  Path planning over spatiotemporal models can be applied to a variety of
applications such as UAVs searching for spreading wildfire in mountains or
network of balloons in time-varying atmosphere deployed for inexpensive
internet service. A notable aspect in such applications is the dynamically
changing environment. However, path planning algorithms often assume static
environments and only consider the vehicle's dynamics exploring the
environment. We present a spatiotemporal model that uses a cross-correlation
operator to consider spatiotemporal dependence. Also, we present an adaptive
state estimation for path planning. Since the state estimation depends on the
vehicle's path, the path planning needs to consider the trade-off between
exploration and exploitation. We use a high-level decision-maker to choose an
explorative path or an exploitative path. The overall proposed framework
consists of an adaptive state estimator, a short-term path planner, and a
high-level decision-maker. We tested the framework with a spatiotemporal model
simulation where the state of each grid transits from normal, latent, and fire
state. For the mission objective of visiting the grids with fire, the proposed
framework outperformed the random walk (baseline) and the single-minded
exploitation (or exploration) path.
