Distance

Description

The distance between the origins of frame_aand of frame_b are determined and provided at theoutput signal connector distance. Thisdistance is always positive. Derivatives of thissignal can be easily obtained by connecting theblockModelica.Blocks.Continuous.Derto distance (this block performs analytic differentiationof the input signal using the der(…) operator).

In the following figure the animation of thesensor is shown. The light blue coordinate system isframe_a, the dark blue coordinate system is frame_b,and the yellow arrow is the animated sensor.

If the distance is smaller then the parameter s_small(in the "Advanced" menu), it is approximated such that its derivative isfinite for zero distance. Without such an approximation, the derivative wouldbe infinite and a division by zero would occur. The approximation is performedin the following way: If distance > s_small, it iscomputed as sqrt(r*r) where r is theposition vector from the origin of frame_a to the origin of frame_b.If the distance becomes smaller then s_small, the "sqrt()"function is approximated by a second order polynomial, such that the functionvalue and its first derivative are identical for sqrt() and the polynomial ats_small.Furthermore, the polynomial passes through zero. The effect is, that the distancefunction is continuous and differentiable everywhere. The derivative at zero distanceis 3/(2*s_small).