Structured Isosurface Mapping of 3-D Scalar Fields While Seeking Extremum With Mobile Sensor Networks

Adaptive navigation (AN) techniques enable autonomous modification of an agent’s trajectory using realtime measurements of the local environment. AN methods can reduce time and energy expended to autonomously explore unknown and dynamic scalar fields representing physical features of real-world phenomena (e.g., pollutants, temperature, radiation) when compared to conventional navigation approaches. A coordinated group of agents, referred to as a mobile sensor network, can improve AN performance through cooperative and spatially dispersed sensing to determine the local scalar field structure and then use that data to inform navigation decisions for the network. This article proposes a novel method for performing structured 3-D isosurface mapping en route to seeking an extremum, which combines the two historically separate categories of extrema seeking and level set/contour tracking in a single mission profile. Characterization of an isosurface shape is achieved through structured mapping of the surface, described as a systematic “rendering” via contour tracing within periodically spaced planes which intersect the surface. Successive mapping planes are set perpendicular to the local scalar field gradient, calculated in realtime from mobile sensor network readings, as the agents follow the path of steepest ascent/descent toward an extremum. The result is a more intuitive and cost-effective characterization of the isosurface shape and gradient direction, that is also simpler for a supervisor to operate. This article presents the multilayer control architecture that maintains the geometry of the uncrewed aerial vehicle (UAV) cluster, uses AN control primitives to specify the direction of cluster motion, and implements a mission-level sequencer to establish the combined isosurface mapping/extremum-seeking functionality. The new controller is verified using high-fidelity simulations that include vehicle dynamics, outdoor wind gust disturbances, position sensor inaccuracy, and scalar field sensor noise.