Leveraging Least Squares for a Unified Methodology in Mobile Robotics and SLAM problems

Intelligent mobile robots require a model of the operating environment to perform their tasks. For example, a vacuum cleaner robot needs a model of the house to efficently cover the space, and to visit all the rooms. An autonomous car needs a model of the surrounding environment, i.e. the traversed city, to move from its starting location to its goal one. Instead, a robot designed for planetary exploration should be able to build such a model, with the goal of safely exploring the surrounding environment. Building such robust systems requires performing a set of mandatory steps. Namely, all the intrinsics and extrinsics parameters of the robot and of the sensors mounted on it has to be accurately estimated; using the sensors readings, the platform has to build a compress, yet informative, representation of the environment; the robot has to be constantly localized in this representation; and it has to safely navigate into it. Calibration, Simultaneous Localization and Mapping (SLAM) and Navigation constitute active fields of research, leading to robust and reliable industrial products. In these thesis we faced all these problems, providing novel contributions to the state- of-the-art approaches. The solution of all these tasks requires the application of a coherent methodology, leveraging least squares solvers. Thus, the contribution of this thesis is twofold. First, we provide novel contributions to calibration-, SLAM- and navigation-related problems, with a particular focus on motion-based calibration, feature-less point cloud registration, environment representation using high-level primitives, and model predictive control. Second, we provide a unified methodology, leveraging least squares, to design and solve mobile robotics and SLAM related problems. The presented methodology is intended to be used as a guideline to face such problems, requiring specific adaptations for each specific application. Thus, for each faced problem we provide the specializations needed to achieve state-of-the-art performance. Moreover, to foster the repeatability of our experiments, we provide our open-source implementation for each one of the solutions presented in this thesis.