Hierarchical Multi-Robot Data Sampling for Environmental State Estimation through Online Gaussian Process

Coverage control presents a promising method for addressing challenges such as environmental monitoring of specific fields. However, when applied to robots, coverage control typically assumes data sampling continuously both in time and space, whereas many external sensors gather data at discrete points and times. To address this issue, this paper investigates a novel cooperative data sampling that reflects the discrete nature of sensors to estimate scalar fields based on the sparse online Gaussian process (SOGP). The control goal of the present problem is formulated by a constraint on the decay rate of the variance function given by the SOGP. We then design a partially distributed constraint-based controller that enforces the constraint in the transient state, while also considering safety constraints. We then point out a drawback inherent in the present "myopic" control strategy through simulation studies. In order to overcome the drawback, we present a hierarchical control architecture, where the high-level path planner generates the optimal path based on a long-term perspective, and the low-level constraint-based control meets the decay rate constraint, while referring to the designed path for designing the nominal control. Finally, the present controller’s effectiveness is demonstrated through simulations.