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Not Cow Tipping - Car Tipping! (page 2)

based on 41 ratings
Author: Lexie S.

Introduction

Terms and Concepts for Background Research

The following terms and concepts were researched for background information:

  • linear velocity
  • angular velocity
  • gravitational force
  • centripetal force

Research Questions

  • How does changing the degree of decline affect the time that a LEGO MINDSTORMS NXT 2.0 robotic vehicle tips in milliseconds (ms)?
  • How does changing the degree of decline affect the point at which a LEGO MINDSTORMS NXT 2.0 robotic tips in 1/200ths of a g-force (1/20ths meters/sec2)?
  • Can a preventative accelerometer-based program that is based upon this knowledge be used to prevent cars from reaching the tipping point and tipping over?

Experimental Procedure

Setup
  1. Be acquainted with accelerometer.
  2. Be acquainted with NXT-G programming software, especially with the advanced blocks, logic blocks, and sensor blocks.
  3. Be sure to have downloaded the accelerometer block from http :// www . hitechnic . com / cgi - bin / commerce . cgi ? preadd = action & key = NAC 1040
  4. Build a robot modeled after a car with an accelerometer build into it.
  5. Test to confirm robot works. It should be:
    1. Able to accelerate quickly
    2. Top-heavy
    3. Able to steer and turn
  6. Clear at least an 8ft x 12ft space.
    1. Lay the piece of plywood out so that one ends rests on the ground and the other ends is supported off the ground to create a ramp.
    2. Use various objects to support and prop the ramp.
  7. Program robot.
    1. Create a program that has the robot drive straight while logging the accelerometer measurements (straight program).
    2. Create a program that has the robot drive straight and then in a circle while logging the accelerometer measurements (trial program).
  8. Test to confirm programs work.
Part I: Trials
  1. Prop the ramp at a 12º from the ground. Measure the angle using a goniometer.
  2. Begin straight trials.
    1. Place the robot so that its back wheels are on the very back edge of the board.
    2. Let go of the robot. Start the robot's straight program and the stopwatch at the same time.
    3. Measure the amount of time in seconds that it takes the back wheels of the robot to go from the top of the ramp to the point at which they are off the bottom of the ramp, using a stopwatch or other device that can operate as a stopwatch that measures centiseconds.
    4. Repeat 4 times so that 5 straights have been completed.
    5. Data is collected in this step.
  3. Repeat step 2, but run the trial program instead of the straight program.
    1. Data is collected now
    2. Repeat 9 times so that 10 trials have been completed.
  4. Repeat steps 1-3 four times, changing the slant of the ramp to 9º, 6º, 3º, and 0º to the ground.
Data collected:

As completing step three, use a stopwatch to determine the approximate time in milliseconds that the robot tips over.

  1. Start stopwatch as the robot begins running the program.
  2. Stop stopwatch when the robot tips over.
  3. Record time under correct course and trial number.

NO accelerometer measurements need to be logged. The NXT brain is already logging the accelerometer measurements in 1/200s of a g-force (about 1/20ths m/sec2) about every 16 milliseconds.

Access the accelerometer measurements.
  1. Be sure to have uploaded all data files to computer.
  2. Files will be saved as Text files (.txt)*
  3. Open file in Microsoft Excel (if Excel is not available for use, open in Notepad or another similar, simple, word-processing program).
  4. Text Import Wizard will open.

i. On step 1, under "Original data type," choose "Delimited - Characters such as commas or tabs separate each field" as file type. The "Start import at row:" should be set to row 1. Leave other options at the default. Click the "Next >" button.

ii. On step 2, under "Delimiters" click on "Tab" so that it is unselected. Then select "Comma." The Data preview will now show two columns of numbers separated by a line. Leave other options as is. Click the "Next >" button.

iii. On step 3, under "Column data format," make sure "General" is selected for both columns. Click the "Finish" button.

  1. Excel should now display two columns of numbers.

i. The first column is the time, in milliseconds. For increased clarity, label the column this.

ii. The second column is the accelerometer measurements in 1/200ths of a g-force. For increased clarity, label the column this.

- *If some of the files were saved as Backup files (.bak), do the following:

  1. Rename the file. It doesn't matter what it is changed to, it just has to be different than what it should be.
  2. Open the file in Notepad.

i. Click on and then right-click on the file.

ii. Select "Open with" by moving the mouse over it.

iii. Click "Choose default program..."

iv. A window titled "Open with" will appear. Underneath the "Recommended Programs," there will be "Other Programs" followed by a line. At the end, there is an arrowhead. It should be facing up. If facing down, click it. A list of programs should appear, with an image next to the program name and program producer.

v. Click "Notepad; Microsoft Corporation." Then click "OK."

vi. The file will now open in Notepad.

  1. Save the file as a .txt file.

i. Click "File," and then "Save as…"

ii. Change the file name back to "__° straight/trial/beep__"

iii. Click the "Save as type:" drop down menu and select "Text Documents (*.txt)."

iv. Click "Save."

v. The file is now saved in a second file as a .txt file under the correct name. The .bak file can now be deleted since it contains the same data.

- Analyze results.
  1. Look at the notes of which course, trial numbers, and times tipped.
  2. Look at accelerometer data matching the course and trial.
  3. Once the robot tips, the data values will be in all different ranges. Look for this abnormality. The value at which this starts is the tipping point.
Part II: Application
  1. Create new programs for robot.
    1. reate a program that has the robot drive straight and then turn in a circle while logging the accelerometer measurements. If the value of the accelerometer measurements reach outside the range of x to y, have the robot cut its power by 50%. Program the robot to emit an alarm sound if this second part of the program occurs. If the values of the accelerometer measurements return to the range of x to y, then have the robot increase its power by 200% so that the power level is back at 100% and have the robot emit a beep. (beep program)See page 20.
    2. x and y represent the extremes of the range at which the robot has not gained enough centripetal force to tip over.
  2. Repeat Part 1 steps 1-4 but run the beep program instead of the straight program or the trial program. Data is collected during these beep trials (beeps).
Data collected

- Record the times at which the following events occur for each trial if they occur. They will most likely not occur for every trial. If it does not occur record a 0 instead of time (this is done for a more accurate average). If the time is unknown but the event occurred, record a "yes" instead of a time.

  1. 1st alarm
  2. 1st beep
  3.   2nd alarm
  4. 2nd beep
  5. 3rd alarm
  6.   3rd beep
  7. tip

- NO accelerometer measurements need to be logged. The NXT brain is already logging the accelerometer measurements in 1/200s of a g-force (about 1/20ths m/sec2) about every 16 milliseconds.

- Access the accelerometer measurements. See Part I Data Collection for instructions on accessing the data logged by the NXT.

- Analyze results.
  1. Look at the notes of which course, trial numbers, and times tipped.
  2. Look at accelerometer data matching the course and trial.
  3. Once the robot tips, the data values will be in all different ranges. Look for this abnormality. The value at which this starts is the tipping point.

If necessary, and the program did not prevent the robot from tipping over, make changes in speed cut and programs, repeat steps 1-2 of Part II, and collect new sets of data.

0 degrees straights
finish time
Trial 1
2560
Trial 2
2630
Trial 3
2640
Trial 4
2620
Trial 5
2560
Average
2602

Results

Data

0° straights and trials:

0° straight 1- time 2.56 sec.

0° straight 2- time 2.63 sec. Lost a back wheel.

0° straight 3- time 2.64 sec. Saved as a .bak file. Converted to a .txt file.

0° straight 4- time 2.62 sec. Lost left back wheel.

0° straight 5- time 2.56 sec.

 

 

0° trial 1- the robot went slow and yet surprisingly still tipped. My plan just officially backfired. The robot was not supposed to tip over. How come it couldn't do this earlier? Tipped onto left side at 2.17 sec.

0° trial 2- tipped again! Originally, this would have been a good thing. But now . . . anyway, the robot was beginning to turn around to come back towards the top of the board when it tipped onto its left side at 2.39 sec. Lying at 90°.

0° trial left- ran the robot to turn the other way this time to see if it was somehow bias to one side. Lying at 90°. Tipped at 2.38 sec onto right side.

0° trial short- ran the robot's motors 270°instead of 1 whole rotation (360°) before turning. Forgot to change the programming so that it turned to the left instead of the right. Tipped to the right, and rolled over onto its left side at 2.11 sec. Saved as a .bak file. Converted to a .txt file.

0° trial 3- the robot was beginning to turn back towards me when it tipped. Lying at 85°. Rocked a little once it had fallen. Tipped onto left side at 2.34 sec.

0° trial 4- the robot was really close to coming back towards me when it tipped. Seemed to spin around; its front wheels pivoted, its back wheels skidded, and then it tipped. Tipped on its left side at 2.48 sec. Lying at 95°.

0° trial 5- tipped just as the robot was beginning to turn back towards me. Fell directly onto its left side. Lying at 75°. Lost left back wheel. Tipped at 2.30 sec. Saved as a .bak file. Converted to .txt.

0° trial 6- the robot tried to come back towards the top of the board when it tipped. The front wheels pivoted and the back ones skidded like in 0° trial 4. It just didn't go quite as far down the board. It's only just on the bottom side of halfway down the board. Lying at 120°. Tipped at 2.42 sec onto its left side.

0° trial 7attempt- hit edge of board. The wheels slipped down and it got stuck when it tried to turn. Lying parallel to bottom edge of board. Tipped at 2.52 sec. Lost left back wheel.

0° trial 7- the real thing. Was coming back towards the top of the board when the robot tipped. Fell onto its left side. Like 0°trial 4 and 0° trial 6, the wheels pivoted and skidded. I guess the radius of curvature is too small. Oh well. Lying at about 87°. Tipped at 2.34 sec.

0° trial 8- Radius of curvature and probably the skinny wheels are definitely the problem. It pivoted, skidded and fell. Lying at about 88° again. Tipped onto left side at 2.24 sec. Lost left back wheel.

0° trial 9- Same problem as in the previous trial. Lying at 95°. Tipped onto left side at 2.38 sec. At least it will make a good frame-by-frame and videotape. Not that I taped this one; I mean the situation.

0° trial 10- Ditto the previous one. Had the same problem again. Lying at about 91°. Tipped onto left side at 2.26 sec.

 

 

0° trial tape- took a video a couple of times. Ran it four times under the same accelerometer log file. The first time it did the usual pivot and skid and fell onto the left side, though the pivot and skid wasn't as obvious as I wanted it to be. This one was taped. The second time it just fell over onto its left side. The third time was the best; it actually went all the way horizontally, and when it turned, it swung its back end all the way around to turn the other way before actually falling over. Figures that the best run is the time that the camera doesn't register that I pressed the button. The fourth time I didn't tape because it rolled off the edge of the board. It kept going on the carpet and surprisingly did a full circle before crashing into the edge of the board and losing its left wheel upon impact.

 

3°straights and trials:

 

3 degrees straights

finish time

Trial 1

1840

Trial 2

1800

Trial 3

1790

Trial 4

1800

Trial 5

1760
Average
1798

 

3° straight 1- time 1.84 sec.

      3° straight 2- time 1.80 sec.
      3° straight 3- time 1.79 sec.

      3° straight 4- time 1.80 sec.

      3° straight 5- time 1.76 sec.

3° trial 1- Was about to start ascent up board when tipped. Twisted itself so that it is hallway between being perpendicular to the board and being backwards (135°). Tipped onto its left side at 1.48 sec.

3° trial 2- Was going horizontal across board when tipped. Tipped onto inside wheels and as it fell, spun itself to 135°position. Tipped onto left side at 1.52 sec.

3° trial 3- Got pretty close to the edge before it turned. Was going horizontal across board when it tipped. Twisted to 135°. Tipped onto left side at 1.73 sec.

3° trial 4- Was beginning upward ascent of board when it tipped. Lying at a 90°. Tipped onto its left side at 1.50 sec. Lost a back wheel.

 

3° trial 5- Was beginning upward ascent of board when it tipped. Twisted around a little more so that it lies at about 150°. Tipped onto its left side at 1.83 sec. Lost a back wheel.

3° trial 6 attempt- Got just a bit too close to the edge of the board. Fell off just as it began to tip [most likely should be turn]. Fell to left, remained balanced on top, leaning to the right. Tipped at 2.00 sec.

3° trial 6- Was beginning upward ascent of board when it tipped. Flipped to its left and flipped around so that it ended up on its right side. Tipped to the left at 1.47 sec. Pictured.

3° trial 7- Was just beginning upward ascent of board when it tipped. Twisted due to front wheel's power so that it was nearly perpendicular to the bottom of the board (around 85°). Tipped to left side and onto right at 1.75 sec. Lost a back wheel.

3° trial 8- Was beginning upward ascent of board when it tipped. Twisted around to 135°. Tipped onto left side at 1.71 sec.

3° trial 9 attempt- Fell off left edge of board. Tipped onto left side. No time because stopwatch did not start. Lost a back wheel.

3° trial 9- real thing, but no time because the stopwatch did not stop. Robot was going horizontal across board and just beginning upward ascent when tipped. Rocked once before tipping. Lying at a 130° angle or so.

3° trial 10 attempt- Ran off edge at 1.06 sec. Had attempted to turn and fell to left side. Lost a back wheel. Saved as both a .bak and a .txt. Kept the .txt file since they were the same.

3° trial 10- Was beginning upward ascent of board when it tipped. As outside wheels were in the air, the inside one kept twisting, causing the robot to twist so that it laid at about 20°. Tipped onto its left side at 1.79 sec.

 

6° straights and trials:

 

6 degrees straights
finish time
Trial 1
2080
Trial 2
2100
Trial 3
1960
Trial 4
1960
Trial 5
1920
Average
2004

 

           

            6° straight 1- time 2.08 sec.

            6° straight 2- time 2.10 sec.
            6° straight 3- time 1.96 sec.
            6° straight 4- time 1.96 sec.
            6° straight 5- time 1.92 sec.
            6° trial 1 attempt- Fell off

6 degrees trials

time of tip in ms

Trial 1
1800
Trial 2
1830

Trial 3

1780
Trial 4
1800
Trial 5
1870

Trial 6

1960

Trial 7

1740

Trial 8

1890
Trial 9
1840

Trial 10

1930
Average
1844

 edge at about 1.91 sec. Angled the robot wrong. Saved as a .bak file. Converted to .txt file.

            6° trial 1- the real thing. Tipped onto left side. Had begun upward ascent up the board when tipped. Appears nearly perpendicular to bottom of board. I guess the wheels didn't bank up enough speed to twist the robot around. Tipped at 1.80 sec. Pictured. Saved as a .bak file. Converted to .txt file.

            6° trial 2- Got really close to edge of board. Robot must have been angled wrong. Just as it was about to go off the edge, it angled in for the turn. Appears to have begun ascent before tipping onto its left side. Tipped at 1.83 sec. Saved as a .bak file. Converted to a .txt file.

            6° trial 3- Was about to begin ascent up board when it tipped. Lying at about 10° off from being perpendicular to the board. Tipped onto its left side at 1.78 sec.

            6° trial 4- Was about to turn to begin upward ascent when it tipped. Lying at about 5° off from being perpendicular to the board. Tipped onto left side at 1.80 sec.

            6° trial 5- Was about to turn to begin upward ascent when it tipped. Lying at 45° off to the right from being perpendicular to the board [about 135°]. Tipped onto left side at 1.87 sec.

            6° trial 6- Going horizontal across the board when it tipped. Lying about 5-10° off from being perpendicular to board. Tipped at 1.96 onto left side at 1.96 sec. Saved as a .bak file. Converted to .txt file.

            6° trial 7- Got real close to the edge of the board before turning. Was going horizontal across board when tipped. It appeared to have been just starting or about to start turn to upward ascent up board, or it had enough power and/or speed in its wheels to twist itself around. Lying halfway between being perpendicular to the board and being backwards [135°]. Tipped onto left side at 1.74 sec. Saved as .bak file. Converted to .bak file.

            6° trial 8- Going horizontal across board when it tipped. Appeared to have twisted itself so that it was perpendicular to the board [90°]. Tipped onto its left side at 1.89 sec.

            6° trial 9- Was about to begin upward ascent of board when it tipped. Lying perpendicular to the board [90°]. Tipped onto left side at 1.84 sec. Saved as a .bak file. Converted to a .txt file.

      6° trial 10- Was going horizontal across the board when it tipped. Started to begin upward ascent of board as it tipped and skidded into a position that is backwards and parallel to board [180°]. Tipped onto its left side at 1.93 sec. Pictured.

9° straights and trials:

 

9 degrees straights

finish time

Trial 1

1860

Trial 2

1830

Trial 3

invalid

Trial 4

invalid

Trial 5

1900
Average
1863.3

 

 

           9° straight 1- time 1.86 sec.

            9° straight 2- time 183 sec.
            9° straight 3- time 1.74 sec.
            9° straight 4- time 1.74 sec.

            9°straights 3 and 4 both have invalid times due to stopwatch being stopped early. It was stopped at the time that the robot's front wheels crossed the bottom of the board instead of when the back wheels crossed the bottom of the board. The data files are valid for these straights.

            9° straight 5- time 1.90 sec.

9 degrees trials

time of tip in ms

Trial 1

1660

Trial 2

1630

Trial 3

1580

Trial 4

1450

Trial 5

1740

Trial 6

1690

Trial 7

1710

Trial 8

1520

Trial 9

1640

Trial 10

1490
Average
1611

            9° trial 1- Was going horizontal across the board when it tipped. Tipped onto left side at 1.66 sec. Facing backwards.

            9° trial 2- Was going horizontal across the board when it tipped forward and to right [should probably be left]. Landed on left side. Tipped at 1.63 sec.

            9° trial 3- While it tipped, its spinning front wheels twisted it around so that they were where the back end should be. Ended on its left side. Tipped at 1.58 sec.

            9° trial 4 attempt- Angled the robot wrong. Fell of[f] edge at about 1.34 sec. Rolled over so that it ended on its right side.

            9° trial 4- the real thing. Robot tipped onto its right side and twisted so its front wheels were in the back, and slid down the board a little. Tipped at 1.45 sec.

            9° trial 5- Tipped onto its left side and then twisted so that it was backwards. Ended on its left side. Tipped at 1.74 sec.

            9° trial 6- Tipped on left side, and wheels twisted robot around by about 180° [lies at 180°]. Ended on its left side. Tipped at 1.69 sec.

            9° trial 7- Was going horizontal across the board when it tipped. Its front wheels twisted the robot around backwards. Ended on left side. Tipped onto its left side at 1.71 sec. Saved as a .bak file. Converted to a .txt file.

            9° trial 8 attempt- Robot was angled badly and went off edge at about 1.58 sec. Robot flipped over, a full flip, and ended up on its wheels. It then proceeded to go in a circle as programmed. The steering motor became disconnected in two places. It was easily reconnected.

            9° trial 8- the real thing. Robot tipped at 1.52 sec. Was going horizontally across board when it tipped onto its left side. The back wheels twisted the robot about 120° around. [lying at 120°]. Ended on left side. Saved as a .bak file. Converted to a .txt file.

            9° trial 9- Was going horizontal across the board when it tipped. As its two outside wheels were in the air, the remaining motor-powered wheel caused the robot to twist about 110°around [lying at 110°]. Ended on its left side. Tipped about 1.64 sec.

            9° trial 10- Was about to begin upward ascent of the board when it tipped. Flipped to its left side and ended up on its back. Tipped at 1.49 sec.

12° straights and trials:

12 degrees straights

finish time

Trial 1
1760
Trial 2
1770
Trial 3
1760
Average
1763.3

          

            12° straight 1- time 1.76 sec.

            12° straight 2- time 1.77 sec.
            12° straight 3- time 1.76 sec.
12 degrees trials
time of tip in ms
Trial 1
1470
Trial 2
1690
Trial 3
1280
Trial 4
1290
Trial 5
1580
Trial 6
1610
Trial 7
1470
Trial 8
1500
Trial 9
1630
Trial 10
1430
Average
1495

            Only three straights were completed for 12° data.

            12° trial 1- Tipped at 1.47 sec. Fell onto right side [should most likely be left side].

            12° trial 2- Twisted around so that its facing the top of the ramp. Ended up on its right side [should most likely be left side]. Tipped at 1.69 sec.

            12° trial 3- Was beginning upwards ascent of board when it tipped so that it ended up on its right side [should most likely be left side]. Looked a lot like last time. Tipped at 1.28 sec.

            12° trial 4 attempt- Put robot too close to edge. Fell off at 1.24 sec. Tipped onto left side.

            12° trial 4- the real thing. Was beginning upwards ascent of board when it tipped and got farther up than last time. Lying on left side. Appears to have begun inwards part of ascent of ramp. Tipped at 1.29 sec.

            12° trial 5 attempt- Turned but ended up off the bottom of ramp this time. Robot must have skidded a little. Had not started ascent at all this time and is backwards. Fell on left side. These tips happen a bit too fast for me to process completely. Tipped at 1.31 sec. It turns out that the file got messed up. It somehow got saved as a .bak file. [file was deleted]

            12° trial 5 attempt 2- Put the robot too close to edge. It fell off and landed on right side. Tipped at 0.86 sec and bounced a little before tipping.

            12° trial 5 attempt 3- Set the robot on the board and it went right off the edge. A couple of pieces went flying. The connections between the steering motor and robot body broke and need fixing. [robot was fixed]

            12° trial 5- the real thing. Robot turned and flipped over. Balanced on its top for a little and then tipped onto left side. Initial tip at 1.58 sec.

            12° trial 6 attempt- Rolled off board and onto carpet. Bounced, then did a flip and landed upright before falling onto right side. Tipped at 0.88 because robot was placed too close to the edge of the board.

            12° trial 6- the real thing. Wobbled before tipping. Appeared to have turned sideways before tip. Fell onto left side. Tipped at 1.61 sec. Wheel fell off.

            12° trial 7- flipped over completely off the side of the board. Landed on left side. Tipped at 1.47 sec.

            12° trial 8 attempt- Put robot too close to edge so it fell off the edge of the board.

            12° trial 8- the real thing. Went right down board and tipped as it went horizontal across board. Tipped at 1.50 sec.

            12° trial 9- Flipped over to its left side as it was going horizontal across the board. Flipped completely over (i.e. onto its back and then onto the other side). Ended on right side. Tipped at 1.63 sec.

            12° trial 10- Was going horizontal across board when it tipped and somehow twisted around and is facing backwards on right side. Tipped at 1.43 sec.

 

0° beeps:

0 degree beeps (ms)
1st alarm
1st beep
2nd alarm
2nd beep
3rd alarm
3rd beep
time of tip
Total

Trial 1

2490
3890
4020
11460
0
0
0
21860

Trial 2

2550
yes
3260
4130
0
0
4130
14070

Trial 3

2650
2750
4200
4670
5760
6140
0
26170

Trial 4

2500
2505
5230
5235
6670
6675
0
28815

Trial 5

2690
2695
9600
0
0
0
0
14985
Average
2576
2960
5262
5099
2486
2563
826
21772

            0° beep 1- no tip! =) 1stalarm - 2.49 sec, beep - 3.89 sec, a second alarm came shortly after, and a second beep about 11.46 sec.

            0° beep 2- robot tipped but this time it was due to wheel. The left back wheel fell off the 2nd time that the robot turned in a circle. 1stalarm - 2.55 sec, beep in between, 2nd alarm 3.26 sec, 2nd beep/tip (about same time) -4.13 sec.

            0° beep 3- no tip! =) 1st alarm - 2.65 sec, beep - 2.75 sec, 2nd alarm - 4.20 sec, 2nd beep 4.67 sec, 3rd alarm - 5.76 sec, 3rd beep - 6.14 sec.

            0° beep 4- no tip! =) 1st alarm/beep - 2.50 sec, 2nd alarm/beep - 5.23 sec, 3rd alarm/beep - 6.67 sec. On this one, the robot got to the "Al" of alarm before beeping so the corresponding alarms and beeps basically occurred at the same time.

            0° beep 5- no tip! =) 1st alarm/beep - 2.69 sec, 2nd alarm - 9.60 sec. The 2nd alarm was due to left back wheel falling off just before end of program, so accelerometer log may have a leap in measurements towards the end.

            It was noted that in both of the 0° beeps in which the robot lost a wheel, the wheel fell off the axle, instead of the whole axle connections falling apart.

3° beeps:

3 degree beeps (ms)
1st alarm
1st beep
2nd alarm
2nd beep
3rd alarm
3rd beep
time of tip
Total

Trial 1

1450
1700
1900
0
0
0
1905
6955

Trial 2

1570
1800
1920
0
0
0
1975
7265

Trial 3

1650
2070
2075
0
0
0
2080
7875

Trial 4

1880
2140
2145
0
0
0
2150
8315

Trial 5

1530
1800
2070
0
0
0
2075
7475
Average
1616
1902
2022
0
0
0
2037
7577

            3° beep 1- Was turning to begin ascent up board when it tipped. Lying at 105°. alarm - 1.45 sec, beep 1.70 sec, 2nd alarm/tip - 1.90 sec. Left back wheel came off during swivel turn and was trapped beneath the robot.

            3° beep 2- Was beginning upwards ascent of board when tipped. Lying nearly perpendicular to the board. 1st alarm - 1.57 sec, beep 1.80 sec, 2nd alarm/tip - 1.97 sec.

            3° beep 3- Was going horizontal across board when it tipped. Lying at 100°. 1st alarm - 1.65 sec, 1st beep/2nd alarm/tip (basically all at once) - 2.07 sec. Lost left back wheel during tip.

            3° beep 4- Was going horizontal across board when it tipped. Fell right over and did not rotate or slide much. Lying at 87°. 1st alarm - 1.88 sec, 1st beep/2nd alarm/ tip (basically all at once) - 2.14 sec.

            3° beep 5- Was going horizontal across board when it tipped. Fell onto left side and did not slide or rotate much. 1st alarm - 1.53 sec, 1st beep - 1.80 sec, 2nd alarm/tip - 2.07 sec. Lost left back wheel as it tipped and swiveled/spun.

6° beeps:

6 degree beeps (ms)
1st alarm
1st beep
2nd alarm
2nd beep
3rd alarm
3rd beep
time of tip
Total

Trial 1

1670
yes
yes
0
0
0
2120
3790

Trial 2

1580
yes
yes
0
0
0
1900
3480

Trial 3

1790
yes
yes
yes
2090
0
2380
6260

Trial 4

1520
1890
2030
0
0
0
2035
7475

Trial 5

1520
1740
1920
0
0
0
1925
7105
Average
1616
1815
1975
0
418
0
2072
7896

            6° beep 1- Was going horizontal across board when it tipped. Slid to bottom of board as momentum rotated robot. Lying at about 80°. 1st alarm - 1.67 sec, final resting spot - 2.12 sec. Fell onto left side.

            6° beep 2- Was going horizontal across board when it tipped. Fell onto left side and slid to bottom of board as robot rotated to 85°. 1st alarm - 1.58 sec, tip/resting spot - 1.90 sec. 1st beep and 2nd alarm somewhere between 1st alarm and tip.

            6° beep 3- Was going horizontal across board when it tipped. Lost left back wheel as tipping and spun around. Flipped onto back and then over onto right side. 1st alarm - 1.79 sec, 1st beep/2nd alarm/2nd beep in between, 3rd alarm - 2.09 sec, tip - 2.38 sec.

            6° beep 4- Was going horizontal across board when it tipped. Momentum made robot slide down board. Lying at 75° on left side. 1st alarm - 1.52 sec, 2nd alarm/tip - 2.03 sec.

            6° beep 5- Was going horizontal across board when it tipped. Lost left back wheel. Spun around and tipped onto back from left side. While tipping onto its back, it rotated to almost 165°. 1st alarm - 1.52 sec, 1st beep - 1.74 sec, 2nd alarm/tip - 1.92 sec.

9° beeps:

9 degree beeps (ms)
1st alarm
1st beep
2nd alarm
2nd beep
3rd alarm
3rd beep
time of tip
Total

Trial 1

1380
1600
0
0
0
0
2170
5150

Trial 2

1350
1620
0
0
0
0
2090
5060

Trial 3

1470
0
0
0
0
0
2050
3520

Trial 4

1420
1730
1740
0
0
0
2060
6950

Trial 5

1500
1750
0
0
0
0
2210
5460
Average
1424
1340
348
0
0
0
2116
5228

            9° beep 1- No qualitative data [Lying at 126°? Writing is illegible.]. 1st alarm - 1.38 sec, 1st beep - 1.60 sec, tip - 2.17 sec.

            9° beep 2- Was going horizontal across board when it tipped. Fell onto left side. Its momentum carried the robot down towards bottom right corner of the board. 1st alarm - 1.35 sec, 1st beep - 1.62 sec, tip - 2.09 sec.

            9° beep 3- Fell onto left side and twisted around to 95°. Slid down board to the bottom. 1st alarm - 1.47 sec, tip - 2.05 sec.

            9° beep 4- Was going horizontal across board when it tipped. Slid down to the bottom of the board. 1st alarm - 1.42 sec, 1st beep - 1.73 sec, 2nd alarm nearly right after 1st beep. Slid to final resting place by 2.06 sec. Fell onto left side. Appeared to have actually just begun upward ascent of board. Left back wheel came loose and was trapped beneath robot.

            9° beep 5- Tipped as turning to cross board. 1st alarm - 1.50 sec, 1st beep - 1.75 sec, tip - 2.21 sec. Slid down board. Lying at about 95°.

12° beeps:

12 degree beeps (ms)
1st alarm
1st beep
2nd alarm
2nd beep
3rd alarm
3rd beep
time of tip
Total

Trial 1

1580
yes
yes
0
0
0
1630
3210

Trial 2

1590
0
0
0
0
0
1620
3210

Trial 3

1530
0
0
0
0
0
1870
3400

Trial 4

1360
1570
0
0
0
0
2710
5640

Trial 5

1400
1620
0
0
0
0
invalid
3020
Average
1492
797.5
0
0
0
0
1957.5
4247

            12° beep 1- forgot to write down qualitative information before picking up robot so there is the possibility of inaccuracy and lack of details. Was going horizontal across board when it tipped. Fell on left side, basically right after the alarm. Lost a back wheel (the left?). 1st alarm - 1.58 sec, 1st beep and 2nd alarm in between, tip - 1.63 sec.

            The obvious flaw in the program is that the loop doesn't break and the robot does not stop until after it is manually turned off, so the files are like 9 kb, compared to the 3-4 kb files of the 6 second long part I trials.

            12° beep 2- Was going horizontal across board when it tipped. Fell onto left side. 1st alarm - 1.59 sec, tip - 1.62 sec.

            12° beep 3- Fell onto left side. Lost both back wheels. The right wheel went flying and the left wheel got stuck under the fallen robot. 1st alarm went off around 1.53 sec, tip - 1.87 sec.

            12° beep 4- Fell to the left and twisted so that nearly backwards. 1st alarm - 1.36 sec, 1st beep - 1.57 sec, tip - 2.71 sec.

            12° beep 5- Fell to the left and twisted so that nearly backwards. 1st alarm - 1.40 sec, 1st beep - 1.62 sec, tip - 1.36 sec [recorded in tables as invalid since it is not possible to have the tip before the beep. The tip was probably 2.98 sec.].

The average of averages is 1790.4 ms, as shown in the last column. The trend of the graph shows how the times get progressively faster as the degree of decline goes up, though the 3 degree trials seem to be an exception. The median of the variation averages, excluding the average of the variation averages, is 1642 ms. The values span 2360 ms to 1495 ms, creating a range of 865 ms.

The average of straight averages is 2006.1332, as shown in the last column. The trend of the graph shows how the times get progressively faster as the degree of decline increases. The 3° straights are clearly an exception, being faster than the 6° average by 306 ms and faster than the 9° average by 35.7 ms. The median of these averages, excluding the average column, is the 9° straight average at 1863.333 ms. The values span 2602 ms to 1763.333 ms, creating a range of 838.667 ms.

The 0° beep 1 had the most events out of all the beep representatives. It had a 1st alarm and beep, and a 2nd alarm and beep. The 3°beep 5 and the 6° beep 4 both had a 1st alarm, 1st beep, 2nd alarm, and a tip, while the 9° beep 1 had a 1st alarm, a 1st beep, and a tip. The 12° beep 3 only had a 1st alarm and a tip. The 0° beep 1 was the only beep representative that did not tip; all the others tipped at about the same time of about 2000 ms.

On this graph, some degrees' averages show startlingly similar results. The 3°average and 6° average both have a 1st alarm, a 1st beep and a 2nd alarm all of which happened at about the same time for both trials at each event; the 3° average's events happened just slightly after the 6° average's events. The same goes for the 9° and 12° averages, whose 1st alarms occur at about the same time. The 9° average's 1st beep occurred slightly after the 12° average's 1st beep. The 1st alarms for 3°, 6°, 9°, and 12° averages all occur at about 1400-1600 ms, and the tips for these averages occur at about the same time of 2000 ms. The 0° average is an outlier.

As shown by the graph, the trial representatives have very similar data trends, especially in the beginning, up to about 1000 ms, and in the end, from about 3000 ms on. This is most evident in places where the lines overlap. From 3000 ms on, 12° trial 8 has the most variation with the occasional downward spike before it juts back up again to join the rest of the data. In the beginning before 1000 ms, 3° trial 8 appears to be most prominent because its data is visible on the ends of most of the ups and downs. In the middle section between 1000 to 3000 ms, the data is jumbled. From about 1000 to 1500 ms, the 3°, 6°, 9°, and 12° data all follow an upwards, elevated trend in which is rises from about 15/200 g-force up to about 125/200 g-force. However, the 0° data remains less than 50/200 g-force and does not elevate to join the other degrees' data, even from 1500 ms to 3000 ms. Even in this, the 0° representative is seen popping out the bottom of the data while all the other degrees' data peaks up and down. Even so, the data of all the degrees follow a similar trend.

The representation beeps' data have similar overall trends to that of the representation trials' data. There are the data sets that have about the same data, which in this case are only 3° beep 5, 6° beep 4, and 9° beep 1. The other 12°representative, unlike last time, has data that is most unlike the other data sets, joining the 0° beep 1 in its differences. All of the data sets start out together until about 700 ms, when all degrees but 0 began to have peaks or rising data. Then by about 1100 ms, the 12° beep 3 data began to decrease, settling into a steady string of small ups and downs around the -200/200 g-force. By 2100 ms, the 0° data hit the top of an arc of data that only peaks to about 75/200 g-force at 2323. It then decreases just in about the same pattern as the rise of the arc and becomes a stream of small ups and downs not unlike the 12° data, except the 0° data is around 20/200g-force. Meanwhile, the 3°, 6°, and 9° data have risen up to around the 200/200-220/200 g-force range, where they too have even smaller ups and downs in their data. Though these beeps have different data trends, especially when compared to the trial representatives', the beeps' data for the most part rises before becoming a streams of small changes in data.

Statistical Analysis

The graphs reveal unpredicted information and prove part of the hypothesis right and part of the hypothesis wrong. The hypothesis first stated that the robot would tip quicker as the angle of decline increased; this was proved right by the first set of graphs, especially the averages graph. The "Average time of vehicle's tip" graph showed this trend, illustrating the decrease in times from the 0° trials' average of 2360 ms, to the 3° trials' average of 1642 ms, the 6° trials' average of 1844 ms, the 9° trials' average of 1611 ms, and the 12° trials' average of 1495 ms, though the 3°trials seem to be an exception. Most of the 3 degree trials were about 1700 ms, but there were 4 that were well below it, in the range of 1470 ms to 1520 ms, that were enough to pull the 3°average down to a low 1642 ms.Still, tipping times decreased overall as the degree of decline increased.

The straight data revealed that for the most part, the values did not exceed the range of     -50/200th g-force (-1/4th g-force or -1/5th meters/sec2) to 50/200th g-force (1/4th g-force or 1/5th meters/sec2). This value was thus chosen to be the parameters x and y as the extreme values for accelerometer data in part II of the experiment.

Graphs in the second set titled "Accelerometer measurements for __° trial __," were chosen to represent each degree based on the based on the following parameters respectively: the trial's tipping time and how close it was to the average; or if an anomaly occurred, such as if the vehicle lost a wheel at the end. The final representatives that were chosen are as follows: 0° trial 10, 3° trial 8, 6° trial 9, 9° trial 2, and 12° trial 8. The information provided in these five graphs,plus one that presents all of the data together for comparison, show that the second part of the hypothesis is wrong and that they are similar despite the changing degree of decline.

In all of the trial graphs, the trends are similar. Most of the tipping times are found before, after, or buried within a series of peaks. For instance, in 0° trial 10, the tipping time is found towards the end of three peaks; in 12° trial 8, the tip is at the beginning of a series of several peaks, and the tipping point in 9° trial 2 is on the second peak in a series of several small peaks. In addition to the somewhat varying locations of tipping times, the actual tip that is represented in data cannot be clearly found in each data set without the aid of the recorded time. The tipping time is found in each graph in the red segment. As illustrated by the graphs, the leap between the data values is not always that much. In 0° trial 10, the tip at time 2260 ms goes from a measurement of 100/200ths g-forces (1/2 g-force) at 2247 ms to a measurement of 104/200ths g-force at 2372 ms. However, in 9° trial 2, the tipping time is 1630 ms. The measurements leap from 117/200ths g-force to 162/200ths g-force at 1618 and 1635, respectively, giving 9° trial 2 the widest leap between measurements of all the representative trials.

The beep trials' times of alarms, beeps, and tips can be found in the third set of graphs under that name. The first of the two graphs show the alarms, beeps, and tips of the representation beeps. To pick these representatives, for each beep trial, all of the event's individual times were added up and compared to the average's total for that trial. The beep trial with the closest total was chosen as the representation beep for that degree. Values of 0 were used if the beep trial did not have a certain event; for example, the 12° representative, 12° beep 3, did not have a 1st beep, as indicated by a value of 0. The averages graph also shows the corresponding events and times for each degree. It is interesting that the 9° and 12° beeps have very similar times and trends, while the 3° and 6° beeps also have similar times and trends, and the 0° beeps were outliers and had very different data from the others, probably due to the fact that the programming actually prevented it from tipping. The 9° beep's average first alarm occurred at 1424 ms and the 12° beep's average first alarm was 1492. Also, the 3° and 6° beeps have the same average first alarm, at a time of 1616 ms. However, the time of the 0° beep's average first alarm was 2576 ms.

The accelerometer graphs reflect the impact of the programming; they show that though the programming did not work on all the degrees of decline, it did slow the robot down and decrease lateral momentum. It decreased the series of peaks. For instance, in the 6° beep 4, the tip was only buried in a series of 3 peaks, as compared to the 6 peaks in the 6° trial 9. This means there was less lateral momentum as the robot turned and tipped. In addition, in 0° trial 10, there is a series of 3 peaks, whereas 0° beep 1 had no peaks since it did not tip. The 9° trial 2 peak series numbered about 7 peaks, as opposed to the 9° beep 1 where it does not have much of a peak series; it is simply rising data values. It also decreased the damages, namely the number of times that a wheel has fallen off. A total number of 11 out of the 50 trials reported lost back wheels compared to the 7 lost back wheels throughout the 25 beep trials. However it must also be noted that lost wheels were not noted in the trials throughout the 9° and 12° trials in the beginning. This partially proves the hypothesis right, that it can prevent the tip on lower degrees, though not the higher ones, and will decrease damages and lateral momentum on all degrees. Therefore, the graphs prove different parts of the hypothesis right and wrong.

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