Design and Implementation of Welding Mobile Robot Using a Proposed Control Scheme Based On Its Developed Dynamic Modeling for Tracking Desired Welding Trajectory

This paper presents a proposed control scheme that makes the combination of a kinematic controller (KC) and an integral sliding mode controller (ISMC) for a welding mobile robot (WMR) to track a desired welding path. First, a posture tracking error vector is defined and a kinematic controller is designed based on kinematic modeling to make the tracking error vector go to zero asymptotically. Second, a sliding surface vector is defined based on the velocity tracking error vector and its integral term. And then, an integral sliding mode dynamic controller is designed based on developed dynamic modeling to make velocity tracking error vector also go to zero asymptotically. The above controllers are obtained by backstepping method. The stability of system is proved based on the Lyapunov stability theory. To implement the designed tracking controller, a control system is developed based on DSP F28355 and ATmega328. A scheme for measuring the posture tracking error vector using torch sensor is presented. The simulation and experiment results are shown to illustrate effectiveness and the applicability to the welding industry field of the proposed controller.

To solve the problem of trajectory tracking of welding mobile robot, this research presents a proposed control scheme that makes the combination of a kinematic controller (KC) based on the kinematic modeling and an integral sliding mode dynamic controller (ISMC) based on the developed dynamic modeling considering at voltage level for the WMR to track a desired welding trajectory at a desired velocity. The above controllers are obtained by backstepping method. The system stability is proved using the Lyapunov stability theory. To implement the designed tracking controller, a control system is developed based on DSP F28355 and ATmega328. A scheme for measuring the posture tracking error vector using torch sensor is presented. The simulation and experiment results are shown to illustrate effectiveness of the proposed nonlinear controller.

II.
SYSTEM DESCRIPTION AND MODELING In this section, the system description, dc servo motor modeling, the kinematic and dynamic models of a welding mobile robot (WMR) are presented. Fig. 1 shows the 3D configuration of a welding mobile robot (WMR) used in this research in three sides. It consists of platform, two wheels, DC servo motors and encoders, welding torch, power supply and a electronic control system, etc. Fig. 2 shows the 2D configuration for geometric model of the WMR. For simplifying the modeling of WMR, the assumptions are given as follows [10][11][12][13][14]:

System description
(1) Kinematic's parameters such as wheel's radius r and distance b are known exactly.
(2) Moment of inertia of WMR is constant during welding process. (3) A disturbance vector exerted on the WMR consists of surface friction and slip phenomenon bewteen wheel and the ground. (4) Motion surface is a smooth horizontal plane. (5) The WMR has two driving wheels for flatform motion, and those are positioned on an axis passed through the WMR geometric center, (6) Two passive wheel which have zero constraint are installed in front and rear of the flatform at the bottom for balance of WMR. So their motion can be ignored in the kinematic and dynamic models. A welding torch is located to coincide the axis through the center of the two driving wheels. The radius of welding curve is sufficiently larger than turning radius of the WMR.

DC Servo Motor Modeling
This section presents the modelingof DC servo motor [9]. Schematic of the the DC servo motor plus wheel is shown in Fig. 3.
The relation between m Torque of DC servo motor is given by ki ta The kinematic equations for the center point of the WMR are set up as the following: is the actual velocity vector.
The relationship between , v  and the angular velocities of right wheel rw  and left wheel lw  is given by In where l is assumed to be constant.

Developed Dynamic Modeling
In Fig. 2, using the references from [10] to [14], the developed dynamic equations of the WMR considering at DC Servo motor voltage level is rewrited as follows: Because torch length l is controllable based on the torch slider. The first derivative of e yields First, the kinematic controller is designed as follows (  )  cos  3 3  3  1 1 33 15) and the length of torch satisfies ,, C C C is a positive values. Second, the developed dynamic controller with voltage control input vector for DC servo motors is designed as follows: The velocity error vector v e is defined as The sliding surface vector S v is defined as Where v K is a positive diagonal matrix and is an integral sliding surface vector.
Third, the auxilary control law The Lyapunov function candidate is defined as follows: where the conponents of the V function are chosen as: With the velocity control input Eq. (15), the 1 V becomes The derivative of S v in Eq. (19) is as the following In other hand, from Eqs. (11) and (17) Subtituting Eq. (28) into the first derivative of 2 V in Eq.

Mesurement of tracking error using tourch
sensor In order to measure the tracking errors, a mechanical measurement scheme using potentiometers is shown in Fig. 5 [9]. Two rollers are placed at points O2 and O3. Two sensors for measuring the errors are needed. That is, they are one linear potentiometer sensor for measuring ds and one rotating potentiometer sensor for measuring the angle between the torch and the tangent line of the wall at the welding point.

International Journal of Advanced Engineering Research and Science (IJAERS)
[ Vol-4, Issue-10, Oct-2017]  https://dx.doi.org/10.22161/ijaers.4.10.13  ISSN: 2349-6495(P) | 2456-1908(O) www.ijaers.com Page | 77 where O2 and O3 are the center points of roller O2 and O3 respectively, O1 is the center point of O2O3, W is the point on torch holder, rs is the radius of the roller, ds is the length measured by the linear potentiometer, and e3 is the angle measured by the rotating potentiometer. In Figure 5, the reference welding path is a line. When the reference welding path is a curve, Eq. (30) is also valid if the distance O2O3 is sufficiently small and the radius of the welding path is enough large. Fig. 6 shows the control system configuration of welding mobile robot. The control system is based on the integration of microcontroller DSP F28335 and ATmega328. The microcontroller ATmega328 are used for two DC servo motor control signal of left wheel and right wheel and torch slider controller. The microcontroller DSP F28335 is used for main controller. The three servo controllers are controlled by main controller. The main controller functionalized as master links to the three servo controllers via I2C communication.

Slave unit 3 ATmega328
Servo controller of wheel 1 Servo controller of wheel 2 Servo controller of torch slider The two A/D ports of the DSP F28355 are connected with the two potentiometers for sensing the tracking errors. The master unit send the commands to the slave controllers via I2C communication,respectively. The master unit can be used to interface other devices such as display and keypad devices for manual control. The sampling time of control system is 10ms. The slave unit integrates ATmega328 with motor drivers for the DC servo motor control. This slave controller can perform a complete servo operation with a closed loop feedback control using an encoder for velocity control of two wheels and position of welding torch. The experimental welding mobile robot is shown in Fig. 7 and its dimensions are shown in Table 3. Fig. 8    The simulation results for tracking welding path are shown in Figs. 9 to 17. Fig.s 9 and 10 show the movement of the WMR along the desired welding trajectory for the time beginning and full time 4000 seconds. The simulation results for error tracking vector during 5 seconds at beginning and 4000 secconds of full time are shown in Fig.s 11 and 12. The errors go to zero from 3 seconds. The linear velocity of welding point is shown in Fig. 13; its is shown that the linear velocity at the welding point W of the WMR has quick change at the first time and converges to the constant velocity in the vicinity of 7.5 / mm s as desired after 1 seccond.  Fig. 16 shows the linear velocity and torch length of WMR. It goes from 145 mm at initial time to 163.3mm after about 3 seconds and keeps the that value for remain time. Fig. 17 shows that the control input voltage vector u changes rapidly at the start time converges to small values from 0.3 second for the full time. Figs. 18 and 19 show the welding process of welding mobile robot and experimental welding line result respectively. The simulation and experimental results are shown that the WMR has good welding path tracking performance. It is so that the welding mobile robot can be applied in the practical welding industry field. VI. CONCLUSION This paper presents the proposed control scheme that makes the combination of a kinematic controller (KC) and an integral sliding mode dynamic controller (ISMC) based on the developed dynamic modeling for the welding mobile robot to track a desired welding trajectory at a desired velocity under external disturbances. The control laws are obtained by backstepping method. The system stability is proved based on Lyapunov theory. The control law stabilizes the sliding surface vector and makes the tracking error vector go to zero asymptotically. To implement the designed tracking controller, the control system is developed based on DSP F28355 and ATmega328. A scheme for measuring the posture tracking error vector using torch sensor is presented. The simulation and experiment results are shown to illustrate effectiveness and the applicability to the welding industry field of the proposed controller.