Subject: Re: Almost Holonomic Drive Built With The NXT - msg#00055

Geoffrey Hyde wrote:
"Rich Thompson" <rich@xxxxxxxxxxxxxxxxx> wrote in message news:JAAttJ.I8z@xxxxxxxxxxxxx

I have been working on a few different designs for a Lego Holonomic Drive or
Killough Platform. I almost have the components right with the robot that I
have built here:

Can you define "holonomic" as that word relates to this project of yours? I looked it up on dictionary.reference.com and it didn't find a dictionary entry for it but did have an encyclopedia entry for it, which made my head spin.

Basically, it's a fancy word meaning that the robot is movable in
every possible direction and can spin in every direction.

A Killough platform is holonomic in a two dimensional world - it
can move forwards, backwards, left and right - and combine them
to go diagonally - all without turning it's body. And it can also
spin around. Those are the only motions possible for an object
that's stuck to a two-dimensional surface like the floor.

In a three dimensional world, a holonomic robot would have to
be able to move up and down - and also roll sideways and pitch
forwards and backwards. A helicopter is a holonomic machine
in that sense.

Here is a great description of a Lego Killough platform:

http://staff.science.uva.nl/~leo/lego/killough.html

Wikipedia has a nice explanation of holonomic systems:

"In robotics holonomicity refers to the relationship between the controllable and total degrees of freedom of a given robot (or part thereof). If the controllable degrees of freedom is equal to the total degrees of freedom then the robot is said to be holonomic. If the controllable degrees of freedom is less than the total degrees of freedom it is non-holonomic. A robot is considered to be redundant if it has more controllable degrees of freedom than degrees of freedom in its task space. Holonomicity can be used to describe simple objects as well.

For example, a car is non-holonomic because although it could physically move laterally, there is no mechanism to control this movement.

A human arm, by contrast, is a holonomic, redundant system because it has 7 degrees of freedom (3 in the shoulder, 1 in the elbow and 3 in the wrist) and there are only 6 physical degrees of freedom in the task of placing the hand (x, y, z, roll, pitch and yaw), while fixing the 7 degrees of freedom fixes the hand."