tag:blogger.com,1999:blog-1222092101762956112.post6036363328506394070..comments2024-03-12T23:03:35.556-07:00Comments on Infinigons, etc.: Whaddya know? Math in the "real world"!Allison Johnsonhttp://www.blogger.com/profile/01731073560005744198noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-1222092101762956112.post-69980651431744920182011-05-21T19:50:41.565-07:002011-05-21T19:50:41.565-07:00This is really cool! I'm confused, however, ab...This is really cool! I'm confused, however, about one thing. The transformation<br /><br />(0, 1) ---> (1, 1)<br />(1, 0) ---> (0, 1)<br />(0, -1) ---> (-1, -1)<br />(-1, 0) ---> (1, 0)<br /><br />is not linear! If you call the transformation F, linearity would require that F(1, 0) = -F(-1, 0), and this condition is not satisfied: (0, 1) is not equal to -(1, 0).<br /><br />Because the transformation isn't linear, it can't be carried out using pure matrix multiplication. That means the matrix formula you wrote down can't be doing what you want it to do.* And, indeed, it doesn't: if you multiply (-1, 0) by the matrix ((0, 1) (1, 1)), you get (0, -1), rather than (1, 0).<br /><br />One possible fix is to use the transformation<br /><br />(0, 1) ---> (1, 1)<br />(1, 0) ---> (-1, 1)<br />(0, -1) ---> (-1, -1)<br />(-1, 0) ---> (1, -1)<br /><br />instead. This transformation is linear, and can therefore be carried out using matrix multiplication. It also gives the robot operator more flexibility, because it allows the left and right wheels to spin in opposite directions. Depending on how your wheel base is set up, this might allow for tighter turns.<br /><br />* Incidentally, this is a nice example of how abstract ideas can be useful in practical situations: knowing a little something about abstract linear transformations makes it way easier to track down the bug in the robot control code. It might even lead you to notice the bug without even testing the code!Aaronhttps://www.blogger.com/profile/18281785407407667986noreply@blogger.comtag:blogger.com,1999:blog-1222092101762956112.post-89181010254222614532011-01-29T13:16:18.589-08:002011-01-29T13:16:18.589-08:00And now you will have a robot that they can see it...And now you will have a robot that they can see it on!<br /><br />Some say I would teach robots all day if I could. They don't realize that in doing so, I am teaching Physics, Math, Engineering, Writing, Business, and Programming. Real world beats textbook any day in my opinion.<br /><br />I especially love how you filled the whiteboard wall with matrices. The brainstorming is half the fun.<br /><br />Thanks to you and the other "A" for all of your help this season.Phil Wagnerhttps://www.blogger.com/profile/08938707552495871086noreply@blogger.com