This paper addresses the problem of simultaneous localization and mapping (SLAM) by a mobile robot. An incremental SLAM algorithm is introduced that is derived from multigrid methods used for solving partial differential equations. The approach improves on the performance of previous relaxation methods for robot mapping, because it optimizes the map at multiple levels of resolution. The resulting algorithm has an update time that is linear in the number of estimated features for typical indoor environments, even when closing very large loops, and offers advantages in handling nonlinearities compared with other SLAM algorithms. Experimental comparisons with alternative algorithms using two well-known data sets and mapping results on a real robot are also presented.

This paper addresses the problem of impedance control for flexible joint robots based on a singular perturbation approach. Some aspects of the impedance controller, which turned out to be of high practical relevance during applications are then addressed, such as the implementation of space stiffness for redundant manipulators, the avoiding of mass matrix decoupling and the related design of the desired damping matrix. Finally, the proposed methods are validated through measurements on the DLR robot.

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.