MinVal

Computes the minimum value of a user specified function, which could be a MotionSolve expression or a user subroutine.

The minimum value of a signal f(q(t)) satisfies the following condition: If T* is the point in time when is f(q(t)) minimum, then f(q(T*))≥f(q(t)) when t ≠T*. If the expression has no minimum value, the initial value will be returned as the minimum value.

A smooth approximation to the MIN function is implemented in MotionSolve, so that its sensitivities are analytically computed. The smooth approximation, known as the alpha soft approximation, is:

Minval(x)=∫T0x(t) eax(t) dt∫T0eax(t) dt

The parameter a<0 is used to control the accuracy of the calculations.
Note: Min(x)=lim⍺→∞Minval(x) .

Example

Assume that you want to put a lower limit on the velocity of a vehicle.

Here is a code snippet that shows how the response should be defined with MinVal:
>>> # Define the minimum of velocity
>>> minVel = MinVal(function = "VZ({},{})".format(p.cm.id,ref.id))