Uncertainty in Localization, Mapping, and Planning: Advanced Methods and Applications

by Joachim Clemens

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.

Reference:

Uncertainty in Localization, Mapping, and Planning: Advanced Methods and Applications (Joachim Clemens), PhD thesis, Cognitive Neuroinformatics, University of Bremen, 2018.

Bibtex Entry:

@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. } }