Information gathering tasks, such as terrestrial search and rescue, aerial inspection, and marine monitoring, require robotic unmanned systems to make decisions on how to travel within an environment to maximize or minimize a path-dependent information objective function. The distribution of information throughout the environment is the result of various processes, either natural or human-caused, and so this distribution exhibits an underlying structure. Existing information gathering algorithms seek to implicitly exploit this structure by selecting paths which maximize the robot's time in high-value regions. We see an opportunity to improve the performance of robots in these information gathering tasks by explicitly reasoning over the structure of information, allowing robots to plan their information gathering missions more efficiently and effectively. Topological representations provide an elegant way to describe the structure of an environment using descriptors that are defined relative to a set of features in the environment. Since these descriptors are inherently global, they provide a way for robots to reason directly about their paths within the global context of their operational environments. This additional context enables robotic systems to efficiently plan non-myopically.
To accomplish this goal, this thesis develops four contributions that allow robotic systems to reason about topological structure in field robotics tasks. The first contribution is a method for formalizing topological path constraints using a Mixed Integer Programming formulation to plan. Our second contribution is a system for exploiting expert-provided domain knowledge to track a topological feature using a team of heterogeneous robots. Both of these contributions provide ways to exploit the existence of topological features in the environment to motivate and constrain information gathering tasks. However, these methods require the features to be defined before planning. While methods to identify features exist for well-constructed indoor environments, they do not extend to the less-structured outdoor environments more common in field robotics applications. Our third and fourth contributions address this problem. The third contribution of this thesis is a hierarchical planning algorithm which identifies hotspot regions in an information function and uses them to construct a high-level planning graph, while the fourth is an algorithm for fitting a Topology-Aware Self-Organizing Map to an information function. The benefits of reasoning about the topology of the information field is demonstrated in simulation and field experiments. By incorporating global context about the information gathering task via topology, our methods are able to plan paths that collect more information than a naïve myopic planner. Furthermore, we are able to produce comparable or superior paths more quickly than state-of-the-art planners that do consider the entire path, such as combinatorial branch and bound algorithms.