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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What sort of curve does the trajectory follow?

Polynom 5th order. All coefficients are known.P(t)=3D C0 + C1*t + C2*t^2

  • C3*t^2 + C4*t^4 + C5*t^5

Why 5th?

Because jerk is limited.

But please read on the Web site:

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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)


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