  We propose a combined analytical-numerical strategy to predict the dynamics
and trajectory of a microswimmer next to a curved spherical obstacle. The
microswimmer is actuated by a slip velocity on its surface and a uniformly
valid solution is provided by utilizing the Reynolds reciprocal theorem in
conjunction with the exact hydrodynamic solution of translation/rotation of a
sphere in an arbitrary direction next to a stationary obstacle. This approach
permits the hydrodynamic interaction of the microswimmer and the obstacle to be
consistently and accurately calculated in both far and near fields. Based on
the analysis, it was shown that while the "point-singularity solution" is valid
when the microswimmer is far from the obstacle, it fails to predict the correct
dynamics when the swimmer is close to the obstacle (i.e. gap size is
approximately twice the characteristic length of the microswimmer). Two
different paradigms for propulsion, so-called "squirmer" and "phoretic" models,
were examined and for each type of microswimmer, various types of trajectories
are highlighted and discussed under which circumstances the swimmer can be
hydrodynamically trapped or guided by the obstacle. The analysis indicates that
it is always easier to capture a microswimmer in a closed circular orbit with a
large sized obstacle ($\sim 20$-$40$ times larger than the microswimmer size)
as in this case the magnitude of rotational velocity can be sufficiently large
that the swimmer can adjust its distance and orientation vector with the
obstacle.
