For some explanations about the variables and the x and y conventions look at Omnidirectional Control page. Below the formulas are given to calculate the velocity and acceleration of the robot. $$ v_x=\omega*r_{wheel}*(2*sin(\phi)+2*sin(\theta))*\frac{z_1}{z_2} $$ $$ v_y=\omega*r_{wheel}*(2*cos(\phi)+2*cos(\theta))*\frac{z_1}{z_2} $$ $$ F_{motor}=\tau/r_{wheel}*\frac{z_2}{z_1} $$ $$ F_x=F_{motor}*(2*sin(\phi)+2*sin(\theta)) $$ $$ F_y=F_{motor}*(2*cos(\phi)+2*cos(\theta)) $$ $$ a_x=F_{x}/m_{robot} $$ $$ a_y=F_{y}/m_{robot} $$
$z_1$ and $z_2$ are the gears teeth, where $z_1$ is the pinion gear attached to the motor and $z_2$ is attached to the wheel.
The formulas above are put in a Python file to calculate the values for the velocity and acceleration. For the new robot, the gear ratio has become 1.
| Specs | Current | New | Unit |
|---|---|---|---|
| $v_x$ | 6.17 | 15.03 | $[m/s]$ |
| $v_y$ | 8.43 | 20.53 | $[m/s]$ |
| $a_x$ | 20.4 | 8.96 | $[m/s^2]$ |
| $a_y$ | 27.87 | 12.24 | $[m/s^2]$ |