DQ-NMPC: Dual-Quaternion NMPC for Quadrotor Flight

TL;DR

The paper addresses the challenge of precise, agile quadrotor control by coupling translation and rotation in a single, globally non-singular framework. It proposes Dual-Quaternion NMPC (DQ-NMPC) that operates directly on the dual-quaternion manifold and uses a left-invariant pose error projected to the Lie algebra to jointly minimize pose and velocity errors. Through simulations and real-world experiments, the approach achieves faster convergence and significant reductions in orientation and position tracking errors (up to about 56%), enabling aggressive maneuvers up to 13.66 m/s and 4.2 g in confined spaces, where baseline NMPC struggles. The work highlights a compact, unified representation for SE(3) control and points to extensions to other robotic platforms and learning-based enhancements for dynamic environments.

Abstract

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.

Figures (12)

• Figure 1: Trajectory tracking experiment comparing Dual-Quaternion NMPC and Baseline NMPC. Green lines indicate the desired trajectory, blue lines show the system's evolution under the DQ-NMPC controller, and orange lines represent the results obtained with the baseline NMPC.
• Figure 2: Aerial system representation with inertial $\mathcal{W}$ and body frames $\mathcal{B}$
• Figure 3: Control block diagram of the proposed DQ-NMPC, illustrating the flow of information through the DQ-NMPC formulation. $\mathbf{x}$ and $\mathbf{x}_d$ represent the current and desired pose of the quadrotor based on decoupled dynamics. These values are transformed into the dual-quaternion space using eqs. \ref{['eq:3']} and \ref{['eq:4.2']} and subsequently used in the DQ-NMPC method.
• Figure 4: Interpretation of the DQ-NMPC formulation: Both the predicted and desired poses of the quadrotor are represented as unit dual-quaternions, and their difference is captured using a left-invariant error. This error lies on the dual-quaternion manifold and is projected onto the Lie algebra and included into the NMPC cost function.
• Figure 5: Comparison of different orientation error cost functions. The baseline cost function lacks sensitivity to large orientation errors, which limits its performance and results in slower convergence