You don't have to have encoders to do that... Encoders help with accuracy... but are considered "extras"...

Imagine that your bot is doing a cycle... The center of mass... is on the cycle, whereas the servo wheels are a bit off...

This means that the inner wheel is moving on a smaller radius cycle while the opposite is in effect for the other wheel...

What you want is that circular speed is maintained while the radius is different...

ω = r*u, where ω is the radial speed of your vehicle, r is the radius of the cycle that the each wheel travel on and u is the speed of the wheel...

So we what that ω is maintained so let's say:

ω1 = ω2 = ω3

ω1 = R1*u1

ω2 = R2*u2

ω3 = R*u

where u1 is the speed of the inner wheel if considered a matter point

u2 is the speed of the outer wheel if considered a matter point

u is the speed of the center of mass of the robot

R1 is the radius the inner wheel travels on

R2 is the radius the outer wheel travels on

R is the radius of the cycle on which the center of mass (center of differential drive) of the robot travels on

So let's say.... ω1 = ω2 => R1*u1 = R2*u2 => u1 = (R2/R1)*u2 => u1 = a*u2 where a = (R2/R1)...

So you have the the proportion of the speeds that wheels should have...

The robot travels on a circle that has a R radius... So if R1 < R2 you will have...

R = R1 + (R1 - R2)/2 = (3R1 - R2)/2

But you also have that R2 = R1 + d, where d is the wheels distance so....

R = R1 + d/2 and R = R2 - d/2 =>

R1 = R - d/2 and R2 = R + d/2

So you finally can have the proportion of the wheels speed only with the radius of the cycle you want your robot to ride...

u1 = ((R - d/2)/(R + d/2))*u2 and that's true cause ((R - d/2)/(R + d/2)) < 1 and u1 < u2....

So that's it.... that how you should calculate servos speed on radius of the cycle your robot rides...

Keep in mind that all calculations are done on the same units.. R is in m/inch, u = m/s or inch/2 and so on...

It's important in calculations that you consider units!!!!!!

Since you are using wheels and servos you may don't need to calculate exact values... u1 and u2 can be pulses

and the parenthesis can be the proportion of this pulses...

That's all for now...

Best Regards, Lefteris

Greece