In geographic data analysis, one is often given point data of different categories (such as facilities of a university categorized by department). Drawing upon recent research on set visualization, we want to visualize category membership by connecting points of the same category with visual links. Existing approaches that follow this path usually insist on connecting all members of a category, which may lead to many crossings and visual clutter. We propose an approach that avoids crossings between connections of different categories completely. Instead of connecting all data points of the same category, we subdivide categories into smaller, local clusters where needed. We do a case study comparing the legibility of drawings produced by our approach and those by existing approaches. In our problem formulation, we are additionally given a graph G on the data points whose edges express some sort of proximity. Our aim is to find a subgraph G′ of G with the following properties: (i) edges connect only data points of the same category, (ii) no two edges cross, and (iii) the number of connected components (clusters) is minimized. We then visualize the clusters in G′. For arbitrary graphs, the resulting optimization problem, Cluster Minimization, is NP-hard (even to approximate). Therefore, we introduce two heuristics. We do an extensive benchmark test on real-world data. Comparisons with exact solutions indicate that our heuristics do astonishing well for certain relative-neighborhood graphs.

There is a great deal of interest in efficient, accurate and reliable high-quality scene modeling: In robotics, especially for autonomous robots and drones, high-quality scene modeling is essential for navigation and interaction within complex environments. In agriculture, farmers require the tool for precision monitoring and cropping. In architecture and construction, engineers use it to assist Building Information Modeling (BIM) in creating detailed 3D representations of buildings and infrastructure. In the entertainment industry, high-quality scene modeling facilitates the cre- ation of immersive experiences in films, video games, and virtual reality (VR). While the process of object and small scene modeling is well developed with implicit representation, precise incre- mental reconstruction on large scenes remains a complex and challenging task, due to the high budget required for loop correction. Besides the geometric modeling, color suffers from the need to accommodate more complex patterns, and supports only inefficient post-training. Semantic modeling also presents a significant challenge. Due to the significantly higher dimensionality, it is even more difficult to model semantic information in continuous space. This thesis deals with the Dense SLAM and the challenges of the new trend of continuous mapping and usage on large scale. To support loop-correction on large scale, IMT-Mapping introduces an SE(3)-transformable implicit map for remapping functions. IFR makes SDF-to- SDF registration without moving the field, thereby providing an efficient way for aligning two sub-maps. Turning from geometry to color, NSLF-OL introduces online-learning of high quality color alongside real-time reconstruction. Analyzing the limitations of previous research, Uni- Fusion proposes Universal Continuous Mapping for all map properties, even high-dimensional CLIP features, without any training. SceneFactory designs a workflow-centric framework that uniformly supports a complete range of Incremental Scene Modeling. The combination of these contributions results in the emergence of a novel general concept in this thesis: Incremental Continuous Scene Modeling (ICSM). ICSM transcends the conventional limitations of dense SLAM, offering a versatile and comprehensive approach to high-quality in- cremental mapping of various features (geometric, color, semantic, and more), sensor setups, and applications (Dense RGB/RGB-D/RGB-L/Depth-only SLAM, Unposed & Uncalibrated MVD, and more). This thesis first introduces the history of robotic mapping and our overall contribution. Then in three separate chapters, we present the geometry, color and semantics components of ICSM. Where we integrate our papers in subsections of corresponding chapters. Besides the broad features supported in ICSM, the subsequent chapter introduces a unified framework for accommodating the diverse sensor configurations and applications. The authors are confident about the contribution to the field. However, there are limitations. Therefore, in the final chapter, together with the conclusion of the thesis, we also indicate the limitations, problems that remain to be explored, and a future direction outlook.

In this thesis, a model of the dynamics during the landing phase of an interplanetary lander mission is developed in a 3 DOF approach with the focus lying on landing by propulsive means. Based on this model, a MATLAB simulation was developed with the goal of enabling an estimation of the performance and especially the required fuel amount of a propulsive landing system on Venus. This landing system is modeled to be able to control its descent using thrusters and to perform a stable landing at a specified target location. Using this simulation, the planetary environments of Mars and Venus can be simulated and the impact of wind, atmospheric density and gravity as well as of using different thrusters on the fuel consumption and landing abilities of the simulated landing system can be investigated. The comparability of these results with the behavior of real landing systems is validated in this thesis by simulating the Powered Descent Phase of the Mars 2020 mission and comparing the results to the data the Mars 2020 descent stage has collected during this phase of its landing. Further, based on the simulation, the minimal necessary fuel amount for a successful landing on Venus has been determined for different scenarios. The simulation along with these results are a contribution to the research of this thesis’s supervisor Clemens Riegler, M.Sc., who will use them for a comparison of different types of landing systems in the context of his doctoral thesis.

Dieser Kurzbericht beleuchtet die Einsatzmöglichkeiten von Kleinsatelliten in der extraterrestrischen Forschung und zeigt auf welche technologischen Herausforderungen sich bei ihrem Einsatz ergeben. Die präsentierten Ergebnisse sind Teil der SATEX Untersuchung (FKZ 50OO2222). In diesem Dokument werden zunächst die allgemeinen Einsatzmöglichkeiten von Kleinsatelliten in der Extraterrestrik anhand ausgewählter Beispielmissionen beleuchtet. Daraufhin erfolgt die Erörterung spezifischer technischer Herausforderungen und Umweltbedingungen bei cislunaren und interplanetaren Kleinsatellitenmissionen, gefolgt von einer kurzen Präsentation von Nutzerwünsche aus Deutschland für Missionen zur Erforschung des Weltraums. Zum Abschluss werden zehn konkrete, im Rahmen der Untersuchung ermittelte, Missionsideen vorgestellt und bewertet. Schließlich erfolgt die Zusammenfassung der wichtigsten Erkenntnisse und Empfehlungen.

Autonomous mobile robots operating in unknown terrain have to guide their drive decisions through local perception. Local mapping and traversability analysis is essential for safe rover operation and low level locomotion. This thesis deals with the challenge of building a local, robot centric map from ultra short baseline stereo imagery for height and traversability estimation. Several grid-based, incremental mapping algorithms are compared and evaluated in a multi size, multi resolution framework. A new, covariance based mapping update is introduced, which is capable of detecting sub- cellsize obstacles and abstracts the terrain of one cell as a first order surface. The presented mapping setup is capable of producing reliable ter- rain and traversability estimates under the conditions expected for the Cooperative Autonomous Distributed Robotic Exploreration (CADRE) mission. Algorithmic- and software architecture design targets high reliability and efficiency for meeting the tight constraints implied by CADRE’s small on-board embedded CPU. Extensive evaluations are conducted to find possible edge-case scenar- ios in the operating envelope of the map and to confirm performance parameters. The research in this thesis targets the CADRE mission, but is applicable to any form of mobile robotics which require height- and traversability mapping.