  Non-flat surfaces pose difficulties for robots operating in unstructured
environments. Reconstructions of uneven surfaces may only be partially possible
due to non-compliant end-effectors and limitations on vision systems such as
transparency, reflections, and occlusions. This study achieves blind surface
reconstruction by harnessing the robotic manipulator's kinematic data and a
compliant tactile sensing module, which incorporates inertial, magnetic, and
pressure sensors. The module's flexibility enables us to estimate contact
positions and surface normals by analyzing its deformation during interactions
with unknown objects. While previous works collect only positional information,
we include the local normals in a geometrical approach to estimate curvatures
between adjacent contact points. These parameters then guide a spline-based
patch generation, which allows us to recreate larger surfaces without an
increase in complexity while reducing the time-consuming step of probing the
surface. Experimental validation demonstrates that this approach outperforms an
off-the-shelf vision system in estimation accuracy. Moreover, this compliant
haptic method works effectively even when the manipulator's approach angle is
not aligned with the surface normals, which is ideal for unknown non-flat
surfaces.
