Adaptive Sampling of a Stationary Gaussian Spatial Process by a Team of Robots With Heterogeneous Dynamics and Measurement Noise Variance

Abstract

This paper presents an algorithm for a team of heterogeneous mobile robots to estimate and adaptively sample a stationary, isotropic, Gaussian process. An estimation framework is proposed to assimilate measurements from robots with differing sensing capabilities (i.e., measurement noise variance). To improve computational efficiency of the Gaussian process regression, the survey area is divided into regions that each use a common semivariogram matrix constructed with a truncated measurement set determined by an adaptive selector. As the mission proceeds, a Voronoi-based algorithm periodically partitions a density function—representing time-varying sampling priority—to identify high-value sampling locations. The path for each robot is modeled as an mechanical system: a sequence of masses (waypoints) are interconnected by springs and dampers and pulled towards Voronoi cell centroids. At each path planning cycle the robots are iteratively simulated with heterogeneous dynamics (e.g., speed, turn radius) following their respective waypoint paths as stiffness/damping parameters are adjusted to satisfy mission time constraints. Numerical simulations show that the proposed approach reduces mapping error when compared to non-adaptive lawnmower coverage of a survey area. The algorithm is demonstrated experimentally using two cooperating autonomous surface vessels to map the bathymetry in a section of Lake Norman near Charlotte, NC.

Keywords

• Adaptive sampling
• Gaussian processes
• multi-robot system
• heterogeneous sensing
• Voronoi partition