Graphics Reference
In-Depth Information
2.8 Graph Complexity Reduction
2.8.1 Complexity Growth
The SLAM graph grows every time a view is created or observed. Even when the
robot stays within a bounded space, the views there are observed repeatedly, adding
pose nodes and edges to the graph and thus increasing the complexity with time. The
storage requirements and graph optimization costs grow with the graph complexity,
so in order to control these costs, the graph complexity must be bounded.
The view nodes correspond to elements of the front end relative to which pose
estimates can be computed. Further, the spatial density of view nodes is bounded
by the front end (as existing views will be recognized from nearby viewpoints), so
operation within a fixed spatial region implies a bounded number of view nodes. The
pose nodes, on the other hand, represent past robot poses that are not directly useful
in subsequent operation, except as a data structure for encoding constraints on other
nodes. The number of pose nodes grows with the number of observations, instead of
with the number of views. The graph complexity can be bounded by removing pose
nodes and limiting node connectivity to keep the complexity of the graph linear in
the number of views and thus linear in the amount of space explored.
2.8.2 Pose Node Marginalization
The graph represents a GMRF over past poses of the robot, so nodes can be removed
in statistically consistent manner by marginalizing out the corresponding pose vari-
ables from the GMRF state. The graph directly encodes the Markov property of the
system: a node is conditionally independent of all nodes to which it is not directly
connected. Thus marginalizing out a node's state involves only the Markov blanket
of the node (all of the nodes within one hop in the graph). Further, because the mar-
ginal distributions of a Gaussian are also Gaussians, the graph resulting from the
removal exactly encodes the appropriate Gaussian distribution over the remaining
variables [
11
].
Removing a node by marginalization induces pairwise constraints between all
pairs of nodes connected to the removed node. If a constraint (edge) already exists
between such a pair, the new constraint is combined with the existing constraint by
multiplication of their Gaussians. A few operations on edges are needed to define
the node marginalization procedure:
2.8.2.1 Edge Reversal
An edge
e
represents an uncertain rigid transformation between its two endpoint
nodes, given by a mean and covariance
(μ,Σ)
in the appropriate Lie group and Lie
