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6.2 CIRCULAR INTERPOLATION
In the ELAU GmbH EPAS-4 library there is a function called MoveC. This function needs the
following parameters:
• Start point, A – Start position for the TCP
• End point, B – End position for the TCP
• Cirlce point, C – Point between start and end points
• Max TCP velocity – The maximum velocity of the TCP when moving along the path
The function moves the TCP on a circular path from the starting position A via the arc point C
to the target position B. Between the end and start point the curve is divided into several points,
see Figure 6.4. Then the distance between every point at the curve is interpolated using cubic
spline.
Figure 6.4, shows circle spline with the motion between point A to point B divided
into several points which are in turn interpolated with cubic spline.
The virtual master determines the velocity of the TCP for each cycle. To contain this velocity
the x, y and z have different velocities so at the end the TCP trajectory has the desired velocity.
6.3 CUBIC SPLINE
Splines represent an alternative approach to data interpolation. In polynomial interpolation, a
single formula, given by a polynomial, is used to meet all the data points. The idea of splines is
to use several formulas, each a low degree polynomial, to pass trough the data points (14). A
cubic spline interpolates between the given data points by degree 3 polynomial. It is used when
one want to make a various path with interpolation between many points. In ELAU GmbHs
robotic library is this function called MoveSB, and can move the robot in a three-dimensional
spline from the start position across a maximum of 100 points to the target position. The cubic
spline calculates the smoothes path between each of the data points so at the end a smooth
trajectory will be held.
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Public Report ELAU GmbH, Marktheidenfeld
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