(Georgia Institute of Technology, 2014)
Indelman, Vadim; Carlone, Luca; Dellaert, Frank
This work investigates the problem of planning
under uncertainty, with application to mobile robotics. We
propose a probabilistic framework in which the robot bases
its decisions on the
generalized belief
, which is a probabilistic
description of its own state and of external variables of interest.
The approach naturally leads to a dual-layer architecture: an
inner estimation layer, which performs inference to predict the
outcome of possible decisions, and an
outer decisional layer
which is in charge of deciding the best action to undertake.
The approach does not discretize the state or control space,
and allows planning in continuous domain. Moreover, it allows
to relax the assumption of
maximum likelihood observations: predicted measurements are treated as random variables and
are not considered as
given. Experimental results show that
our planning approach produces smooth trajectories while
maintaining uncertainty within reasonable bounds.
(Georgia Institute of Technology, 2014)
Carlone, Luca; Kira, Zsolt; Beall, Chris; Indelman, Vadim; Dellaert, Frank
Factor graphs are a general estimation framework
that has been widely used in computer vision and robotics. In
several classes of problems a natural partition arises among
variables involved in the estimation. A subset of the variables
are actually of interest for the user: we call those
target
variables. The remaining variables are essential for the formulation of the optimization problem underlying maximum a
posteriori (MAP) estimation; however these variables, that we
call
support
variables, are not strictly required as output of the
estimation problem. In this paper, we propose a systematic way
to abstract support variables, defining optimization problems
that are only defined over the set of target variables. This
abstraction naturally leads to the definition of
smart factors, which correspond to constraints among target variables. We
show that this perspective unifies the treatment of heterogeneous problems, ranging from structureless bundle adjustment
to robust estimation in SLAM. Moreover, it enables to exploit
the underlying structure of the optimization problem and the
treatment of degenerate instances, enhancing both computational efficiency and robustness.