Axis Mapping: The Estimation of Surface Orientations and its Applications in Vehicle Localization and Structural Geology

The map representation of an environment should be selected based on its intended application. For example, a geometrically accurate map describing the Euclidean space of an environment is not necessarily the best choice if only a small subset its features are required. One possible subset is the orientations of the flat surfaces in the environment, represented by a special parameterization of normal vectors called axes. Devoid of positional information, the entries of an axis map form a non-injective relationship with the flat surfaces in the environment, which results in physically distinct flat surfaces being represented by a single axis. This drastically reduces the complexity of the map, but retains important information about the environment that can be used in meaningful applications in both two and three dimensions. This thesis presents axis mapping, which is an algorithm that accurately and automatically estimates an axis map of an environment based on sensor measurements collected by a mobile platform. Furthermore, two major applications of axis maps are developed and implemented. First, the LiDAR compass is a heading estimation algorithm that compares measurements of axes with an axis map of the environment. Pairing the LiDAR compass with simple translation measurements forms the basis for an accurate two-dimensional localization algorithm. It is shown that this algorithm eliminates the growth of heading error in both indoor and outdoor environments, resulting in accurate localization over long distances. Second, in the context of geotechnical engineering, a three-dimensional axis map is called a stereonet, which is used as a tool to examine the strength and stability of a rock face. Axis mapping provides a novel approach to create accurate stereonets safely, rapidly, and inexpensively compared to established methods. The non-injective property of axis maps is leveraged to probabilistically describe the relationships between non-sequential measurements of the rock face. The automatic estimation of stereonets was tested in three separate outdoor environments. It is shown that axis mapping can accurately estimate stereonets while improving safety, requiring significantly less time and effort, and lowering costs compared to traditional and current state-of-the-art approaches.

Language, Logos, and Social Ontology: Naturalist and Post-Naturalist Narratives of Human Rationality and Social Reality

I distinguish two ways that philosophers have approached and explained the reality and status of human social institutions. I call these approaches “naturalist” and “post-naturalist”. Common to both approaches is an understanding that the status of mind and its relation to the world or “nature” has implications on a conception of the status of institutional reality. Naturalists hold that mind is explicable within a scientific frame that conceives of mind as a fundamentally material process. By proxy, social reality is also materially explicable. Post-naturalists critique this view, holding instead that naturalism is parasitic on contemporary science—it therefore is non-compulsory and distorts how we ought to understand mind and social reality. A comparison of naturalism and post-naturalism will comprise the content of the first chapter. The second chapter turns to tracing out the dimensions of a post-naturalist narrative of mind and social reality. Post-naturalists conceive of mind and its activity of thought as sui generis, and it transpires from this that social institutions are better understood as a rational mind’s mode of the expression in the world. Post-naturalism conceives of social reality as a necessary dimension of thought. Thought requires a second person and thereby a tradition or context of norms that come to both structure its expression and become the products of expression. This is in contrast to the idea that social reality is a production of minds, and thereby derivative. Social reality, self-conscious thought, and thought of the second person are therefore three dimensions of a greater unity.