Dual-Quaternion Based Nonlinear Model Predictive Control for Quadrotor Leader-Follower Formation

Abstract

To effectively address the challenges of cooperative control for quadrotor formations in complex environments, this paper extends the dual-quaternion based nonlinear model predictive control (DQ-NMPC) framework to leader-follower formation. Unlike conventional methods that treat translation and rotation separately, the dual-quaternion based model achieves a unified and compact representation of rigid-body motion using only eight real numbers without singularities, enabling global description on SE(3). Through the logarithmic map, the pose error is mapped from the Lie group to its Lie algebra, resulting in a quadratic cost function that naturally resolves the dimensional inconsistency between position and attitude errors, thereby simplifying weight tuning and improving numerical stability. Building on this formulation, a UAV formation controller is developed, where the relative motion between leader and follower is concisely described using dual quaternions, and a minimum safe distance constraint is explicitly incorporated to avoid collisions and maintain safe separation. In formation scenarios, the follower autonomously accomplishes chasing, rendezvous, and formation keeping under various trajectories, including straight-line pursuit and Lissajous curves. Moreover, the stability of formation control is validated under non-ideal conditions such as communication delay, mass mismatches, and constant external disturbances. Furthermore, the optimal weight combination is determined through grid search, which further improves formation tracking accuracy and control smoothness. In addition, the proposed framework inherently supports time-varying formation patterns, such as dynamic switching between different relative configurations and adaptive scaling. Computational efficiency analysis shows that the average solution time per control cycle is far below the sampling interval, validating real-time feasibility. Overall, the DQ-NMPC framework provides a unified, robust, and efficient solution for quadrotor formation control under both ideal and perturbed environments.