We describe a model of "trust" in human-robot systems that is inferred from their interactions, and inspired by similar concepts relating to trust among humans. This computable quantity allows a robot to estimate the extent to which its performance is consistent with a human’s expectations, with respect to task demands. Our trust model drives an adaptive mechanism that dynamically adjusts the robot's autonomous behaviors, in order to improve the efficiency of the collaborative team. We illustrate this trust-driven methodology through an interactive visual robot navigation system. This system is evaluated through controlled user experiments and a field demonstration using an aerial robot.