Optimal Acquisition of Laser Scan Data
In this talk, we illustrate how one of the classical areas of computational geometry has gained in practical relevance, which in turn gives rise to new, fascinating geometric problems. In particular, we demonstrate how the mobile robot platform Irma3D can produce high-resolution, virtual 3D environments, based on a limited number of laser scans. Computing an optimal set of scans amounts to solving an instance of the Art Gallery Problem (AGP): Place a minimum number of stationary guards in a polygonal region, such that the whole region is guarded. While this problem is NP-hard, the equivalent in the mobile mapping case, is solvable efficiently. Here a single mobile guard, i.e. a watchmen has to find a tour, that covers the whole scene. In addition to discussing the AGP and Watchmen problem, we will look at the online exploration problem and apply mobile mapping in the case, where the scene geometry is not know before.