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Re: Geometry & Trig Quiz
Given I tried solving this in between lectures, I am not certain of my solution.
First, let us define an angle Phi that is the angle in radians from the +y axis to the vector of intended motion <x1-x0,y1-y0>. Phi is equal to the sum of the two angles Alpha (The angle from +y to the front of the robot) and Sigma (The angle from the front of the robot to the direction of the wheels).
Since both angles are measured clockwise from their respective reference lines, the angles are added together.
Constructing a right triangle with <x1-x0,y1-y0> as the hypotenuse and the legs parallel to the Cartesian axes, we find the Angle from +y to the vector of intended motion to be arctan((x1-x0)/(y1-y0)). This may look odd at first, but the use of the change in x and y terms in the arctangent function is due to measuring the angle with respect to the y axis instead of the x axis.
Phi = arctan((x1-x0)/(y1-y0))
Phi = Alpha + Sigma
Alpha + Sigma = arctan((x1-x0)/(y1-y0))
Sigma = arctan((x1-x0)/(y1-y0)) - Alpha
Additionally, the wheels must be turned Sigma - Beta from their initial configuration. (not that the problem asked for it.)
I disregarded the width and length of the wheelbase because the initial and final coordinates were already based on the center of geometry, meaning I could treat this as an omnidirectional unicycle bot (I challenge someone to make it).
This is my solution for the posted problem; I trust it has errors, but I am not certain where they are, so any critiques or suggestions are welcome.
I have included a somewhat mediocre drawing of what this looks like.
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2016:
Alamo, Bayou, and Lone Star Regional FTAA
2015:
Dallas, Alamo, Bayou, and Lone Star Regional FTAA
2014:
Alamo, Dallas, and Lone Star Regional FTAA
Alamo Regional Robot Inspector
2013:
Einstein Champion and 2013 World Champion (Thanks 1241 & 610), Galileo Division Champion, Razorback Regional Winner, Alamo Regional Semifinalist, Bayou Regional Semifinalist, Lone Star Regional Quarterfinialist
2012:
Curie Division Semifinalist, Lone Star Regional Finalist, Bayou Regional Winner, Alamo Regional Winner
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