation process, each step is a basic rotation or translation; represents a rotation along the X axis i-1 angle; Indicates moving a along the X axis i-1 distance; represents a rotation along the Z axis θ i angle; Indicates movement d along the Z axis i distance.

[0025] Furthermore, an analytical method is used to establish the twin attribute model based on inverse kinematics;

[0026] Criteria for solving the twin attribute model based on inverse kinematics include: selecting a solution based on joint space limitations, selecting a solution based on the shortest distance, and selecting a solution based on obstacle avoidance principles.

[0027] Furthermore, the kinematic attribute model is optimized using the Adam optimization method to obtain an optimized attribute model; specifically including:

[0028] Step 1: Set the initial parameters of Adam optimization; the initial parameters include learning rate, first-order moment estimation decay rate, second-order moment estimation decay rate and maximum number of iterations N;

[0029] Step 2: Read the true value of the joint angle and joint angle experimental values Calculate initial error

[0030] Step 3: Initialize the first-order moment and the second-order moment to zero vectors, and set the time step t = 0;

[0031] Step 4: Enter the iterative optimization process and calculate the gradient g at each iteration t ;

[0032] Step 5: Update the first-order moment and the second-order moment, and perform deviation correction;

[0033] Step 6: Update the joint angle experimental value according to the Adam formula

[0034] Step 7: Check whether the maximum number of iterations has been reached. If not, return to step 4 and continue optimization. If reached, output the optimized result.

[0035] Furthermore, in Automation Studio TM A dynamic simulation model of the hydraulic system is constructed in the paper; a modular modeling approach is adopted to divide the hydraulic system into a power source module, a control module, an execution module, a load module, a sensor module, and a signal control and feedback loop; each module is connected through a standard hydraulic interface to form a complete closed-loop control hydraulic system.

[0036] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a hydraulic manipulator modeling and optimization method based on digital twin technology, which has the following beneficial effects:

[0037] This paper constructs a digital twin model of a hydraulic robot, comprising a physical model (i.e., a virtual geometric model) and an attribute model. Furthermore, to address the insufficient accuracy of the attribute model, the Adam optimization algorithm is used to optimize the model, improving the accuracy of each joint angle of the robot's digital twin. This improves the modeling accuracy of the hydraulic manipulator arm.

[0038] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0040] Figure 1 A schematic flow chart of a hydraulic robotic arm modeling and optimization method based on digital twin technology provided in an embodiment of the present invention.

[0041] Figure 2 Schematic diagram of the five-dimensional digital twin system architecture of the hydraulic robotic arm provided in an embodiment of the present invention.

[0042] Figure 3 Schematic diagram of the digital twin system construction framework provided in an embodiment of the present invention.

[0043] Figure 4 A schematic diagram of the communication system architecture for a virtual geometric model provided by an embodiment of the present invention.

[0044] Figure 5Schematic diagram of the connecting rod coordinate system of the hydraulic mechanical arm provided in an embodiment of the present invention.

[0045] Figure 6 A schematic diagram of the Adam algorithm optimization process provided by an embodiment of the present invention.

[0046] Figure 7 This is a physical schematic diagram of the hydraulic execution system provided by an embodiment of the present invention.

[0047] Figure 8 This is a schematic diagram of the hydraulic system principle after the model in the actual hydraulic system is replaced according to the embodiment of the present invention.

[0048] Figure 9 A schematic diagram of a robot toolbox simulation provided by an embodiment of the present invention.

[0049] Figure 10 A schematic diagram comparing joint angles of a robotic arm provided in an embodiment of the present invention.

[0050] Figure 11 A schematic diagram of joint angle error provided by an embodiment of the present invention.

[0051] Figure 12 A schematic diagram of the optimized joint angle error provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0052] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0053] The embodiment of the present invention discloses a hydraulic manipulator modeling and optimization method based on digital twin technology, see Figure 1 As shown, the following steps are included:

[0054] Based on the geometric performance parameters of the hydraulic manipulator, a corresponding virtual geometric model is established through modeling software;

[0055] Based on the joint position and posture data of the hydraulic manipulator, the corresponding kinematic attribute model is established;

[0056] The kinematic attribute model is optimized using the Adam optimization method to obtain the optimized attribute model;

[0057] Construct a dynamic simulation model of the hydraulic system based on the working status data of each component in the hydraulic system;

[0058] Integrate the virtual geometric model, optimized property model, and dynamic simulation model to obtain a digital twin model of the hydraulic manipulator.

[0059] The operating status data of the hydraulic mechanical arm is collected in real time, and the status of the digital twin model is updated based on the operating status data.

[0060] In the embodiment of the present invention, a five-degree-of-freedom hydraulic manipulator is specifically used. Next, based on the five-degree-of-freedom hydraulic manipulator, the hydraulic manipulator modeling and optimization method based on digital twin technology provided by the present invention is described in detail.

[0061] 1. Digital twin architecture and implementation of a five-degree-of-freedom hydraulic robotic arm:

[0062] 1.1. Five-dimensional digital twin system architecture of hydraulic robotic arm:

[0063] In order to build a digital twin system for hydraulic manipulators, the embodiment of the present invention designs a complete digital twin architecture for hydraulic robots based on the five-dimensional model theory of digital twins. The overall architecture consists of five parts: physical layer, twin layer, data layer, connection layer, and service layer. Figure 2 As shown. Among them:

[0064] (1) Physical layer:

[0065] The physical layer, the foundation of the digital twin system, includes the hydraulic manipulator, the hydraulic system, and various sensors deployed in various locations. Its primary task is to collect real-time operational data on the hydraulic manipulator, providing real-time operational data support for the entire digital twin system.

[0066] (2) Twin layer:

[0067] The twin layer is the core of the hydraulic manipulator's digital twin system. This layer constructs a virtual geometric model based on the physical manipulator's structural layout, assembly logic, and appearance features, achieving precise mapping of appearance and proportions. Furthermore, by integrating the motion characteristics and component interactions experienced in actual operations, a kinematic property model and a dynamic simulation model of the hydraulic system are established. This fully reflects the manipulator's motion behavior and hydraulic response, enabling synchronized mapping and real-time linkage between the virtual and real systems in terms of structure and dynamic state.

[0068] (3) Data layer:

[0069] The data layer processes and analyzes real-time status and operating data transmitted from the physical hydraulic manipulator, as well as the virtual entity's operating data. This information is accurately transmitted to the digital twin model and used to generate drive data to update the digital twin model's status in real time, accurately reflecting the current state of the hydraulic manipulator itself.

[0070] (4) Connection:

[0071] Connection is the data hub of the digital twin system. It enables the interconnection of all parts of the digital twin and serves as a bridge between the hydraulic manipulator body and the digital twin model.

[0072] (5) Service layer:

[0073] The service layer is the functional integration part of the digital twin system. It refers to the service packaging of various types of data, models, algorithms, simulations, and results required in the digital twin application process to realize functions such as data visualization, human-computer interaction, fault diagnosis, and life prediction.

[0074] 1.2. Implementation of the Digital Twin System for Hydraulic Robotic Arms:

[0075] In the embodiment of the present invention, in order to realize the digital twin of the hydraulic robotic arm and establish the linkage between the real robotic arm and the virtual robotic arm, the construction of the digital twin system of the hydraulic robotic arm is divided into four stages, and the corresponding technical routes are as follows: Figure 3 shown. Specifically:

[0076] During the 3D modeling stage, by analyzing the physical structure and mechanism of the hydraulic robotic arm, the 3D modeling software is used to complete the digital modeling of its geometric shape to obtain a virtual geometric model; ensuring that the virtual geometric model is highly consistent with the hydraulic robotic arm entity in terms of size, shape and mass distribution, providing an accurate geometric basis for subsequent modeling.

[0077] During the attribute modeling phase, the focus was on modeling and optimizing the kinematic attributes of the hydraulic manipulator to ensure that the attribute model accurately reflected the manipulator's motion behavior and physical characteristics. The hydraulic system was then modeled to obtain a dynamic simulation model of the hydraulic system.

[0078] During the experimental simulation phase, kinematic simulations were conducted using the CoppeliaSim and MATLAB co-simulation platform. Joint optimization algorithms were introduced to adjust joint angles to ensure the virtual robot's motion accuracy and stability. This process verified the robot's motion performance under different operating conditions, providing data support for subsequent control strategies.

[0079] During the digital twin phase, the virtual geometric model, optimized property model, and dynamic simulation model are integrated to construct a high-fidelity digital twin. Using real-time data interaction technology, the hydraulic manipulator's sensor feedback, control strategy, and operating status are mapped to the virtual model, ensuring that the virtual simulation model accurately reflects the real-time behavior of the physical manipulator, providing reliable technical support for real-time monitoring, fault diagnosis, and prediction of the manipulator.

[0080] 2. Establishment of virtual geometric model of hydraulic manipulator:

[0081] Based on the actual structure of the hydraulic robotic arm, SolidWorks was used for geometric modeling to accurately restore its size, shape, and mass distribution, laying the foundation for subsequent property modeling and digital twin construction.

[0082] 2.1. Description of the geometric model:

[0083] In this embodiment of the present invention, a 5+1-axis hydraulic manipulator is studied. The basic structure of the manipulator is made of hard-anodized aluminum alloy and equipped with a protective layer. The manipulator has five main axis joints, including upper arm deflection, upper arm pitch, forearm pitch, wrist pitch, and wrist rotation. An additional gripper opening and closing function, serving as the "+1 axis," enables independent control of the gripper.

[0084] 2.2. Establishment of virtual geometric model and lightweight processing:

[0085] Establishing a virtual geometric model of the hydraulic manipulator is fundamental to achieving real-time monitoring and dynamic simulation. An accurate model provides data support for subsequent control systems and performance optimization. To build an accurate and efficient virtual geometric model, the hydraulic manipulator's 3D physical model must first be drawn and assembled in SolidWorks. Then, lightweight processing is used to optimize the model's computational performance to meet the requirements of real-time simulation and dynamic control.

[0086] (1) Drawing and assembling virtual geometric models in SolidWorks:

[0087] The virtual geometric model of the hydraulic manipulator, a physical model, was initially created using SolidWorks software. During this phase, 3D models of each component were created according to the design requirements, including the manipulator's joints, segments, grippers, and hydraulic system components. Each component was precisely modeled based on its actual size and function, ensuring that its coordination with other components met the design requirements.

[0088] Component Modeling: Based on the design specifications of the hydraulic manipulator, each component was 3D modeled in SolidWorks. The design process for each component required considering its shape, size, and functional requirements.

[0089] Component Fit and Constraints: After completing the modeling of individual components, the assembly phase begins. During the assembly process, the assembly constraints in SolidWorks are used to combine the components into a complete hydraulic manipulator model.

[0090] (2) Lightweighting in 3ds Max:

[0091] Because digital twin models typically require real-time computation and simulation, model complexity must be kept within reasonable limits. While high-precision 3D models are crucial for initial design and static analysis, excessive geometric detail and complex structures can increase the computational burden and hinder simulation efficiency in real-time digital twin simulations. Therefore, to improve the computational performance and real-time responsiveness of virtual geometric models, they must be lightweight.

[0092] Lightweight modeling significantly reduces computational burdens by removing unnecessary details and simplifying geometric structures. This process is crucial for real-time monitoring, dynamic simulation, and control system implementation. In hydraulic manipulator applications, real-time dynamic simulation requires rapid calculation of hydraulic system responses, manipulator position changes, and joint motion. Therefore, simplifying the virtual geometric model can effectively improve simulation speed and accuracy.

[0093] Specifically, after completing the 3D solid model of the hydraulic manipulator and assembling it, the model was imported into 3dsMax for lightweighting. 3dsMax is a widely used 3D modeling and animation software that provides optimization and simplification capabilities for engineering models. During this process, the model was exported to STEP format and simplified using 3dsMax's optimization tools to achieve lightweighting.

[0094] Export and Load: The hydraulic manipulator model from SolidWorks was exported to STEP format, a standard 3D exchange format that ensures the model can be loaded smoothly into 3ds Max while maintaining high geometric accuracy. The exported STEP file was loaded into 3ds Max for further simplification.

[0095] Model simplification and optimization: In 3ds Max, the first step in lightweighting a virtual geometry model is to reduce unnecessary details. Many small geometric features (such as subtle surface textures and delicate connections) have no substantial impact on the dynamic simulation and control of the hydraulic manipulator. Removing these details can reduce model complexity.

[0096] The main optimization measures include:

[0097] ① Reduce the number of polygons and vertices: Using the "ProOptimizer" tool in 3ds Max, set the vertex merge threshold to 0.1mm and the edge fold angle threshold to 15° to optimize the number of polygons in the virtual geometry model. By reducing redundant faces and vertices, the volume of the virtual geometry model and the amount of computation required were significantly reduced.

[0098] ② Simplify the geometry: Remove unnecessary complex geometries, such as overly detailed housings of mechanical parts, and merge similar parts to reduce computational requirements.

[0099] ③Optimize surface smoothness: For parts that do not affect the simulation effect, reduce the amount of calculation and optimize rendering performance by reducing the surface smoothness.

[0100] After lightweight processing, the number of polygons in the virtual geometric model of the hydraulic robotic arm was reduced by 43.7%, and the number of vertices was reduced by 43.5%, which reduced memory usage, improved computing performance and running frame rate during real-time simulation, reduced computing burden, and accelerated running speed.

[0101] 2.3. Virtual scene construction of hydraulic robotic arm:

[0102] Export the designed model to STL file format, a universal 3D model data exchange format. Finally, import the STL file into CoppeliaSim to obtain the hydraulic manipulator physical model, that is, the final virtual geometric model.

[0103] After importing the model, the first step is to color it. Then, add rotational joints and pose information to the robot. Importing rotational joint data to each joint ensures the robot's motion capabilities. Furthermore, the robot's various mechanical structures must be connected, establishing parent-child relationships to form a complete tree structure. This structure allows all robot components to follow the rotation of the joints, ensuring the robot's realistic and accurate reflection of physical motion in the simulated environment.

[0104] 2.4. System communication architecture design:

[0105] To monitor equipment status, the collected equipment operating data must be mapped to the virtual system in real time, ensuring synchronization between the virtual model and the actual equipment. Furthermore, the virtual system must convert the output of the virtual model into control instructions, enabling remote control of the actual equipment.

[0106] To ensure efficient collaboration between devices and virtual systems, the system's communication architecture must have the following characteristics:

[0107] Real-time: Data transmission must have low latency to ensure real-time synchronization between the virtual model and the actual device.

[0108] Reliability: The communication system needs to be highly fault-tolerant and able to cope with equipment or network failures to ensure stable system operation.

[0109] High bandwidth: Device operation data usually has a large amount of data, so the communication architecture needs to provide sufficient bandwidth to ensure efficient data transmission.

[0110] Two-way communication: The system not only needs to transmit data from the device to the virtual system, but also needs to transmit control instructions from the virtual system to the device to ensure the efficiency of two-way communication.

[0111] By designing a reasonable communication architecture, we can ensure efficient and stable collaboration between the virtual system and the actual equipment, thereby achieving accurate equipment monitoring and remote control. Figure 4 As shown. Among them:

[0112] (1) Physical layer: The physical layer is primarily responsible for data collection and transmission at the device end. At this layer, the hydraulic manipulator connects to the controller via the UDP / IP protocol, collecting real-time device status information, such as the hydraulic system pressure and displacement sensor values. The data provided by these sensors is processed by the physical layer and transmitted to the upper-layer system via the network protocol.

[0113] (2) Virtual layer: The virtual layer connects the physical entity with the high-level application, enabling communication between the digital twin and MATLAB via the TCP / IP protocol. At this layer, the digital twin model can receive device data transmitted from the physical layer in real time and use MATLAB for data processing and simulation. MATLAB's powerful functionality enables the virtual layer to accurately model and analyze device states and display the working status of the robotic arm through a virtual model.

[0114] (3) Application service layer: The application service layer is responsible for storing, processing, and visualizing the data transmitted by the virtual layer. The functions of this layer include not only real-time display of the working status and position of the robot arm, but also dynamic display of the robot arm's movement process through a three-dimensional model, achieving all-round monitoring. The system will update the status of the robot arm in real time based on the data analyzed by the virtual layer, and store this data in a database to provide a basis for subsequent analysis and optimization. In addition, the application service layer can also display relevant data to users through a graphical interface, support data query, historical record viewing, and alarm management, and provide comprehensive service support for operators and managers.

[0115] 3. Establishment of kinematic property model of hydraulic manipulator:

[0116] Based on the physical characteristics of the hydraulic manipulator, a kinematic attribute model is established. By comparing actual operating data with the model output, the source of errors is analyzed. Based on the error analysis results, the kinematic attribute model is optimized to gradually improve the model's accuracy and reliability. The kinematic attribute models in this embodiment of the present invention include twin attribute models based on forward kinematics and twin attribute models based on inverse kinematics.

[0117] 3.1. Establishment of twin attribute model based on forward kinematics:

[0118] Forward kinematics for a robotic arm involves calculating the position and posture of the end effector in the workspace, given the angle information of each joint. A twin attribute model based on forward kinematics is established using an improved DH parameter method. Compared to the standard DH method, this method effectively reduces modeling errors caused by redundant parameters of adjacent joints, making it particularly suitable for the high-precision kinematic modeling requirements of hydraulic drive systems.

[0119] The connecting rod coordinate system of the hydraulic manipulator is as follows Figure 5 As shown, in the embodiment of the present invention, taking a 5-DOF hydraulic manipulator as an example, its corresponding DH parameters are shown in Table 1.

[0120] Table 1: Improved DH parameters of hydraulic manipulator

[0121]

[0122]

[0123] After defining the coordinate system for all links, the constant parameters of each link can be listed based on the established joint coordinate system. The joint coordinate system established based on the DH parameter method derives the coordinate transformation between adjacent links, which is the general form of the coordinate transformation between each link. These transformations are then multiplied sequentially to obtain the forward kinematic equations of the robotic arm.

[0124] Based on the DH parameters provided in Table 1, the specific position and posture of the end relative to the base within its space can be determined. A link coordinate system is established for each joint of the multi-DOF serial manipulator. Using the four key variables in Table 1, the transformation matrix of the i-th link's coordinate system relative to the i-1-th link's coordinate system can be derived; where the i-th link and the i-1-th link are two adjacent links; the transformation matrix is ​​expressed as:

[0125]

[0126] in, represents the transformation matrix of the coordinate system of the i-th link relative to the coordinate system of the i-1-th link; α i-1 represents the rotation angle of the i-1th connecting rod; a i-1represents the length of the i-1th connecting rod; d i represents the offset of the i-th connecting rod; θ i represents the joint angle corresponding to the i-th link; Represents the total transformation matrix from the coordinate system of the i-th link to the coordinate system of the i-1-th link; and There are 4 steps in the whole transformation process, each step is a basic rotation or translation; Represents a rotation along the X axis α i-1 angle; Indicates moving a along the X axis i-1 distance; Represents a rotation along the Z axis θ i angle; Indicates movement d along the Z axis i distance.

[0127] Multiply the transformation matrices between each two links in sequence to obtain the twin attribute model equation based on forward kinematics. Taking a 5-DOF hydraulic manipulator as an example, its twin attribute model equation based on forward kinematics is expressed as:

[0128]

[0129] n x =c1c 234 c5+s1s5,n y =s1c 234 c5-c1s5,n z =s 234 c5

[0130] o x =-c1c 234 s5+s1c5,o y =-s1c 234 s5-c1c5,o z =-c 234 s5

[0131] a x =-c1c 234 ,a y =-s1s 234 ,a z =c 234

[0132] p x =c1(a2c2+a3c 23 -d5s 234 )-d2s1

[0133] p y =s1(a2c2+a3c 23-d5s 234 )-d2c1

[0134] p z =-a2s2-a3s 23 +d2c1

[0135] c 1···i =cos(θ1+···+θ i ),s 1···i =sin(θ1+···+θ i )

[0136] i=1···5

[0137] in, represents the transformation matrix when i=1, which represents the transformation between the base and link 1; represents the transformation matrix when i=2, representing the transformation of link 1 and link 2; represents the transformation matrix when i=3, representing the transformation of link 2 and link 3; represents the transformation matrix when i=4, representing the transformation of link 3 and link 4; Represents the transformation matrix when i=5, representing the transformation of link 4 and link 5; connecting these five represents the position and posture of link 5 relative to the base; n x ,n y ,n z Represents the direction vector of the x-axis of the hydraulic manipulator end coordinate system in the base coordinate system; x ,o y ,o z Represents the direction vector of the y-axis of the hydraulic manipulator end coordinate system in the base coordinate system; a x ,a y ,a z p represents the direction vector of the z-axis of the hydraulic manipulator end coordinate system in the base coordinate system; x ,p y ,p z represents the coordinates of the end of the hydraulic manipulator in the base coordinate system; a2 represents the length of the second connecting rod; a3 represents the length of the third connecting rod; d2 represents the offset of the second connecting rod; d5 represents the offset of the fifth connecting rod; θ i represents the joint angle corresponding to the i-th link; c1 represents Cosθ1, s1 represents sinθ1, c 23 represents cos(θ2+θ3), and so on.

[0138] 3.2. Establishment of twin attribute model based on inverse kinematics:

[0139] The inverse kinematics problem for robotics involves converting the motion of the end effector in the operating space into the corresponding motion in the joint space. Specifically, given a desired end effector position, the solution is found that ensures that the joint angles of the robotic arm meet that desired position.

[0140] The analytical method can directly derive the solution of each joint angle through geometric relationships, avoiding the iterative process commonly seen in numerical methods, and is therefore suitable for robotic arms with a small number of joints and a relatively simple structure. Through geometric derivation, the analytical method can accurately and efficiently calculate the inverse kinematics solution on the basis of satisfying the above criteria. In addition, when faced with a multi-solution problem, the analytical method can optimize multiple solutions according to specific criteria, thereby selecting the most appropriate solution to ensure that the robotic arm can complete the task in the best way. Therefore, the embodiment of the present invention adopts an analytical method to model and calculate the inverse kinematics of the robotic arm, and uses the forward kinematics model of the robotic arm to infer the inverse kinematics problem. The reason for choosing the analytical method is that it can directly derive the solution of each joint angle through geometric relationships, and is suitable for robotic arms with a small number of joints and a relatively simple structure. The analytical method can not only efficiently calculate an accurate solution, but also can handle problems with multiple solutions.

[0141] According to the twin attribute model equation based on forward kinematics (i.e., according to the above formula (2)), the homogeneous transformation matrix T of the hydraulic manipulator can be obtained. The inverse matrix T of the homogeneous transformation matrix T is -1 It can be obtained by transposing the rotation matrix and the translation vector. It can be expressed as:

[0142]

[0143] Where R represents the rotation matrix (3×3) and P represents the translation vector (3×1).

[0144]

[0145] Based on the above formula, the specific solution process is as follows:

[0146] Let the elements in the 2nd row and 4th column of the matrix be equal, and we get:

[0147] -S1p x +C1p y =0 (6)

[0148] First, perform trigonometric identity transformation, let:

[0149] p x =ρcos(φ), (7)

[0150] p y =ρsin(φ) (8)

[0151] in:

[0152]

[0153] φ=atan2(p y ,p x ) (10)

[0154] cos(θ)sin(φ)-sin(θ)cos(φ)=-d / ρ (11)

[0155] Where d represents the connecting rod offset; based on this, we can further obtain:

[0156]

[0157] in:

[0158] p x 2 +p y 2 -d 2 ≥0 (13)

[0159] Let the elements in the 2nd row and 1st column of the matrix be equal, and the elements in the 2nd row and 2nd column be equal, and we get:

[0160] -S1n x +C1n y =S5 (14)

[0161] S1o x -C10 y =C5 (15)

[0162] From formulas (14) and (15), we can further obtain:

[0163] θ5=arctan2(S1n x -C1n y ,S1o x -C1o y ) (16)

[0164] Let the elements in the first row and first column of the matrix be equal, and the elements in the third row and second column be equal, and we get:

[0165] -S 234 =C1n x +S1n y (17)

[0166] -C 234 =n z (18) From formulas (17) and (18), we can further obtain:

[0167]

[0168] θ234 =arctan2(C1n x +S1n1,n z ) (20)

[0169] Comparing the elements on both sides of the matrix (the elements in the 1st row and 4th column, and the elements in the 3rd row and 4th column), we can get:

[0170] C1p x +S1p y =a3C 23 +a2C2+d5S 234 (twenty one)

[0171] p z -d1=-(a3S 23 +a2S2+d5C 234 ) (twenty two)

[0172] Eliminate θ 23 , which is simplified to:

[0173] -AS2+BC2=C (23)Based on:

[0174]

[0175] In order to solve θ2, we must have A 2 +B 2 -C 2 ≥0, there is a solution.

[0176] After solving for θ2, substitute into equations (19) and (20) to obtain:

[0177]

[0178]

[0179] According to θ4=θ 234 -θ 23 , θ3=θ 23 -θ2. Solve for θ3 and θ4.

[0180] We can get:

[0181]

[0182] θ4=Atan2(s 234 ,c 234 )-θ 23 (29)

[0183] In many practical applications, a robot can reach the desired end-position from multiple directions or multiple postures, resulting in multiple different joint angle solutions. In this case, the inverse kinematics equation has multiple solutions. To select the most appropriate solution, it is usually necessary to optimize according to some criteria:

[0184] Select solutions based on joint space constraints: Ensure that all calculated solutions are within the allowed angle range of each joint and exclude solutions that exceed the motion limits.

[0185] Select the solution based on the shortest stroke: If there are multiple solutions, select the one that is closest to the current hydraulic manipulator configuration to minimize the joint motion stroke, thereby improving work efficiency and reducing energy consumption.

[0186] Select a solution based on the obstacle avoidance principle: In some actual working environments, the robot needs to avoid collisions with obstacles. Therefore, it is also necessary to comprehensively consider the obstacles in the workspace and select a solution that does not interfere with the obstacles.

[0187] 3.3. Compensation of joint angle errors in the kinematic attribute model based on the Adam optimization algorithm:

[0188] In the control process of the digital twin robotic arm, the optimization of the joint angle is crucial to improving the accuracy and dynamic response of the system. In order to narrow the gap between the digital twin robotic arm and the physical robotic arm, the output data of the virtual model must be compensated. This not only improves the accuracy of the system, but also enables more precise control and optimization. Therefore, an embodiment of the present invention proposes a robotic arm joint angle compensation method based on the Adam (Adaptive Moment Estimation) optimization algorithm, which aims to improve the accuracy and reliability of the robotic arm movement by optimizing experimental data and adjusting the deviation between the digital twin and the entity.

[0189] The Adam optimization algorithm combines the advantages of Momentum and RMSProp, and improves the stability and convergence speed of parameter updates by adaptively adjusting the first-order moment and second-order moment of the gradient. Its calculation steps are as follows:

[0190] Step 1: Set the initial parameters of Adam optimization; the initial parameters include learning rate α, first-order moment estimation decay rate β1, second-order moment estimation decay rate β2 and maximum number of iterations N;

[0191] Step 2: Read the true value of the joint angle and joint angle experimental values Calculate initial error

[0192] Step 3: Initialize the first-order moment and the second-order moment to zero vectors, and set the time step t = 0;

[0193] Step 4: Enter the iterative optimization process and calculate the gradient g at each iteration t ; expressed as:

[0194]

[0195] Where L represents the mean square error (MSE) loss function;

[0196] Step 5: Update the first-order moment m t and the second moment v t , and make deviation corrections; where:

[0197] First-order moment m t and the second moment v t The update is expressed as:

[0198] m t =β1·m t-1 +(1-β1)·g t (31)

[0199]

[0200] The bias correction is expressed as:

[0201]

[0202] in, represents the corrected first-order moment at step length t; represents the corrected second-order moment at step length t; represents the decay rate of the first-order moment estimate at step size t; represents the decay rate of the second-order moment estimate at step size t;

[0203] Step 6: Update the joint angle experimental value according to the Adam formula Make it close to the theoretical value; expressed as:

[0204]

[0205] Among them, ε is a numerical stability term, which is generally taken as 1e-8.

[0206] Step 7: Check whether the maximum number of iterations has been reached. If not, return to step 4 and continue optimization. If reached, output the optimized result. Figure 6 shown.

[0207] 4. Modeling and analysis of hydraulic manipulator drive system:

[0208] 4.1. Working principle of hydraulic system:

[0209] A hydraulic system is a mechanical transmission system that uses liquids to transmit energy and signals. Its core principle, based on the incompressible nature of liquids, converts mechanical energy into hydraulic energy and, through the transmission of pressurized liquid, achieves force and motion control. A typical hydraulic system primarily consists of a hydraulic pump, a reservoir, hydraulic control valves, and hydraulic actuators. The hydraulic pump draws hydraulic oil from the reservoir and pressurizes it for delivery to the hydraulic system, providing the entire system with power. The reservoir stores the hydraulic oil and provides heat dissipation and impurity precipitation to ensure stable operation of the hydraulic system. Hydraulic control valves (including directional valves, pressure valves, and flow valves) regulate the direction, pressure, and flow of the liquid, thereby precisely controlling the system's operating state. Hydraulic actuators (such as hydraulic cylinders or hydraulic motors) convert hydraulic energy into mechanical energy, achieving force transmission and motion control. During hydraulic system operation, the hydraulic pump draws liquid from the reservoir and delivers it into the hydraulic pipeline. After adjustment by the control valves, the pressurized oil flows to the hydraulic actuators, causing them to produce displacement or rotational motion, thereby driving the various joints of the robotic arm. Hydraulic systems offer advantages such as high power density, high output force, smooth motion, easy adjustment, and high reliability. Consequently, they are widely used in mechanical equipment subject to high loads, precision control, and harsh environments. In the embodiments of the present invention, the actuation of a five-degree-of-freedom hydraulic manipulator relies on the linear motion of a hydraulic cylinder. Therefore, detailed modeling of the hydraulic system is required, combined with digital twin technology to simulate the motion of the hydraulic system and the manipulator.

[0210] 4.2. Hydraulic system modeling based on Automation StudioTM:

[0211] Each of the hydraulic manipulator's five moving joints is equipped with high-precision photoelectric encoders, which capture real-time angle and position information for each joint and feed it back to the control system, forming the foundational data link for closed-loop motion control. To further enhance the system's state awareness, dynamic pressure sensors are integrated at the inlet and outlet ports of the hydraulic actuators for joints 2 (shoulder), 3 (elbow), and 4 (wrist pitch) to monitor hydraulic circuit pressure waves in real time. The motion parameters of each joint are as follows: The 1st-axis chassis is driven by a swing cylinder, capable of ±90° rotation (total travel of 180°); the 2nd-axis shoulder, 3rd-axis elbow, and 4th-axis wrist pitch joints are driven by linear cylinders, with ranges of motion of 110°, 100°, and 95°, respectively; the 5th-axis wrist rotation joint is driven by a swing cylinder, with a rotation range of 300°; the end-of-line parallel gripper is driven by a linear cylinder, achieving a 0-100mm opening and closing travel, adapting to a variety of grasping tasks.

[0212] The hydraulic system is powered by a hydraulic pump station, with hydraulic oil delivered through pipelines to each actuator. Each joint's hydraulic actuator is controlled by a proportional valve to regulate fluid flow and achieve precise control of movement speed. The hydraulic oil transmits pressure energy within the system, driving the joints to move, enabling the robotic arm to complete its intended movements.

[0213] The hydraulic actuator system consists of six hydraulic actuators, including linear cylinders and swing cylinders. The linear cylinders are used to drive the robot's 2nd, 3rd, and 4th axes and the end gripper to achieve linear reciprocating motion; the swing cylinders drive the 1st and 5th axes to achieve rotary motion. Figure 7 As shown, Figure 7 Figure (a) is a schematic diagram of the linear cylinder. Figure 7 Figure (b) is a physical diagram of the linear cylinder.

[0214] Automation Studio by Famic Technologies TM AS is an integrated design and simulation software widely used for modeling and simulating various industrial automation technologies, including hydraulics, pneumatics, electrical control, PLCs, and HMIs. Using AS to model the hydraulic drive system, we focused on simulating the dynamic characteristics of key components in the hydraulic circuit. By combining the kinematic models of the hydraulic system and the robotic arm, we constructed a digital twin system for the hydraulic robotic arm, providing reliable data support for subsequent electromechanical-hydraulic coupling analysis.

[0215] Compared to traditional hydraulic schematics, schematics created by AS offer enhanced visualization and intuitiveness. Traditional schematics are often represented using symbols, lacking a visual representation of actual system components, hindering system debugging and understanding. However, AS allows users to directly select hydraulic components from the component library that match the actual system. This not only graphically replicates the actual equipment, but also allows for configuration of specific model parameters, achieving a "what you see is what you get" simulation modeling experience.

[0216] After replacing the components in the schematic diagram according to the models in the actual hydraulic system, Figure 8 As shown in the figure, the system diagram covers key components such as the hydraulic pump group, oil filter, servo valve, hydraulic cylinder, control module and sensor connection. Among them, the mark ① is the hydraulic oil tank; ② is the oil tank thermometer; ③ is the air-cooled cooler; ④ is the oil pump; ⑤ is the filter; ⑥, ⑧ and is the overflow valve; ⑦ is the flow meter; ⑨ and is a reversing valve;⑩ is a pressure gauge; and It is a swing cylinder; and It is a linear cylinder; For check valves, all components are selected from the AS standard hydraulic library to ensure the comparability and repeatability of modeling results, and also facilitate subsequent parameter adjustment and function expansion.

[0217] In Automation Studio TMWhen modeling the hydraulic system in [1], a modular modeling approach was adopted, dividing the system into a power source module (hydraulic pump and motor), a control module (servo valve, proportional valve, etc.), an actuator module (hydraulic cylinder or hydraulic motor), a load module (joints connected to the robotic arm), a sensor module (pressure, displacement, etc.), and a signal control and feedback loop. Each module is connected via standard hydraulic interfaces to form a complete closed-loop hydraulic actuator system.

[0218] Integrating the robot's structural parameters, the hydraulic system model not only reproduces the hydraulic energy conversion process but also enables collaborative simulation with the kinematic model in Simulink through an interface. The angular displacement, velocity, and load reaction force of each joint of the robot are acquired in real time through measurement elements within the AS and fed into the kinematic model for feedback and correction, laying the foundation for building a digital twin system.

[0219] 5. Experimental simulation and analysis:

[0220] 5.1.MATLAB kinematics simulation verification:

[0221] Modeling and simulation are the core tasks of hydraulic robot digital twin applications. TM It is industrial automation development and simulation software suitable for modeling and simulation in multiple fields, including electrical, pneumatic, and hydraulic systems. MATLAB excels in robot kinematic analysis and trajectory planning. CoppeliaSim has powerful 3D modeling and simulation capabilities. MATLAB excels in robot kinematics, but its robotics toolbox still has certain limitations in visualizing 3D spatial configurations, such as insufficient 3D visualization capabilities. CoppeliaSim supports high-precision robot modeling but lacks algorithm verification capabilities. Combining the two, leveraging their respective strengths, is expected to achieve efficient virtual-real data interaction while balancing computational accuracy and visualization effects.

[0222] In order to verify the accuracy of the kinematic modeling, the embodiment of the present invention uses the Simulink platform in MATLAB and the Robot Toolbox to perform kinematic simulation on a five-degree-of-freedom robotic arm.

[0223] (1) Build a 3D model of the robotic arm using the Simulink platform. Use the "Rigid Body Tree" module in the Robotics System Toolbox in Simulink to construct the robotic arm model. Define the multiple rigid bodies and joints of the robotic arm. Add Body and Joint modules to each joint, representing the connector and joint of the robotic arm, respectively. Each joint can be set as a rotational or translational joint. Select the appropriate joint type based on your robotic arm structure. Use the Scope module to monitor the changes in the angles of each joint and the position of the end effector of the robotic arm over time in real time.

[0224] (2) Using the SerialLink class in the Robot Toolbox, the robot model was generated by improving the DH parameters of the robot arm. The accuracy of the kinematic model was ensured by setting the rotation and displacement of the five joints. Then, using the forward kinematics method, different joint angles were set and the position and posture of the end effector were calculated to verify the feasibility and accuracy of the model. Figure 9 shown.

[0225] By comparing the actual robotic arm with the simulation results, it is shown that the model successfully realizes the kinematic modeling of the robotic arm and can effectively describe the position and posture changes of the end effector in the workspace.

[0226] 5.2.CoppeliaSim and MATLAB co-simulation:

[0227] Interaction between MATLAB and CoppeliaSim typically relies on the remote API (remote.API) provided by CoppeliaSim. This API establishes a communication interface between an external program (such as MATLAB) and the CoppeliaSim simulation environment, enabling MATLAB to send control commands to CoppeliaSim, adjust simulation states, and receive simulation data for subsequent processing. This interaction process can be divided into several key steps to ensure efficient data transmission and precise control between the two platforms.

[0228] (1) Add path and configure remote API:

[0229] Before interacting with CoppeliaSim in MATLAB, you first need to add the CoppeliaSim remote API library path to the MATLAB working path. To do this, use the addpath function in MATLAB to add the remoteApi folder path in the CoppeliaSim installation directory to the MATLAB search path.

[0230] In CoppeliaSim, you need to configure the "Remote API" option in the "Simulation" menu. In this setup, you need to specify a port number (for example, the default port is 19999) so that MATLAB can connect to CoppeliaSim. To start the remote service, add a non-threaded script to the CoppeliaSim scene and insert the command simRemoteApi.Start(19999) at the top of the script to start the remote API service. The port number on both the MATLAB and CoppeliaSim terminals should be the same to ensure a successful connection.

[0231] (2) Establish connection and verification:

[0232] Establishing a connection is the first step in interacting with CoppeliaSim. Use the vrep.simxStart function in MATLAB to establish a connection with CoppeliaSim. Once connected, use the MATLAB control panel to control the joints of the CoppeliaSim robot and use the vrep.simxGetJointPosition function to query the current position or angle of a specific joint.

[0233] (3) Collecting actual joint motion data of the robotic arm:

[0234] A data acquisition script was run in MATLAB, connecting to the actual hydraulic robot's sensor system to collect real-time motion data from the robot's five joints. The sampling period was from 10:00 AM to 10:05 AM on October 22, 2024, with a sampling period of 1 / 30 second. A total of 9,000 joint angle data points were collected for the digital twin robot. Due to space limitations, only 10 of these are shown, as shown in Table 2.

[0235] Table 2: Robotic arm joint angle timing data (partial)

[0236] Joint1 Joint2 Joint3 Joint4 Joint5 30.19 30.145 4.266 0.173 0.128 30.191 30.134 4.583 0.181 0.123 30.191 30.123 4.922 0.177 0.123 30.191 30.108 5.281 0.179 0.118 30.192 30.099 5.664 0.181 0.119 30.192 30.091 6.016 0.182 0.12 30.192 30.084 6.398 0.184 0.125 30.193 30.072 6.801 0.185 0.125 30.193 30.061 7.224 0.186 0.125 30.193 30.051 7.666 0.188 0.125

[0237] (4) Twin drive and synchronization:

[0238] The collected joint motion data of the robotic arm is loaded into MATLAB. This joint data is then sent to CoppeliaSim to control the motion of the robotic arm in the simulation model. To ensure synchronization between the digital twin and the real robotic arm, MATLAB needs to read the real robotic arm data at regular intervals and send it to CoppeliaSim.

[0239] (5) Close the connection:

[0240] After all data exchange and simulation control are completed, the connection between MATLAB and CoppeliaSim needs to be closed. This operation is achieved through the MATLAB command vrep.simxFinish(clientID) to release resources and ensure the normal operation of the system.

[0241] 5.3. Analysis and Optimization:

[0242] In order to verify the accuracy of the digital twin of the hydraulic manipulator, this section compares and analyzes the joint angle measurement data during the actual operation of the manipulator with the joint angle data output by the digital twin.

[0243] Compare it with the actual robotic arm. Figure 10 As shown, the joint error is Figure 11 shown.

[0244] Depend on Figure 10 、 11 The overall accuracy of the digital twin is good, but the error increases significantly as the robotic arm's joints move to and from the target angle (30°). During the stable joint motion phase (i.e., during the non-starting and stopping phases), the error decreases significantly, demonstrating that the digital twin's simulation accuracy is high in steady state and can well reflect the kinematic characteristics of the actual robotic arm.

[0245] Error source analysis:

[0246] 1) During the robot's startup and shutdown phases, the acceleration varies significantly, resulting in differences in the dynamic response between the actual robot and its digital twin. The digital twin may not fully simulate the dynamic characteristics of the actual robot, such as the nonlinear behavior of the hydraulic system or changes in joint friction, which may affect the accuracy of the angle.

[0247] 2) The actual joint angle data of the robotic arm may be affected by sensor noise, especially in the initial and final stages of movement, where the impact of noise is more significant.

[0248] To solve these problems, we use the Adam optimization algorithm to compensate for the joint angles of the digital twin. The algorithm parameters have the following value ranges:

[0249] Learning rate α = 0.001 ~ 0.005, first-order moment decay rate β1 = 0.85 ~ 0.95, second-order moment decay rate β2 = 0.990 ~ 0.999, maximum number of iterations N = 500 ~ 2000.

[0250] In this paper, the initial learning rate is 0.001, the first-order moment decay rate is 0.9, the second-order moment decay rate is 0.999, the maximum number of iterations is 1000, and the numerical stability term is set to 1e-8. The results after optimization are as follows Figure 12 As shown, the red curve represents the original angle error of the digital twin, and the green curve represents the error curve after optimization by the Adam algorithm.

[0251] from Figure 12 As can be seen, after optimization using the Adam algorithm, the joint angle error is significantly reduced. The optimized error curve (green) is generally lower than the original error curve (red), indicating a significant reduction in the error amplitude. The error changes are shown in Table 3 below.

[0252] Table 3: Error variation

[0253] Scenario Original maximum error Maximum error after optimization Error reduction rate Movement phase 0.65° 0.15° 76.9％ Steady-state phase 0.15° 0.08° 46.7％

[0254] As can be seen from the table above, after optimization by the Adam algorithm, the twin robots:

[0255] 1) Improvement in the dynamic stage: During the start-up and stop phases of the robot arm, the fluctuation of the error curve after optimization is significantly reduced, indicating that the Adam algorithm effectively alleviates the impact of dynamic response differences.

[0256] 2) Improved steady-state accuracy: During the stable joint motion stage, the optimized error further approaches zero, indicating that the steady-state simulation accuracy of the digital twin has been further improved.

[0257] In summary, the Adam optimization algorithm performs exceptionally well in improving joint angle accuracy. After optimization, the joint angles in the simulation model more closely match those of the real robot arm, with a reduced margin of error. This optimization effectively reduces joint jitter, resulting in more accurate trajectory tracking and enhanced dynamic responsiveness of the system. The optimized digital twin robot arm more accurately simulates the motion characteristics of the real robot arm, improving the reliability of the digital twin system and laying the foundation for further intelligent optimization and control.

[0258] 6. Implementation of hydraulic robot digital twin system:

[0259] Based on the framework proposed in this paper, a digital twin visualization platform for hydraulic manipulators was built. The platform includes three modules: state detection and virtual-real synchronization, visualization display, and human-computer interaction.

[0260] (1) Virtual and real synchronization function

[0261] Virtual-reality synchronization is a core function of the hydraulic robotic arm digital twin platform. This module uses high-precision sensors to collect real-time operational data from the robotic arm and synchronizes the current state of the physical robotic arm with the virtual model. The virtual robotic arm can reflect the joint position, posture, and operating status of the physical robotic arm in real time, achieving virtual-reality synchronization.

[0262] (2) Visual display

[0263] The visualization module utilizes 3D modeling and data visualization technologies to intuitively present the hydraulic manipulator's operating status, trajectory, and key performance parameters. Specific functions include: real-time display of the manipulator's joint angles, end-effector position, and trajectory; combining a color mapping algorithm to dynamically display hydraulic system data such as pressure and temperature; and using 3D animation to display the manipulator's operational flow and tasks in real time. Furthermore, by overlaying historical trajectory lines, users can trace the manipulator's operational history, helping them analyze operational patterns and optimize work paths.

[0264] (3) Human-computer interaction function

[0265] The human-computer interaction module is designed to enhance the user experience of operating the hydraulic manipulator, enabling quick access to key information and flexible control of the arm. Specific features include: virtual model interaction, allowing users to scale, rotate, and switch perspectives on the manipulator model, allowing users to observe the manipulator's operating status from multiple angles; parameter adjustment, allowing users to dynamically adjust the manipulator's motion parameters, such as joint angles and load; and support for designing task trajectories and issuing operational commands through a simple graphical interface.

[0266] 7. Conclusion:

[0267] The embodiment of the present invention integrates the technical advantages of CoppeliaSim and MATLAB, and combines AutomationStudio TM To further enhance the modeling capabilities of hydraulic systems, a modeling and optimization method for a hydraulic manipulator based on digital twin technology was proposed. First, a technical solution was developed for the hydraulic manipulator, encompassing 3D models, attribute models, co-simulation, and twin system development. Furthermore, the 3D model of the hydraulic manipulator was constructed in CoppeliaSim, and the attribute model was established in MATLAB. An optimization algorithm was then introduced to address modeling errors.

[0268] In the hydraulic system modeling, Automation Studio is used TM Detailed modeling of key components, including the hydraulic pump, proportional valve, hydraulic cylinder, and swing cylinder, was performed to construct a dynamic model of the hydraulic system. Using the Simulink platform, the hydraulic system and the robotic arm kinematic model were co-simulated, forming a complete electromechanical-hydraulic coupling modeling framework and improving the accuracy and responsiveness of the digital twin system.

[0269] Subsequently, this paper constructed a virtual-reality fusion simulation experimental platform, enabling real-time data interaction and simultaneous verification between physical devices and digital twin models. The platform focused on evaluating the effectiveness of the Adam algorithm in optimizing joint angle modeling errors. Finally, a digital twin visualization system for hydraulic robots was developed, exploring feasible paths for the practical application of this paper's research findings.

[0270] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0271] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A hydraulic manipulator modeling and optimization method based on digital twin technology, characterized in that: include: Based on the geometric performance parameters of the hydraulic manipulator, a corresponding virtual geometric model is established through modeling software; Based on the joint position and posture data of the hydraulic manipulator, a corresponding kinematic attribute model is established; Optimizing the kinematic attribute model using the Adam optimization method to obtain an optimized attribute model; Constructing a dynamic simulation model of the hydraulic system based on the working status data of each component in the hydraulic system; Integrating the virtual geometric model, the optimized property model, and the dynamic simulation model to obtain a digital twin model of the hydraulic robotic arm; The operating status data of the hydraulic mechanical arm is collected in real time, and the status of the digital twin model is updated based on the operating status data.

2. The hydraulic manipulator modeling and optimization method based on digital twin technology according to claim 1 is characterized in that: Lightweight the established virtual geometric model; The lightweight processing includes: reducing the number of polygons and vertices of the virtual geometric model, simplifying the geometric structure and optimizing the surface smoothness.

3. The hydraulic manipulator modeling and optimization method based on digital twin technology according to claim 1 is characterized in that: The kinematic attribute model includes a twin attribute model based on forward kinematics and a twin attribute model based on inverse kinematics.

4. The hydraulic manipulator modeling and optimization method based on digital twin technology according to claim 3 is characterized in that: The twin attribute model based on forward kinematics is established by adopting the improved DH parameter method; For multiple links in a hydraulic manipulator, the improved DH parameters of the i-th link include: the rotation angle of the i-1th link, the length of the i-1th link, the offset of the i-th link, and the joint angle corresponding to the i-th link; Among them, the i-th connecting rod and the i-1-th connecting rod are two adjacent connecting rods.

5. The hydraulic manipulator modeling and optimization method based on digital twin technology according to claim 4 is characterized in that: The improved DH parameter method is used to establish the twin attribute model based on forward kinematics, specifically including: Based on the improved DH parameters of the i-th link, a transformation matrix is ​​established for the coordinate system of the i-th link relative to the coordinate system of the i-1-th link. The transformation matrices between each two links are multiplied in sequence to obtain the twin property model equation based on forward kinematics. Wherein, the transformation matrix is ​​expressed as: Among them, α i-1 represents the rotation angle of the i-1th connecting rod; a i-1 represents the length of the i-1th connecting rod; d i represents the offset of the i-th connecting rod; θ i represents the joint angle corresponding to the i-th link; Represents the total transformation matrix from the coordinate system of the i-th link to the coordinate system of the i-1-th link; and There are 4 steps in the whole transformation process, each step is a basic rotation or translation; represents a rotation along the X axis i-1 angle; Indicates moving a along the X axis i-1 distance; represents a rotation along the Z axis θ i angle; Indicates movement d along the Z axis i distance.

6. The hydraulic manipulator modeling and optimization method based on digital twin technology according to claim 3 is characterized in that: An analytical method is used to establish the twin attribute model based on inverse kinematics; Criteria for solving the twin attribute model based on inverse kinematics include: selecting a solution based on joint space limitations, selecting a solution based on the shortest distance, and selecting a solution based on obstacle avoidance principles.

7. The hydraulic manipulator modeling and optimization method based on digital twin technology according to claim 1 is characterized in that: The method of optimizing the kinematic attribute model using the Adam optimization method to obtain an optimized attribute model specifically includes: Step 1: Set the initial parameters of Adam optimization; the initial parameters include learning rate, first-order moment estimation decay rate, second-order moment estimation decay rate and maximum number of iterations N; Step 2: Read the true value of the joint angle and joint angle experimental values Calculate initial error Step 3: Initialize the first-order moment and the second-order moment to zero vectors, and set the time step t = 0; Step 4: Enter the iterative optimization process and calculate the gradient g at each iteration t ; Step 5: Update the first-order moment and the second-order moment, and perform deviation correction; Step 6: Update the joint angle experimental value according to the Adam formula Step 7: Check whether the maximum number of iterations has been reached. If not, return to step 4 and continue optimization. If reached, output the optimized result.

8. The hydraulic manipulator modeling and optimization method based on digital twin technology according to claim 1 is characterized in that: In Automation Studio TM A dynamic simulation model of the hydraulic system is constructed in the paper; a modular modeling approach is adopted to divide the hydraulic system into a power source module, a control module, an execution module, a load module, a sensor module, and a signal control and feedback loop; each module is connected through a standard hydraulic interface to form a complete closed-loop control hydraulic system.

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