  Recent research in robot exploration and mapping has focused on sampling
environmental hotspot fields. This exploration task is formalized by Low,
Dolan, and Khosla (2008) in a sequential decision-theoretic planning under
uncertainty framework called MASP. The time complexity of solving MASP
approximately depends on the map resolution, which limits its use in
large-scale, high-resolution exploration and mapping. To alleviate this
computational difficulty, this paper presents an information-theoretic approach
to MASP (iMASP) for efficient adaptive path planning; by reformulating the
cost-minimizing iMASP as a reward-maximizing problem, its time complexity
becomes independent of map resolution and is less sensitive to increasing robot
team size as demonstrated both theoretically and empirically. Using the
reward-maximizing dual, we derive a novel adaptive variant of maximum entropy
sampling, thus improving the induced exploration policy performance. It also
allows us to establish theoretical bounds quantifying the performance advantage
of optimal adaptive over non-adaptive policies and the performance quality of
approximately optimal vs. optimal adaptive policies. We show analytically and
empirically the superior performance of iMASP-based policies for sampling the
log-Gaussian process to that of policies for the widely-used Gaussian process
in mapping the hotspot field. Lastly, we provide sufficient conditions that,
when met, guarantee adaptivity has no benefit under an assumed environment
model.
