Research on unmanned navigation and PID control method for aircraft tractor

Unmanned navigation and control systems are gaining traction in various industries, including aviation. The related issues of control systems are also hot topics in research. This paper comprehensively studies the application of unmanned navigation and the implementation of proportional integral differential (PID) control methods for aircraft tractors. Aiming at the characteristics of large deviation of turning trajectory angle error and long lag time in the process of an unmanned tractor, the dynamic characteristics and state equation of the unmanned tractor are established by the PID method, and the motion equation is established by the Cartesian coordinate system. Finally, the simulation results show that the proposed method has good dynamic stability and rapidity. Compared with proportional control or integral control alone, the PID control system has better stability and a faster frequency response, which can be obtained that the PID control algorithm can effectively improve the work efficiency of the unmanned tractor and reduce its instability and slow response.


Introduction
Aircraft often need to move within the confines of hangars, covered bridges, aprons and maintenance workshops when stopped, and this process is usually completed by manually operated aircraft tractors.The efficiency and safety of aircraft traction processes depend on the operator's operating experience and proficiency, and repeated position adjustment leads to cumbersome operation process and low work efficiency of aircraft tractors.It is urgent to effectively improve the accuracy and work efficiency of tractor movement.Today's driverless technology can better meet the general requirements for vehicle control.Driverless technology can reduce human error to enhance vehicle safety, get smoother driving modes, and improve route planning to improve efficiency [1][2][3].The aircraft tractor uses the clamping lifting device to lift the front wheel of the aircraft, relying on the gravity of the body and the front wheel part of the aircraft to bear the adhesion of the ground [4][5].At present, car driverless technology mainly adopts GPS navigation and inertial navigation combined navigation technology [6][7].PID control has been widely used in the field of trajectory tracking, and its advantages are its simple structure, small calculation amount, and control parameters can be obtained by trial.Nowadays, there are two main types of aircraft tractors, namely rodless tractors and rodless tractors.The difference is that the rodless tractor directly uses the wheel holding mechanism to pick up the aircraft front landing gear tyres, resulting in fast speed, large traction, high work efficiency, etc., but the stability of the operation is not as good as that of the rod tractor [8].Tractors are usually towable by the driver or handheld remote control devices, which depends on the operator's proficiency and experience.Therefore, unmanned technology has been focusing on it.Compared with traditional tractors, unmanned tractors can effectively reduce the wear caused by operator errors, improve the efficiency of airports, and add a PID control system to the navigation control system of unmanned tractors, which can well reduce the error of the angle of the turning trajectory, thereby improving the work efficiency of unmanned tractors.In this paper, the PID control method is used to establish the PID control model of the unmanned aircraft tractor; the current position of the vehicle is obtained according to GPS and inertial sensors; the interpolation calculation is calculated between the reference point and the deflection angle; and the PWM wave is output to control the vehicle.Matlab was used to simulate and verify whether the theory proposed in this paper could be applied.

Literature review
Gour Karmakar used two models using DNN deep learning algorithms to measure the trust level of driverless cars, and experiments showed that the model they built can evaluate confidence scores well [9]; Li Jing et al. use the blockchain technology system to reasonably plan the route of the tractor, and the experiment also shows that the addition of the blockchain system is to reduce the frequency and intensity of daily supervision from the theory, so that hidden dangers are controlled first [10]; Wang yin et al. based on GPS/BDS positioning system, using lateral deviation path tracking algorithm and PID control method composite navigation control algorithm, designed an unmanned navigation control system for agricultural tractors, and experiments also show that the system has good lateral error control accuracy [11].Liu et al., combined with the nonlinear characteristics of rodless tractor-aircraft and obstacle avoidance considerations, adopted offline path planning and online trajectory tracking, which better realized the unmanned simulation of aircraft tractor in the deck scene, but the scope used for obstacle avoidance was too large compared with the aircraft and tractor system, which may lead to greater redundancy in the planned path [12].These studies have achieved important theoretical results, which provide a profound theoretical and applied foundation for the research of this paper.The innovation of this paper lies in how to use PID control to improve the steering accuracy of unmanned tractors, thereby reducing their lateral errors.Where the parameter r(t) is the input quantity given by the system, y(t) is the actual output of the system, e(t) is the difference between the actual output and input of the system, and u(t) is the control output parameter after proportional, integral, and differential operations on the difference.Its calculation formula is:

Method
In the formal:   is a scale factor;   is an integration time constant;   is a differential time constant.

GPS and inertial combined navigation system design.
GPS has a positioning function with high positioning accuracy; accuracy will not change with the change of positioning time.While inertial navigation systems can provide extremely accurate motion displacement, a more accurate positioning function cannot be achieved.A combination of GPS and inertial navigation systems can work effectively.The input parameters and deviation calculation of this system are mainly used to calculate the deflection angle of the servo.In the combined application process with GPS as the main system and the position of the point in the coordinate system as input and detection parameters, the inertial navigation system plays an auxiliary role.When combined with the application, it can effectively improve the ability to track satellites, ensure dynamic performance, and provide anti-interference to further improve the accuracy of navigation and positioning.The block diagram of the control system for an unmanned tractor is shown in Figure 2.

Aircraft tractor kinematic modeling.
According to the motion characteristics of the tractor, based on the steering of the traction system, the numerical modelling analysis of the kinematics of the whole vehicle is done.Establish the Cartesian coordinate system xoy, define the rear axle center M1 of the tractor, the center M2 of the rear axle of the aircraft, the heading angle  of the tractor under the steering, the angle  formed between the aircraft and the tractor, the rotation angle of the aircraft under the steering of the aircraft, the declination angle of the universal front wheel declination of the tractor , the drive wheel base L of the tractor, the wheelbase of the aircraft d1, and the wheelbase of the tractor d2, as shown in Figure 3.
In this equation, x, y is the coordinate of the center M1 of the rear axle of the tractor, and v is the speed of the center of the rear axle of the tractor M1.
is a angular speed of vehicle steering: From  and vehicle speed v, the steering radius R and the deflection angle of the front wheels can be obtained :

Analysis of simulation experiment results
The realization of PID control in aircraft tractor navigation is divided into four steps: 1.Through the sensor data collection of vehicle navigation, the data of the GPS and inertial test unit is uploaded to the system to obtain the real-time position of the aircraft and tractor; 2. Error calculation: this step is used to compare the current position and direction of the tractor to calculate the error so as to reduce it.3.
Adjust the PID control system to adjust the PID gain to the best.4. Finally, the calculated data will be output to accurately navigate the tractor.
When the vehicle is driving in a straight line, the equilibrium point attachment gives the vehicle an initial rotation signal, the deflection angle is 1rad, and the PID controller parameters are tuned by the optimal PID parameter setting method, it can be well observed that when the gain is increased, the faster the step response, the value is   = 1.46,   = 0.151, and the corresponding of the system can be simulated, as shown in Figure 4.     Figure 5, Figure 6, and Figure 7 are representative gain values, and the gain values are 3, 20, and 30, respectively.Figure 8 is a linear plot composed of overshoot points with a gain of 3 to 30.It can be seen that the greater the gain, the faster the frequency response, and the larger the overshoot.Then, combined with the previous Figures 4, 5, 6, and 7, it is found that these overshoots will not have a great impact on the PID control system, and these overshoots can be controlled by modifying the size of   .Compared with proportional control or integral control alone, the PID control system has better stability and a faster frequency response, which can be obtained that the PID control algorithm can effectively improve the work efficiency of the unmanned tractor and reduce its instability and slow response.

Discussion
The method used in this paper is a relatively simple PID control theory, and the selected data is not comprehensive enough, but the basic principle of PID control systems shows that the theory is valid.There are better options in terms of path and algorithm, such as using a combination of the lateral deviation path algorithm and the PID control method or the MPC algorithm to design a track tracking controller.Both algorithms can be combined with PID control methods and have been well experimented with in other papers.Fuzzy PID algorithms can also be added to PID control, which can make the system's judgement more humane.

Conclusion
The application of PID control in the navigation and control system of aircraft tractor greatly improves the accuracy, stability and safety of the ground operation.Adding unmanned technology to aircraft tractors can not only improve the overall safety of the airport but also greatly improve the overall efficiency of the airport.Unmanned technology is an important project now and in the future, and the development of these technologies into the aviation industry in advance can raise the aviation industry to a new level.
3.1.Experiment preparation3.1.1.PID control theory.The PID control algorithm is based on three control terms: proportional (P), integral (I), and differential (D).The ratio term provides an output proportional to the current error between the desired position and the actual position.The integral term considers the sum of past errors to eliminate steady-state errors and takes into account errors accumulated over time.Derivative terms predict future errors based on the rate of change of the current error, helping to improve the stability and responsiveness of the system(Figure1).

Figure 1 .
Figure 1.Schematic Diagram of PID Control System.

Figure 3 .
Figure 3. Schematic Diagram of vehicle motion modeling.