3
$\begingroup$

enter image description here

What would the equations be for the robot's angular and linear velocity at P and also P2? I think I'm doing it wrong...

WL = left wheels angular velocity WR = right wheels angular velocity

For P I had for example the linear velocity = (1/3)rWL + (2/3)2rWR

Am I on right track?

$\endgroup$
  • $\begingroup$ Can you explain that diagram? If I'm reading it properly, it looks like the boxes on the outside are supposed to be the wheels, and the r and 2r labels are radii (even though drawn as diameters). Is that correct? $\endgroup$ – Ian Feb 24 '14 at 16:50
  • $\begingroup$ diameter. The below has examples of how this works, i just cant figure it out. rose-hulman.edu/~berry123/Courses/ECE425/Spring07_files/… $\endgroup$ – user3893 Feb 25 '14 at 21:41
2
$\begingroup$

The linear velocity $v$ of a differential drive robot is the average of the velocities of its wheels [^]. In mathematical terms:

$$ v = \frac{v_L + v_R}{2} $$

Where $v_L$ and $v_R$ are respectively the linear velocity of the left and right wheels. These are functions of their angular velocities and radii, such that:

$$ v_L = r_L \omega_L $$

$$ v_R = r_R \omega_R $$

Where $r_L$ and $r_R$ are respectively the radii (not the diameters!) of the left and right wheels, and $\omega_L$ and $\omega_R$ likewise the angular velocities.

The angular velocity $\omega$, on the other hand, is the average of the opposing contributions of left and right wheels: the left wheel contributes clockwise ("negative") motion, whereas the right wheel contributes counter-clockwise ("positive") motion. In mathematical terms:

$$ \omega = \frac{\phi_R - \phi_L}{2} $$

Where the wheel contributions $\phi_L$ and $\phi_R$ are given by:

$$ \phi_L = \frac{r_L \omega_L}{l_L} $$

$$ \phi_R = \frac{r_R \omega_R}{l_R} $$

And $l_L$ and $l_R$ are respectively the left and right shaft lengths between the center of rotation and the left and right wheels.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.