Group 7
Lab Notebook - Lesson 9
Date: 07/05 2015
Group members participating: Ivan Grujic, Lasse Brøsted Pedersen, Steffan Lildholdt, René Nilsson
Activity duration: 5 hours
Goal
The goal of this exercise is to investigate how the method of odometry and the tachocounter can be used to keep track of position of a LEGO car with differential drive.
Plan
The plan is to follow the plan described in [1].
Odometry
For this exercise the standard base vehicle from Lesson 6 is used together with the PilotSquare.java program provided in this lesson. The parameters of the LEGO car in this program is defined as the following.
| Parameter | Value |
|---|---|
| Left wheel diameter | 5.5 cm |
| Right wheel diameter | 5.5 cm |
| Track width | 16 cm |
The program makes the car drive 20 cm straight forward, turn 90 degrees to the left and repeat this 4 times in order to get back to the initial position. A special piece of paper with multiple grids on it is used to measure the accuracy of the system. This is shown in the following image.
Optimally, the LEGO car should end up in the exact same position as prior to the execution of the program. However this is not the case due to both systematic and non-systematic errors. The result of the 3 test runs are summarized in the following table.
| Attempt | Measured x | Measured y | Calculated x | Calculated y |
|---|---|---|---|---|
| 1 | -2.00 mm | -2.00 mm | 1.00 mm | -1.60 mm |
| 2 | -2.00 mm | 2.00 mm | 0.40 mm | -0.60 mm |
| 3 | -4.00 mm | 3.50 mm | 2.50 mm | -1.90 mm |
"Measured" x and y is the physical error measured by a ruler and "Calculated" x and y is computed error displayed in the LCD on the NXT.
The Non-systematic involves variations in the surface and the internal uncertainty of ~2% [2]. These errors are difficult to cope with. However the systematic errors involves incorrect definition of the LEGO car parameters and these can be corrected by calibration which is described in the following.
Calibration of wheel diameter and the track width
Initial square run with calibrated values
| Parameter | Value |
|---|---|
| Left wheel diameter | 5.539 cm |
| Right wheel diameter | 5.544 cm |
| Track width | 16.27 cm |
| Attempt | Measured x | Measured y | Calculated x | Calculated y |
|---|---|---|---|---|
| 1 | -10.00 mm | -13.00 mm | 1.30 mm | -1.30 mm |
| 2 | -10.00 mm | -10.00 mm | 2.80 mm | -2.80 mm |
| 3 | -13.00 mm | -15.00 mm | 3.00 mm | -1.80 mm |
Tweaking parameters according to square run with left turns.
| Parameter | Value |
|---|---|
| Left wheel diameter | 5.539 cm |
| Right wheel diameter | 5.544 cm |
| Track width | 16.4 cm |
5.5950.99 = 5.539 5.60.99 = 5.544
| Attempt | Measured x | Measured y | Calculated x | Calculated y |
|---|---|---|---|---|
| 1 | 5.00 mm | 5.00 mm | 0.60 mm | -0.60 mm |
| 2 | -1.25 mm | 2.50 mm | 1.90 mm | -2.10 mm |
| 3 | 2.00 mm | 3.00 mm | 6.30 mm | -1.80 mm |
| 3 | -1.00 mm | 0.00 mm | 1.80 mm | -2.30 mm |
Reversed square with right turns
| Attempt | Measured x | Measured y | Calculated x | Calculated y |
|---|---|---|---|---|
| 1 | 30.00 mm | 40.00 mm | 1.30 mm | 2.30 mm |
| 2 | -27.50 mm | -30.00 mm | 5.20 mm | 2.70 mm |
Final parameters
| Parameter | Value |
|---|---|
| Left wheel diameter | 5.539 cm |
| Right wheel diameter | 5.544 cm |
| Track width | 16.27 cm |
Why this behavior?
Quantization error in tacho counter in each step of the trip. Orientation of back wheel.
500 mm kørt distance. Afstand fra mål ~0.5 mm = dist_err = 0.001 Rotation error ~0.5 degrees. 0.5/360 = 0,00138
Position tracking by means of particle filters
Hastighed ændret fra 5 til 15
Distance noise factor = 0.005
Angle noise factor = 2.5
Conclusion
References
[1] http://legolab.cs.au.dk/DigitalControl.dir/NXT/Lesson10.dir/Lesson.html [2] http://lejos.sourceforge.net/nxt/nxj/tutorial/WheeledVehicles/WheeledVehicles.htm