@phdthesis{clemens2018phd,
  title     = {Uncertainty in Localization, Mapping, and Planning: Advanced Methods and Applications},
  author    = {Clemens, Joachim},
  year      = {2018},
  school    = {Cognitive Neuroinformatics, University of Bremen},
  address   = {Bremen},
  abstract  = {Localization, mapping, and planning are three of the most fundamental tasks not only
in mobile robotics but also for many applications that involve moving vehicles. The first
is concerned with estimating the pose (position and orientation) of a robot, the second
aims to create a map of the environment, and the goal of the third is to plan the further
course of action. In all three areas, it is essential to correctly handle and represent the
inherent uncertainty of the processed information. The sensor data used to estimate the
pose and to create the map is usually noisy and incomplete. Furthermore, measurements
recorded at different time steps or using multiple sensors may contradict each other. The
different types of uncertainty have to be considered during the fusion process and need
to be reflected by the estimate. The result is in turn used as basis for planning, where
the uncertainty has to be taken into account as well in order to make optimal decisions.

This thesis investigates advanced theoretical methods for representing uncertainty in
the four areas localization, mapping, simultaneous localization and mapping (SLAM), as
well as planning. In the field of localization, we focus on pose estimation in 3D Euclidean
space, where a particular challenge arises from the complex topology of the rotation
space. This problem is addressed by utilizing a formalism that uses a globally consistent
parametrization to represent elements in the state space manifold, while deviations and
uncertainty are expressed in a local vector space. The mapping between both spaces is
encapsulated in order to allow for a seamless integration into fusion algorithms. Based on
that methodology, we derive different Bayesian filters, in particular a particle filter and
an extended Kalman filter, for multi-sensor fusion and pose estimation. Furthermore, an
algorithm for multi-robot localization using graph optimization is presented. In the area
of mapping, we extend the representation of uncertainty in occupancy grid maps by the
use of the belief function theory, which results in so-called evidential grid maps. This
framework allows one to explicitly represent different dimensions of uncertainty in the
input data and the estimate, which makes it possible to identify and distinguish between
different causes for uncertainty. That mapping method is further extended to a full
SLAM algorithm, which is, to the best of our knowledge, the first evidential approach
to the SLAM problem. Additionally, we present a probabilistic approach to extend
the representation of uncertainty in SLAM, where beta distributions are employed to
model the uncertainty of the occupancy probabilities. In both cases, we derive all SLAM
equations based on the respective map representation and propose different measures for
quantifying the uncertainty in those maps. Regarding the topic of planning, we consider
the utilization and the minimization of uncertainty in localization and mapping. We
present an approach to active perception, which aims to actively choose the best actions
for making observations that reduce the uncertainty of the pose estimate. Furthermore,
we show how the extended representation of uncertainty in the maps estimated by the
SLAM algorithms can be utilized for path planning and active exploration. In the case
of the former, the robot needs to plan a path to a predefined goal state, where we
can control the cautiousness of the robot by defining different costs depending on the
type of uncertainty. The goal of active exploration is to plan a path in order to reduce
the uncertainty in the map. It benefits from the detailed representation of uncertainty
because the robot can decide which uncertainty type shall be minimized, which allows
for conducting the exploration in a more targeted manner.

All developed algorithms are applied to multiple applications and are evaluated using
both simulation and real-world data. The first application is navigating an autonomous
spacecraft through deep space, which is a simulation scenario used as an example for
investigating the topics of localization and active perception. The second application
considers the navigation of multiple melting probes through ice, where one of these
probes is maneuverable. The corresponding system was tested on different European
and Antarctic glaciers, while a simulation environment is available as well. In that
context, we study single-robot and multi-robot localization as well as evidential mapping.
Finally, the third application is the autonomous exploration of an office environment
using a wheel-driven robot, where we also utilize simulation and real-world datasets.
This scenario is used to investigate and evaluate the two SLAM approaches as well as
the algorithms for path planning and active exploration. However, the proposed methods
are not limited to those applications. They are quite generic and can be applied to other
fields as well, like underwater navigation and highly automated driving.
}
}