  We present RoadMapping, a full-likelihood dynamical modelling machinery that
aims to recover the Milky Way's (MW) gravitational potential from large samples
of stars in the Galactic disk. RoadMapping models the observed positions and
velocities of stars with a parametrized, three-integral distribution function
(DF) in a parametrized axisymmetric potential. We investigate through
differential test cases with idealized mock data how the breakdown of model
assumptions and data properties affect constraints on the potential and DF. Our
key results are: (i) If the MW's true potential is not included in the assumed
model potential family, we can - in the axisymmetric case - still find a robust
estimate for the potential, with only <~ 10% difference in surface density
within |z| <= 1.1 kpc inside the observed volume. (ii) Modest systematic
differences between the true and model DF are inconsequential. E.g, when
binning stars to define sub-populations with simple DFs, binning errors do not
affect the modelling as long as the DF parameters of neighbouring bins differ
by < 20%. In addition, RoadMapping ensures unbiased potential estimates for
either (iii) small misjudgements of the spatial selection function (i.e., <~
15% at the survey volume's edge), (iv) if distances are known to within 10%, or
(v) if proper motion uncertainties are known within 10% or are smaller than
delta mu <~ 1 mas/yr. Challenges are the rapidly increasing computational costs
for large sample sizes. Overall, RoadMapping is well suited to making precise
new measurements of the MW's potential with data from the upcoming Gaia
releases.
