Blending function

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)?



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Isn't P(t) a multivalued function? In other words, doesn't each coefficient have two components, one for x and the other for y?

P1 and P2 each have two components...

- Daniel

Reply to
D Herring

Hi Leo,

This is interesting stuff,

Can you please explain the function more?:

if you only have two axis, then the polar coordinate system:

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be of some use?


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