The goal of this research is to develop a navigation methodology for robots using relational geometric models that are constructed and evaluated using minimal sensing. The use of qualitative states is both intuitive to human perception, and amenable to long-term operations in robotics because of the inherent scalability and simplicity in sensing. The technical approach consists of four tasks. The first task is to create a mathematical representation that supports relational sensing/maps/navigation. The second task is to extend the representation and methods to include uncertainties, which allows the work to be of practical significance. The third task is to develop a hypothesis based navigation methodology that naturally enables planning over minimal, uncertain relational maps and sensor data. Finally, the theory will be validated using an increasingly complex set of experimental validation tests. This research enables robust navigation of robots in applications such as autonomous driving and personal robotics, as well as applications that have unstructured environments with no GPS access, such as exploration (under water, planetary, caves), disaster relief and search and rescue. The research is particularly well suited to robots that have sensing and computational constraints. In the long term, it is envisioned that the algorithms and software enable life-long learning in robotics because of the ability to scale to long-term operations.
