A couple things:
There's more to speed on the motor. You need to be more concerned with torque. The BaneBot RS775 18V operating at 12V is a bit different.
Can you post a sketch of your drivetrain geometry? Is it a square? Wide base? Please provide dimensions, wheel material, and tire width
You will need to answer these questions:
- What is the scrub force of the robot?
- What is the torque/force of each wheel needed to turn the robot to overcome the scrub force?
- What is the torque needed to accelerate the robot to maximum speed in an acceptable time?
- What motor and gearbox combination will achieve this?
- Anything I missed

You've already got a good starting point with the requirement of 1.5-2 m/s. From here, you need to figure out how much force provided by each wheel is required to rotate the robot in place (this will be the most demanding operation of your setup). Also, keep in mind that the motor torque ratings are given at a certain RPM. This RPM may be at full power. If you use a full-power rating, you may not have control when throttling down (low speed or fine motion).
Quote:
Originally Posted by ArchVince
Side question, as long as I have a thread: If I have the wheels as close to the gears on the output shaft as possible, would I still need to worry about supporting the shaft to protect the planetary gearbox?
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Post a photo or CAD file of your design. My initial suggestion would be to support that end since the shaft is only supported by one 3/8" thick bearing on the output of the gearbox if I recall correctly. This may be easy or difficult depending on your design. It may be possible to stack a bearing block with the appropriate bearing press fit on the output end of the gearbox to help alleviate the moment arm.