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 [DPRG] Robot math problems Message index sorted by: [ date ] [ thread ] [ subject ] [ author ] Previous message: [DPRG] Robot math problems Next message: [DPRG] Robot math problems Subject: [DPRG] Robot math problems From: Chuck McManis cmcmanis at mcmanis.com Date: Wed Feb 13 14:08:02 CST 2002 ```At 11:37 AM 2/13/02 -0800, Clay Timmons wrote: >Just working out a few robot navigation issues >and thought I'd share a couple math problems >I've encountered. Have fun! Took me about >10 minutes. You've got to build more tracked robots :-) This is essential knowledge for doing inverse kinematics computations to position one's bot. >If a 12" wide robot with 3" diameter wheels >has one wheel going 1/2 the speed of the other >it will go in a circle. > > 1) What diameter is that circle? > > 2) To make the robot go in a circle with > a 9" radius on the inside wheel > what speed should the inside wheel > go as a percentage of the outside wheel? I'm going to assume that the centerline of the two wheels are 12" apart, since your robot is "12 inches wide" that cannot be true in practice as you either measured from wheel edge to wheel edge in which case the center line is 1 wheel width less than 12", or you measured the body and the wheels were outside of that meaning they are 1 wheel width + 12" apart. Given that, there is no solution for #2 because the smallest radius turn you could possibly make that is *centered on the inside wheel* is 12". However by rotating one wheel in reverse you can translate the center of rotation along the axle between the two wheels. Allow me to suggest a third component to this question: 3) Assume the separation between your wheels is n inches, and the radius of your wheels are r inches. Given two wheel speeds, Sl (left) and Sr (right), derive the equation that describes the rate of angular rotation as a function of time, and derive the equation that describes the radius of the arc traversed, both for a fixed input (Sl, Sr). theta (degrees/second) = f(Sl, Sr) Diameter (inches) = g(Sl, Sr) Once you have those two equations, you have the necessary model for being able to put your robot from where it is, to where it needs to be at the correct orientation (facing the right direction). You can then specify things like, "I want my robot to be over by that wall and perpendicular to the wall." (of course that assumes you know where you are at the moment!) --Chuck ``` Previous message: [DPRG] Robot math problems Next message: [DPRG] Robot math problems Message index sorted by: [ date ] [ thread ] [ subject ] [ author ] More information about the DPRG mailing list