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.
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.
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