Exploring Topological Environments

Simultaneous localization and mapping (SLAM) addresses the task of incrementally building a map of the environment with a robot while simultaneously localizing the robot relative to that map. SLAM is generally regarded as one of the most important problems in the pursuit of building truly autonomous mobile robots. This thesis considers the SLAM problem within a topological framework, in which the world and its representation are modelled as a graph. A topological framework provides a useful model within which to explore fundamental limits to exploration and mapping. Given a topological world, it is not, in general, possible to map the world deterministically without resorting to some type of marking aids. Early work demonstrated that a single movable marker was sufficient but is this necessary? This thesis shows that deterministic mapping is possible if both explicit place and back-link information exist in one vertex. Such 'directional lighthouse' information can be established in a number of ways including through the addition of a simple directional immovable marker to the environment. This thesis also explores non-deterministic approaches that map the world with less marking information. The algorithms are evaluated through performance analysis and experimental validation. Furthermore, the basic sensing and locomotion assumptions that underlie these algorithms are evaluated using a differential drive robot and an autonomous visual sensor

Exploring Topological Environments

Simultaneous localization and mapping (SLAM) addresses the task of incrementally building a map of the environment with a robot while simultaneously localizing the robot relative to that map. SLAM is generally regarded as one of the most important problems in the pursuit of building truly autonomous mobile robots. This thesis considers the SLAM problem within a topological framework, in which the world and its representation are modelled as a graph. A topological framework provides a useful model within which to explore fundamental limits to exploration and mapping. Given a topological world, it is not, in general, possible to map the world deterministically without resorting to some type of marking aids. Early work demonstrated that a single movable marker was sufficient but is this necessary? This thesis shows that deterministic mapping is possible if both explicit place and back-link information exist in one vertex. Such 'directional lighthouse' information can be established in a number of ways including through the addition of a simple directional immovable marker to the environment. This thesis also explores non-deterministic approaches that map the world with less marking information. The algorithms are evaluated through performance analysis and experimental validation. Furthermore, the basic sensing and locomotion assumptions that underlie these algorithms are evaluated using a differential drive robot and an autonomous visual sensor

Robot Map Verification of a Graph World

: In the map verification problem, a robot is given a (possibly incorrect) map M of the world G with its position and orientation indicated on the map. The task is to find out whether this map, for the given robot position and orientation in the map, is correct for the world G. We consider the world model with a graph G = (V G ; EG ) in which, for each vertex, edges incident to the vertex are ordered cyclically around that vertex. (This holds similarly for the map M = (V M ; EM ).) The robot can traverse edges and enumerate edges incident on the current vertex, but it cannot distinguish vertices and edges from each other. To solve the verification problem, the robot uses a portable edge marker, that it can put down and pick up as needed. The robot can recognize the edge marker when it encounters it in G. By reducing the verification problem to an exploration problem, verification can be completed in O(jV G j \Theta jE G j) edge traversals (the mechanical cost) with the help of a singl..