Nice rebuttal, Ether!
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Originally Posted by Ether
However, words enter the English language through repeated usage which facilitates communication, and in the field of robotics the adjective "holonomic" when applied to a robot has come to mean that the robot can translate (X,Y) and rotate (theta) simultaneously and independently.
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I grudgingly agree, I am fighting a losing battle, but it is fun to rant about it once in a while.
Quote:
Originally Posted by Ether
A unicycle has nonholonomic constraints (see Mason, pages 31 & 32), so is it not omnidirectional?
What is your definition of omnidirectional? Do you consider a “crab” drive to be omnidirectional? If not, what technical term do you suggest be used? But if so, what word should then be used for, say, a mecanum, to distinguish its freedom of motion from a crab’s?
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I would not classify either a unicycle or a crab drive as omnidirectional. 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.
I don't have an alternate term to describe the nature of the crab drive, but I'm not sure there needs to be one. Speaking mathematically, I do not see any qualitative difference between a crab drive and unicycle or an Ackerman steered car. All are controllable, kinematic systems with nonholonomic constraints, they just have different degrees of difficulty associated with doing the actual control. We might consider the crab drive to be a member of the class of vehicles with fully articulated wheels, but I don't know of an agreed upon name for that class of vehicles.
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Originally Posted by Ether
The above is a good non-technical way to explain it. Some experts, when arguing the finer points, would say however that there are nonholonomic constraints which do result in an algebraic constraint on the position of the robot (Mason, p27)... although Mason goes on to say "the robotics literature often neglects this point, and in fact this book will henceforth also neglect it".
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That is a great quote, I love Mason's style. But in that passage he was referring to unilateral constraints, which are different beasts altogether than the bilateral equality constraints we face with wheeled vehicles.
These are all minor details and I admit that they don't matter much from a practical perspective. But I like to think about them and talk about them, and I sincerely appreciate your interest and indulgence.
-George