Re: GA in electronics

[Wesley Smith]

Eduardo Jose Bayro-Corrochano has done a lot of work in GA and
robotics. You could read up on his research:
http://www.gdl.cinvestav.mx/~edb/ . Also, for implementing GA, the
Gaigen dissertation by Fontijne is quite nice:
http://staff.science.uva.nl/~fontijne/

On Thu, Feb 28, 2013 at 3:49 PM, Juan Jose Cespedes Gutierrez
<antar...@gmail.com> wrote:
> Hi everyone, my name is Juan José and i am a student of electronics
> engeneering in Bolivia, and i am preparing my dissertetion about the
> implementation of GA in microcontrollers for basic applications in robotics,
> studying the efficience of the code. Anybody works in this area??? i would
> thank any help.
>
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[Juan Jose Cespedes Gutierrez]

Thanks for the references, actually i've already read the books of both, and im using them as a base for my dissertation, however, i would like to know if my hypothesis is right, i mean, i am implementing the different products in a microcontroller, and studying the time they take to solve, for example, the inverse kinematics problem of a robotic arm of 5 DOF. I want to know how fast would be a microcontroller solving this problem and executing GA operations. I know that GA operations need a lot of computation, specially in conformal GA, of course, implemented in a PC with a processor running at 2GHz, the time required for this operations is relatively short, but using a microcontroller which runs at 20MHz even 80MHz, the time required is longer. Making the experiments i found that the microcontroller i am using solves the IK of the arm in 236 ms, i think it is an acceptable result right???.
I woul appreciate ay suggestions. Thanks

[Juan Jose Cespedes Gutierrez]

Also i would like to understand exactly which are the real advantages of GA?? Specially i don´t understand why they say that GA works in a free coordinate system. Thanks again

[yang Li]

I think "coordinate free" is a nice feature when expressing the relation between two geometric objects, however, when you come to calculate something, you never get rid of coordinates...

I might be wrong! Correct me!

2013/3/1 Juan Jose Cespedes Gutierrez <antar...@gmail.com>

Also i would like to understand exactly which are the real advantages of GA?? Specially i don´t understand why they say that GA works in a free coordinate system. Thanks again

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Thanks for reading!

Yang Li
Electronic Engineering, Fudan University

[Fred lunnon]

I was mystified by the expression "coordinate-free" when first encountering
GA , since the whole subject was quite obviously concerned with little else
than coordinates!

Eventually I realised that people generally have come to regard "coordinates"
as a singular term denoting an algebraic (vector) representation of some
geometric entity (point, line, plane, quadric, or whatever); whereas what a
Victorian mathematician called "coordinates" would now more be referred
to more specifically as "components".

It's the same kind of subtle shift in meaning that has overtaken the word
"data", originally the plural of "datum" denoting of a single reading of some
experimental quantity. Such evolution may well be significant, in reflecting
a greater level of abstraction in the way we think about these matters.

So the idea behind coordinate-freedom is rather to suppress reference
to individual components, which are ideally restricted to a standard
implementation layer, that --- once specified --- remains out of sight.

To some extent of course, this notion was already present even in
the usual Gibbs-Heaviside vector calculus: GA just carries it further.

Fred Lunnon

[eskki paramasivan]

Dear Lunnon

The modern mathematics of geometry has entered new phase of both
conceptualising and concretising the therotical physics.Riemann's
dismissal of Euclidean geometry carved out a space from thin air.The
coordinate geometry though moved in this direction of course lost its
own charms of "coordinates".
Edward Witten has taken a great leap with his tool of
"homotopic"flavour to entertain the space-time warps etc with
metrization of C^r diffeomorphism of smooth manifolds.Now this made a
great rendezvous of unifying the QFT and GR.The super string theory
moored on this ,weaves through a Super Symmetric cosmic model towards
grand design of the Universe."The invariance" is the key from
"Einstein"upto "Witten" to deform of algebraic as well as geometic
configuration of "space".The much celebrated measure theory rendering
to "Lebesgue" measure that hits the rock bottom of the "abstraction"
of the geometry
and continuity with discrete packets (QUATUM FOAM).We deduce
beautifully "a loop quantum gravity" to reach richer and richer
heights.

I invite discussions from this angle of "discoordinated" coordinate
geometry freeing from the x y z ets axis orientations.

Paramasivan Esakki