  A key problem of robotic environmental sensing and monitoring is that of
active sensing: How can a team of robots plan the most informative observation
paths to minimize the uncertainty in modeling and predicting an environmental
phenomenon? This paper presents two principled approaches to efficient
information-theoretic path planning based on entropy and mutual information
criteria for in situ active sensing of an important broad class of
widely-occurring environmental phenomena called anisotropic fields. Our
proposed algorithms are novel in addressing a trade-off between active sensing
performance and time efficiency. An important practical consequence is that our
algorithms can exploit the spatial correlation structure of Gaussian
process-based anisotropic fields to improve time efficiency while preserving
near-optimal active sensing performance. We analyze the time complexity of our
algorithms and prove analytically that they scale better than state-of-the-art
algorithms with increasing planning horizon length. We provide theoretical
guarantees on the active sensing performance of our algorithms for a class of
exploration tasks called transect sampling, which, in particular, can be
improved with longer planning time and/or lower spatial correlation along the
transect. Empirical evaluation on real-world anisotropic field data shows that
our algorithms can perform better or at least as well as the state-of-the-art
algorithms while often incurring a few orders of magnitude less computational
time, even when the field conditions are less favorable.
