This dissertation presents a basic information-driven sensor management problem, referred to as treasure hunt, that is relevant to mobile-sensor applications such as mine hunting, monitoring, and surveillance. The objective is to classify/infer one or multiple fixed targets or treasures located in an obstacle-populated workspace by planning the path and a sequence of measurements of a robotic sensor installed on a mobile platform associated with the treasures distributed in the sensor workspace. The workspace is represented by a connectivity graph, where each node represents a possible sensor deployment, and the arcs represent possible sensor movements. A methodology is developed for planning the sensing strategy of a robotic sensor deployed. The sensing strategy includes the robotic sensor's path, because it determines which targets are measurable given a bounded field of view. Existing path planning techniques are not directly applicable to robots whose primary objective is to gather sensor measurements. Thus, in this dissertation, a novel approximate cell-decomposition approach is developed in which obstacles, targets, the sensor's platform and field of view are represented as closed and bounded subsets of an Euclidean workspace. The approach constructs a connectivity graph with observation cells that is pruned and transformed into a decision tree, from which an optimal sensing strategy can be computed. It is shown that an additive incremental-entropy function can be used to efficiently compute the expected information value of the measurement sequence over time. The methodology is applied to a robotic landmine classification problem and the board game of CLUE$^{\circledR}$. In the landmine detection application, the optimal strategy of a robotic ground-penetrating radar is computed based on prior remote measurements and environmental information. Extensive numerical experiments show that this methodology outperforms shortest-path, complete-coverage, random, and grid search strategies, and is applicable to non-overpass capable platforms that must avoid targets as well as obstacles. The board game of CLUE$^{\circledR}$ is shown to be an excellent benchmark example of treasure hunt problem. The test results show that a player implementing the strategies developed in this dissertation outperforms players implementing Bayesian networks only, Q-learning, or constraint satisfaction, as well as human players. / Dissertation