  We present a cost-efficient and versatile method to map an unknown 3D
freeform surface using only sparse measurements while the end-effector of a
robotic manipulator moves along the surface. The geometry is locally
approximated by a plane, which is defined by measured points on the surface.
The method relies on linear Kalman filters, estimating the height of each point
on a 2D grid. Therefore, the approximation covariance for each grid point is
determined using a radial basis function to consider the measured point
positions. We propose different update strategies for the grid points
exploiting the locality of the planar approximation in combination with a
projection method. The approach is experimentally validated by tracking the
surface with a robotic manipulator. Three laser distance sensors mounted on the
end-effector continuously measure points on the surface during the motion to
determine the approximation plane. It is shown that the surface geometry can be
mapped reasonably accurate with a mean absolute error below 1 mm. The mapping
error mainly depends on the size of the approximation area and the curvature of
the surface.
