We use the well-known Iterative Closest Points (ICP) algorithm to
calculate a rough approximation of the transformation while the
robot is acquiring the 3D scans. The ICP algorithm calculates
iteratively the point correspondence. In each iteration step, the
algorithm selects the closest points as correspondences and
calculates the transformation () for minimizing the
equation
It is shown that the iteration terminates in a minimum [3]. The assumption is that in the last iteration step the point correspondences are correct. In each iteration, the transformation is calculated by the quaternion based method of Horn [10].
To digitalize environments without occlusions, multiple 3D scans have to be registered. After registration, the scene has to be globally consistent. We designed a method called simultaneous matching to generate overall consistent scenes by minimizing the global error [12]. The computed transformations are applied to the robot pose and thus a relocalization of the robot is done after every 3D scan. Therefore the simultaneous localization and mapping problem (SLAM) is solved.