# Roto-Translation Invariant Formation of Fixed-Wing UAVs in 3D: Feasibility and Control

## TL;DR

This paper explores the feasibility and control of roto-translation invariant formations of fixed-wing UAVs in 3D, considering nonholonomic constraints and input saturation, with stability proofs and simulations.

## Contribution

It introduces new feasibility conditions and a formation controller for fixed-wing UAVs in 3D roto-translation invariant formations, accounting for realistic constraints.

## Key findings

- Feasibility conditions for RTI formations are established.
- A stable formation control method is designed and verified.
- Simulations confirm the theoretical results.

## Abstract

This paper investigates the formation of fixed-wing UAVs in 3D, which communicate via a directed acyclic graph. Different from common formation problems, we consider the roto-translation invariant (RTI) formation, where the "roto-translation" refers to a rigid-body motion obtained by composing rotation and translation. Besides, the fixed-wing UAV is modelled by a 3-D nonholonomic constrained rigid body instead of a particle agent. The main results of this paper include proposing the formation feasibility conditions and designing the formation controller. Firstly, we define the RTI formation and propose the conditions to guarantee that the formations are feasible for the fixed-wing UAVs under the nonholonomic and input saturation constraints. Secondly, given feasible formations, we design a formation controller by introducing a virtual leader and employing the compensation of rotation, followed by proving the stability of the closed-loop system. Finally, simulation examples are presented to verify the theoretical results.al with the motion coupling among multiple robots. Finally, numerical simulations are conducted to verify the theoretical results.