Multi-Robot Adaptive Exploration and Mapping for Environmental Sensing Applications

Recent research in robot exploration and mapping has focused on sampling hotspot fields, which often arise in environmental and ecological sensing applications. Such a hotspot field is characterized by continuous, positively skewed, spatially correlated measurements with the hotspots exhibiting extreme measurements and much higher spatial variability than the rest of the field. To map a hotspot field of the above characterization, we assume that it is realized from non-parametric probabilistic models such as the Gaussian and log-Gaussian processes (respectively, GP and `GP), which can provide formal measures of map uncertainty. To learn a hotspot field map, the exploration strategy of a robot team then has to plan resource-constrained observation paths that minimize the uncertainty of a spatial model of the hotspot field. This exploration problem is formalized in a sequential decision-theoretic planning under uncertainty framework called the multi-robot adaptive sampling problem (MASP). So, MASP can be viewed as a sequential, non-myopic version of active learning. In contrast to finite-state Markov decision problems, MASP adopts a more complex but realistic continuous-state, non-Markovian problem structure so that its induced exploration policy can be informed by the complete history of continuous, spatially correlated observations for selecting paths. It is unique in unifying formulations of non-myopic exploration problems along the entire adaptivity spectrum, thus subsuming existing non-adaptive formulations and allowing the performance advantage of a more adaptive policy to be theoretically realized. Through MASP, it is demonstrated that a more adaptive strategy can exploit clustering phenomena in a hotspot field to produce lower expected map uncertainty. By measuring map uncertainty using the mean-squared error criterion, a MASP-based exploration strategy consequently plans adaptive observation paths that minimize the expected posterior map error or equivalently, maximize the expected map error reduction. The time complexity of solving MASP (approximately) depends on the map resolution, which limits its practical use in large-scale, high-resolution exploration and mapping. This computational difficulty is alleviated through an information-theoretic approach to MASP (iMASP), which measures map uncertainty based on the entropy criterion instead. As a result, an iMASP-based exploration strategy plans adaptive observation paths that minimize the expected posterior map entropy or equivalently, maximize the expected entropy of observation paths. Unlike MASP, reformulating the cost-minimizing iMASP as a reward-maximizing dual problem causes its time complexity of being solved approximately to be independent of the map resolution and less sensitive to larger robot team size as demonstrated both analytically and empirically. Furthermore, this reward-maximizing dual transforms the widely-used non-adaptive maximum entropy sampling problem into a novel adaptive variant, thus improving the performance of the induced exploration policy.