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

TL;DR

This paper introduces a cost-effective method for robotic surface mapping using sparse measurements and local plane approximations, validated through experiments with laser sensors achieving sub-millimeter accuracy.

Contribution

The method combines local geometry approximation with Kalman filtering and radial basis functions, enabling accurate surface mapping with minimal measurements during robotic tasks.

Findings

Mean absolute error below 1 mm in surface mapping

Mapping accuracy depends on approximation area size and surface curvature

Effective for real-time robotic surface tracking

Abstract

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.