  For the shape control of deformable free-form surfaces, simulation plays a
crucial role in establishing the mapping between the actuation parameters and
the deformed shapes. The differentiation of this forward kinematic mapping is
usually employed to solve the inverse kinematic problem for determining the
actuation parameters that can realize a target shape. However, the free-form
surfaces obtained from simulators are always different from the physically
deformed shapes due to the errors introduced by hardware and the simplification
adopted in physical simulation. To fill the gap, we propose a novel deformation
function based sim-to-real learning method that can map the geometric shape of
a simulated model into its corresponding shape of the physical model. Unlike
the existing sim-to-real learning methods that rely on completely acquired
dense markers, our method accommodates sparsely distributed markers and can
resiliently use all captured frames -- even for those in the presence of
missing markers. To demonstrate its effectiveness, our sim-to-real method has
been integrated into a neural network-based computational pipeline designed to
tackle the inverse kinematic problem on a pneumatically actuated deformable
mannequin.
