Hierarchical optimization on manifolds for online 2D and 3D mapping

In this paper, we present a new hierarchical optimization solution to the graph-based simultaneous localization and mapping (SLAM) problem. During online mapping, the approach corrects only the coarse structure of the scene and not the overall map. In this way, only updates for the parts of the map that need to be considered for making data associations are carried out. The hierarchical approach provides accurate non-linear map estimates while being highly efficient. Our error minimization approach exploits the manifold structure of the underlying space. In this way, it avoids singularities in the state space parameterization. The overall approach is accurate, efficient, designed for online operation, overcomes singularities, provides a hierarchical representation, and outperforms a series of state-of-the-art methods.