Foreword
Truck-mounted cranes can be applied to missile weapon equipment transportation, semi-automatic missile loading systems, hazardous environment rescue, and fruit tree and agricultural product spraying and harvesting. When applied to missile weapon equipment, missiles require transportation from production to combat training and battlefield use, including ship transport, vehicle transport, and personnel transport. Equipment reliability is closely related to the quality of its transportation performance, and the transportation environment affects missile performance. In semi-automatic missile loading systems, the function is to load missiles ready for launch onto the launch pad. The loading device mainly consists of a machine that loads or unloads missiles from the launch pad. To replace manual loading and ensure missiles automatically enter their precise positions on the launch pad, the missiles to be loaded are first transported to the corresponding positions on the launch pad, and then, through a simple rotation, the missiles are loaded individually or simultaneously onto the corresponding launch pads. In the field of rescue robots, facing increasingly complex and dangerous rescue strategies and frequent man-made and natural disasters worldwide, robots assisting or even replacing humans in rescue work has become an important issue and means of rescue efforts. The application of robots in agriculture can greatly reduce labor intensity, increase labor productivity, and solve the problem of labor shortage. Modern agricultural robots are machines that integrate multiple technologies such as detection technology, sensing technology, artificial intelligence technology, image recognition technology, and communication technology.
my country only began researching truck-mounted crane systems in the 1970s and 80s. Due to this late start, domestic research on truck-mounted crane robotic arms lags significantly behind that of developed countries. Under the leadership of Academician Wang Tianran, seven collaborating institutions, including Zhejiang University, Beijing University of Aeronautics and Astronautics, Dalian University of Technology, Northwestern Polytechnical University, and the China Academy of Machinery Science and Technology, have developed a hydraulically driven rescue truck-mounted crane robotic arm. The hydraulically driven rescue truck-mounted crane robotic arm features: alternating hydraulic and electric power; dual-arm operation with wheel-track composite movement; and the ability of the robotic arms at the ends of the two arms to quickly switch between different functions depending on the needs of the operation or rescue site. This allows the hydraulically driven rescue truck-mounted crane robotic arm to rapidly complete loading, unloading, dismantling, and emergency rescue operations.
The kinematic model of a truck-mounted crane's robotic arm is fundamental to structural analysis. It facilitates the analysis of the mechanism's velocity and acceleration, and provides a convenient basis for studying dynamic-related problems. Common methods include the DH parameter representation and the homogeneous transformation matrix method. The advantage of this method is its ease of use in calculating the Jacobian matrix and force analysis. However, it has a fundamental technical problem: while it can fully describe robotic arms that move only along the x and z axes, it becomes inapplicable when considering motion along the y-axis. Furthermore, the mechanical mechanisms of automatic loading systems for truck-mounted cranes are complex, often involving multiple joints such as rotation, slewing, and extension. This poses significant challenges to setting joint coordinates using the DH parameter method. Therefore, employing the homogeneous transformation rotation matrix method for kinematic modeling of hydraulic truck-mounted crane robotic arms used in outdoor operations offers a simpler and more intuitive approach.
1. Establishment of mathematical model
This paper first establishes a coordinate system using the Denavit-Hartenberg method (DH method), and then derives the motion equations of the robotic arm based on the coordinate system established by the DH method. The DH method is a matrix method for establishing relative pose. Proposed by Denavit and Hartenberg in 1995 and named after them, the DH method uses homogeneous transformations to describe the spatial geometric relationships of each link relative to a fixed reference frame. The spatial relationship between two adjacent links is described by a 4x4 homogeneous transformation matrix, thus allowing the derivation of the coordinate transformation matrix of the end effector's coordinate system relative to the base coordinate system, and establishing the motion equations of the manipulator.
To solve the forward kinematics of a robotic arm, the angles of each joint must be known. Then, the desired pose of the end effector must be calculated based on the angles of each joint. The standard method for studying robotic arm kinematics is to use the DH method for analysis and modeling. The basic idea is: first, establish a reference coordinate system at each joint of the robotic arm; second, determine the transformation matrix between any two adjacent coordinate systems and multiply the resulting matrices sequentially; finally, obtain the total transformation matrix from the base to the end effector.
Figure 1 Six-DOF modular robotic arm
A robotic arm can be viewed as a series of links connected by joints. Based on the structural characteristics of this robotic arm, the DH method is used to establish a base coordinate system and coordinate systems for each joint. A six-DOF robotic arm is a spatial mechanism with six joints. Only by establishing a coordinate system at each joint can the attitude and position of the robotic arm's end effector in space be described.
2. Introduction to MATLAB
MATLAB is a high-level technical computing language that plays a vital role in data visualization, algorithm development, numerical computation, and data analysis. MATLAB offers capabilities such as plotting functions and data graphs, performing matrix operations, writing programs in languages like C and C++, and creating user interfaces. MATLAB's greatest strength lies in numerical computation. Its plotting functions, matrix operations, user interface creation, and integration with other programming languages can fulfill requirements for image processing, engineering calculations, control design, and signal detection. Matrices are the fundamental unit of data in MATLAB, and their forms used in engineering and mathematics are very similar to its command expressions. Because of this, solving problems with MATLAB is much simpler and more concise compared to languages like C and FORTRAN. MATLAB's advantages and features
1) Enables computational programming and result visualization, with comprehensive graphics processing capabilities;
2) To facilitate users, a variety of application toolboxes have been established, such as the communication toolbox and the signal processing toolbox;
3) It has powerful symbolic and numerical computation functions, which can avoid complicated mathematical operations and analysis;
4) The natural language of mathematical expressions and user interface makes it easier to learn and master.
MATLAB can be considered a collection of computational functions that enable users to perform all the computational tasks they need. This collection includes over six hundred computational algorithms used in engineering and research. Under the same computational requirements, programming using other methods would be significantly more laborious than programming with MATLAB. MATLAB's function sets (such as eigenvectors, complex matrix functions, and Fourier transforms) can solve many computational problems in engineering (such as optimization problems, solving systems of differential and partial differential equations, Fourier transforms, and statistical data analysis).
In graphics processing, MATLAB has made significant progress and development. It not only supplements the functions generally available in other software, such as processing and plotting 2D curves and 3D surfaces, but also demonstrates outstanding processing capabilities for functions not found in other software, such as color processing, 4D data processing, and lighting manipulation. MATLAB also features data visualization capabilities, a feature inherent from its development, which facilitates user interaction by expressing matrices and vectors graphically. Advanced plotting, including 2D and 3D image processing, visualization, expression, and animation, can be used for engineering drawing and scientific computing. MATLAB has also designed corresponding functions for users at different levels who have specific requirements for graphical interfaces and similar tasks.
3. Kinematic simulation
Kinematic simulation of a robotic arm is performed. To make the robotic arm's movements more three-dimensional and intuitive, the simulation results can be represented graphically. This includes whether the robotic arm can meet the spatial operation requirements, whether the movements are smooth, and whether there are any interference phenomena. Compared with simulation using data curves or the data itself, graphical simulation can analyze a large amount of important information, while simulation using data curves or the data itself cannot reveal the robot's motion laws.
3.1 Verification of Forward Kinematics
Figure 3. End-effector pose of the eighth robotic arm
3.3 Results of Interference Programming
The following is the vertical grasping trajectory planned using interpolation. This paper simulates the spatial curve trajectory, velocity, and acceleration, as shown in Figures 4, 5, and 6.
Figure 4 Curves of each coordinate axis
Figure 5 Spatial Curve Trajectory
Figure 6 Joint velocity curves
4. Conclusion
The forward kinematics analysis of the truck-mounted crane was performed using the DH method to establish a coordinate system and solve for the DH parameters of the robotic arm. Based on the coordinate position of the end effector of the robotic arm and the forward kinematics solution, 16 sets of inverse kinematic solutions were derived. This paper also uses interpolation to plan the trajectory of the truck-mounted crane robotic arm and divides the kinematics into seven stages using the Cartesian space trajectory planning method, solving for the uniform velocity stage and the variable acceleration stage separately. Finally, the forward and inverse kinematics were simulated. By setting the length of the rod and assuming the joint degrees, eight sets of solutions were obtained. Comparing these eight sets of solutions with the original data, it was found that the two sets of data were similar, which fully proves that the solution of the inverse kinematics is correct.
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