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Unread 06-05-2011, 22:50
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Re: Offseason Project: Holonomic Kiwi Drive Robot

Quote:
My definition of omnidirectional is that the kinematics allow instantaneous velocity in all directions in the configuration space. Omni drives and mecanum drives satisfy this definition. A crab drive can seemingly move in every direction at once (especially with some of the ridiculously skilled FRC drivers at the helm) but a closer look reveals that it must first take the time to properly orient it's wheels. Viewed instantaneously, a crab drive only has two (or fewer in some wheel configurations) degrees of freedom at any given instant.
Let's compare a 4-wheel mecanum robot (Robot1) to a robot with 4 independently steerable and independently driven standard wheels (Robot2).

For Robot1, any instantaneous combination of dX/dt plus dY/dt plus dTheta/dt vehicle motions resolves into an instantaneous set of 4 wheel speeds [see reference 1]. As the desired vehicle dX/dt and dY/dt and dTheta/dt changes over time, the wheel speeds must "instantaneously" change to produce the new vehicle motion values. So Robot1 is limited by the dynamic response of the wheel speeds which is limited by the motor power and the vehicle mass, etc.

For Robot2, any instantaneous combination of dX/dt plus dY/dt plus dTheta/dt vehicle motions resolves into an instantaneous set of 4 wheel speeds AND 4 wheel steering angles [see reference 2]. As the desired vehicle dX/dt and dY/dt and dTheta/dt changes over time, the wheel speeds and the wheel steering angles must "instantaneously" change to produce the new vehicle motion values. So Robot2 is limited by the dynamic response of the wheel speeds and the wheel angles which is limited by the motor power and the vehicle mass and the turning friction, etc.

So the only difference is dynamic response. Within its dynamic capabilities, Robot2 can do anything (that is, mimic any motion, however complicated) that Robot1 can do. In that sense, from a kinematic standpoint they are equivalent.


[1] http://www.chiefdelphi.com/media/papers/download/2722

[2] http://www.chiefdelphi.com/media/papers/download/3027