(Georgia Institute of Technology, 2015-05)
Carlone, Luca; Tron, Roberto; Daniilidis, Kostas; Dellaert, Frank
Pose graph optimization is the non-convex optimization problem underlying pose-based Simultaneous Localization and Mapping (SLAM). If robot orientations were known, pose graph optimization would be a linear least-squares problem, whose solution can be computed efficiently and reliably. Since rotations are the actual reason why SLAM is a difficult problem, in this work we survey techniques for 3D rotation estimation. Rotation estimation has a rich history in three scientific communities: robotics, computer vision, and control theory. We review relevant contributions across these communities, assess their practical use in the SLAM domain, and benchmark their performance on representative SLAM problems (Fig. 1). We show that the use of rotation estimation to bootstrap iterative pose graph solvers entails significant boost in convergence speed and robustness.
(Georgia Institute of Technology, 2015)
Tron, Roberto; Carlone, Luca; Dellaert, Frank; Daniilidis, Kostas
Bearing-only localization can be formulated in
terms of optimal graph embedding: one has to assign a 2-D or
3-D position to each node in a graph while satisfying as close as possible all the bearing-only constraints on the edges. If the
graph is parallel rigid, this can be done via spectral methods. When the graph is not rigid the reconstruction is ambiguous, as different subsets of vertices can be scaled differently. It is
therefore important to first identify a partition of the problem into maximal rigid components. In this paper we show that the
cycle basis matrix of the graph not only translates into an algorithm to identify all rigid sub-graphs, but also provides a more intuitive way to look at graph rigidity, showing, for
instance, why triangulated graphs are rigid and why graphs with long cycles may loose this property. Furthermore, it provides practical tools to enforce rigidity by adding a minimal
number of measurements.