Tying Knots in the Air: Reducing the Number of Quadrotors for Aerial Knot Formation

Abstract

Knots provide compact, lightweight, and mechanically stable configurations that are invaluable for aerial transportation and construction. However, autonomous knot formation in midair remains an open challenge due to the dexterity and complexity of manipulating flexible cables. In this paper, we present a method for midair knot formation that employs two types of aerial robots: lifting robots, which hold the cable endpoints, and support robots, which stabilize intermediate spans to enable interlacing. Our approach focuses on minimizing the number of support robots required while ensuring that the knot’s topology is preserved. Our method proceeds in three stages: (i) encode the knot projection as a grid of directional segments and crossings, (ii) apply our Loop Consistency Filter (LCF) to identify the minimal set of support robots required to preserve topology, and (iii) reconstruct continuous Cartesian trajectories using a cable model governed by a spring–damper force and a straightening force. Our results show a reduction in the required robots to form a knot of at least fifty percent compared to the baseline grid-based method. We demonstrate that our method is effective on actual robots, enabling the formation of knots with multiple quadrotors.