Abstract: When robots perform tasks involving contact with the environment, such as assembly, spatial docking, and medical surgery, position control is required to achieve optimal operational performance. This paper introduces a robot position control system based on a fuzzy neural network. This paper combines fuzzy control with neural networks, utilizing the neural network to implement fuzzy inference, and applies it to the trajectory tracking control of a two-jointed robot. Simulation results show that this network has excellent performance in robot trajectory tracking control, making it an effective control method.
Keywords : fuzzy neural network, robot, position control
Intermediate Classification Number : TP 9 Document Identification Code: B
0 Introduction
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.
In recent decades, fuzzy systems based on fuzzy logic have become a very active field. Some algorithms have shown considerable capability in the design of controllers for complex systems, and fuzzy mathematics theory has also provided an extremely superior tool for constructing knowledge models.
Because neural networks possess excellent self-learning, self-adaptation, and associative intelligence, they can adapt to the complex and ever-changing dynamic characteristics of systems. The combination of fuzzy control and neural networks has become a key research focus. This research originated in Europe and America, but achieved significant development in Japan in the late 1980s. Currently, in the field of knowledge and information processing, it has reached a unique research stage, independent of fuzzy logic and neural network technologies. The integration of fuzzy and neural network technologies overcomes the shortcomings of neural networks and fuzzy logic in knowledge processing, possessing functions such as supervised learning, processing experiential knowledge, and online learning based on language expression. The nonlinear mapping and self-learning capabilities of neural networks are used to adjust fuzzy control, giving it a certain degree of adaptability while also enabling the neural network to acquire the reasoning and inductive capabilities of fuzzy control. This paper studies the application of fuzzy neural networks in robot control and proposes a fuzzy neural network-based robot trajectory tracking control. Simulation results show that this control method can effectively track the robot trajectory.
1. Establishment of Robot Control System
In this system, the stereo positioning system serves as the primary data input channel, accurately acquiring the precise relative position between the target location and the robot. This real-time spatial information is then integrated into the previously established spatial model. During this process, it is necessary to determine the transformation relationship between the previous model and the actual 3D space, i.e., registration.
Then, the robot performs motion operations according to the motion plan formulated by the computer-aided system. During the motion, the stereo positioning system continuously collects the spatial position of the robot relative to the target, and performs visual control in conjunction with the robot's multi-axis controller. The robot control system is shown in Figure 1. In the block diagram, the input is the feedback current of the robot's walking drive servo motor, and the output is the robot's walking speed, which is achieved by servo speed regulation.
Figure 1 Robot Control System
This paper designs a six-degree-of-freedom (DOF) robot: three rotational and three translational. The robot's six DEFs work together to complete spatial motion. Considering the robot's small size, the goal is to minimize weight. This necessitates limiting the overall load on the mechanism due to reduced stiffness, while also considering stability during high-speed motion. Furthermore, the stiffness design of this multi-DOF mechanism depends on the speed and direction of motion.
2. Fuzzy Neural Network
2.1 Control System Structure
The control system structure is constructed by combining the robot positioning system, as shown in Figure 2, with the robot position as the controlled variable.
Figure 2. Fuzzy Neural PID Control Structure Diagram
In the figure, e and ec represent the error and the rate of change of error, respectively. The input r is the robot position, and the output y is the actual output of the robot.
2.2 Structure of Fuzzy Neural Networks
The fuzzy neural network has four layers, as shown in Figure 3. Layer 1 is the input layer; layer 2 is the fuzzification layer; layer 3 is the fuzzy inference layer; and layer 4 is the output layer. The fuzzy neural network structure is 2–6–6–3.
Figure 3. Structure of a fuzzy RBF neural network
(l) Input Layer. This layer takes the input error e and the actual system output y(k) as inputs to the next layer. The activation function is:
Therefore, the outputs of this layer are e and y(k).
(2) Blurring layer. The activation function is the membership function. Therefore, the output is:
Where i = 1, 2; j = 1, 2, ..., 6. cij and bij are the mean and standard deviation of the membership functions of the j-th fuzzy set of the i-th input variable of the Gaussian function, respectively.
(3) Fuzzy Inference Layer. The output value of this layer is obtained by multiplying the fuzzy quantities in the upper layer pairwise. Therefore, the activation function of this layer, i.e., the output, is:
Here, k = 1, 2, 3, 4, 5, 6.
(4) Output Layer. This layer outputs the parameters of the PID controller. The output value of this layer is the weights multiplied by the output of the third layer using a matrix multiplication method. Therefore, the output of this layer is:
The control quantity of incremental PID control is
The objective function is:
Where r(k) is the desired output.
2.3 Robust Controller
To ensure the stability and good control performance of the closed-loop system, the real-time controller consists of a fuzzy neural network controller (NNC) and a robust controller (RC). The output signals of these two controllers are weighted and synthesized, and then used as the control input of the system [8-10], forming a variable robust controller u(k):
In the formula: un(k) is the output of the NNC; ur(k) is the output of the robust controller; γ is the identification accuracy of the system model NNI, called the robustness factor. γ is expressed as:
(4)
In the formula: τ is the variable robustness coefficient of the robustness factor; Em is the square of the difference between the NNI output and the actual system output.
3 System Simulation Research
To verify the effectiveness of the proposed fuzzy neural network control algorithm, a fuzzy neural network was created in MATLAB. The abstract fuzzy rules were transformed into training samples for the fuzzy neural network using membership functions and fuzzy rules. The hidden layer used the Tansig function, which is differentiable at any point, as the transfer function, and the output layer used the commonly used non-negative Sigmoid function.
The response curves of the system to a step signal are shown in Figure 3 when conventional PID control and fuzzy neural network control are used. Figure 3 shows the error response curves of the conventional PID controller and the fuzzy neural network controller for tracking a sinusoidal signal. By comparison, it can be seen that the fuzzy neural network controller is significantly better than the conventional PID controller in terms of dynamic performance, and can reduce the sinusoidal response error from 0.02 rad to 0.001 rad.
(a) PID control (b) Fuzzy neural network control
Figure 3. System sinusoidal error response curve
4. Conclusion
This paper combines fuzzy control with neural networks to design a robot position control system based on fuzzy neural networks, and applies it to a robot trajectory tracking control system. Simulation results show that the control system can effectively overcome the influence of nonlinearity and coupling in robot systems, making it a good control method.
