Distributed 3D Navigation of Swarms of Non-Holonomic UAVs for Coverage of Unsteady Environmental Boundaries

Abstract

A team of non-holonomic constant-speed under-actuated unmanned aerial vehicles (UAVs) with lower-limited turning radii travel in 3D. The space hosts an unknown and unpredictably varying scalar environmental field. A space direction is given; this direction and the coordinate along it are conditionally termed as the “vertical” and “altitude”, respectively. All UAVs should arrive at the moving and deforming isosurface where the field assumes a given value. They also should evenly distribute themselves over a pre-specified range of the “altitudes” and repeatedly encircle the entirety of the isosurface while remaining on it, each at its own altitude. Every UAV measures only the field intensity at the current location and both the Euclidean and altitudinal distances to the objects (including the top and bottom of the altitudinal range) within a finite range of visibility and has access to its own speed and the vertical direction. The UAVs carry no communication facilities, are anonymous to one another, and cannot play distinct roles in the team. A distributed control law is presented that solves this mission under minimal and partly inevitable assumptions. This law is justified by a mathematically rigorous global convergence result; computer simulation tests confirm its performance.