Quote:
Originally Posted by Ether
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.
|
Yes, if you allow discontinuous steering angles the associated infinite steering velocities then the crab drive is omnidirectional. But this may be where we reach an amiable impasse, because I do not allow infinite velocities in my kinematic analysis. If infinite velocities are allowed, then any controllable kinematic system can be made omnidirectional through the use of infinitely fast, infinitesimally small Lie bracket maneuvers.
Now, once dynamics are taken into consideration, then I admit that the crab drive becomes practically indistinguishable from (what I would call) true omnidirectional systems. With dynamic constraints in effect, the laws of nature dictate that trajectory must be smooth in the sense that it has continuous velocities. As a result, any dynamically feasible vehicle trajectory would not require discontinuous steering angles and the crab can do anything the mecanum can do. In fact, the crab can probably do more because it can generate larger reactions forces against the floor and thus achieve higher accelerations.
Thanks, by the way, for pointing out your papers on the subject. They will come in handy if I ever convince my students to attempt and omnidirectional (or pseudo-omnidirectional
) chassis.
-George