MAVs have great potential to assist humans in complex tasks, with applications ranging from logistics to emergency response. Their agility makes them ideal for operations in complex and dynamic environments. However, achieving precise control in agile flights remains a significant challenge, particularly due to the underactuated nature of quadrotors and the strong coupling between their translational and rotational dynamics. In this work, we propose a novel NMPC framework based on dual-quaternions (DQ-NMPC) for quadrotor flight. By representing both quadrotor dynamics and the pose error directly on the dual-quaternion manifold, our approach enables a compact and globally non-singular formulation that captures the quadrotor coupled dynamics. We validate our approach through simulations and real-world experiments, demonstrating better numerical conditioning and significantly improved tracking performance, with reductions in position and orientation errors of up to 56.11% and 56.77%, compared to a conventional baseline NMPC method. Furthermore, our controller successfully handles aggressive trajectories, reaching maximum speeds up to 13.66 m/s and accelerations reaching 4.2 g within confined space conditions of dimensions 11m x 4.5m x 3.65m under which the baseline controller fails.

翻译：微型飞行器在协助人类完成复杂任务方面具有巨大潜力，其应用范围涵盖物流配送至应急响应等多个领域。其敏捷性使其成为在复杂动态环境中执行任务的理想平台。然而，在敏捷飞行中实现精确控制仍然是一个重大挑战，这主要源于四旋翼系统的欠驱动特性及其平动与旋转动力学之间的强耦合关系。本研究提出了一种基于对偶四元数的新型非线性模型预测控制框架（DQ-NMPC）用于四旋翼飞行控制。通过在对偶四元数流形上直接表示四旋翼动力学与位姿误差，本方法构建了紧凑且全局非奇异的数学模型，完整刻画了四旋翼的耦合动力学特性。我们通过仿真与实物实验验证了所提方法的有效性，结果表明：相较于传统基准NMPC方法，本控制器具有更优的数值稳定性，并显著提升了轨迹跟踪性能——位置与姿态跟踪误差分别降低达56.11%与56.77%。此外，本控制器能成功执行激进轨迹跟踪任务，在11m×4.5m×3.65m的受限空间内实现了最高13.66 m/s的飞行速度与4.2 g的加速度，而基准控制器在此条件下已失效。