The progressive processing model allows a system to trade off resource consumption against the quality of the outcome by mapping each activity to a graph of potential solution methods. In the past, only semi-linear graphs have been used. We examine the application of the model to control the operation of an autonomous rover which operates under tight resource constraints. The task structure is generalized to directed acyclic graphs for which the optimal schedule can be computed by solving a corresponding Markov decision problem. We evaluate the complexity of the solution analytically and experimentally and show that it provides a practical approach to building an adaptive controller for this application.