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vx, vy, and vz are in meters/sec. vth is in radians/second.

Take a look at this site.

One thing I would add about finding distance travelled and theta:

To get distance, and therefore (x,y) position, you will have to know wheel circumference. Encoder counts gives you how much the motor has turned, but if that motor is attached to a larger wheel, then the distance will obviously be greater.

Example:

If your robot was just riding on the motor shafts and your motor shafts were 4 cm in circumference. If you rotated your motor one full rotation, you will have traveled 4 cm.

However, if your motor shaft was fixed to a wheel with a circumference of 25 cm and you rotated your motor one full revolution, then you will have traveled 25 cm (ignoring friction and drag).

vx, vy, and vz are in meters/sec. vth is in radians/second.

Take a look at this site.

One thing I would add about finding distance travelled and theta:

To get distance, and therefore (x,y) position, you will have to know wheel circumference. Encoder counts gives you how much the motor has turned, but if that motor is attached to a larger wheel, then the distance will obviously be greater.

Example:

If your robot was just riding on the motor shafts and your motor shafts were 4 cm 0.04 m in circumference. If you rotated your motor one full rotation, you will have traveled 4 cm. 0.04 m.

However, if your motor shaft was fixed to a wheel with a circumference of 25 cm 0.25 m and you rotated your motor one full revolution, then you will have traveled 25 cm 0.25m (ignoring friction and drag).