  Extracting the proton charge radius from electron scattering data requires
determining the slope of the charge form factor at $Q^2$ of zero. But as
experimental data never reach that limit, numerous methods for making the
extraction have been proposed, though often the functions are determined after
seeing the data which can lead to confirmation bias. To find functional forms
that will allow for a robust extraction of the input radius for a wide variety
of functional forms in order to have confidence in the extraction from upcoming
low $Q^2$ experimental data such as the Jefferson Lab PRad experiment, we
create a general framework for inputting form-factor functions as well as
various fitting functions. The input form factors are used to generate
pseudo-data with fluctuations intended to mimic the binning and random
uncertainty of a given set of real data. All combinations of input functions
and fit functions can then be tested repeatedly against regenerated
pseudo-data. Since the input radius is known, this allows us to find fit
functions that are robust for radius extractions in an objective fashion. For
the range and uncertainty of the PRad data, we find that a two-parameter
rational function, a two-parameter continued fraction and the second order
polynomial expansion of $z$ can extract the input radius regardless of the
input charge form factor function that is used. We have created an easily
expandable framework to search for functional forms that allow for a robust
extraction of the radius from a given binning and uncertainty of pseudo-data
generated from a wide variety of trial functions. This method has enabled a
successful search for the best functional forms to extract the radius from the
upcoming PRad data and can be used for other experiments.
