  Robotic systems often operate with uncertainties in their dynamics, for
example, unknown inertial properties. Broadly, there are two approaches for
controlling uncertain systems: design robust controllers in spite of
uncertainty, or characterize a system before attempting to control it. This
paper proposes a middle-ground approach, making trajectory progress while also
accounting for gaining information about the system. More specifically, it
combines excitation trajectories which are usually intended to optimize
information gain for an estimator, with goal-driven trajectory optimization
metrics. For this purpose, a measure of information gain is incorporated (using
the Fisher Information Matrix) in a real-time planning framework to produce
trajectories favorable for estimation. At the same time, the planner receives
stable parameter updates from the estimator, enhancing the system model. An
implementation of this learn-as-you-go approach utilizing an Unscented Kalman
Filter (UKF) and Nonlinear Model Predictive Controller (NMPC) is demonstrated
in simulation. Results for cases with and without information gain and online
parameter updates in the system model are presented.
