Controlling and modeling of an automated guided vehicle Daniel Antal, Ph.D. student Robert Bosch department of mechatronics University of Miskolc Miskolc, Hungary antal.daniel@uni-miskolc.hu Tamás Szabó, Ph.D. Associate Professor Robert Bosch department of mechatronics University of Miskolc Miskolc, Hungary szabo.tamas@uni-miskolc.hu Abstract In this paper the designing aspects of a path controlled three wheeler vehicle is discussed. Two of the three wheels are driven independently by DC motors. Incremental encoders are used to give feedbacks. The position of the vehicle is calculated by kinematical model assuming ideal rolling of the driven wheels. PWM signals are used to drive the motors with a given angular velocity. The separate driving electronic is controlled via I 2 C protocol. A comparison is made between the real and the calculated positions of the vehicle. Keywords-path control; automated guided vehicle, I. INTRODUCTION In logistics automated guided vehicles are used for decades. These machines are operating without any human intervention. The area of operation is static in general, hence the path can be marked with permanent methods, e.g. inductive loop, optical marks etc. Cameras and radio transmitters can also be used to verify positions because it is necessary to follow the path properly due to the lack of space. The advantage of these methods is the exact and fast execution. The disadvantage is the fixed predefined path, which is hard to modify time to time. In an open area, where the given path should not be strictly followed, simpler and cheaper methods can be used. This paper presents a method, in which the path is prescribed by polygon, and the corner points are the inputs for the control program. II. ORIENTATION AND LOCATION DETERMINING METHODS According to the introduction, guiding on a flexible path requires a position and orientation sensing methods, whereby the moving of the vehicle is controlled. These methods are based on different types of sensors, which provide feedbacks for the calculations. The orientation and position sensing methods can be divided into three groups [4], odometric method is based on step counting and is carried out by summarizing the relative motion information, absolute method is based on distance measuring from objects at known positions and other methods. The odometric distance measuring gives indirect information about the movement [2], which can be: A. Rotary encoder Rotary encoders can be divided into an absolute or an incremental one depending on the specific construction. The two methods can be distinguished by the applied rotating disc and the assigned signal processing. These encoders are mounted on the shaft. Using an incremental encoder with large resolution can give an adequate result. B. Measuring the revolution in the drivetrain Measuring can be performed with sensing the revolution of the motor in the drive train with optical, inductive, capacitive or hall sensor. Magnets can be easily applied on the side of the gears, in case of using hall-sensors, also the teeth of the gears can be detected by using different sensors. C. Independent movement measurement Motor independent movement sensing system can be realized with a measuring wheel or a measuring ball, e.g., mechanical computer mouse. The odometric distance measuring methods are having regular and irregular errors. The measuring error is incremental so the calculated position should be refined regularly by absolute distance measuring methods. During absolute distance measuring the position is calculated by known position objects called marker points. These points can be active or passive, and natural or artificial depending on the construction. Absolute distance measuring methods [3]: D. Optical marker technique. Setting or using visually distinguishable points in the area. E. Radio principle positioning system. One need to set up a radio based local positioning system or can utilize an existing system, e.g., GPS (Global Positioning System).
F. Laser and ultrasonic technique. Instruments based on triangulation method are using the beam to set the direction. Instruments based on phase modulation or radar principle are using the beam as an electromagnetic wave to determine the distance between the measuring equipment and the signal point. Comparing the odometric distance measuring, to the absolute distance measuring one can state that the later has only a regular error which is constant. However, the absolute technique is a time consuming or expensive method, so it can be only used rarely. It means that the less expensive odometric position determination can be refined by an expensive one time to time. There are also other location and orientation determining methods, e.g., Doppler sensor or a system provided by accelerometers, gyroscopes or their combinations. III. DESIGNING ASPECTS In this part of the paper the designing of a path controlled vehicle will be shown. The main goal of the designing is to realize a vehicle which can be used to reach specific points in an area. During marking the points, one needs to consider the potential obstacles, passable ways etc. When it is necessary to roam a curved path between the given points additional intermediate points needs to be added. Several methods were shown in the previous chapter to determine the position, from which the rotary encoder will be preferred. Using a simple and cheap method is essential in our case. A. Selecting the rotary encoder and the DC motor The resolution of the rotary encoder will fundamentally determine the resolution of the movement. When selecting the resolution one first need to specify the required accuracy during the motion control. The diameter of the rotated wheel and the gear ratio of the transmission are also important during the theoretical accuracy calculations. In our case the movement will be performed in a closed area, where the ground is negligibly rough. The exact path should be given since several obstacles can be found in the area. The desirable accuracy under these circumstances should be less than a centimeter. DC motors will be used to actuate the vehicle, because it is relatively easy to control the angular velocity. The control electronic will be supplied with 12V DC voltage hence it is practical to use a DC motor with the same rated voltage. It is important to note at this point, that one need to also consider the expected power consumption. According to the load, the voltage can drop below the threshold of the electronic and it can produce unexpected functional disorders. The motors should be able to move the vehicle dynamically, with the structure and the battery. B. DC motor controlling First we have to select the drive for the motors. High frequency, fast signals are expected in our case, due to the controlling method. The motors should be able to rotate in both directions. Relays imal switching frequencies are limited by the inertia of the contacts, hence the drive cannot be built up with these electrical components. BJT s or MOSFET s as the microelectronic alternative of the relays should be used. Simple circuits can be found to provide the appropriate drive for the motors. The most common circuit is the H-bridge designed with transistors. C. Computing Calculations are based on step-by-step calculations. Two electrical motors will be used on the sides of the vehicles, and a third wheel on the front of the car. In each step the rotary encoders are giving a positive or negative impulse on the sides. The principle is shown in Figure 1. It is clearly visible, how the vehicle is moving along the arc α, if only one of the sides is driven with one increment. Figure 1. Roamed arc belonging to one increment The displacement is calculated with the following formulae: step _ left + step _ right step = (1) 2 step _ right step _ left α = 2 wheel _ offset α 0 x x + step cos α + 2 α y y + step sin α + 2 step α < 0 x x + step cos α π + 2 α y y step sin α π + + 2 The new vehicle direction can be calculated with: α = α + α (4) These calculations are made for each step. One can see that all the variables should be float type. Since calculations with float variables are time consuming processes calculation ability is essential, which needs to be considered during the designing. (2) (3)
D. Mechanical construction The mechanical construction will basically affect some important properties of the path controlled vehicle, e.g. the wheel offset. The motors should be mounted co-axially to prevent the resultant errors from the construction. The wheels should have the same diameter, to prevent turning during the movement. To ensure the pointwise contact between the road and the wheel, the tread suggested to be peaked shaped. In Figure 2 an appropriate construction can be seen. It is ideal for small or medium robotic applications, providing cost effective drive and feedback for the user. It also includes a standard noise suppression capacitor across the motor windings. The EMG30 is supplied with a 6 way JST connector [1]. The connections are given in Table 1, and the motor specification is shown in Table 2. Wire colour Purple (1) Blue (2) Green (3) Brown (4) Red (5) Black (6) TABLE 1. Connection Hall Sensor B Vout Hall sensor A Vout Hall sensor ground Hall sensor Vcc + Motor - Motor MOTOR CONNECTIONS IV. Figure 2. Peaked shaped wheel tread to minimize error REALIZATION OF A PATH CONTROLLED VEHICLE In this chapter the selection of the components will be shown for the realized vehicle. As it was discussed in the previous chapter, the vehicle should be able to travel the path under idealized circumstances in a closed area. The desired accuracy will be less than one centimetre, and positions will be calculated to the tenth of a millimetre. To reach such an accuracy one should select a high resolution encoder and build the appropriate mechanical construction as well. The control should also be capable to process the data. A. Rotary encoder and DC motor selection To reach the desired theoretical accuracy is depending on the followings: Rotary encoder resolution Transmission ratio Wheel diameter As a power supply a 12V 4Ah Redpoint battery is used, hence the DC motors rated voltage will be the same. In our case a compact driving system will be used. The EGM30 is a 12V motor fully equipped with encoder and 30:1 reduction gearbox. The encoder resolution is shown in the Table 2 which results 0.872 mm displacement per an impulse for the selected wheel. The encoder provides two square waves in quadrature. The direction can be detected e.g. with sensing the falling signal after overlapping. The typical output of an incremental can be seen in Figure 3. Figure 3. Output signals for an incremental rotary encoder when the axis is rotating clockwise TABLE 2. MOTOR SPECIFICATION Specification Rated voltage 12 V Rated torque 1.5 kg/cm Rated speed 170 rpm Rated current 530 ma No load speed 216 rpm No load current 150 ma Stall Current 2.5 A Rated output 4.22 W Encoder counts per output shaft turn 360 This construction provides a wheel revolution from 1.5 rpm to 200 rpm off load when supplied with 12 V power supply. B. DC motor controlling The selected driving system also contains the motor driver electronics: MD23, Dual 12Volt 3Amp H Bridge. The drive electronics has the following properties: Reads motors encoders and provides counts in registers for determining distance traveled and direction. Drives two motors with independent or combined control, only 12 V supply is required to power the module. Motor current is readable through registers. Onboard 5v regulator can supply up to 1A peak, 300mA continuously to external circuitry. Motors can be commanded to turn by I 2 C register value. Several registers can be changed through I 2 C communication e.g. acceleration, power regulation. MD 23 uses PIC16F873 microcontroller to control the motor drivers, and reading the encoder values. As the encoder signals are changing rapidly, using external interrupts are essential to handle each. I 2 C communication is used to communicate with the microcontroller. MD 23 provides the protection of the H-bridge with NOR gates (74HC02), and with delayed switching. LM5104 integrated circuits are used to
drive the ZXMN3A04DN8 n-channel MOSFETs. The MD 23 motor drive can be seen in Figure 4. 1 if α0 α > δlim v12 = v α0 α else δ lim (9) α 0 is standing for the angle at which the vehicle should turn to reach the target, α is the vehicles actual moving direction and δlim is the limit angle difference for turning in one place. The (8) and (9) equations are only applied if α0 > α π and 0 < α0 α <. The control should be written for all the 2 quarters of a circle unit in bothα 0 > α and α0 < α cases. Figure 4. MD 23 motor drive The drive is using PWM signals to control the revolution speed of the motors. The speed parameter is defining the speed for both motors, and can be changed from -128 to 127. The numbers are indirectly affecting the pulse width, in a cycle. Negative values are forcing both motors to rotate backwards. The speed control is realized in two steps. In the first step the speed is regulated accordingly the distance from the target. C. Computing For performing the calculations, relatively large calculation ability is required, because the number of float calculations. A PIC32MX4 multimedia board is selected for this purpose, by the MikroElektronika company. The media board is equipped with a PIC32MX460F512L 32bit microcontroller. The multimedia board can be seen in Figure 5 with the shielded cable connected to the I2C1 connections. 1 if spath > 1000 spath v = v if 200 < spath < 1000 1000 0.2 if spath < 200 (5) Figure 5. PIC32MX4 MMB with the I2C communication cable The interpretation of the turn parameter is: v v if v 0 v1 = v + v if v < 0 v + v if v 0 v2 = v v if v < 0 In the second step, the turn parameter is determined, which is also affecting the speed: 0 if α0 α > δlim v = v α0 α δlim else δ lim (6) (7) (8) The microcontroller is operating with 3.3V, hence the V cc.cannot be common with the V cc of the MD 23 motor drive. The media board is equipped with a large LCD display. Important information can be displayed on the display e.g. actual position, distance from the target etc. The computation method interpreted previously is used during the calculations. The control is operating with 80 Mhz clock, and consuming less than 100mAs. D. Mechanical construction The mechanical construction is supporting the DC motors, drive electronic, multimedia control board and the battery. For the experimental vehicle a simple wooden plate were used to support the elements. A switch is used to power up the system. The top view of the path controlled vehicle can be seen in Figure 6. The bottom part of the vehicle can be seen in Figure 7. The reference point of the vehicle is located in the midpoint of the rear axis and denoted by a black circle. Since the third wheel rotates freely it does not constrain the motion of the vehicle.
( v = 60 ) given in last row of Table 3, the path is shown in Figure 10. The worst test run shown in Figure 11 was carried out by the parameters given in the first row of Table 3. The repetition accuracy was also investigated. Performing 10 times the cycle shown in Figure 8, the very last target point was approached with error 215mm in x direction and 220mm in y direction. 7 y 5 0,2,4,6,8 1 x Figure 6. Upper view of the path controlled vehicle 3 Figure 8. Test path Figure 7. Bottom view of the path controlled vehicle E. Test runnings A prescribed path is shown in Figure 8. The numbers denote the sequence of the targets. The distance between each neighboring targets is 1000 mm. A series of computations has been performed at different values of the velocity v, turn parameter v and limit angle δ lim. For each test run the imum deviation x from the prescribed path and the length s path of the travelled path are determined on the last branch of path, i.e., between 6-7-8 target points along a length of 1580mm section. The obtained results are shown in Table 3. The test run is considered optimal if the x = 0 and s path = 1580 mm. The last but one row of the Table 3 corresponds to the best test run, and its path is shown in Figure 9. We notice that it was performed at a low speed ( v = 20 ). Also good solution was obtained at a reasonable high speed TABLE 3. v v lim TEST RUNNINGS δ [ ] x [mm] s path [mm] 60 5 40 236 1708 60 90 40 64 1613 60 10 40 63 1612 60 30 80 53 1599 60 30 10 22 1599 120 30 40 51 1598 60 60 40 27 1597 60 20 40 36 1596 100 30 40 41 1594 60 37.5 40 19 1593 60 30 40 24 1591 60 30 20 16 1591 60 30 30 25 1590 60 45 40 21 1589 20 30 40 5 1585 60 30 60 15 1584 Figure 9. The best test run at low speed ( v = 20)
Figure 10. Good test run at reasonable high speed ( v = 60) kinematic model. Running tests have been performed for different velocities and limit turning angles. As a result of test runnings the followings can be concluded: The vehicle is able to reach every position in a flat area with acceptable accuracy. At high speed the vehicle may overrun the target point which is corrected with local zig-zag motions. After a number of repetitions of the same cycle the error is increasing due to slip of the driving wheels. Arbitrary high accuracy cannot be achieved with kinematical model due to slip of the wheels and uneven road conditions. ACKNOWLEDGMENT The described work was carried out as part of the TÁMOP- 4.2.2./B-10/1-2010-0008 project in the framework of the New Hungarian Development Plan. The realization of this project is supported by the European Union, co-financed by the European Social Found. Figure 11. The worst test run at reasonable high speed ( v = 60) REFERENCES [1] MD23 - Dual 12Volt 3Amp H Bridge Motor Drive Technical documentation: http://www.robot-electronics.co.uk/htm/md23tech.htm [2] J. Borenstein and Liqiang Feng, Measurement and Correction of Systematic Odometry Errors in Mobile Robots Robotics and Automation, Vol 12, No 6, December 1996, pp. 869-880. [3] M. Vogel Ipari robotjárművek helymeghatározó rendszerei Műszerügyi és méréstechnikai közlemények, 37.-68, 2001. [4] B. Koleszár: Szárazföldi robottechnikai eszközök tervezésének és alkalmazásának biztonsági szempontjai, V. CONCLUSIONS An automated guided vehicle has been investigated. The control of the independently driven wheels is based on a