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.