Adaptive Multirobot Virtual Structure Control using Dual Quaternions

This paper presents a dual-quaternion-based control strategy for the coordinated formation flying of small UAV teams. A virtual structure is used to define the formation, enabling a unified and global representation of its pose and of the geometric variables that shape the formation. Dual quaternions provide a compact and singularity-free representation in SE(3), allowing the pose controller to operate consistently even when the formation undergoes large rotational motions or when its orientation is only partially defined. Building on existing dual-quaternion kinematic controllers, we extend the formulation by introducing two key enhancements. First, we propose a geometry-adaptive control law whose gains vary online according to the formation inertia. Stability guarantees are established for the adaptive case by extending the convergence results of the fixed-gain controller. Second, we introduce a partial dual-quaternion representation that enables the same pose-control structure to be applied across formations with fully or partially defined orientation. This allows seamless transitions between configurations—such as when a formation loses one agent and reduces to a smaller structure—without redesigning the control law. The proposed method is validated through simulations and experiments, including comparative studies that quantify the benefits of the adaptive strategy and practical demonstrations of formation transitions. The results show improved tracking performance and robustness under varying formation geometries.