| This dissertation proposes minimal models for solving visibility-based robotic tasks. It introduces strategies that handle sensing and actuation uncertainty while avoiding precise state estimations. This is done by analyzing the space of sensing and actuation histories, the history information space. The history information space is compressed into smaller spaces, called derived information spaces, which are used for filtering and planning. By designing and analyzing the derived information spaces, we determine minimal information requirements to solve the robotic tasks. In this context, minimal information refers to the detection combinatorial properties of the environment necessary to complete the task. Examples of these combinatorial properties are the order type of a configuration of landmarks, or the inflection arrangement of a polygonal boundary. By establishing that certain tasks can be solved using simple sensors that detect these properties, formal performance guarantees are made while avoiding substantial modeling challenges. From this perspective, the thesis provides novel strategies for classical robotic tasks, such as navigation in unknown planar environments, navigation among unknown sets of landmarks, and visibility-based pursuit-evasion. Information is recovered from combinatorial events with models of sensors unable to gather metric information (e.g., distances or angles), or global reference frames (e.g., without a compass, or a global positioning system). These combinatorial events served as the base of a sensor beam abstraction, from which several inferences about the path followed by the robot are made. |
