Two abilities fundamental to any robot equipped with a camera and functioning within an unknown, three-dimensional environment are exploring the environment and planning a collision-free path to reach a desired location. The focus of this research project is on the development of strategies that have provable properties, operate in real-time, and rely on efficiently-computable, qualitative visual information to control the motion of the robot. Because the robot moves in the environment in a continuous fashion, exploration and path planning is modeled as continuous, dynamic processes where motion planning and visual sensing are tightly coupled and occur simultaneously. The connection between these two processes becomes stronger as the geometric constraints imposed on the environment's obstacles get weaker. At some level of uncertainty, this connection induces a qualitative jump in the complexity of path planning, making visual exploration of the environment's obstacles necessary. To address these problems, the dynamics of the boundary separating the explored from the unexplored parts of the environment are studied. The strategies developed aim to structure the motion of the robot so that the representation of this boundary is simple and qualitative, can be efficiently derived from qualitative visual information, and its dynamic evolution is predictable and can be used to further guide the motion of the robot. This research should provide a better understanding of the connection between motion planning in three dimensions and visual sensing, and lead to the development of active, exploratory strategies for problems such as reaching a desired location, surveying unknown environments (e.g., a ship wreck),recognizing objects, or learning the shape of an unknown object.
