L₁ Adaptive Control-Based Formation Tracking of Multiple Quadrotors Without Linear Velocity Feedback Under Unknown Disturbances

Abstract

This paper addresses the problem of formation control for a quadrotor swarm (QS) system with directed graph topology under external environmental disturbances and unreliable internal state acquisition. The proposed distributed robust control framework, based on a gemetric controller, incorporates ${\mathcal {L}}_{1}$ adaptive controllers and differentiator systems. First, the geometric formation controller is designed to implement the formation control of the nominal system. Then, ${\mathcal {L}}_{1}$ adaptive controllers are designed separately for each quadrotor’s position loop and attitude loop subsystems to address the effects of uncertainties such as external time-varying disturbances (matched and unmatched disturbances) and different mass variations of quadrotors. Furthermore, the differentiator system is devised to accurately estimate the higher-order derivatives of the non-directly-measurable velocity information and the virtual translation control signal, which enhances system accuracy while reducing computational complexity. The Lyapunov stability theory is employed to analyze the stability of the closed-loop system. Finally, the effectiveness and exceptional performance of this approach in QS formation control were validated through numerical simulation and experimental results. Note to Practitioners—The inspiration for this article comes from the issue of formation control in a cluster of quadrotor drones, which is also applicable to formation control in other types of drones. In this paper, a formation control algorithm based on ${\mathcal {L}}_{1}$ adaptive control strategy and arbitrary-order differentiation is designed. This algorithm can address not only the issue of time-varying wind disturbances frequently encountered during quadrotor drone flights but also the effects of unpredictable velocities and inconsistent masses of quadrotor drones. The disturbance rejection capability of this scheme enables quadrotor drones to be applied more safely and reliably in complex environments for search and rescue missions and surveillance tasks. Eliminating the need for linear velocity measurements reduces sensor costs and enhances system reliability and stability. The proposed formation control scheme allows the QS system to have different masses for each UAV, which can be applied to tasks such as collaboration logistics transportation, material delivery and crop spraying. Preliminary physical experiments have validated the feasibility of the proposed scheme, although it has not been applied in practical scenarios yet. In future research, we intend to equip each drone in the QS system with objects of different masses to achieve collaboration material transportation and delivery in complex environments.