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--- turtlebot:adventures:sensing101_thetaerror [2015/10/27 19:38] – pvela
+++ turtlebot:adventures:sensing101_thetaerror [2024/08/20 21:38] (current) – external edit 127.0.0.1
@@ Line 3: / Line 3: @@
 It turns out that these two parts used correspond to a planar quaternion, which is basically just a complex number $ z = x + jy$.  Be careful though because the quaternion version has half the phase.  When you unpack the quaternion into a complex number, be sure to square it first so that it has the correct phase. Also make sure that you set the proper parts to be the real and the complex coordinates.
 OK, let's assume that you have a desired orientation that gets created as a complex number
-$$ z_{des} = e^{j \theta_{des}} = \cos(\theta_{dsc}) + j \sin(\theta_{des})$$
+$$ z_{des} = e^{j \theta_{des}} = \cos(\theta_{des}) + j \sin(\theta_{des})$$
 In python, one would use the [[https://docs.python.org/2/library/cmath.html|cmath]] package and the ''rect'' function to create the complex number.  Naturally, since only rotations are the concern, the magnitude should be 1 (to create a unit length complex number).  Basically $z_{des}$ lives on the unit circle, which makes it equivalent to an orientation.