3D scene graphs hierarchically represent the environment appropriately
organizing different environmental entities in various layers. Our previous
work on situational graphs extends the concept of 3D scene graph to SLAM by
tightly coupling the robot poses with the scene graph entities, achieving
state-of-the-art results. Though, one of the limitations of S-Graphs is
scalability in really large environments due to the increased graph size over
time, increasing the computational complexity.
To overcome this limitation in this work we present an initial research of an
improved version of S-Graphs exploiting the hierarchy to reduce the graph size
by marginalizing redundant robot poses and their connections to the
observations of the same structural entities. Firstly, we propose the
generation and optimization of room-local graphs encompassing all graph
entities within a room-like structure. These room-local graphs are used to
compress the S-Graphs marginalizing the redundant robot keyframes within the
given room. We then perform windowed local optimization of the compressed graph
at regular time-distance intervals. A global optimization of the compressed
graph is performed every time a loop closure is detected. We show similar
accuracy compared to the baseline while showing a 39.81% reduction in the
computation time with respect to the baseline.

通过利用层次结构和压缩冗余机器人姿态来减小图的规模，我们提出了改进版的 S-Graphs，相较于基线，实现了类似的准确性，并在计算时间上减少了 39.81%。

基于层次利用 S - 图进行更快优化

Faster Optimization in S-Graphs Exploiting Hierarchy

State-of-the-art techniques for simultaneous localization and mapping (SLAM)
employ iterative nonlinear optimization methods to compute an estimate for
robot poses. While these techniques often work well in practice, they do not
provide guarantees on the quality of the estimate. This paper shows that
Lagrangian duality is a powerful tool to assess the quality of a given
candidate solution. Our contribution is threefold. First, we discuss a revised
formulation of the SLAM inference problem. We show that this formulation is
probabilistically grounded and has the advantage of leading to an optimization
problem with quadratic objective. The second contribution is the derivation of
the corresponding Lagrangian dual problem. The SLAM dual problem is a (convex)
semidefinite program, which can be solved reliably and globally by
off-the-shelf solvers. The third contribution is to discuss the relation
between the original SLAM problem and its dual. We show that from the dual
problem, one can evaluate the quality (i.e., the suboptimality gap) of a
candidate SLAM solution, and ultimately provide a certificate of optimality.
Moreover, when the duality gap is zero, one can compute a guaranteed optimal
SLAM solution from the dual problem, circumventing non-convex optimization. We
present extensive (real and simulated) experiments supporting our claims and
discuss practical relevance and open problems.

本文提供了 Lagrangian duality 用于多智能体下载定位与地图制作中关于质量评价的解决方案。我们讨论了 SLAM 推理问题改良后的概率基础形式，推导了相应的拉格朗日对偶问题，并讨论了原始问题和对偶问题之间的关系。我们证明了可以在从对偶问题获得的情况下，计算 SLAM 问题的最优解并提供质量证书。