Multi-Robot Adaptive Sampling based on Mixture of Experts Approach to Modeling Non-Stationary Spatial Fields

This paper presents an adaptive sampling strategy for a team of robots to model non-stationary spatial fields – i.e., fields with uneven variations – in large environments, with a desired predictive accuracy. Modeling non-stationary heterogeneous fields is essential for many applications, like monitoring air quality or contamination level in lakes. Mainstream adaptive sampling strategies assume stationarity of the environmental phenomenon and use a single model to explain such fields, resulting in inaccurate characterization of unique localized variations. In this paper, we model a non-stationary field as a collection of (infinite, in theory) non-overlapping layers of stationary homogeneous subfields. This approach allows for modeling non-stationary fields using a mixture of experts, where each expert is assigned a particular homogeneous subregion to map. This approach decomposes the environment into smaller homogeneous regions, which allows real-time modeling of large environments. We design a data-driven approach to adaptively identify each stationary layer and define its relationship to other layers. We model the relationship between various subregions as a network of experts – the rapidly-sampling adaptive graph. Each robot incrementally builds its own sub-network of experts, which is used to determine where to sample. Several experiments in realistic simulation demonstrate competitive accuracy and sampling efficiency compared to other state-of-the-art methods.