2.3. Calibration of the Potentiometer, IMUs, and Encoders

The potentiometer (at point H in Figure 4) measured the articulation angle. Figure 4 shows the aerial view of the right turning center articulated rover. When the rover was straight, P₁ was parallel to P₂ and the potentiometer digital signal read 493. P₁ is the center point between front tires, while P₂ is the cnter point between the rear tires. The distance between P₁ and P₂ is Z. The length of l₁ and l₂ was 0.91 m each. To obtain the articulation angle γ, manual measurements were made and applied using the Cosine rule progression below (Equation (1));

Potentiometer Calibration. Potentiometer calibration involves measurements of the voltage reported by the potentiometer in relation to the changing angle θ of the rover when turning left or right. Assume all the points are in a cartesian coordinate system.

To calibrate the angle, the rover was turned left or right. The angle was measured by the potentiometer, which was digitized with a 10-bit ADC, and the signal values ranged from 0 to 1023. The angle was recorded when turning left and right in 20 digital signal intervals from 493 (Figure 5a,b). Assume 493 as the center position and going left is negative while going right is positive. The angle γ was plotted together with the potentiometer signal (Figure 5). The potentiometer signal decreased when turning left and increased when turning right. The Equation obtained from the plots for the left was y = 0.190225x, and for the right was y = 0.1932075x (Figure 5). The Equations were implemented in Algorithm 1 at lines 15 to 19. The left/right Equations were slightly different due to potentiometer errors, human errors, and the slight misalignment of the vehicle.

Gain Kp is equal to 1

p <– Kp * (γk+1 – γk)

WHILE p > Et

 Declare and assign 0 to increment i

 Declare and assign 0 to temp

 WHILE i < 20

   Delay for one microsecond

   Read the analog signal from the high precision potentiometer γk

   temp add the γk to temp

   Increment i

 }

 Get the average temp

 Assign temp to γk+1

 IF temp > analog signal 493

   γk+1 = (temp-493) * 0.1932075;

 ELSE

   γk+1 = (temp-493)*0.190225;

 END IF

 p <- Kp * (γk+1 - γk)

 IF p > -Et

   Set the left relay HIGH

   Set the right relay LOW

 ELSE IF –p < Et

   Set the left relay LOW

   Set the right relay HIGH

 ELSE

   Set the left relay LOW

   Set the right relay LOW

 END IF

END WHILE

Return all the error

The calibration of the potentiometer and articulation angle. The left image (a) presents the relationship of the left articulation angle versus the potentiometer signal. The left image (b) shows the relationship of the right articulation angle versus the potentiometer signal.

Both IMUs were calibrated as advised by the manufacturer’s users guide (Phidgets Inc., Calgary, CA, USA). The magnetic error correction was done by the compass calibrator software downloaded from the Phidgets website. The two IMUs were placed at two different locations on the vehicle, as described in the section “Robot components and System Setup.” The IMU was calibrated by connecting the IMU to the embedded computer, which had the Phidget compass calibration program installed. The magnetic field estimated value for Tifton, Georgia, was 0.47459 T obtained online from the NOAA website (http://www.ngdc.noaa.gov/geomag-web/#igrfwmm). After entering the magnetic field value, the program was started, and the rover was driven in a circle behind the Engineering Annex fields (31.475340N, 83.528968W) in Tifton, Georgia, to generate the calibrated compass parameters. After the calibration, the IMUs were then used for localization and navigation experiments.

Encoder calibration was conducted by finding the circumference of the rover wheels and then converting the signal of the encoder to distance for each encoder count. The rotary encoders used a 10-bit Analog-to-digital converter. To make sure that the encoders were accurately calibrated, the tires of the rover were rotated 360°, and the count of the encoders increased from 0 to 1023. Since the circumference of the tire was 1915.1 mm, the distance per count (resolution) was 1915.1/1024 = 1.87 mm.