  Ideally, robots should move in ways that maximize the knowledge gained about
the state of both their internal system and the external operating environment.
Trajectory design is a challenging problem that has been investigated from a
variety of perspectives, ranging from information-theoretic analyses to
leaning-based approaches. Recently, observability-based metrics have been
proposed to find trajectories that enable rapid and accurate state and
parameter estimation. The viability and efficacy of these methods is not yet
well understood in the literature. In this paper, we compare two
state-of-the-art methods for observability-aware trajectory optimization and
seek to add important theoretical clarifications and valuable discussion about
their overall effectiveness. For evaluation, we examine the representative task
of sensor-to-sensor extrinsic self-calibration using a realistic physics
simulator. We also study the sensitivity of these algorithms to changes in the
information content of the exteroceptive sensor measurements.
