0 Introduction
Fuzzy control technology has become an important branch of intelligent control technology, representing an advanced algorithmic strategy and a novel technique. Since British engineer E. H. Mandani first used a fuzzy controller based on fuzzy set theory for steam engine control in 1974, fuzzy control technology has experienced widespread and rapid development over the past 30 years. Currently, fuzzy control is widely applied in metallurgical and chemical process control, industrial automation, intelligent home appliances, instrumentation automation, and computer and electronic technology applications. It demonstrates strong application value, particularly in traffic intersection control, robotics, manipulator control, aerospace flight control, automotive control, elevator control, nuclear reactors, and home appliance control. Dedicated fuzzy chips and fuzzy computers are now available for selection. China began researching fuzzy controllers in 1979 and has achieved significant results in the definition, performance, algorithms, robustness, circuit implementation methods, stability, and rule self-adjustment of fuzzy controllers. The renowned scientist Qian Xuesen pointed out that fuzzy mathematics theory and its applications are related to China's national strength and destiny in the 21st century.
In recent years, with the development of robotics and control technology, robots have been widely used in daily life and industrial and agricultural production. A robot is a nonlinear, strongly coupled, multivariable system. During its motion, due to uncertainties such as friction and load changes, it is also a time-varying system. Traditional robot control technologies are mostly model-based control methods, which cannot achieve satisfactory trajectory tracking results. The development of artificial intelligence, such as fuzzy control and neural networks, has provided new ideas for solving the robot trajectory tracking problem. The control rules of ordinary fuzzy control are mostly summaries of human experience. They lack self-learning and adaptive capabilities and are often influenced by human subjectivity. Therefore, they cannot effectively control time-varying and uncertain systems.
Mobile robots are comprehensive systems integrating environmental perception, dynamic decision-making, behavior control, and execution. Motion control is a crucial research area in mobile robotics and forms the foundation for trajectory control, localization, and navigation. Traditional motion control often employs PID control algorithms, characterized by simplicity, robustness, and high reliability. However, it requires a precise mathematical model to achieve good control results for linear systems, and its performance on nonlinear systems is less than ideal. Fuzzy control, on the other hand, does not require a precise mathematical model of the controlled object, thus offering flexibility and adaptability. However, any pure fuzzy controller is essentially a nonlinear PD control, lacking integral action, making it difficult to eliminate steady-state errors in fuzzy control systems. To address this problem, and considering the actual operating conditions of the motion control system, a fuzzy PID control method is designed to achieve large-range error adjustment of the wheel speed of a fast-moving robot. Fuzzy control and PID control are combined to form a parametric fuzzy self-tuning PID algorithm for servo motor control. This allows the controller to possess both the flexibility and adaptability of fuzzy control and the high precision of PID control. This enables the motion control system to meet design requirements such as high real-time performance, robustness, and stability. Furthermore, by expanding the fuzzy control rule base, other functions can be easily added to the motion control system.
1. Kinematic Analysis of an All-Way Mobile Robot
This research focuses on a fully autonomous mobile robot platform. The robot employs a four-wheel omnidirectional motion system. This omnidirectional capability allows the robot to move linearly in any direction without requiring rotational movement. Furthermore, this wheel system can simultaneously perform linear motion and rotation, achieving any desired posture angle in the final state. The application of this omnidirectional wheel system will endow the soccer robot with advantages such as rapid and flexible movement, stable ball control, strong offensive capabilities, and ease of control, making it more competitive on the field.
1.1 Omnidirectional wheel
The robot uses omnidirectional wheels with smaller wheels evenly distributed around a large wheel. The large wheel is driven by a motor, while the smaller wheels can rotate freely. This type of omnidirectional wheel effectively avoids the non-holonomic constraints caused by the inability of ordinary wheels to laterally slide, giving the robot all three degrees of freedom for planar motion and enhancing its maneuverability. Based on the above analysis, this type of omnidirectional wheel was chosen.
1.2 Kinematic Analysis
Before establishing the robot's motion model, the following assumptions are made:
(1) The car moves on an ideal plane, and the irregularity of the ground can be ignored.
(2) The car is a rigid body and its deformation can be ignored.
(3) The wheel and the ground meet the condition of pure rolling, and there is no relative sliding.
The omnidirectional mobile robot is driven by four omnidirectional wheels, evenly distributed at 90° intervals, as shown in Figure 1. Here, xw-yw is the absolute coordinate system, and xm-ym is the relative coordinate system fixed to the robot body, with its origin coinciding with the robot's center. θ is the angle between xw and xm, δ is the angle between the wheel and ym, L is the distance from the robot's center to the wheel's center, and vi is the velocity of the i-th wheel along the driving direction.
Figure 1. Motion model of the robot
The kinematic equations can be derived as shown in equation (1):
Because the wheels are symmetrically distributed and the constant δ is 45°, the motion model of the omnidirectional mobile robot is obtained as follows:
V=Ps
Where v=[v1v2v3v4]T is the speed of the wheel, s= is the overall expected speed of the robot, and P is the transformation matrix.
In this way, the overall desired speed of the robot can be calculated into the speed of each of the four wheels, and the data can be transmitted to the controller to complete the control of the robot.
2 Design of a motion controller based on fuzzy PID
Currently, conventional PID controllers are widely used in the field of automation. However, conventional PID controllers do not have the function of online tuning of control parameters kp, ki, and kd, and cannot meet the self-tuning requirements of PID parameters for different deviations e and the rate of change of deviation ec. Therefore, they are not suitable for nonlinear system control.
This paper, based on the actual operating conditions of the motion control system, designs and adopts fuzzy PID control to achieve large-range error adjustment of the wheel speed of a fast-moving robot. By combining fuzzy control and PID control, a parametric fuzzy self-tuning PID algorithm is constructed for the control of the servo motor. This allows the controller to have both the advantages of fuzzy control (flexibility and adaptability) and the high precision of PID control. The motion control system thus takes into account the design requirements of high real-time performance, strong robustness, and stability. Furthermore, by expanding the fuzzy control rule base, other functions can be easily added to the motion control system.
2.1 Structure of Parameter Fuzzy Self-Tuning PID
The structure of the fuzzy PID control system is shown in Figure 2. The input of the system is the wheel speed given by the controller, and the feedback value is the digital value fed back by the photoelectric encoder of the motor. Δkp, Δki, and Δkd are correction parameters.
Figure 2 Adaptive Fuzzy Controller Structure
2.2 Fuzzification of Speed Control Input and Output Variables
The inputs to this speed controller are the deviation value e between the actual speed and the set speed , and the rate of change of the deviation value ec . The outputs are the correction values Δkp, Δki, and Δkd of the PID parameters, including their linguistic variables, basic universe of discourse, fuzzy subsets, fuzzy universe of discourse, and quantization factors.
After determining the linguistic variables and universe of discourse of fuzzy variables E and EC, as well as the output quantities ΔKP, ΔKI, and ΔKD, it is necessary to determine the membership degrees of the fuzzy linguistic variables. Commonly used membership functions include B-spline basis functions, Gaussian membership functions, and trigonometric membership functions. Considering the requirements of design simplicity and real-time performance, this paper adopts the trigonometric membership function.
2.3 Parameter Self-Tuning Rules
The core of fuzzy control design is to summarize the technical knowledge and practical experience of engineering designers, establish a suitable fuzzy rule table, and obtain fuzzy control tables tuned for the three parameters kp , ki , and kd respectively. Based on the respective roles of the three parameters kp , ki , and kd, fuzzy control rules can be formulated. Taking kp as an example, the rules are listed in Table 2 ; ki and kd can be derived similarly.
Fuzzy self-tuning of PID parameters involves finding the fuzzy relationship between the three PID parameters Kp, Ki, and Kd and e and ec . During operation , e and ec are continuously monitored, and the three parameters are tuned online based on the principle of fuzzy control .
Setting PID parameters relies on experience and familiarity with the process , referencing the measured value vs. setpoint curve to adjust the values of Kp, Ki, and Kd. Fuzzy control rules are used to correct the PID parameters; these rules are derived based on the process's step response. The rules are as follows:
(1) Pre-select a sufficiently short sampling period for the system to operate;
(2) Add only the proportional control loop until the system exhibits critical oscillation in response to a step input . Record the proportional gain and the critical oscillation period at this point.
(3) Modify the PID controller parameters according to the specific rules below until you are satisfied.
Based on the fuzzy control rules described above, the following PID parameter adjustment rules are adopted, as shown in Tables 1, 2, and 3.
Table 1 Kp Rule Adjustment Table
Table 2 KI Rule Adjustment Table
Table 3 KD Rule Adjustment Table
2.4 Output Defuzzification
After determining the output quantity according to the speed fuzzy control parameter tuning rules, what is obtained is only a fuzzy set. In practical applications, a precise quantity must be used to control the controlled object. The process of selecting the single value that best represents the fuzzy set is called the defuzzification decision.
Commonly used defuzzification algorithms include the maximum membership method and the weighted average method. Based on the actual situation, the weighted average method is used for defuzzification. The flowchart of the fuzzy PID control program is shown in Figure 3.
Figure 3 Flowchart of fuzzy PID control program
3 Experimental Results
To verify the effectiveness of the parametric fuzzy self-tuning PID controller, experiments were conducted on a DC motor using both conventional PID control and fuzzy PID control. The set wheel speed in the experiments was 50 r/min. Compared to the conventional PID control algorithm, the parametric fuzzy self-tuning PID algorithm significantly reduced overshoot, accelerated response speed, and improved the control system's performance in controlling wheel speed.
4. Conclusion
The robot motion control system is the actuator of the entire Robocup robot system, and its performance on the field directly affects the entire soccer robot system. This paper uses a soccer robot as a platform, and considering the system's time delay and nonlinearity, adopts a combination of fuzzy control and PID control. Experimental research on speed control was conducted on a self-developed soccer robot. The results show that this method overcomes the shortcomings of conventional PID control in robot motion speed control, such as large overshoot and long response time, and can achieve ideal results.
