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

Common estimation algorithms, such as least squares estimation or the Kalman filter, operate on a state in a state space S that is represented as a real-valued vector. However, for many quantities, most notably orientations in 3D, S is not a vector space, but a so-called manifold, i.e. it behaves like a vector space locally but has a more complex global topological structure. For integrating these quantities, several ad-hoc approaches have been proposed.Here, we present a principled solution to this problem where the structure of the manifold S is encapsulated by two operators, state displacement : S × R n → S and its inverse : S × S → R n . These operators provide a local vector-space view δ → x δ around a given state x. Generic estimation algorithms can then work on the manifold S mainly by replacing +/− with / where appropriate. We analyze these operators axiomatically, and demonstrate their use in least-squares estimation and the Unscented Kalman Filter. Moreover, we exploit the idea of encapsulation from a software engineering perspective in the Manifold Toolkit, where the / operators mediate between a "flat-vector" view for the generic algorithm and a "named-members" view for the problem specific functions.

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Abstract-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.