Re: Blending function

On 21 Mai, 19:52, pnachtwey <pnacht...@xxxxxxxxx> wrote:
On May 21, 5:25 am,leo<e1e120032...@xxxxxxxxx> wrote:



Hi friends

We have the portal robot with two axis X and Y. For each axis we have
the servo drive that we can write in the trajectory values every 2
msec.

From this trajectory the drive will calculate the velocity and
acceleration. If we have two points P1 with coordinates X1 and Y1 and
P2 with coordinates X2 and Y2 we have to find the blendig function
between these two points. It would be the function P(t) which is a
polynom of the 5th order with coeficients C0, C1, C2, C3 and C4. The
coeficients are known if we know the velocity, acceleration and
coordinates of the points P1 and P2.

My question is: How can I get values X(t) and Y(t) at the moment t if
I have the function P(t).

For example at the moment t=2msec the value of the polynom would be:

P(2msec) = C0 + C1*2msec + C2*(2msec)^2 + C3*(2msec)^3 + C4 *
(2msec)^4 + C5 * (2msec)^5

How can I get values X(2msec) and Y(2msec)?

Thanks.

Leo

This isn't clear.  What does P(t) represent?  A position in one
dimension?  Is P(t) supposed to return a x(t) and y(t)?  If so then
why mess with P(t) and just figure out how to get from x0,y0 to  x1,y1
in a given amount of time?

x(t)=A0+A1*t+A2*t^2+A3*t^3+A4*t^4+A5*t^5
y(t)=B0+B1*t+B2*t^2+B3*T^3+B4*t^4+B5*t^5

calculating a motion profile from x(0), y(0) to x(T),y(T) is easy if
you know T.  You know the inital conditions for the two polynomials
and you know the final conditions, the problem is what should T be to
keep from exceeding velocity, acceleration and jerk limts.  That
requires a little math.  That is also why not many people use 5th or
7th order controllers.   If you have a graphical tool then you can
adjust the time and check the speeds, accelerations etc. but this
requires everything be worked out ahead of time.  This works for many
robotic applications because everything is known ahead of time.

I am assuming you are still working on your x, y robot.  I have seen
your posts on other forums.

Peter Nachtwey- Zitierten Text ausblenden -

- Zitierten Text anzeigen -

Hi Peter

Thanks for your answer. But please read on the Web site:

http://www.cim.mcgill.ca/~haptic/publications.html#Y1993

this publication:
Lloyd, J. E and Hayward, V. 1991. Real-Time Trajectory Generation
Using Blend Functions

Can you explain me on page 2 (785) what is X(t) on the graph? You can
read path displacemant. I think this is vector distance.
And how can I calculate for every axis distance if I have distance for
vector?(in time)

Regards

Leo

.

Relevant Pages

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