(Georgia Institute of Technology, 2010)
Ni, Kai; Dellaert, Frank
We propose a novel batch algorithm for SLAM
problems that distributes the workload in a hierarchical way.
We show that the original SLAM graph can be recursively partitioned
into multiple-level submaps using the nested dissection
algorithm, which leads to the cluster tree, a powerful graph
representation. By employing the nested dissection algorithm,
our algorithm greatly minimizes the dependencies between two
subtrees, and the optimization of the original SLAM graph can
be done using a bottom-up inference along the corresponding
cluster tree. To speed up the computation, we also introduce a
base node for each submap and use it to represent the rigid
transformation of the submap in the global coordinate frame.
As a result, the optimization moves the base nodes rather
than the actual submap variables. We demonstrate that our
algorithm is not only exact but also much faster than alternative
approaches in both simulations and real-world experiments.
(Georgia Institute of Technology, 2010)
Dellaert, Frank; Carlson, Justin; Ila, Viorela; Ni, Kai; Thorpe, Charles E.
In this paper we propose an efficient preconditioned
conjugate gradients (PCG) approach to solving large-scale
SLAM problems. While direct methods, popular in the
literature, exhibit quadratic convergence and can be quite
efficient for sparse problems, they typically require a lot of
storage as well as efficient elimination orderings to be found. In
contrast, iterative optimization methods only require access to
the gradient and have a small memory footprint, but can suffer
from poor convergence. Our new method, subgraph preconditioning,
is obtained by re-interpreting the method of conjugate
gradients in terms of the graphical model representation of the
SLAM problem. The main idea is to combine the advantages of
direct and iterative methods, by identifying a sub-problem that
can be easily solved using direct methods, and solving for the
remaining part using PCG. The easy sub-problems correspond
to a spanning tree, a planar subgraph, or any other substructure
that can be efficiently solved. As such, our approach provides
new insights into the performance of state of the art iterative
SLAM methods based on re-parameterized stochastic gradient
descent. The efficiency of our new algorithm is illustrated on
large datasets, both simulated and real.