# Robot command translation: Calculating circle radius from forward velocity and yaw rate.

I'm writing a driver for a robot control program.
The robot only understands a command with arguments of (Forward velocity, Radius).

ex: (200mm/s, 200mm) will cause the robot to move in a circle of radius 200mm at a tangential velocity of 200mm/s

The control software written sends me commands containing (Forward velocity, Yaw rate) arguments.

How can I calculate the radius of the circle, a robot would make, with a certain yaw rate and forward velocity?

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I think you may need to define "yaw rate" for us. –  Trevor Wilson Feb 7 '13 at 4:49
I'd like to have it defined too. That's all the documentation says. That I will be provided tangential speed and yaw rate, and that needs to be translated to tangential speed and circle radius... I THINK it means the angular velocity of the robot. Still confusing to think about. –  vilive Feb 7 '13 at 22:27

If the yaw rate is $r$ degrees per second (I will use degrees here - radians would work just as well), it will take $360/r$ seconds to turn a full circle.
If the velocity is $v$ meters per second, in $360/r$ seconds it will travel $v*360/r$ meters. Since this will be a full circle with circumference $v*360/r$ meters, the radius will be the circumference divided by $2 \pi$ or $v*360/(r*2 \pi) = 180v/(\pi r)$ meters