Distributed multi-UAV shield formation based on virtual surface constraints

TL;DR

The paper tackles distributed formation control for UAV swarms to form a shield along a 3D quadric surface $S$, ensuring almost uniform surface coverage and a Delaunay triangulation to guarantee local rigidity. It combines a simple surface-based target formation design with a gradient-based control that enforces both inter-agent distances and confinement to $S$, and extends a local 2D Delaunay test to the 3D surface. A Lyapunov-based analysis demonstrates local asymptotic stability of the shield formation, even though the surface constraint alters standard rigidity notions. The approach is validated through simulations on ellipsoidal and spherical shields and a real-time Crazyflie 2.1 experiment with 12 UAVs, confirming convergence of $d_{ij}$ to $d_{ij}^*$ and confinement to the quadric surface. This framework offers a scalable, distributed means to deploy UAV swarms for infrastructure protection with minimal global information requirements.

Abstract

This paper proposes a method for the deployment of a multi-agent system of unmanned aerial vehicles (UAVs) as a shield with potential applications in the protection of infrastructures. The shield shape is modeled as a quadric surface in the 3D space. To design the desired formation (target distances between agents and interconnections), an algorithm is proposed where the input parameters are just the parametrization of the quadric and the number of agents of the system. This algorithm guarantees that the agents are almost uniformly distributed over the virtual surface and that the topology is a Delaunay triangulation. Moreover, a new method is proposed to check if the resulting triangulation meets that condition and is executed locally. Because this topology ensures that the formation is rigid, a distributed control law based on the gradient of a potential function is proposed to acquire the desired shield shape and proofs of stability are provided. Finally, simulation and experimental results illustrate the effectiveness of the proposed approach.

Figures (12)

• Figure 1: Example of the possible triangulations for the set of points $\{A,B,C,D,E\}$. Only the one on the left is a Delaunay triangulation.
• Figure 2: View of the shield examples given in Table \ref{['tab:shieldexample']}: Semi-ellipsoid (left), cylinder (middle), cone (right).
• Figure 3: Target formation example. A team of $N=50$ agents forms a semi-spherical shield.
• Figure 4: The triangle formed by $\{A,B,C\}$, its circumcircle, and its circumcenter $m_{ABC}$.
• Figure 5: 3D view (left) and projection over the XY plane (right) of the trajectories of the system (in red) for Example 1. Red crosses represent positions at which errors $e_{ij}$ are 0.

Theorems & Definitions (33)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Definition 5
• Definition 6
• Example 1
• Remark 1
• Example 2
• Remark 2