Distributed robotic sampling of non-homogeneous spatio-temporal fields via recursive geometric sub-division

Environmental monitoring, an important application for robots, has begun to be addressed recently with linear least squares regression techniques because they estimate the values of measured attributes and their uncertainty. But several challenges remain when performing adaptive sampling in a communication-constrained distributed multi-robot setting. When the attributes of interest evolve over time (as is natural for many environments) any non-homogeneous spatial variability may necessitate continual re-modeling of the field dynamics and/or re-sampling of the field. This raises questions about the robots´ division of labor and workload balance that can be difficult to address when sample information is not stored centrally. This paper tackles these coordination problems efficiently by introducing a sub-division-based modeling technique appropriate for distributed decision-making. We augment Ordinary Kriging to enable representation of a field´s (potentially non-homogeneous) evolution through Bayes filtering that characterize the underlying dynamics. This approach not only enables adaptive path planning in the field, but the sub-divided areas lead to a straightforward formulation of the optimal workload distribution through modification of an approximate graph partitioning algorithm. Using a simulated multi-robot sampling scenario, we demonstrate and validate the approach. The experiments show good performance in terms of cross-validation using real values and illustrate how hotspots are identified and modeled, in turn affecting the division of labor.