We present a novel data structure, the Bayes tree, that provides an algorithmic foundation enabling a better understanding of existing graphical model inference algorithms and their connection to sparse matrix factorization methods. Similar to a clique tree, a Bayes tree encodes a factored probability density, but unlike the clique tree it is directed and maps more naturally to the square root information matrix of the simultaneous localization and mapping (SLAM) problem. In this paper, we highlight three insights provided by our new data structure. First, the Bayes tree provides a better understanding of the matrix factorization in terms of probability densities. Second, we show how the fairly abstract updates to a matrix factorization translate to a simple editing of the Bayes tree and its conditional densities. Third, we apply the Bayes tree to obtain a completely novel algorithm for sparse nonlinear incremental optimization, named iSAM2, which achieves improvements in efficiency through incremental variable re-ordering and fluid relinearization, eliminating the need for periodic batch steps. We analyze various properties of iSAM2 in detail, and show on a range of real and simulated datasets that our algorithm compares favorably with other recent mapping algorithms in both quality and efficiency.

Abstract-We present incremental smoothing and mapping (iSAM), a novel approach to the simultaneous localization and mapping problem that is based on fast incremental matrix factorization. iSAM provides an efficient and exact solution by updating a QR factorization of the naturally sparse smoothing information matrix, therefore recalculating only the matrix entries that actually change. iSAM is efficient even for robot trajectories with many loops as it avoids unnecessary fill-in in the factor matrix by periodic variable reordering. Also, to enable data association in real-time, we provide efficient algorithms to access the estimation uncertainties of interest based on the factored information matrix. We systematically evaluate the different components of iSAM as well as the overall algorithm using various simulated and real-world datasets for both landmark and pose-only settings.

Solving the SLAM (simultaneous localization and mapping) problem is one way to enable a robot

We present a new SLAM system capable of producing high quality globally consistent surface reconstructions over hundreds of metres in real-time with only a low-cost commodity RGB-D sensor. By using a fused volumetric surface reconstruction we achieve a much higher quality map over what would be achieved using raw RGB-D point clouds. In this paper we highlight three key techniques associated with applying a volumetric fusion-based mapping system to the SLAM problem in real-time. First, the use of a GPU-based 3D cyclical buffer trick to efficiently extend dense every frame volumetric fusion of depth maps to function over an unbounded spatial region. Second, overcoming camera pose estimation limitations in a wide variety of environments by combining both dense geometric and photometric camera pose constraints. Third, efficiently updating the dense map according to place recognition and subsequent loop closure constraints by the use of an "as-rigid-as-possible" space deformation. We present results on a wide variety of aspects of the system and show through evaluation on de facto standard RGB-D benchmarks that our system performs strongly in terms of trajectory estimation, map quality and computational performance in comparison to other state-of-the-art systems.

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