Worksheet Answer Key: Scanning and Mapping Projects > Mine Mapping > Investigation 2

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Suzanna Hines
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1 Worksheet Answer Key: Scanning and Mapping Projects > Mine Mapping > Investigation 2 Ruler Graph: Analyze your graph 1. Examine the shape formed by the connected dots. i. Does the connected graph create a pattern? This answer will depend on the student. In general, the dots should have created a shape on the paper that is rectangular or polygonal. But the fidelity of this image to the actual environment that they are mapping will depend on the precision of measurements and of plotting. ii. If so, what does it represent in the real world? This pattern represents the outline of the simulated environment, i.e. it shows the locations of the walls of the environment, as well as their distance away from the center of measurement, which is at the origin of the polar graph. iii. Are there any places where the pattern does not hold? Again, this will depend on the student. If measurements were taken and plotted methodically and precisely, then the pattern should be true to the simulated environment at all points. Some skewing may occur at the corners of the plotted image, which can be attributed to difficulty in measuring to those points. As students will see later, this skewing becomes much more pronounced when using the Ultrasonic Sensor to measure the distance to a corner. 2. Find the point on the graph farthest from the origin? i. What is the longest distance represented by a point on the graph? Exact measurements will depend on the student. In general, measurements should be between 20 and 30cm. This will be the distance of the point on the farthest ring from the origin. It should be one of the points at a corner of the plotted shape, since the corners of the area are the farthest distance from the center of measurement in the real area. ii. Is it the same as the longest distance to a wall in the real area? Why or why not? It should be. The distance that is plotted on the graph is taken directly from the measurement of this distance made with the ruler. Only minor differences should be present between the distance that these points represent, and the actual distance. These differences can be considered the results of human error in measuring and then plotting. Note: This question is not asking about the actual distance between the origin and the farthest point from it the question is asking for the distance represented by this point. The two actual distances will not be the same, as the plot is a scaled down model of the real thing. The actual distance on the graph should only be a few centimeters, while the distance in the simulated environment should be between 30 and 45cm. 3. Find two points or lines that can tell you the distance from the left wall to the right wall in the testing area. i. Based on the graph, estimate the width of the testing enclosure. Given the setup shown in the Investigation, the width should be between 25 and 45cm. This can be found by finding two points on the graph that are directly across from one another, and determining how far to the right or left of the center line each one is, and then adding the two distances together. This is 1/7

2 easiest to do using the points that lie along the 0 and 180 degree lines. In that case, all you need to do is to read off how far they each are from the origin of the graph, and then add the two measurements. If students have used a different type of setup that isn t based around the size of NXT bins, then their answers will vary widely. They may even need to rewrite the scale that is printed on the polar graph paper to accommodate a larger (or smaller) area. ii. Measure the width of the physical area. How close was your prediction? This will depend on the student, as well as the accuracy of the measurements. This question should be answered using phrases such as Very Close or Pretty Far Off rather than numerical error calculations. Ruler Graph: Map Object 4. Compare this graph to the one you made without the object. What clues does the graph give you that show the object s location? On the graph of the area with the object, there should be at least one or two data points that seem out of place compared to the other graph. These points should be much closer to the origin than their counterparts on the first graph. 5. How could you get a better idea of the size and shape of the object by scanning like this? By scanning from a different angle. This single scan gives you only a very rough estimate of the location of the object, but it cannot tell you how large the object is. For instance, by scanning from this location, you cannot tell whether or not the object extends all the way back to the wall of the enclosure, or if the object is just a very thin board. If you rotated your view by 180 degrees, however, and redid the scan from a zero point located on the back wall of the enclosure, then you can compare that data to the data from the first scan and get a better idea of the overall size of the object. The more scans you take and overlay, the more complete a picture you will get. This applies to any sort of scanning and mapping. The key is to weigh the completeness of the picture against the time it takes to acquire the additional data, and decide just how much data to take based on that. By taking more data points. By increasing the number of measurements that you take over the entire area, you will get a more accurate image of what the area looks like. You can do this by measuring every 5 degrees, or even every degree, if you are good! Sensor Graph: Map Object 6. Compare this sensor-based graph to the original obstacle-free ruler graph. i. Are the graphs similar? This will depend on which sensor the students used. For example, the Sound Sensor will produce no useful readings, and so if students measured the area with a Sound Sensor, their plots would be completely different from the one made with the ruler. Something similar would occur with the Light and Touch Sensors. The best sensor to use for this application is the Ultrasonic Sensor, which may have provided slightly different data than students were able to measure with a ruler, but produces a graph that is similar. There is one notable exception to this similarity, which is covered in the next question. Check the two graphs and make sure the student s answer is appropriate. ii. Which features are the same? Which are different? This will depend on the student and the sensor they chose. Using the Ultrasonic Sensor, there may be points along the left or right walls of the pattern that may seem slightly out of place when graphed with 2/7

3 the sensor. Most of the erroneous or out-of-place points will be located in and around the corners of the simulated environment. The Ultrasonic Sensor will often measure these points as farther away than they actually are, and so, when plotted, they will tend to skew the plot, giving it sharp corners that don t exist in the real environment. This happens because the ultrasonic waves will hit side of a corner and then, instead of bouncing back to the sensor to be collected, they will be deflected towards the other side of the corner. So, when the waves finally do come back to the sensor, they have traveled a longer distance, and this is what the sensor records. If the group chose to use one of the other three sensors, check their two graphs to see if they answered this question appropriately. For example, if the sensor graph shows no clear pattern while the ruler graph makes a perfect rectangle, then it is not appropriate to say that all features are the same. Use judgment to make sure the answer suits the data provided. iii. Which graph is more accurate? Explain your reasoning. This question is difficult to answer, and students may choose either graph as the more accurate, so long as the fully explain their reasoning. For example, a student may determine that the graph created by measuring with a ruler is more accurate than the one created with the sensor, because the pattern that it shows looks more like the outline of the area that they were mapping. However, this argument could go both ways. Another student may argue that the graph made with the Ultrasonic Sensor is more accurate, because they found it difficult to take the measurements with the ruler. It will be up to the student to make and support this judgment. Sensor Graph: Map Object 7. Can you tell by the graph where the object is located? The answer to this question will depend on the student. Using an appropriate sensor, the results from this graph should be similar to the results from the ruler-measured graph with the object, and so, yes, the object should be apparent on the plot. However, if using an Ultrasonic Sensor, it may be possible to angle the object in such a way that the ultrasonic waves would bounce off of it and not back to the sensor, and so the object would be effectively invisible to the sensor, where the ruler could have measured it. This can also happen with the Light Sensor, if the object is of a particular color or opacity. The Sound Sensor readings should give you no clear indication of the object s location. Conclusions 8. Trade the graph you made with a ruler and object with the same graph from another group. i. Identify the location of the object in the other group s graph. This is for the individual or group to do. The answer should be marked or otherwise identified on the graph of the other group. This set of questions is meant to give the group practice interpreting the graphs to identify objects that they have no seen, and do not know the location of beforehand, as this is what they will have to do with the information that comes from the mining robot. ii. Check the location of the object in the other team s actual test area. Did you correctly identify the object? This answer will depend on the group, as well as their identification of the object on the other group s graph. iii. If you misidentified any points, what factors led to the confusion? 3/7

4 Again, this will depend on the group. Some factors that may lead to confusion as to object location are: misplotted points, a messy graph, skewed data points, or data points that seem out of place on the graph. 9. Trade the graph you made with a sensor and object with the same graph from another group. i. Identify the location of the object in the other group s graph. This is for the individual or group to do. The answer should be marked or otherwise identified on the graph of the other group. Again, this set of questions is meant to give the group practice interpreting the graphs to identify objects that they have no seen, and do not know the location of beforehand, as this is what they will have to do with the information that comes from the mining robot. ii. Check the location of the object in the other team s actual test area. Did you correctly identify the obstacle? This answer will depend on the group, as well as their ability to discern the location of the object on the other group s graph. The clarity of the pattern on the other group s graph will have a huge impact on their ability to discern the object. iii. If you misidentified any points, what factors led to the confusion? Again, this will depend on the group. Some factors that may lead to confusion as to object location are: faulty sensor readings, the lengthening phenomenon produced when the sensor tries to read the distance to a corner, misplotted points, a messy graph, skewed data points, or data points that seem out of place on the graph. 10. Consider the following questions for both the ruler and sensor versions of the graph. i. Did the graph show the physical area realistically, or was the image distorted? The image was probably slightly distorted on both graphs, but more so on the sensor graph, depending on which sensor was used. Distortion can be due to inaccuracy of measurements, as well as difficulty in plotting precisely, unreliability of the sensor, or poor choice of sensor for this capacity (e.g. the Sound Sensor). Also, using the Ultrasonic Sensor to take measurements will most likely produce a lengthening of the points around the corners. The answers will differ from group to group, and their various graphs should be considered when considering their answer. ii. If you saw distortion, was there a pattern? This will depend on which sensor was used. The Sound Sensor should produce a completely random graph, while the Light Sensor should produce values that are all fairly uniform (if it is held in place at the origin and not moved to be closer to the walls). If using the Ultrasonic Sensor to graph, the major distortion occurs around the corners of the environment. There should not be any major distortions (of the same scale) in the ruler-based graph. iii. What might have caused the distortion, if any? The answer to this question depends on the answers above. If students had answered that there was no distortion on either graph, then there would be nothing to say here. However, they should point out causes for distortion if they identified any in part (ii). These causes may include, but are not limited to: faulty sensor readings, the lengthening phenomenon produced when the Ultrasonic Sensor tries to read the distance to a corner, misplotted points, poor choice of sensor, a messy graph, skewed data points, or data points that seem out of place on the graph iv. Is the level of distortion acceptable for the planned uses of the map? Students should reach their own conclusions to answer this question. Some may conclude that, yes, this distortion is acceptable for determining distances and the location of objects within the mine. If you can still tell where the objects are, and measure width and depth of the area, then it should be fine to use inside the mine. Others may look at the sensor-based graph and determine that the results are much 4/7

5 too skewed to give an accurate representation of the dimensions of the mine or the location of objects. If there is no clear answer based on a student s findings, ask students to justify their answer. 11. Compare the readings that you took with the sensor to the readings that you took using the ruler. i. Were there any areas of the map that were consistently different between the ruler and sensor-based versions? Again, this will depend on which sensor was used. If students used the Ultrasonic Sensor to graph, the corners of the area will be consistently skewed, because the sensor can be easily tricked by ultrasonic waves bouncing off walls. If they used the Light sensor, the graph would be consistently skewed by any light sources nearby, or by the ambient light in the room. The graph created by a Touch Sensor may be different depending on the angle at which the sensor came in contact with flat surfaces. The Sound Sensor should produce a graph that shows no consistent results whatsoever, so there is no real way to answer this question. ii. Consider the operation of the sensor. Propose at least one possible reason that would explain why the sensor value is different. This will depend on the sensor. For more information on sensors and how they work, See the Basics Section. Touch Sensor: sensor value could be different due to a missed press, or the fact that the axle slid along the surface for a bit before the sensor actually triggered a press. Also, if the touch Sensor is extended with a hand beyond the origin of the graph, it may be difficult to measure exactly how far the hand extended before the touch sensor was pressed, which may lead to bad data points. Sound Sensor: Because the Sound Sensor does not give us back useful data to begin with, it s hard to say what would cause the values to be different from the ruler-measured values. There is no way to answer this question. Light Sensor: The Light Sensor could give back readings that are different from the ruler measurements for a myriad of reasons. First of all, to give readings in centimeters, the user needs to have some sort of method for calibrating the Light Sensor. They need to either create a look-up table of light sensor values and their counterpart distance measurements, or to have some other method, possibly a function, to translate from one to the other. Then they need to make sure that the experimental set up is precisely the same (including ambient light values) as the set up when they did the calibration. Causes of distortion of sensor values could lie anywhere along this process. The calibration could have been done incorrectly, of the translation from light readings to centimeters could have been incorrect, or the experimental setup could be slightly lighter or darker one day than it was when the calibration was done. Additionally, skewed numbers could come from not accounting for variations in color, which the Light Sensor will detect. Ultrasonic Sensor: The Ultrasonic Sensor values will be skewed if the ultrasonic wave sent out by the sensor does not come directly back to it once it has bounced off of an object. For example, in the corner of a box, the wave may reflect off of one side of the corner, and bounce toward the other side, and then retrace its path back to the sensor. This would account for the sensor reading the distance as slightly longer than it actually is. Also, the Ultrasonic sensor may not sense a gap in between two objects, because it will read the waves bouncing off of the objects rather than the wave bouncing through the gap and back. iii. Is the ruler or sensor version closer to the actual physical region? No matter which sensor was used, the ruler version is a closer description of the actual physical region. This is because the ruler measurements are exact (or close to it), and have passed through a human approval process before getting recorded on the graph. Sensor readings, on the other hand, are not physical data that the human can check or recheck. Light Sensor readings, for example, have no true physical counterpart, like centimeters on a ruler. When taking readings with a ruler, a human will instinctively double check the measurements and make sure they make sense in the scheme of things. With a sensor, on the other hand, the human must take the sensor value as it is. There is no good way of checking its accuracy. 5/7

6 12. Taking a ruler into the mine is not possible. Based on your experimentation, do you think your sensor is a reasonable substitute? This will depend on the student and the sensor they chose. Note that this is similar to Question 10, Part (iv). In general, students should conclude that the Ultrasonic Sensor is a reasonable substitute, but that each of the other sensors pose significant problems that must be overcome in order to use them for this mapping purpose. Have students justify their answers to this question if you do not feel that they are appropriate. 13. Conclusion: Is the sensor-based, polar graphing method of gathering and representing positional data acceptable for your purposes? Explain the capabilities and limitations of this approach in general, and justify your conclusion as to the suitability or non-suitability of this method. If you decide that this method is not acceptable, propose a different method instead that could accomplish the same goals. Responses to this question will vary widely, depending on the sensor used. However, the response should not include a discussion of the sensor, but rather of the method. The student who supports this method may include some or all of these main points in the discussion: The approach is sound, and simplistic. Having the robot wait in the entrance to the mine while it maps the area is a good idea. You would not want the robot to go very far into the mine to begin mapping, because it may come across an obstacle on its way in. This approach also requires only minimal programming to map the room, which leaves less room for things to go wrong during programming. The robot does not need to plan its path according to the sensor data, or to convert the sensor data into any other form. It just needs to take the data from its position in the entrance of the mine, and send it back to the Monitoring NXT. The approach is limited by several things. o It is limited by the range of the sensor. The Light Sensor, for example, can really only sense objects within a few centimeters. The Touch Sensor has a range that is as long as the physical sensor itself. The range of the Ultrasonic Sensor is from 0 to 255 centimeters. The Sound Sensor has a very large range, but does not give back useful readings about the static objects in the environment. o The approach is also limited by the accuracy of the measurement that the sensor gives. The Light Sensor, for example, will give you different readings, even given the same lighting conditions, depending on the color of the object. So its accuracy is questionable. The Ultrasonic Sensor is less accurate in rooms with more obstacles, because there is more for the ultrasonic waves to bounce off of and cause interference. Students may also have concluded that the approach is not sound, and may have listed some of these reasons: The sensor did not do as good of a job at mapping as the ruler did. Some sensors, in fact, produce results that are not discernable as results. If the student used the Sound Sensor, for instance, then the plot that it produced would be random, which may lead them to conclude that this is a poor method of mapping the mine. The object was not discernable from the sensor results. This result is very possible, but it combines with factors such as the accuracy of the person who made the plot, and the skill with which the measurements were taken. Lack of a distinct object on the plot may not be entirely the fault of the sensor, or the method. Student may come up with another reason. Look for a good, logical argument based on scientific observation. I don t want to because it s hard is not a good reason to avoid one method over another. Possible different methods may include: Having the robot drive by pressing the Touch Sensor against the walls of the mine, and use the rotation sensor to measure how far it has traveled. This will require the robot to use another 6/7

7 Touch Sensor to know when it has finished with one wall and must turn to follow the next one. This strategy, however, has the disadvantage that if there is an obstacle in the center of the mineshaft, the robot may not detect it, since it is only using touch to detect object. A further disadvantage of this strategy is that because the robot is traveling around inside of the mine, it may be difficult for it to find it s way back out. The robot needs to use its rotation sensors to know where it is, as well as what direction it is facing, and this can be quite a challenge. Additionally, in the fragile environment of an abandoned mine, rubbing against the walls may not be the best idea. Similar to the method above, the robot can use a Light Sensor to keep a constant distance along the wall, so that it does not have to run into it. This approach is subject to all of the same considerations as the method above, but does not require the robot to come in contact with the wall to run along it, which may be a saving grace in an abandoned mine. The robot could measure by staying in one place and extending a long stylus with a Touch Sensor on the end. It would need to keep track of which direction the stylus was aimed, and how far out it had to be extended in that direction before the Touch Sensor was pressed. Other methods are indeed possible, and should students suggest something different, they should be encouraged to think critically about it, and possibly even test it. 7/7

Department of Physics & Astronomy Lab Manual Undergraduate Labs. A Guide to Logger Pro

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