Exploiting Non-Minimal Parametrizations in Graph-Based SLAM

To date, technology is in constant development, and researchers all over the world are pushing its boundaries every day further. In particular, Robotics is one of the fields that is currently in great expansion, entering into our daily lives in many ways - e.g. autonomous driving cars, service robots, video-games. Intelligent systems have several basic requirements to safely accomplish tasks in the real world. Among them we include i) having a digital map of the environment in which these agents are placed and ii) the ability to localize themselves in such a map. The problem of building a map while estimating the agent’s pose is known in Robotic research as Simultaneous Localization and Mapping (SLAM). As an example, an autonomous car that is asked to reach a location and, thus, has to traverse the city, needs to know the configuration of its surroundings in real-time, including the position of pedestrians, cars, bikes, and every other dynamic (or static) obstacle. Global positioning infrastructures - e.g. GPS - do not provide information on the surroundings and their signal is not always available. For this reason, other sensing modalities are generally used to accomplish such tasks efficiently. This thesis focuses on SLAM, investigating ways to increase the robustness and scalability of the solutions to this problem. More in detail, we will aim the attention to graph- based SLAM systems, which represent the most common choice in state-of-the-art pipelines. In such formalization, Least-Squares optimization represents the foundation of the entire estimation process, allowing it to achieve good accuracy without violating the real-time constraint of Robotic applications. In particular, we will investigate how non-minimal over-parametrizations of the optimization entities contribute to the accuracy, robustness, and scalability of the system. Traditionally, minimal parametrizations are used in the Least-Squares estimation process at different levels: i) to apply small increments to state variables, ii) to represent measurements, and iii) to express local distances between prediction and measurement. Still, such minimal parametrizations might be hard to compute, leading to complex mathematical derivations in the minimization algorithm. Conversely, extended parametrizations introduce additional parameters in the estimation process, possibly leading to a relaxed version of the original problem which can be solved more easily. Leveraging on this concept, we introduced a non-minimal error function in the context of global optimization, aiming to enlarge the converge basin and the overall robustness to noise. Then, we addressed how the map is represented, exploiting a novel extended landmark formalization that allows representing multiple geometric primitives as a unique object. Finally, we present a novel Least-Square optimization framework, which is specifically designed for SLAM pipelines and that can be easily extended to accommodate new solutions - such as the ones previously proposed. All of our contributions are open-source and publicly available to the research community. We believe that this is an important aspect of research, allowing to easily reproduce the results obtained in the proposed experiments while fostering the collaboration with other members of the community.