| This dissertation studies optimal exploration, defined as the collection of information about given objects of interest by a mobile agent (the explorer) using imperfect sensors. The key aspects of exploration are kinematics (which determine how the explorer moves in response to steering commands), energetics (which determine how much energy is consumed by motion and maneuvers), informatics (which determine the rate at which information is collected) and estimation (which determines the states of the objects). These aspects are coupled by the steering decisions of the explorer. We seek to improve exploration by finding trade-offs amongst these couplings and the components of exploration: the Mission, the Path and the Agent.;A comprehensive model of exploration is presented that, on one hand, accounts for these couplings and on the other hand is simple enough to allow analysis. This model is utilized to pose and solve several exploration problems where an objective function is to be minimized. Specific functions to be considered are the mission duration and the total energy. These exploration problems are formulated as optimal control problems and necessary conditions for optimality are obtained in the form of two-point boundary value problems. An analysis of these problems reveals characteristics of optimal exploration paths. Several regimes are identified for the optimal paths including the Watchtower, Solar and Drag regime, and several non-dimensional parameters are derived that determine the appropriate regime of travel. The so-called Power Ratio is shown to predict the qualitative features of the optimal paths, provide a metric to evaluate an aircrafts design and determine an aircrafts capability for flying perpetually. Optimal exploration system drivers are identified that provide perspective as to the importance of these various regimes of flight.;A bank-to-turn solar-powered aircraft flying at constant altitude on Mars is used as a specific platform for analysis using the coupled model. Flight-paths found with this platform are presented that display the optimal exploration problem characteristics. These characteristics are used to form heuristics, such as a Generalized Traveling Salesman Problem solver, to simplify the exploration problem. These heuristics are used to empirically show the successful completion of an exploration mission by a physical explorer. |
