Blending function

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

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

That depends on a lot of things.  If your system has two
independent axis, then you might just work out the x and y
velocities needed to be in the right place on each axis at
the right time.  Basically, you just figure out how long the
movement should take, and the velocity in each direction is
simply the change in location divided by time.

If your system is a more complex system with interdependent
axis, then you should probably work out the model for the
system, and base your movements on that.

If you assume that you will have upper level controls which
will tell the system where to go, then lower level controls
can take over with working out where the robot should be
every few milliseconds, and reading its location.  It then
would use a PID or similar control to adjust itself so that
it arrived at the right spot at the right time.  Note that
reading the location of the robot may take more than 2 ms.

You can use servo or stepper motors with feedback in order
to control the movement and position fairly accurately.

Michael

On 22 Mai, 05:46, "Herman Family"

I know how to make this with software and hardware. We use 1
industrial PC, Ethercat and servo drives.
I don't have any problem with software and hardware. I have problem
with algorithm.

Regards
Leo

Why not the obvious?
theta=arctan((y1-y0)(/x1-x0))
x(t)=cos(theta)*p(t);
y(t)=sin(theta)*p(t);

Peter Nachtwey

Are you sure that theta is constant? I am not sure.

HOW AM I SUPPOSED TO KNOW.  YOU ARE THE ONE ASKING THE QUESTIONS. WHAT
DO YOU MEAN YOU AREN'T SURE?  That is the problem I have with your
posting.  You don't know enough to ask the right questions or provide
the right data for us to provide an intelligent answer.  Is the path
between point x0,x0 and x1,x1 a straight line or not?  Don't you think
this makes a difference to the answer?  If the path is a straight line
then the answer is as simple as what I provided.  If the path is a
curve then the calculations get difficult quickly.  Since you don't
understand the question I doubt you would understand the answer.  It
looks like you are having problems with grasping the basics like point
to point moves using 5th order polynomials.

I have seen the posts on sci.math.  There you say you have a problem
with acceleration.  Limiting acceleration while using 5th order
polynomials is a problem but if you are accelerating from one constand
speed to another the peak acceleration will be 1.5 times the average
acceleration.   You can calculate the average acceleration using
simple second order math.

Peter Nachtwey

I wrote:

It would be the function P(t) which is a
polynom of the 5th order with coeficients C0, C1, C2, C3 and C4

I think, my question is very clear.

So how does one get a x and y component from your function of P(t)?
P(t) says nothing about direction. So it isn't clear and if you don't
understand that you will not understand the answer just like you
didn't understand my answer about superimposed moves earlier this
year.

Peter Nachtwey

I got a .pdf in the mail from leo that describe what I think he wants
to do.  P(t) describe the motion of a part on a conveyor.  Assume the
conveyor moves at a constant speed.  There is a 4 axis robot that must
make contact and follow the position of the part on the conveyor.
The robot has a rotate, a shoulder, a fore arm for placement and a
wrist to keep the tool vertical.
I think leo wants to know how the robot can match the position of the
part while moving.  This isn't what I had imagined the math is still
complicated.   The .pdf leo sent me is very old and uses a technique
called blending to blend the transition between one motion path and
another motion path.  The blending function is a 5th or hermite
blending function that returns values from 0 to 1 over the period of
the blending period.  The blending function is a 5th order so the
function will be continuous after taking the derivative twice so there
will be a smooth transition for the velocity and acceleration as well
as the position.  There is some formulas about mapping the linear
position of the part to the rotational positions of the robot but this
doesn't seem to be the main thrust of the article.  The article seem
to be more concerned with the motion path the robot must take as a
function of the part position and velocity

Leo  , I didn't see a page two.  The pdf file seems to start at page
370 or something.  I didn't see the number 785.   The text does number
the equations so use the equation numbers.

This is still very complicated and too much to explain on a user
group.

Peter Nachtwey

Two more things.
1.  It is the distance over which the blending occurs that affects how
rounded ( the acceleration ) the transition will be.
2. Blending is just one technique.  Super imposed moves and splicing
are two other techniques to do the same thing.  They all have
advantages and disadvantages.  I wouldn't have used blending because
two motion segments need to be calculated and the blending function.
Super imposed moves require that two functions must be computed.
Splicing ends one function at the same position, velocity and
acceleration that are the initial conditions for the next segment.
This means the blending .pdf may not apply.  You really should ask the
robot control manufacturer about the algorithm they used.

Peter Nachtwey

I think Peter you don't have enough experience with robots. This
blending function is very good (you can see in .pdf mathematical
prove why.I try to explain this .pdf and I am asking for help.

Leo

OK, get your answers to your nonsense questions elsewhere.

Peter Nachtwey

Can you explain me Super imposed moves  technique?

Thanks

Leo