The research presented in this work focuses on several aspects of the remote operation of ground vehicles, notably Navigation and Mapping for autonomous robots and the effects of time delay in tele-operated vehicles. Navigation and mapping of large, unstructured spaces is achieved by accumulating constraints on the geometrical relationships between landmarks. These relationships are tracked using two qualitative representations of space, one based on qualitative angles between landmark triples, and a second which also considers qualitative edge lengths. For the first representation, measurements and graph inference are performed by way of manually computed lookup tables based on geometrical constraints on qualitative states. For the second representation, measurements are generated online using a branch-and-bound algorithm to solve a set of nonlinear feasibility problems, while lookup tables for inference are generated using a similar, offline approach. Estimates of the Relative Neighborhood Graph are extracted from the qualitative map and used to perform long-distance navigation. The effects of human control of remote vehicles are considered, focusing on the question of how operators are able to compensate for time delays when teleoperating vehicles in continuous motion. Statistical models fit to experimental data using the Least Angle Regression and Sparse Multinomial Regression algorithms show that human operators anticipate future control needs by predicting rover motion forward through time to determine predicted off-track errors. The relative contributions of environmental features to model predictive power is used to determine how feature 'importance' varies as a function of time delay.