# Trajectory Tracking Control of a Manipulator Based on an Adaptive Neuro-Fuzzy Inference System
## 1 Introduction  
In recent decades, with the rapid development of agriculture, more and more pieces of intelligent agricultural equipment has appeared. Among them, manipulators used for fruit picking and hedge trimming have become a hot research topic nowadays; they reduce labor costs and improve production accuracy and efficiency. The prerequisite for a manipulator to complete a task is that it can track the target trajectory more accurately. This paper takes trimming hedges as the task, designs an automatic manipulator and studies its trajectory tracking control method. At present, the driving modes of manipulators mainly include motor drive and hydraulic drive. Hydraulic drive is widely used in the industrial field because of its small size, large driving force, etc. However, due to the leakage of liquid and the existence of friction force, the system is highly nonlinear and extremely uncertain. In addition, when the manipulator performs tasks, there are also great uncertainties, such as the inaccuracy of sensors and the unpredictability of environment characteristics, etc. These make it difficult to establish an accurate mathematical model and bring huge challenges to its control; therefore, a reasonable control method is particularly important. [PERSON] et al. [1; 2] proposed an adaptive sliding mode control system to solve the problem of external parameter uncertainty in the manipulator. [PERSON] et al. [3; 4] evaluated the stability of the control system by using the Lyapunov theory, and proposed a nonlinear tracking control method based on the Lyapunov function. [PERSON] [5] established the dynamic model of hydraulic robot and adopted a fuzzy algorithm for control. [PERSON] et al. [6] designed a genetic algorithm based on matrix coding on the basis of fuzzy control to optimize fuzzy variables and improve the performance of the fuzzy controller. The PID controller has a simple algorithm, high reliability, fast response and low cost, so it is widely used in industrial control. However, for complex nonlinear and uncertain systems, its control precision is low. Usually, it is combined with other control methods. As a model of intelligent control, the fuzzy logic controller has a nonlinear linguistic mapping between the input and output and does not need an accurate mathematical model [7]. Therefore, many scholars combine PID control with fuzzy intelligent control. [PERSON] et al. [8; 9; 10; 11] put forward a FPID control strategy to control the manipulator and compared its performance with the conventional PID controller. The results proved that the FPID controller had higher control precision. This method, which uses the fuzzy logic algorithm to adjust the PID parameters, improves the precision of the system to a certain extent. However, the fuzzy controller relies too much on expert experience and lacks anti-interference ability. Once the fuzzy controller is determined, the fuzzy rules are also determined accordingly, so it is easy to fall into the local optimum, which reduces the adaptive ability [12]. An artificial neural network is a mathematical model that imitates the structure and function of a biological neural network. It can change the internal structure on the basis of external information and has strong adaptive and learning capabilities. [PERSON] et al. [13; 14; 15; 16; 17] applied the artificial neural network to the manipulator to solve the uncertainty and strong interference of the system and obtain a better control effect. However, as the artificial neural network is similar to a black box and lacks transparency; it cannot well express the inference function of the human brain. The fuzzy system has strong inference ability but lacks self-adaptive ability. Therefore, the ANFIS method was proposed by [PERSON] [18], which consists of a complete collaboration between the activities of a fuzzy system, developed by [PERSON], and a neural system.