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I am working on building a simple robot. Basically, I have a small platform with two motorized wheels and rotary encoders on the edges. So, using the rotary encoders I can estimate the velocity of the two wheels. I then need to use this information to calculate the path that the robot follows. I am having difficulty working out the equation to define the robot's total velocity.

I'm basically looking at it as a rigid bar of length 2L, where the velocities of the right and left edges (v1 and v2 respectively) are known. It is also constrained such that v1//v2. And θ is the angle of the bar with the x axis.

I believe the equation for θ should be:

[itex]\dot{θ}[/itex] = (v1-v2)/L

And, that the magnitude of the total velocity should be the minimum of v1 and v2, plus the component of v2 tangent to the rotation.

v = min(v1,v2) + (v1-v2)/2

Then I just calculate the path it takes by integrating.

I'm sorry if my attempted answer isn't very clear, but I think the question should be. Calculate the velocity of the centre point of a rigid bar where the velocities of it's 2 end points are known, and are always parallel.

Any assistance would be much appreciated.