Dual Quaternion

Dual quaternions offer a powerful mathematical framework for representing and manipulating 3D rigid body motions, combining rotation and translation into a single entity. Current research focuses on applying this representation to control problems in robotics, particularly for unmanned aerial vehicles (UAVs) and manipulators, often employing adaptive control strategies like backstepping and sliding mode control to achieve robust and efficient pose tracking. This compact and singularity-free representation improves the accuracy and efficiency of motion planning and control algorithms, impacting fields ranging from robotics and computer graphics to spatial audio processing and human motion modeling.