Comments on: The TacoCopter? – a gimmick for integration review /blog_archive/2012/03/25/the-tacocopter-a-gimmick-for-integration-review/ iteration, making, building, and coding in education Mon, 26 Mar 2012 01:18:07 +0000 hourly 1 https://wordpress.org/?v=5.7.6 By: Evan Weinberg /blog_archive/2012/03/25/the-tacocopter-a-gimmick-for-integration-review/#comment-59 Mon, 26 Mar 2012 01:18:07 +0000 http://evanweinberg.com/?p=449#comment-59 In reply to John Burk.

Good idea – I think it would be a good place to talk about it, though the details I think are a bit trickier. Perhaps they fit a polynomial to the acceleration data and integrate the error function with respect to time. Or I could give them a set of acceleration data with the Gaussian noise turned off and have them compare the results of the two. You might see my question at the end about the effects of integration on noisy data. We have differentiated noisy position data and seen the effect on velocity, though we did not explicitly talk about it in Calc since it was during Physics which doesn’t share all of the Calc students. That would also lead to a discussion comparing integration error vs. error coming from noise.

I also envision a possible second part to this exploration that involves working directly with the PD differential equation used to control acceleration. It could be a situation where I give them the solution and have them verify it, or have them use Wolfram Alpha to get it:

http://www.wolframalpha.com/input/?i=solve+ODE+%7By%27%27+%3D+a*y+-+b*y%27%7D

Lots to think about, plenty of options. Thanks for the suggestions, as always.

]]> By: John Burk /blog_archive/2012/03/25/the-tacocopter-a-gimmick-for-integration-review/#comment-58 Mon, 26 Mar 2012 00:55:44 +0000 http://evanweinberg.com/?p=449#comment-58 Evan,
One more thought—it seems like this might be a prime opportunity to ask students to deal with some uncertainty. Shouldn’t it be possible for them to try to predict a range for the final position along with their measurement? This is something that was lacking from almost all of my math classes in high school, but this might be a perfect place to introduce the idea. You might even be able to push them to do some calculations to figure out how good the accelerometer data would need to be in order to calculate the position with a certain range.

]]> By: Evan Weinberg /blog_archive/2012/03/25/the-tacocopter-a-gimmick-for-integration-review/#comment-57 Mon, 26 Mar 2012 00:47:13 +0000 http://evanweinberg.com/?p=449#comment-57 In reply to John Burk.

Thanks, John!

They do use a range of sensors – laser scanners, cameras, GPS, and I think another short range distance sensor such as ultrasonic or IR is used for additional information about obstacles. The car use a range of techniques to identify its location and map out its path. The class has been really fantastic in how it teaches you implementation of Monte Carlo localization, Kalman filters (which I’ve tried to teach myself before unsuccessfully), particle filters, and mapping. The thing that has benefited me the most is having an excuse to work in Python on a regular basis – really enjoying learning how to use it. Best part is finding easy ways to bring it into my classes.

]]> By: John Burk /blog_archive/2012/03/25/the-tacocopter-a-gimmick-for-integration-review/#comment-56 Mon, 26 Mar 2012 00:35:52 +0000 http://evanweinberg.com/?p=449#comment-56 Evan,
I love this assignment—this is so much more interesting than learning obscure integration techniques, and it really gets students seeing how calculus is put to use in real-world applications.

Since you’re taking the Udacity course on robotic cars, does the these autonomous cars track their position based on accelerometer data alone? My understanding was that many of them augment that data with ultrasonic or laser rangefinders, etc.

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