弦間スパース性を活用した因子グラフによる大域的最適推定
Exploiting Chordal Sparsity for Globally Optimal Estimation with Factor Graphs
因子グラフでモデル化されたロボットの状態推定問題に対し、凸緩和を用いた大域的最適解を自動構築し、ベイズ木構造を利用してSDPを分解することで計算を高速化する手法を提案した。
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著者: Avinash Subramanian, Connor Holmes, Timothy D. Barfoot, Frank Dellaert, Frederike Dümbgen
分類: cs.RO, math.OC
原文アブストラクト
Robust and efficient state estimation is crucial for perception, navigation, and control in robotics. State estimation problems are conveniently modeled using the factor-graph framework as enabled by modern software packages such as GTSAM or g2o. However, the standard solvers included in such frameworks are local and may converge to poor local minima, posing significant safety concerns. Conversely, techniques based on convex relaxations have been shown to provide a means of globally solving or certifying many state estimation problems. However, these relaxations 1) often require substantial effort to formulate, and 2) may incur significantly higher cost compared to efficient local solvers, as they require solving a large semidefinite program (SDP). In this work, we address both shortcomings by 1) creating a new procedure within the GTSAM framework for automatically constructing convex SDP relaxations for any factor graphs with common factor and variable types, and by 2) exploiting the Bayes tree constructions native to GTSAM to decompose the SDP problem, leading to significant speedup in solver time for chordally sparse problems. We demonstrate the favorable scaling of this structure-exploiting global estimator compared to standard local solvers for two case studies: A 3D pose-graph SLAM problem with a ring factor graph and a 2D localization problem with a chain factor graph. The software framework is available at https://github.com/borglab/gtsam.
