Mood Brightener: ...more from Stay Homas. (Confination III)
Questions/Answers from Reflection on Previous Days:
Perhaps, upon reflection, you have some more questions as a result of previous days discussions?
[Placeholder for Q/A]
Where?
For many robots the question of where they are is critical. Whether it is a welding robot or an autonomous vehicle or a spacecraft where is an important question and there are a variety of ways to determine it. We will take some time to discuss a number of different systems for describing where we are along with some terms that are helpful to understand.
X-Y Grid:
This is the system that you probably learned in a math class at some point. We choose a set of perpendicular axes (usually called x and y but not always) and we define the location of points on the sheet of paper using a 2 dimensional grid. The x value tells us how far to go in the x direction (+ or -) and the y value tells us similarly how far to go in the y direction to identify to desired point or location. Your math teachers hope that you remember that this point is also the intersection of a line of constant x and a line of constant y. The units that we use to measure the x and y values can be anything although we will use the SI (International System) in this class since it is the system used around the world with a few notable exceptions. While you may be more comfortable with the Imperial (British) system of units it is time for us all to move on and join the rest of the world.
It is important to note that it is critical that the origin of the x-y grid be clearly understood. Knowing that an object is located at 431 cm in x and -64 cm in y is useless if we don't know where the origin (the location described by 0,0) is located.
An interesting example of an x-y grid system for describing location is our system of addresses used in most places in this country. Consider the address 61170 SE 27th St in Bend. Do you have a sense of where it is in Bend? Why? Where is the origin of the x-y grid for Bend? The same service is available at 1355 NE Hemlock in Redmond. Why is this harder for many people to know where this is in Redmond? Where is the origin of the x-y grid in Redmond? Both of these addresses are legitimate and correct.
These are the Humane Society addresses in Bend and Redmond. If you went there would you be where you intended to be? Would everybody who goes to this address knock on the same door or park the same place? This distinction creates a need to discuss....
Accuracy and Precision:
Accuracy is the question of whether the location given is where you intended to be. Precision is the question of whether every time someone goes there do they end up at exactly the same place. Are these addresses accurate? Are they precise? Explain your thinking.
On a sphere:
Because a sphere isn't really flat we can't use and x-y grid to define where we are broadly across the globe. Locally x-y works quite well but it leads to errors at larger scales. On the globe the traditional solution has been to use latitude and longitude. If you haven't explored this location system for the earth here is a presentation from the aviation folks to get you started.
Can you articulate clearly where the origin of the lat/long system is on the globe? Be careful if you're hunting for treasure using a vary old pirate map since there have been several origins for this system over the centuries. In the current latitude/longitude system the location of the Bend Humane Society is
44°01'19.2" N 121°15'46.0" W
This is a very complex location description and requires some effort to determine where it is on a map because of the minutes and seconds.
GPS:
We are all very used to GPS though we may not think about how it knows where a location is. As it turns out GPS is also a latitude/longitude description of location but uses only degrees expressed in decimals (as discussed briefly in the video above). What do you notice about the GPS version of the location of the Humane Society in Bend?
44.022003, -121.262777
Hopefully you notice that there are no N/S or E/W labels only + and - and a lot of digits. What can you tell me about where you expect this location to be? What does the - sign on the latitude suggest? The + sign on the longitude? You can, of course, put this GPS address into Google Maps and it will tell you what's there. I will leave that up to you.
-33.856265, 151.215408
GPS and Accuracy/Precision:
If I take the Humane Society GPS (44.022003, -121.262777) and change the last digit we get some sense of the precision of this location system. What happens if I change just the last digit of the GPS address -- does it still get me the right place? What happens if I only use 3 (or 4) decimal places instead of the 6 shown? After playing with this a little you should have some sense of the precision and accuracy of this system of location.
What if I want to tell you where my office is using this system? This is the GPS address of my office in Redmond - 44.256640, -121.166008. Can you tell where it is in the building? What if I make a mistake in the second decimal?...or the third? Depending on how the GPS location is being communicated it is relatively easy to make an error that takes you to a significantly different location. Next time we will discuss how the GPS system works to determine where you are.
It's worth mentioning another geolocation system that seeks to address certain types of communication challenges. Much of the world has no effective addressing system and yet they seek to participate in the global economy. In many places mapping systems and communication are more challenged. In the process of sharing a GPS address multiple times it is easy to imagine an error creaping into the many digits or a - sign gets lost due to a spell checker. what3words is project that seeks to address this challenge by defining locations on earth using 3 words in the local language. The idea is that it is easier to successfully communicate 3 words successfully rather than 10 or 12 digits. Each 3 m x 3 m square on the planet is labelled with 3 distinct words that do NOT relate to the words in adjacent squares nor do they sound similar. This allows you to ask for the delivery of a package to a particular rock in the Namibian desert if you wish. One of the coffee roasters in Bend tried this to deliver packages to his finca in Guatemala in an area where there are no addresses. what3words is currently available in 44 langauges (not translated from one to the other -- that has potential for confusion). My office in Redmond is defined by
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Assignment Breadcrumb Reading: Bb Assignment
Favorite Location
Determine your favorite coffee shop, bakery, or ice cream store. Find
i) the street address
ii) the latitude and longitude in degrees, minutes, and seconds. How to: Google Maps
iii) the GPS location in degrees with 6 or more decimal places
iv) the what3words label for this location. what3words
Do not describe what you get at this location. We will use these for some activities during class.
Before Next Class:
Assignment HW: Bb Assignment
GPS Waypoints
Find two locations at least 5 blocks apart (could be in your town or elsewhere) where you have to take a least 1 90 degree turn to walk from one to the other. Provide a list of GPS locations (waypoints) that will take you between these two locations by traveling directly (straight lines) between successive waypoints. (This is how the path for the autonomous vehicles in the DARPA Grand Challenge were defined). Make sure your list of way points is clear and organized since another student will be asked to figure out your path from your data.
Assignment HW: Bb Assignment
what3words Waypoints
Repeat the previous problem using what3words locations for way points. Again, be clear and organized since another student will be asked to determine your path from your answers.
Looking Ahead:
Look ahead to the next Breadcrumb: Where: Math
Assignment Breadcrumb Reading: Bb Assignment
Thunder and Lightning!
Knowing that sound travels at 343 m/s on earth and light travels at 3.108 m/s calculate the delay time between the arrival of the light from the lightning and the arrival of the sound when the lightning is 1600 m (1 mile) away. Show each calculation and articulate a simplified rule to teach your kids and your family members to determine how far away lighting is.
