Abstract : This paper describes the control system and structural composition of a robotic arm, and establishes and defines the relevant coordinate system. The forward kinematics equations of the system are obtained through a homogeneous transformation matrix, and the inverse kinematics problem of the truck-mounted crane is studied based on this. The pure particle algorithm is used to calculate the solution of the inverse kinematics, and the advantages and disadvantages of the algorithm are analyzed for different cases. Finally, simulation results of the inverse kinematics of the truck-mounted crane are presented through experimental simulation.
Keywords : PLC, servo; control system;
Intermediate Classification Number : TP 9 Document Identification Code: B
0 Introduction
With the development of the economy and modern technology, the practicality of robot products has not only solved practical problems that are difficult to solve by human labor alone, but also greatly promoted the process of industrial automation. Furthermore, they are of great significance for ensuring personal safety, improving the working environment, reducing labor intensity, increasing labor productivity, saving raw material consumption, and reducing production costs. Automated machinery can complete different tasks through program updates; however, this capability is not well demonstrated in actual engineering. For some unpredictable or constantly changing tasks, such as excavating machinery, manual operation is often used. As the application fields of robots expand, for industrial processes with relatively fixed working conditions, defined tasks, and high control precision requirements, manual operation is often labor-intensive and fails to meet the requirements. In such cases, there is an urgent need for robots that are easy to automatically control to replace manual operation, thereby completing the entire work process efficiently and accurately.
Truck-mounted cranes are automated mechanical devices that use lifting mechanisms and telescopic systems to grab, rotate, and transport goods. They generally consist of a boom, turntable, frame, and outriggers. The mechanical movements of a truck-mounted crane are achieved through the motion of luffing, telescopic, slewing, and winching mechanisms; different combinations of these mechanisms accomplish different tasks. Because truck-mounted cranes can provide high torque at high speeds and possess characteristics such as high durability, robustness, high power-to-weight ratio, and fast response, they are widely used in high-risk operations such as infrastructure construction, coal chemical industry, and nuclear industry. Truck-mounted cranes offer advantages such as simple operation, flexible movement, stable performance, and long service life. Currently, truck-mounted cranes are classified by type as telescopic, straight-arm, and folding-arm; and by maximum lifting capacity as various models. Due to their rapid response and high power-to-weight ratio, hydraulically driven truck-mounted cranes are widely used in industrial operations, such as assembly tasks, material processing, construction, and mining.
In robotics, forward kinematics is simple to calculate and yields a unique result; however, inverse kinematics is more complex, often resulting in multiple solutions and sometimes no solution at all. Traditional algebraic methods (i.e., inverse transformation methods) are intuitive but require multiple matrix inverse multiplications; iterative methods rely on the starting point, are computationally intensive, and have complex programming, making real-time control difficult. In recent years, with the rise of intelligent control, more and more scholars have applied intelligent control to solve the problem of robot inverse kinematics. The solution approach of intelligent control methods is to transform the robot's motion equations into a control problem, mainly including genetic algorithms and neural network algorithms. This paper presents a kinematic model of a truck-mounted crane using the homogeneous transformation matrix method, considering the structural characteristics of a 6-DOF truck-mounted crane robotic arm.
1. Description of the crane arm model
The truck-mounted crane's robotic arm is mounted at the rear of the vehicle and is mainly used for lifting large loads and transferring objects between the truck and the transport vehicle. Its control system is hydraulically driven and consists of a fixed displacement pump, outrigger cylinders, luffing cylinders, folding cylinders, and telescopic cylinders. The luffing, folding, and telescopic cylinders utilize built-in magnetostrictive sensors to achieve precise control and feedback of the extension/retraction amount, as shown in Figure 1.
Figure 2.1 Schematic diagram of the hydraulic drive system of the robotic arm
The truck-mounted crane's robotic arm consists of five rotary joints and three telescopic joints, as shown in Figure 2. The crane's base has one degree of freedom for rotation around the z-axis, used to adjust the spatial orientation of the crane when gripping a package, i.e., controlling the transport angle. To enable the crane to reach farther target locations, it requires not only two rotary joints (degrees of freedom 2 and 3) but also a three-section telescopic arm (degrees of freedom 4, 5, and 6) to expand its working range. Since the object being gripped carries a large load, a wrist joint (degree of freedom 7) is added to reduce the additional torque generated by the heavy load at the end of the load during transport, ensuring it remains vertically downward. The gripper's gripping (or releasing) of the package must maintain its orientation, requiring an additional degree of freedom 8 for adjusting the end-effector's posture.
Figure 2. Schematic diagram of the robotic arm model
2. Model Simplification
According to the formula, the base slewing joint 1, connecting rods 2 and 3, and the telescopic connecting rod are not in the same plane of motion. The base slewing joint moves in a plane, controlling the spatial orientation of the transported packaging box; connecting rods 2 and 3 and the telescopic rod move in a plane, and their main task is to grasp the packaging box. Therefore, the spatial orientation of the truck-mounted crane during its movement can be uniquely determined using a bivariate tangent function, the inverse of which is given by [formula missing]. Based on this analysis, the spatial problem of a multi-degree-of-freedom truck-mounted crane can be transformed into a planar three-degree-of-freedom problem.
3. Particle Swarm Optimization Algorithm
Particle swarm optimization (PSO) is a collaborative stochastic search algorithm developed by simulating the foraging behavior of bird flocks. It is generally considered a form of swarm intelligence. It can be incorporated into multi-agent optimization systems and was invented by Dr. Eberh and Dr. Kennedy. PSO simulates the foraging behavior of bird flocks.
Chaotic particle swarm optimization (PSO) algorithms, while lacking the complex operations of genetic algorithms such as encoding/decoding, selection, crossover, and mutation, require fewer parameters, have a simple structure, and are fast. However, like other intelligent algorithms, PSO suffers from premature convergence and poor local optimization capabilities. When a particle encounters a local extremum during its flight, all particles rapidly converge towards it and remain there, causing the algorithm to become trapped in a local optimum, resulting in premature convergence. Therefore, chaotic optimization is introduced into PSO, leveraging the characteristic of chaotic motion to traverse all states without repetition within a certain range, thus achieving global optima.
Following the idea of the chaotic particle swarm optimization algorithm, initial particles are first established using chaotic search. Then, the basic operations of the particle swarm optimization algorithm are performed until the particles enter local convergence. Afterward, chaotic search is performed to escape local optima and quickly converge to the global optimum. Figure 3 shows the flowchart of the particle swarm optimization algorithm.
Figure 3. Flowchart of Particle Swarm Optimization Algorithm
4 Simulation Results
By analyzing the working space of the truck-mounted crane, its working area can be pre-determined using a bivariate tangent function; this simplifies the truck-mounted crane model into a computational problem involving redundant joint variables in a planar space. By selecting the minimum position error, the minimum change in joint angle, and the minimum change in extension length relative to the initial state as additional constraints, a set of feasible solutions can be obtained.
Assuming an initial population size of 30, a maximum number of generations of evolution of 100, and a maximum number of chaotic searches of 30,...
Initial state of each joint:
Good, and highly accurate.
Figure 4 Simulation diagram of particle swarm optimization algorithm
5. Conclusion
This paper introduces the basic structure of a truck-mounted crane and presents a simplified model of the robotic arm. For the complex truck-mounted crane model, this paper uses a particle swarm optimization (PSO) algorithm to analyze the inverse kinematics problem. To solve the inverse kinematics problem of the spatial robotic arm, a set of feasible inverse kinematic solutions is obtained by using the PSO algorithm under the condition of selecting an appropriate optimization function. Finally, a simulation study of the PSO algorithm is conducted.
