Navigating the Edge: UAS Boundary Tracing for Efficient Volcanic Plume Monitoring

We present the implementation and validation of Sketch, an algorithm that uses two Unpiloted Aerial Systems (UASs) to trace the boundary of volcanic plumes. Sketchguarantees asymptotically optimal flight distance and turning by maintaining a sandwich invariant where one UAS stays inside the plume boundary (defined by a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\textbf{CO}_{2}$</tex> concentration threshold) and the other UAS stays outside. The UASs adjust their flight paths based on real-time CO<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>measurements to maintain this invariant. This paper details the implementation of Sketchon a real-world UAS platform, the Dragonfly drone. We evaluate the efficacy of Sketchthrough extensive testing in physics-based simulations and real-world outdoor environments using virtual plumes. The algorithm is compared to a single-UAS baseline algorithm called Zigzag. Results show that Sketchmeets the expectations set by theory, and it is more efficient than Zigzag, achieving shorter flight paths, less turning, and faster mapping times. While Zigzagexhibits slightly higher accuracy in estimating plume area and boundary, Sketchoffers a more efficient real-time volcanic plume monitoring approach, especially in time-sensitive situations. These results demonstrate the feasibility and efficacy of Sketchfor real-time volcanic plume monitoring, paving the way for accurate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\textbf{CO}_2$</tex> emission estimation in hazardous and challenging environments.