Re: Almost Holonomic Drive Built With The NXT

Geoffrey Hyde wrote:
> "Rich Thompson" <[email protected]> wrote in message 
> news:[email protected]...
> 
>> 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."