Teacher Answer Key: Field of View
Introduction to Mobile Robotics > Field of View
Phase 1: Find Detection Boundary – Evaluate your Findings
Observations:
1. Mentally “connect the dots” for the pattern of marks you made.
i.
Do your marks seem to fall into any kind of pattern, trend or outline of a
shape? If so, describe it.
This is a complicated question to answer, because the shape
that the Ultrasonic Sensor readings will make can vary greatly.
Sometimes the “dots” will produce a shape similar to the one
shown on the screen next to this question. Students may
describe this shape as a two circles or ovals or “a snowman.” It
is comprised of a smaller circle close to the robot, and a larger
circle farther away.
On the other hand, the “dots” can also produce a shape that is
more like a cone. It is narrower near the sensor, and then
wider as you get farther away, but has a very well-defined
“end.” This is similar to the first shape, but does not have the
distinctive two-circle appearance.
Other patterns may indeed be possible. If you have concerns about the validity of a
student’s “shape,” verify it on your own by moving the object onto their markings and
noting where the sensor can detect and cannot detect it.
Either of the shapes may be skewed either to the right or the left of the center line. This
can happen organically because of the natural tendencies of the sensor, or it can be a
function of the fact that the sensor was aimed slightly to the left or the right.
ii.
What does this “outline” represent in terms of what the sensor can
detect?
This outline represents the farthest points in all directions at which the sensor will
be able to detect the object. Everything within the shape is the detectable area for the
sensor detecting this object.
2. Locate the tracing that is farthest from the Ultrasonic Sensor. Place the object at this
location again, and record the sensor’s reading from the NXT’s viewscreen.
i.
What is the maximum distance that the Ultrasonic Sensor could detect for this
object?
This will differ from student to student, and will be different depending what surface the
test was performed on. In general, for this object, the maximum reading should be
somewhere in the range of 60 to 100cm. If the student has reported a value larger than
200cm, there is something amiss.
ii.
Where was the object located in relation to the sensor at this distance?
The object will be detected the farthest away when it is directly in front of the
sensor. This will be more or less along the line of tape that runs vertically, if the sensor
was aimed correctly.
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3. Find the two points along the same horizontal line that are the farthest apart. This is
the farthest to the side that your sensor can detect for an object of this size.
i.
Is this “widest detection range” wider or narrower than the robot’s physical
width?
This is the distance in between the two points the furthest apart horizontally, from the
inside of one of the tracings to the inside of the other. For this object, it should be around
50cm, depending on the setup. Larger widths are possible, but take care that they are not
wider than the length of the detection area, as this should not happen. As the robot is
approximately 17cm wide, this width is much larger than the robot.
ii.
If the robot moves in a straight line, is the Ultrasonic Sensor’s detection
“width” wide enough to make sure that it will detect an object of this size
before it runs into it? Hitting the very edge of a tire still counts as a collision!
Yes, the robot itself is much less wide than this, so it will be able to detect objects
to either side of it and can avoid hitting them.
Phase 2: Scale Model – Measure and Plot
4. What is the actual distance between two horizontal lines on the Graph Sheet?
This distance is 2 cm. It is found by measuring with a ruler.
5. What distance is represented by the gap between two lines on the Graph Sheet?
The lines are all labeled in increments.
The lines represent distances 10cm apart. They are actually labeled in 10cm increments.
6. What is the scale (size ratio) between the graph paper distance and the physical
distance it represents? Express your answer as a ratio in the format 1:__.
It is a 1:5 ratio. The size ratio is the ratio of the distance between two lines on the paper, and the
distance between two lines on the actual board. The distance between two lines on the paper
was 2cm, and the distance that represented on the board was 10cm, so the ratio is 2:10, or,
simplified, 1:5.
Phase 2: Scale Down – Evaluate Your Findings
7. Look at your graph sheet.
i.
In what important ways is the scale model the same as the full-size pattern?
The scale model has the same width relative to its length as the full-size pattern.
This is important because it allows us to measure directly from the scale model to
determine key aspect of the full-size pattern. For instance, we can measure the distance
between two points on the scale model, and then multiply it by 5 to get the distance
between those same two points on the actual pattern. If we had shrunk the information in
one direction and not the other (shrunk the length, but kept the width the same, for
example) then it would be more complicated to determine the distance between points
using the scale model.
ii.
Are there any ways in which the scale model is not the same as the full-size
pattern?
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The scale model and the full-size pattern are clearly different sizes. One fits on a
sheet of paper, the other takes up over a square meter of space!
iii.
On the whole, do you feel that the scale model is an acceptable way to store
the information from this experiment?
A scale model is a very good way to store information. It is very common to take objects
(data sets, buildings, etc.) and shrink them down so that they fit in a more reasonable
space. This makes the information easier to present and store.
However, this question asks students how they feel about scale models, so any answer is
acceptable. Students may feel that something is lost when a scale model is created, and
may prefer to keep the original data intact. It is entirely up to them.
8. Recall the scale factor (size ratio) that you calculated in question 6.
The scale factor we calculated was 1:5. For every one centimeter on the paper it represents
five centimeters on the actual pattern.
i.
Explain what this scale factor means.
A scale factor is the amount that you shrunk the information by to fit it on the
page. For this project, you had to take the distance from the sensor in both the vertical
and horizontal directions and shrink them (divide them by 5) so they would fit on the
paper.
ii.
If two points on the full-size pattern were 22 cm apart, how far apart should
they be on the scale model?
To get from the full-size pattern to the paper size, we divided by 5. So if two points are
22cm apart in the full-size pattern, we should divide by 5 to get their distance apart.
22cm/5 = 4.4cm
iii.
If two points measure 2.3 cm apart on your scale model, how far apart should
they have been on the full-size pattern?
If we shrunk things down by 5 times to get them from the board to the paper, then we
need to blow them up (multiply) 5 times to get from the paper to the board. So take the
distance on the paper and multiply it by 5 to get the distance on the real pattern.
2.3cm x 5 = 11.5cm
9. Locate the tracing that is farthest from the 0 cm marking on the graph sheet.
i.
Where was the object located in relation to the sensor at this distance?
If the sensor is correctly aimed, then the object will be sensed the farthest away
when it is directly in front of the sensor, more or less along the dark line that runs
vertically through the data collection sheet.
ii.
Measure the distance from the 0 cm marking to the farthest marking. How far
is it on the graph sheet?
This will differ from student to student, and from robot to robot. On the paper, the
maximum reading should be less than 23cm (because that is the length from the bottom
line to the top of the paper. Generally, the answer should be between 12cm and 18cm,
though longer or shorter distances are possible.
iii.
Using your scale factor (size ratio), calculate how far the object should
actually be. How far away should it be?
This is done simply by multiplying the answer from Part (ii) by the scale factor (5).
For example, if the distance on the graph sheet were 14cm, then the actual distance that
the sensor should be able to detect this about should be 14cm x 5 = 70cm.
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iv.
What is the maximum distance the Ultrasonic Sensor can detect a can-sized
object, and in what direction must it be?
The maximum distance is whatever the student found when they first did the test. This
can be between 60 and 100cm, depending on the surface and the configuration of the
robot. The can should be directly in front of the sensor for maximum detection distance.
This is the distance in between the two points the furthest apart horizontally.
10. The NXT Ultrasonic Sensor has 2 modes that it switches between automatically: a
short-range mode and a long-range mode.
i.
Is there any evidence of this switch happening in the pattern of the detection
area? If so, what do you see that suggests there is some kind of mode
switching happening?
If the pattern that was created has the “snowman” shape, then yes, there is evidence of
these two different modes in the pattern that was created. The two distinct “circles” are
created by the two different modes. The short-range mode detects things in the smaller
circle that is closer to the sensor, and the long-range mode detects the object in the
larger circle, farther away from the sensor.
If the pattern has the “oval” or “egg” shape, then this does not point to any modes of the
sensor.
ii.
At what distance does the transition from short-range mode to long-range
mode appear to occur?
The transition appears to occur somewhere between 25 and 30cm in the
“snowman” shape. It is not quite clear where the exact point is, as the two mode of
operation may overlap some.
iii.
Why might a sensor need multiple modes of operation?
The sensor may need this because one mode alone doesn’t provide the desired results.
For example, if the sensor only had the short-range mode, then it really wouldn’t be able
to detect the object beyond that first small circle, which isn’t very useful. The long-range
mode was added on top of the short range mode in order to increase the detection area.
There are many other reasons to use multiple modes of sensing, as well. It might be
useful to be able to switch back and forth at any given time, or turn one off completely.
Students should be encouraged to think critically about the needs of robot and roboticists
when answering this question, and to be creative with their answers.
Analysis and Conclusions: Conclusions & Exercises
Conclusions
11. The Ultrasonic Sensor works by sending out high-frequency sound waves and
measuring the amount of time it takes for the sound to reflect off an object and come
back.
Explain the shape of the detectable area in terms of where and how far sound
must travel in order to be sent out and received back.
Hint: Areas where the sensor could not detect an object mean that the sound
waves did not reach those areas, did not return to the sensor from those
areas, or were too weak to be detected by the time they returned.
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The detectable area is defined in width by the angle at which sound waves sent out
by the sensor will bounce off the object and come back to the sensor. If the object is
too wide (too far to one side or the other), then sound waves sent out may bounce off the
object, but they will get deflected somewhere else, so the sensor will not read them.
The detectable area is defined in length by the strength of the waves bouncing
back. A larger object has a larger surface area for the waves to bounce off of, so what
bounces back to the sensor is a stronger sound. The less surface area, the weaker the
signal sent back to the sensor, until it reaches a point at which it does not detect
anything. This is why larger objects are ‘visible’ from farther away.
The detectable area is usually broken up into two main “circles” by the two different
modes of the sensor. In one mode, the sensor sends out low power pulses of sound, and
is very sensitive about what it gets back, so it can detect objects in a close range. In the
other mode, the sensor kicks it up a notch and sends out stronger ultrasonic pulses, so
they can bounce off things that are farther away and still send back enough sound to be
detected by the sensor. This is the area bounded by the larger circle. Sometimes these
two modes are not apparent in the outline, but they do exist.
12. Write a paragraph or two describing how you conducted your experiment, including
step by step instructions so that someone could recreate your experiment in the
future. Make sure to include instructions on how to store this data in a manageable
from for future use.
The experiment was conducted with the following steps.
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Set up the data collection area by marking a centerline, and then 10cm increments down
the line.
Set the robot up on the centerline, with the Ultrasonic Sensor pointing forward. View the
sensor readings.
Place the object far down the centerline, and push it towards the sensor until the sensor
is able to read it steadily.
Take the object, put the center of it in line with the line 10cm away from the sensor, but
so far to the left or right that the sensor cannot detect it
Slowly push the object toward the center line. Stop when the Ultrasonic Sensor can
detect it and gives you a reading.
Mark the object’s position with a piece of tape.
Do this on the other side of the centerline.
Do this for every 10cm increment line on the board.
Take this information, and scale it down to fit on the sheet of paper.
A good paragraph will include these steps, and some explanation as to why some of the
tracings are out of line with the rest of them and how the scaling down of the information was
done.
Exercises
13. On the left is the data taken from a
scientist’s test of a similar
ultrasonic sensor. She ran the
experiment with the same method
that you used, by sliding an object
along until the sensor was able to
detect it, and then marking that
point.
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i.
What was the maximum range of her sensor, and in which direction did it
occur?
The maximum distance that the sensor could detect the object was at
approximately 52cm, directly out in front of the sensor (along the centerline). This is
determined from reading the distance of the furthest point from the data graph.
ii.
What was the widest part of the detection area, and how far from the sensor
is it?
The widest part of the detection area occurs at a distance of 40cm away from the
sensor. The detection area at this point is about 30cm wide.
14. Another, much larger, sensor was tested here, but the detection range was so big
that the scale of the graph had to be changed.
i.
What was the maximum range of her sensor, and in which direction did it
occur?
Her sensor could read an object approximately 170cm away, straight out in front of
the sensor.
ii.
What was the widest part of the detection area, and how far from the sensor
is it?
This is a judgment call. Based on the scaled-down data sheet, the widest part of the
detection area could be at a distance of 75cm from the sensor, or a distance of 100cm
from the sensor. The width at either of these distances is about 110cm. the more
accurate way to find this would be to use a ruler and measure, but you can also estimate
using the gridlines on the paper.
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15. Sound travels approximately 340m/s at sea level.
i.
Identify the longest distance you detected an object in this exploration.
Students will answer this by either measuring off of their data sheet and scaling up, or
replacing the object in the spot farthest from the Ultrasonic Sensor, and reading off the
view screen again. Distance will vary from student to student.
For our example, let’s say this distance is 75cm.
ii.
How long did the ultrasonic wave take to reach the object? Remember that
your readings are in cm.
To answer this question, students will convert their distance into meters (divide number of
centimeters by 100) and then divide the answer by 340 m/s to get a number in seconds.
It should be a very small number. See example below:
Distance = 75cm = .75m
Time = .75m / (340m/s) = 0.00221s
iii.
How long did it take for the wave to return to the sensor from the object?
The distance to the object is the same as the distance from the object. Since the distance
is the same, then this answer will be the same as the answer for Part (ii).
Time = .75m / (340m/s) = 0.00221s
iv.
How long did the wave take to travel through the air, in total?
Add the results from Part (ii) and Part (iii), or, multiply Part (ii) by 2.
Total time = time to go one way x 2 = 0.00221s x 2 = 0.00442s
v.
If the object had been 1cm farther (the smallest increment the Ultrasonic
rangefinder will detect), what would its sound wave travel time have been?
For our example distance:
Original distance = 75 cm
New Distance = 76 cm
76cm = .76m
.76m / (340m/s) = 0.00224s
Total Time = 0.00224s x 2 = 0.00448s
This is about 0.0006s longer than the first reading, or 0.6 milliseconds.
vi.
What does this comparison tell you about the sensitivity of the timing circuitry
in the NXT and the Ultrasonic Sensor?
The timing can tell the difference between each half of a millisecond. Let’s put this in
perspective: each time you blink it takes about a tenth of a second, or roughly about 200
times as long as this. That’s some fast circuitry!
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