Controller Design of Automatic Guided Vehicle for Path-Following Using Input-Output Feedback Linearization Method

In this paper, the controller design for path-following using input-output feedback linearization method for the automatic guided vehicle with uncertainties and external disturbances is proposed. The dynamic model of the system with uncertainties and external disturbances is presented. An auxiliary control input vector is designed using input-output linearization technique. The auxiliary control input vector transforms the overall system into two linearized subsystems of the position control subsystem and velocity control subsystem. Based on the two linearized subsystems, a new control law vector for path-following is designed. The new control input vector for path-following guarantees that the tracking errors vector converges exponentially to zero. In addition, a scheme of measuring the errors for experiment by a USB camera is also described. The simulation and experimental results are presented to illustrate effectiveness of the proposed controller.


I. INTRODUCTION
Generally, AGV have been used extensively in several industrial and service fields such as transportation, military, security, space, household, office automation and scientific laboratory systems. Recently, many research results of AGV have been implemented via feedback linearization. In most researches, AGV was considered as a mobile robot. The control problems of a mobile robot include trajectory tracking, to control the robot to follow a desired trajectory starting from a given initial configuration, and point stabilization, to drive a robot from a given initial point to target point. Point stabilization of mobile robot via statespace exact feedback linearization based on dynamic extension approach was proposed in [1]. The objective of this controller is to stabilize a mobile robot at a given target point in the polar coordinate. In [2,3], feedback linearization technique was also used for trajectory tracking and point stabilization of mobile robot systems.
All the above controllers show that they have a good performances and the tracking errors to go to zero in both case but consider only the kinematic model. Many control schemes have been proposed to deal with the mobile robot control problem including the mechanical system dynamic. In [4], Kalman-based active observer controller (AOB) was applied to the path IROORZLQJ ,W JXDUDQWHHV WKH RYHUDOO V\VWHP ¶V VWDELOLW\ even in the presence of uncertainries. The performance of the proposed control algorithm is verified via simulation results but consider only in discrete model. Jeon et al. [5] also proposed the feedback linearization controller based on dynamic model for lattice type welding with seam tracking sensor that shows a good results in simulation but did not consider uncertainties and external disturbances. Control of welding mobile robot or mobile robot for tracking trajectory considering uncertainties and external disturbances using sliding mode control with good tracking performance are presented in [6]- [9]. This paper proposed the path-following controller design method using input-output feedback linearization technique for the automatic guided vehicle with uncertainties and external disturbances. The dynamic model of the system with uncertainties and external disturbances is presented. An auxiliary control input vector is designed using input-output linearization technique. The auxiliary control input vector transforms the overall system into two linearized subsystems of the position control subsystem and velocity control subsystem. Based on the two linearized subsystems, a new control input vector for path-following is designed. The new control input vector for path-following guarantees that the tracking errors vector converges exponentially to zero. In addition, a scheme of measuring the errors for experiment by a USB camera is also described. The simulation and experimental results are presented to illustrate effectiveness of the proposed controller.  Fig. 1 shows configuration of the AGV. It consists of frame, two driving wheels, two passive casters, one rotation wheel, control system and USB camera etc. Fig.  2 shows the configuration for geometric model of the AGV. The two driving wheels are independently driven by two dc motors to achieve a desired motion and orientation. The two driving wheels have the same radius denoted by r and are separated by 2b . The center of mass of the AGV is located at C ; point P is the intersection of a straight line passing through the middle of the vehicle and an axis of the two driving wheels and is rotation center of AGV. The distance between the two points is denoted by d . The body length of the AGV is

Kinematic Modeling
Consider a robot mobile system having an n-dimensional configuration space with a generalized coordinate vector 1 nu • ƒ q and the robot is subjected to m independent constraints of the following form [4-[6]: is a full rank matrix associated with the nonholonomic constraints.
is defined to be a full rank matrix formed by a set of smooth and linearly independent vector fields, spanning the null space of . A(q) Thus, the result of multiplication of these matrices can be written as follows: A(q)S(q) = 0 (2) Supposing pure rolling conditions with no slip of the wheels, the following kinematics constraints ( 3) m can be written: and where the constant ( / 2 ) c r b .
From the constraint Eq. (1), q must be in the null space of . A(q) It where rw lw , where j O are Lagrange multipliers associated with th j Lagrangian is defined as: According to Eqs. (6), (9) and (11), the dynamic model is written as: is the centripetal and Coriolis forces matrix; •ƒ is the vector of constraint forces. It is assumed that the disturbance vector can be expressed as a multiplier of matrix M as follows [6]:

III. CONTROLLER DESIGN FOR PATH-FOLLWING USING INPUT-OUTPUT FEEDBACK LINEARIZATION METHOD
Consider the following MIMO (multi-input/multi-output) nonlinear system.
is the output vector. The objective of this part is to design a path-following controller that allows the AGV to follow a desired path in the Cartesian space starting from a given initial configuration with a desired linear velocity.
Let the output equation be represented by a vector y as follows: > @ > @  So the decoupling matrix d -for the above equations is given as follows: where the Jacobian matrices in Eq.
The necessary and sufficient condition for the system Eq.
(22) to be input-output linearized form and to be controllable is that the determinant of the following decoupling matrix Eq. (31) is not zero, det( ) 0 z d - [8]. where d -is singular if the 0 X axis is perpendicular to the straight line. From Eqs. (29)-(31), the decoupling matrix is used to establish the input-output feedback linearization as shown below, Assuming that the condition det( ) 0 z d -is satisfied and the transformation of state variables is a diffeomorphism, the auxiliary control input vector for achieving inputoutput linearization is given by where z is the vector of wheels velocities; 2 1 u • ƒ is defined as a new control input vector in the following form.
where a tracking error vector with the position and linear velocity errors is defined as follows: which are exponentially stable [9]. The path-following control scheme is presented in Fig. 3. In Fig. 3

Mesurement of tracking error using camera
To achieve the controller, the errors have to be detected. The reference path is a straight line as a desired trajectory marked on a floor. A camera is mounted in front of the AGV to capture directly an image of the tracking line. The errors detecting scheme is shown in Fig. 4.

Hardware and Control System
The configuration diagram of the total control system is shown in Fig. 5. The control system is based on the integration of notebook and PIC-based controller. The hardware of the system is composed of two-level control: the image processing control as high level computer control and the device control as low level microcontroller control. High-level image processing control algorithms are written in VC++ and run with a sampling time of 15 ms on the notebook (a Pentium IV-

International Journal of Advanced Engineering Research and Science (IJAERS)
[ Vol-4, Issue-10, Oct-2017]  https://dx.doi.org/10.22161/ijaers.4.10.25  ISSN: 2349-6495(P) | 2456-1908(O) www.ijaers.com Page | 162 2GHz processor). The notebook communicates with the PIC-based controller on the AGV through a COM port. For the operation, QuickCam SDK is used to capture the image stream into memory in bitmap format with size 320pixel u 240pixel via a USB camera at speed of 30 frames per seconds. The image is processed by VC++ program to extract the parameters of bounding box, center and direction of line. These parameters are used to determine oreintation angle and shortest distance as errors detecting scheme in Fig. 4. The input-output feedback linearization controller is designed to calculate the demand velocity of wheels. These demand torques are sent to the PIC-based controller to control the AGV motion. The tracked desired trajectory is shown on the computer interface of image processing in Visual C++ as shown in Fig. 6. The configuration of the PIC-based controllers for the low level control is shown in Fig. 7. It consists of PLFURFRQWUROOHUV 3,& ) ¶V ZKLFK DUH RSHUDWHG ZLWK the clock frequency 40MHz. The microcontroller performs three basis tasks: 1) communicating with the higher-level controller through RS232; 2) reading number of pulses from encoders; and 3) generating PWM duty cycle. The low level controller is composed of two parts: master controller and slave controller. The master controller functions as the low level control, that is, to receive demand velocities from the computer via RS232 and, in turn, to send the commands to the two slave controllers via I2C communication, respectively. The VODYH FRQWUROOHU LQWHJUDWHV WZR 3,& ) ¶V ZLWK WZR motor drivers LMD18200 for the DC motor control. The sampling time of low level control system is about 10ms. The experimental AGV developed for this paper is shown in Fig. 8. SIMULATION AND EXPERIMENTAL RESULTS To verify the effectiveness of the proposed controller, simulations have been done for a AGV following a straight line. Fig. 9  simulation and experiment are given in Table 1 and Table  2.  show the movement of the AGV along the desired trajectory for full time 40 seconds and the beginning time. As shown in Fig. 12, the tracking point a P of the AGV is able to reach the straight line path and stay on the path for full time. Fig. 13   linearization technique, two decoupled linearized SISO system are obtained: a second-order position model, and a first-order velocity model. A new control input vector is chosen to make the tracking error vector go exponentially to zero. To implement the proposed controller, a control system is developed based on PIC microcontroller and USB camera. The simulation and experimental results are presented to illustrate the good applicability to AGV of the proposed control algorithm.