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.
Highlights
The need to explore various environmental boundaries has motivated extensive research on using mobile robotic platforms for such a purpose; see, e.g., Refs. [1,2,3,4,5,6,7,8,9,10,11,12,13] and the literature therein
This study aimed to design and analyze a distributed navigation and collision avoidance strategy for a team of unmanned aerial vehicles (UAVs) traveling in a 3D environment
Among the complicating factors was the lack of access to the field gradient, absence of communication facilities, non-holonomy, under-actuation, and a finite control range of the UAVs
Summary
The need to explore various environmental boundaries has motivated extensive research on using mobile robotic platforms for such a purpose; see, e.g., Refs. [1,2,3,4,5,6,7,8,9,10,11,12,13] and the literature therein. Examples include finding the flows of air pollutants or contaminant clouds [14] and tracking zones of turbulence or high radioactivity level, to name just a few In such missions, typical challenges include a paucity of a priori information about the field, obsolescence of the data collected online due to the field changes, and the capacity of the available sensors to measure only the field value at the current location via immediate contact with the sensed entity, e.g., with a transparent gas. The possibility to directly measure the field’s gradient is uncommon, whereas reliable gradient estimation from noisy measurements of the field value is still an intricate challenge in a practical setting [19,20] Such estimation calls for measurements in neighboring locations distributed across all dimensions, whereas exploration of an environmental boundary motivates to place the sensors on this lower-dimensional structure. Communication constraints may hinder transfers of field measurements to the gradient estimator, wherever it may be built
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