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calculating position using follower wheels
A certain robot with a 3 degree-of-freedom drivetrain (FWD, STR, RCW) is on a flat level floor. At time T=0, its center of geometry (CoG) is located at the origin of an XY coordinate system fixed with respect to the floor; it is facing 15 degrees clockwise from the +Y axis; and it has the the following robot-centric constant motions: forward = 5 ft/sQuestion 1: What are the coordinates 3 seconds later, and what direction is the robot facing? Students, Mentors, engineers, and professors welcome. |
Re: calculating position using follower wheels
It is at the origin, facing 15 degrees clockwise from the +Y axis.
EDIT: 120 deg/sec * 3 sec = 360 degrees -- it just goes in a circle. |
Re: calculating position using follower wheels
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Question 2: What's the radius of the circle? |
Re: calculating position using follower wheels
Spoiler for solution:
EDIT: Perfectly matched text color w/ background color. EDIT2: Oops, it's 5 ft/s forward and 4 ft/s strafing, not 4 ft/s and 3 ft/s EDIT3: Changed colored text to a spoiler -- thank you EricH |
Re: calculating position using follower wheels
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This one is quite a bit more difficult: Question 3: Exactly the same as Question 1, except the FWD speed is a function of time, as follows: FWD = 5.0 + 1.0*T. In other words, FWD starts with the value 5.0 at T=0, and increases smoothly and linearly at a rate of 1 ft/sec/sec. The STR and RCW remain constant at 4 ft/sec and 120 deg/sec respectively. |
Re: calculating position using follower wheels
Spoiler for Solution:
Can this be done without integrals? |
Re: calculating position using follower wheels
Not answering the math questions... just this one.
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Spoiler for This is a spoiler:
And now back to the math... |
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Spoiler for Question 3:
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Re: calculating position using follower wheels
I did have it rotate counter-clockwise (oops). Corrected answer is the same, with both coordinates their opposites.
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Re: calculating position using follower wheels
2 Attachment(s)
Great work, Jacob and Ryan. Reps to you both. Ryan: what CAS did you use for that? The syntax you used was rejected by Maxima, Octave, and SciLab. (I got it to work in Maxima by changing the syntax a bit) Jacob: You got the right answer, but didn't show your work. How did you solve it? This has a potential practical application for FRC. If you put 3 omni follower wheels -- in the the correct configuration -- on a robot, you can get FWD, STR, and RCW information from them. Then you can use something like the attached C code to get the position and orientation of the robot. |
Re: calculating position using follower wheels
I used Microsoft mathematics, which only allows radians in calculus functions:
X: integral((5+1t)cos((90-15)(pi/180)-120pi/180t)+3sin((90-15)(pi/180)-120pi/180t), t, 0, 3) Y: integral((5+1t)sin((90-15)(pi/180)-120pi/180t)+3cos((90-15)(pi/180)-120pi/180t), t, 0, 3) |
Re: calculating position using follower wheels
Question 4: In the code block highlighted in blue at the bottom of post 11 the following code appears for calculating position and heading: Code:
Code:
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Re: calculating position using follower wheels
Spoiler for Justification:
It is not the best proof, but it explains the general reasoning. |
Re: calculating position using follower wheels
1 Attachment(s)
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See attachment for additional explanation using geometry and a bit of calculus. |
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