  Many robotic systems deal with uncertainty by performing a sequence of
information gathering actions. In this work, we focus on the problem of
efficiently constructing such a sequence by drawing an explicit connection to
submodularity. Ideally, we would like a method that finds the optimal sequence,
taking the minimum amount of time while providing sufficient information.
Finding this sequence, however, is generally intractable. As a result, many
well-established methods select actions greedily. Surprisingly, this often
performs well. Our work first explains this high performance -- we note a
commonly used metric, reduction of Shannon entropy, is submodular under certain
assumptions, rendering the greedy solution comparable to the optimal plan in
the offline setting. However, reacting online to observations can increase
performance. Recently developed notions of adaptive submodularity provide
guarantees for a greedy algorithm in this online setting. In this work, we
develop new methods based on adaptive submodularity for selecting a sequence of
information gathering actions online. In addition to providing guarantees, we
can capitalize on submodularity to attain additional computational speedups. We
demonstrate the effectiveness of these methods in simulation and on a robot.
