# Reconfigurable formations of quadrotors on Lissajous curves for surveillance applications

## TL;DR

This paper develops smooth trajectory planning methods for reconfiguring multi-quadrotor formations on Lissajous curves, enabling collision-free surveillance and area coverage with theoretical analysis, simulations, and real-world experiments.

## Contribution

It introduces a novel calculus of variations-based approach for collision-free reconfiguration of quadrotor formations on Lissajous curves, validated through simulations and real experiments.

## Key findings

- Successful collision-free reconfiguration demonstrated in simulations.
- Validated trajectory planning with quadrotors in a motion capture environment.
- Effective area coverage and rogue target detection capabilities confirmed.

## Abstract

This paper proposes trajectory planning strategies for online reconfiguration of a multi-agent formation on a Lissajous curve. In our earlier work, a multi-agent formation with constant parametric speed was proposed in order to address multiple objectives such as repeated collision-free surveillance and guaranteed sensor coverage of the area with ability for rogue target detection and trapping. This work addresses the issue of formation reconfiguration within this context. In particular, smooth parametric trajectories are designed for the purpose using calculus of variations. These trajectories have been employed in conjunction with a simple local cooperation scheme so as to achieve collision-free reconfiguration between different Lissajous curves. A detailed theoretical analysis of the proposed scheme is provided. These surveillance and reconfiguration strategies have also been validated through simulations in MATLAB\reg for agents performing parametric motion along the curves, and by Software-In-The-Loop simulation for quadrotors. In addition, they are validated experimentally with a team of quadrotors flying in a motion capture environment.