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Abstract：When the AGV affected by external uncertainties under the prescribed path.， it will deviates from the specified path.In order to make the AGV run toward the established path in the process of operation，we establish the kinematics model of the AGV to analyze the relationship between the deviation and speed，to calculate the relationship between the deviation and output voltage of the motor.Through the kinematic analysis of the AGV and the establishment of state equation，it provides the theoretical basis for the design of the controller.
Key words：AGV； Kinematic mode；Deviation；State equation
1 Introduction
With the advancement of science and technology， AGV （Automated Guided Vehicle） has been widely used in industry， agriculture， logistics and military fields[1]. The industrial AGV operation environment is complex and diverse.In order to complete the task ，the motion control technology has become the key research techniques of the AGV path planning and path tracking[2]. AGV is a kind of strongly coupled， time-varying and highly nonlinear complex system. It is easy to be interfered by many nonlinear and uncertain factors in the course of operation[3].In order to understand the AGV motion model，we establish the kinematics model of the AGV to analyze the relationship between the deviation and speed，to calculate the relationship between the deviation and output voltage of the motor.
2 Kinematic Analysis of AGV
In this paper ，we choose the four-wheel AGV as the research object. The front two wheels of the AGV are free wheels， and the latter two wheels are driven wheels independently. The change of the motion state is mainly achieved by adjusting the wheel speed of the left-right drive wheels. Therefore， without affecting the kinematic analysis，the motion model can be reduced to the motion of the left and right drive wheels[4]. As shown in Fig 1.
According to the simplified model，the coordinate system is established.In the figure，is the plane coordinate system， O1 and O2 are the center of the left and right drive wheels respectively，and O3 is the instantaneous center of the body when it moves. O1O2 is the shaft spacing of two-wheel， and the length is D. Vl、Vr、Vo are the speed. R is the instantaneous radius. α is the angle between the running direction and the-axis. Assuming that ω is the instantaneous angular velocity.
Fig.1 The kinematic model of left and right driving wheel difference steering According to kinematic analysis：
The instantaneous angular velocity ω and instantaneous steering radius R can be obtained：
（1）
By changing the relationship between Vl and Vr ，it can realize the change of the motion mode of the AGV.
After a short p time △t， the center of the vehicle moves to the state as showing in Fig1. Assume that the deviation distance in the movement direction isand the angle deviation is β.After a short time △t， the angle between the movement direction and the x-axis is γ.
Angular deviation and positional deviation of the AGV are related to the left and right drive wheel speeds in the motion state.
（2）
In the course of exercise， β amount is generally small， so when deal with the formula （2） in the way of sinβ≈β， we can get the simplified formula：
（3）
In order to accurately describe the relationship between the left-right wheel driving speed and angular deviation or position deviation，the motion error equation is combined with the voltage transfer function of the drive system to establish the dynamic response equation of the system[5].
The drive system uses the same two permanent magnet DC motor. Through the MATLAB toolbox， the high-order system can be changed into the low-order system.The relationship between the speed， voltage and transfer function of the drive motor is as follows
（4）
In formula：K is a constant； U is the armature voltage； Tm is the time constant of the motor.
When the AGV moves out of the predetermined travel path under the outside interference during the process of driving， the control system receives the voltage signal with deviation distance feedback and changes the armature voltage at both ends of the motor to adjust the left and right driving wheel rotation speed， and corrects the position deviation of the AGV and angle deviation. Without changing the speed of the vehicle body，the mathematical relationship between voltage increment and speed increment are shown as follows：
（5）
It can be seen through the transfer function that we can change the voltage to control the speed of the left and right drive wheel，then achieve the purpose of differential steering and correction.The relation between voltage increment and running deviation are shown in Fig2.
Fig.2 The schematic diagram of voltage increment
and velocity deviation and position deviation
Making：
So x=（△t，β，L） is the variable state； △U is the input； L is the distance deviation； β is the angle deviation and the output. The equation of state is as follows： （6）
（7）
3 Conclusions
By establishing the equation of state of the whole control system， it can be seen that the position deviation and angular deviation of the AGVhave a complex nonlinear relationship with the AGV trajectory.At the same time， the relationship between the input voltage and the angle deviation or the position deviation can be clearly displayed from the state equation， which provides the theoretical basis for the design of the controller.
References
[1] Zhao Chen-yu，Chen Xi-kun. Study on Fuzzy control of an agricultural dedicated AGV with differential steering[J]. Journal of Agricultural Mechanization Research.2016（11）：123-125.
[2] Liao Hua-li，Zhou xiang，Dong feng et al. AGV navigation algorithm based on Fuzzy control[J]. Journal of Harbin Institute of Technology. 2005（7）：896-898.
[3] Ren Ke-yan，Gu xi-sheng. Deviation-correcting control of AGV based on Fuzzy PID[J]. Control Engineering of China. 2006（s2）：54-57.
[4] Qing chuang.Design and simulation research of AGV control system based on DSP[D].Haerbin：Harbin Institute of Technology，2014.
[5] Liu jing-ling.Research on AGV path tracking control[D]. Jiangxi：：Jiangxi University of Science and Technology，2015.
Corresponding author： Luo Weiping（1967-）， female， professor. Disciplinary direction for the detection technology and intelligent control， signal and information processing， research areas for digital textile equipment. E-mail：l_wp1@163.com.
The first author： Long Bin（1988-）， male， master. Research direction for the mechanical and electrical control and automation technology. E-mail：604918583@qq.com
Key words：AGV； Kinematic mode；Deviation；State equation
1 Introduction
With the advancement of science and technology， AGV （Automated Guided Vehicle） has been widely used in industry， agriculture， logistics and military fields[1]. The industrial AGV operation environment is complex and diverse.In order to complete the task ，the motion control technology has become the key research techniques of the AGV path planning and path tracking[2]. AGV is a kind of strongly coupled， time-varying and highly nonlinear complex system. It is easy to be interfered by many nonlinear and uncertain factors in the course of operation[3].In order to understand the AGV motion model，we establish the kinematics model of the AGV to analyze the relationship between the deviation and speed，to calculate the relationship between the deviation and output voltage of the motor.
2 Kinematic Analysis of AGV
In this paper ，we choose the four-wheel AGV as the research object. The front two wheels of the AGV are free wheels， and the latter two wheels are driven wheels independently. The change of the motion state is mainly achieved by adjusting the wheel speed of the left-right drive wheels. Therefore， without affecting the kinematic analysis，the motion model can be reduced to the motion of the left and right drive wheels[4]. As shown in Fig 1.
According to the simplified model，the coordinate system is established.In the figure，is the plane coordinate system， O1 and O2 are the center of the left and right drive wheels respectively，and O3 is the instantaneous center of the body when it moves. O1O2 is the shaft spacing of two-wheel， and the length is D. Vl、Vr、Vo are the speed. R is the instantaneous radius. α is the angle between the running direction and the-axis. Assuming that ω is the instantaneous angular velocity.
Fig.1 The kinematic model of left and right driving wheel difference steering According to kinematic analysis：
The instantaneous angular velocity ω and instantaneous steering radius R can be obtained：
（1）
By changing the relationship between Vl and Vr ，it can realize the change of the motion mode of the AGV.
After a short p time △t， the center of the vehicle moves to the state as showing in Fig1. Assume that the deviation distance in the movement direction isand the angle deviation is β.After a short time △t， the angle between the movement direction and the x-axis is γ.
Angular deviation and positional deviation of the AGV are related to the left and right drive wheel speeds in the motion state.
（2）
In the course of exercise， β amount is generally small， so when deal with the formula （2） in the way of sinβ≈β， we can get the simplified formula：
（3）
In order to accurately describe the relationship between the left-right wheel driving speed and angular deviation or position deviation，the motion error equation is combined with the voltage transfer function of the drive system to establish the dynamic response equation of the system[5].
The drive system uses the same two permanent magnet DC motor. Through the MATLAB toolbox， the high-order system can be changed into the low-order system.The relationship between the speed， voltage and transfer function of the drive motor is as follows
（4）
In formula：K is a constant； U is the armature voltage； Tm is the time constant of the motor.
When the AGV moves out of the predetermined travel path under the outside interference during the process of driving， the control system receives the voltage signal with deviation distance feedback and changes the armature voltage at both ends of the motor to adjust the left and right driving wheel rotation speed， and corrects the position deviation of the AGV and angle deviation. Without changing the speed of the vehicle body，the mathematical relationship between voltage increment and speed increment are shown as follows：
（5）
It can be seen through the transfer function that we can change the voltage to control the speed of the left and right drive wheel，then achieve the purpose of differential steering and correction.The relation between voltage increment and running deviation are shown in Fig2.
Fig.2 The schematic diagram of voltage increment
and velocity deviation and position deviation
Making：
So x=（△t，β，L） is the variable state； △U is the input； L is the distance deviation； β is the angle deviation and the output. The equation of state is as follows： （6）
（7）
3 Conclusions
By establishing the equation of state of the whole control system， it can be seen that the position deviation and angular deviation of the AGVhave a complex nonlinear relationship with the AGV trajectory.At the same time， the relationship between the input voltage and the angle deviation or the position deviation can be clearly displayed from the state equation， which provides the theoretical basis for the design of the controller.
References
[1] Zhao Chen-yu，Chen Xi-kun. Study on Fuzzy control of an agricultural dedicated AGV with differential steering[J]. Journal of Agricultural Mechanization Research.2016（11）：123-125.
[2] Liao Hua-li，Zhou xiang，Dong feng et al. AGV navigation algorithm based on Fuzzy control[J]. Journal of Harbin Institute of Technology. 2005（7）：896-898.
[3] Ren Ke-yan，Gu xi-sheng. Deviation-correcting control of AGV based on Fuzzy PID[J]. Control Engineering of China. 2006（s2）：54-57.
[4] Qing chuang.Design and simulation research of AGV control system based on DSP[D].Haerbin：Harbin Institute of Technology，2014.
[5] Liu jing-ling.Research on AGV path tracking control[D]. Jiangxi：：Jiangxi University of Science and Technology，2015.
Corresponding author： Luo Weiping（1967-）， female， professor. Disciplinary direction for the detection technology and intelligent control， signal and information processing， research areas for digital textile equipment. E-mail：l_wp1@163.com.
The first author： Long Bin（1988-）， male， master. Research direction for the mechanical and electrical control and automation technology. E-mail：604918583@qq.com