Joachim Clemens

An evidential approach to SLAM, path planning, and active exploration

Probability theory has become the standard framework in the field of mobile robotics because of the inherent uncertainty associated with sensing and acting. In this paper, we show that the theory of belief functions with its ability to distinguish between different types of uncertainty is able to provide significant advantages over probabilistic approaches in the context of robotics. We do so by presenting solutions to the essential problems of simultaneous localization and mapping (SLAM) and planning based on belief functions. For SLAM, we show how the joint belief function over the map and the robots poses can be factored and efficiently approximated using a Rao-Blackwellized particle filter, resulting in a generalization of the popular probabilistic FastSLAM algorithm. Our SLAM algorithm produces occupancy grid maps where belief functions explicitly represent additional information about missing and conflicting measurements compared to probabilistic grid maps. The basis for this SLAM algorithm are forward and inverse sensor models, and we present general evidential models for range sensors like sonar and laser scanners. Using the generated evidential grid maps, we show how optimal decisions can be made for path planning and active exploration. To demonstrate the effectiveness of our evidential approach, we apply it to two real-world datasets where a mobile robot has to explore unknown environments and solve different planning problems. Finally, we provide a quantitative evaluation and show that the evidential approach outperforms a probabilistic one both in terms of map quality and navigation performance. A belief-function-based approach to SLAM for mobile robots is presented.Different types of uncertainty are explicitly represented in evidential grid maps.Optimal navigation and exploration based on evidential grid maps is shown.Evidential forward and inverse models for range sensors are provided.The approach is evaluated using real-world datasets recorded by a mobile robot.

Multi-Sensor Fusion Using Evidential SLAM for Navigating a Probe through Deep Ice

We present an evidential multi-sensor fusion approach for navigating a maneuverable ice probe designed for extraterrestrial sample analysis missions. The probe is equipped with a variety of sensors and has to estimate its own position within the ice as well as a map of its surroundings. The sensor fusion is based on an evidential SLAM approach which produces evidential occupancy grid maps that contain more information about the environment compared to probabilistic grid maps. We describe the different sensor models underlying the algorithm and we present empirical results obtained under controlled conditions in order to analyze the effectiveness of the proposed multi-sensor fusion approach. In particular, we show that the localization error is significantly reduced by combining multiple sensors.

Optimal rotation sequences for active perception

One major objective of autonomous systems navigating in dynamic environments is gathering information needed for self localization, decision making, and path planning. To account for this, such systems are usually equipped with multiple types of sensors. As these sensors often have a limited field of view and a fixed orientation, the task of active perception breaks down to the problem of calculating alignment sequences which maximize the information gain regarding expected measurements. Action sequences that rotate the system according to the calculated optimal patterns then have to be generated. In this paper we present an approach for calculating these sequences for an autonomous system equipped with multiple sensors. We use a particle filter for multi- sensor fusion and state estimation. The planning task is modeled as a Markov decision process (MDP), where the system decides in each step, what actions to perform next. The optimal control policy, which provides the best action depending on the current estimated state, maximizes the expected cumulative reward. The latter is computed from the expected information gain of all sensors over time using value iteration. The algorithm is applied to a manifold representation of the joint space of rotation and time. We show the performance of the approach in a spacecraft navigation scenario where the information gain is changing over time, caused by the dynamic environment and the continuous movement of the spacecraft

Dimensions of Uncertainty in Evidential Grid Maps

We show how a SLAM algorithm based on belief function theory can produce evidential occupancy grid maps that provide a mobile robot with additional information about its environment. While uncertainty in probabilistic grid maps is usually measured by entropy, we show that for evidential grid maps, uncertainty can be expressed in a three-dimensional space and we propose appropriate measures for quantifying uncertainty in these different dimensions. We analyze these measures in a practical mapping example containing typical sources of uncertainty for SLAM. As a result of the evidential representation, the robot is able to distinguish between different sources of uncertainty (e.g., a lack of measurements vs. conflicting measurements) which are indistinguishable in the probabilistic framework.

Rigid Body Attitude Control Based on a Manifold Representation of Direction Cosine Matrices

Autonomous systems typically actively observe certain aspects of their surroundings, which makes them dependent on a suitable controller. However, building an attitude controller for three degrees of freedom is a challenging task, mainly due to singularities in the different parametrizations of the three dimensional rotation group SO(3). Thus, we propose an attitude controller based on a manifold representation of direction cosine matrices: In state space, the attitude is globally and uniquely represented as a direction cosine matrix R ∈ SO(3). However, differences in the state space, i.e., the attitude errors, are exposed to the controller in the vector space 3. This is achieved by an operator, which integrates the matrix logarithm mapping from SO(3) to so(3) and the map from so(3) to 3. Based on this representation, we derive a proportional and derivative feedback controller, whose output has an upper bound to prevent actuator saturation. Additionally, the feedback is preprocessed by a particle filter to account for measurement and state transition noise. We evaluate our approach in a simulator in three different spacecraft maneuver scenarios: (i) stabilizing, (ii) rest-to-rest, and (iii) nadir-pointing. The controller exhibits stable behavior from initial attitudes near and far from the setpoint. Furthermore, it is able to stabilize a spacecraft and can be used for nadir-pointing maneuvers.

Towards the exploitation of formal methods for information fusion

When an autonomous system has to act in or interact with an environment, a suitable representation of it is required. In the past decades, many different representation forms – especially spacial ones – have been proposed and even more information fusion techniques were developed in order to build these representations from multiple information sources. However, most of these algorithms do not exploit the full potential of the available information. This is caused by the fact that they are not able to handle the full complexity of all possible solutions compatible with the information and that they rely on restrictive assumptions (i.e. independencies) in order to make the computation feasible. In this work, a new methodology is envisioned that utilizes formal methods, in particular solvers for Pseudo-Boolean Optimization, to drop some of these assumptions. In order to illustrate the ideas, information fusion based on belief functions and occupancy grid maps are considered. It is shown that this approach allows for considering dependencies among multiple cells and thus significantly reduces the uncertainty in the resulting representation.

Multi-robot in-ice localization using graph optimization

We present a graph-based algorithm for jointly estimating the positions of multiple ice-melting probes. The probes determine the distances relative to each other by measuring the signal propagation time of acoustic pulses. Furthermore, multiple other sensors, like an inertial measurement unit and a differential magnetometer system, are used to calculate the relative movement of the probes. The positions of the probes are represented by nodes of a graph, while those nodes are constrained by edges, which result from the sensor measurements. Finally, the localization task is solved by optimizing the node positions with respect to the error resulting from the constraints. Our approach is compared to other algorithms for multi-robot localization in different scenarios.

Formal methods for reasoning and uncertainty reduction in evidential grid maps

Information fusion is the task of combining data collected from different sources into a unified representation. Here, a main challenge is to deal with the inherent uncertainty contained in the information, such as sensor noise, conflicting information, or incomplete knowledge. In current approaches, one usually employs independence assumptions in order to reduce the complexity. Because of this, the full potential of the gathered data is often not fully exploited and the fusion may lead to additional uncertainty. In order to reduce this uncertainty, further information in form of background and expert knowledge can be utilized, which is often available for real-world scenarios. However, reasoning on this knowledge is a computational complex task. In this work, we propose a methodology which utilizes formal methods for that reasoning, which allows to relax some of the independence assumptions. We demonstrate the proposed methodology using evidential grid maps – a belief function-based environment representation, in which different kinds of uncertainty are represented explicitly. Our methodology is evaluated based on basic structures as well as on real-world data sets. The results show that the uncertainty in the maps is significantly reduced by considering dependencies among cells.