Quote:
Originally Posted by Siri
Independent-turn pivot does allow X & Y-bias snake drive, which (as far as I know), one can't do in mecanum or omni.
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A rigid vehicle operating on a flat surface has a maximum of only 3 degrees of freedom: 2 translational and 1 rotational.
Any possible motion of the vehicle (on the flat surface) can be accomplished by the appropriate combination of these three degrees of freedom. Any motion your drive can do (on a flat surface) can also be done with a mecanum or omni vehicle.
For example, if you want the vehicle to revolve around a central point while at the same time rotating about its own axis (like the Moon around the Earth), that motion can be specified in terms of the 3 degrees of freedom mentioned above, and the mecanum, omni, and your drive can do it.
Or, if you want the vehicle to spin its back end around and pivot around a point located between the front wheels, a mecanum or omni can do that as well (again, as a combination of the 2 translational and 1 rotational degrees of freedom of the vehicle).
Or if you want the vehicle to go forward in a straight line while simultaneously spinning around its center, a mecanum or omni can do that too. (Although it would require a very talented and dextrous driver to do so!)
Any conceivable vehicle motion on the flat surface can be accomplished by the proper (time-varying) instantaneous wheel speeds (and angles). As long as the drive motors have the necessary dynamic response to create the necessary time-varying wheel speeds (and angles), the desired vehicle motion can be accomplished.
The "inverse kinematic problem" is to determine, given a desired instantaneous vehicle motion, what each of the four wheel speeds should be (in the case of mecanum or omni), or what each of the four wheel speeds plus wheel angles should be (in the case of your drive), to achieve the desired instantaneous vehicle motion.
The "forward kinematic problem" is to determine what vehicle motion will result from an
arbitrary choice of wheel speeds (and angles). In general, this has no solution. Only properly coordinated sets of speeds (and angles) will result in vehicle motion without "scrubbing" the wheels on the floor.
Considering the above, the way to give your driver "complete manual control" is to allow them to independently command forward/reverse, strafe left/right, and spin CW/CCW. All possible motions of the vehicle can be accomplished by these three degrees of freedom. But, this may NOT be the best "driver presentation", depending on what types of motion the driver wants to do, because it may be too difficult for the driver to think that fast. For example, as mentioned above a mecanum or omni vehicle
is mechanically capable of going in a straight line while simultaneously spinning, but I highly doubt a driver could do it without computer assistance. If a competition required this type of motion, you would want to provide a gyro and/or accelerometer or whatever on the vehicle so that the driver commands could be interpreted as field-oriented commands and then translated on-the-fly by the cRIO into the correct wheel speeds (and angles).
There's an excellent text which discusses this (cf especially Chapter 3) if you want to research it further:
Mechanics of Robotic Manipulation
Mason, Matthew T.
Cambridge, Mass. : MIT Press, c2001
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