Emergent Structure in Multi-agent Systems Using Geometric Embeddings

TL;DR

This work proposes a decentralized control system architecture that produces a globally stable emergent structure from local observations only; there is no requirement for agents to share a global plan or follow prescribed trajectories.

Abstract

This work investigates the self-organization of multi-agent systems into closed trajectories, a common requirement in unmanned aerial vehicle (UAV) surveillance tasks. In such scenarios, smooth, unbiased control signals save energy and mitigate mechanical strain. We propose a decentralized control system architecture that produces a globally stable emergent structure from local observations only; there is no requirement for agents to share a global plan or follow prescribed trajectories. Central to our approach is the formulation of an injective virtual embedding induced by rotations from the actual agent positions. This embedding serves as a structure-preserving map around which all agent stabilize their relative positions and permits the use of well-established linear control techniques. We construct the embedding such that it is topologically equivalent to the desired trajectory (i.e., a homeomorphism), thereby preserving the stability characteristics. We demonstrate the versatility of this approach through implementation on a swarm of Quanser QDrone quadcopters. Results demonstrate the quadcopters self-organize into the desired trajectory while maintaining even separation.

Figures (11)

• Figure 1: The flight path of a UAV forms a dumbbell curve in space, visible from a top-down perspective where the vehicle's curve is traced on the horizontal plane. This trajectory was recorded through the light painting technique, and it tracks the position of LEDs mounted on the top of the UAV. The two red "X" on the floor are $1.5$ m distant from each other and can be used as a visual reference. They are not centralized in the trajectory due to the camera perspective.
• Figure 2: A Dumbbell curve being described by a swarm of three UAVs following the same path. The with three UAVs following the same path.
• Figure 3: System-level architecture containing the control strategy implemented on each UAV. The numbers in parentheses denote the equations implemented at each step.
• Figure 4: Quanser QDrone used for physical experiments.
• Figure 5: Test area for autonomous flight.