Iterative Surface Mapping Using Local Geometry Approximation with Sparse Measurements During Robotic Tooling Tasks

We present a 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 by the projected distance to the measured points' positions. We propose different update strategies for the grid points, where the approximation is valid to consider the locality of the planar approximation. We experimentally validate the approach 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. These points determine the approximation plane, which updates the mapping. 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.