Dual Quaternion Quintic Blends: \(\mathcal {C}^2\) -Continuous, Time-Optimized Interpolation with Unit Dual Quaternion Pose Representation

The manufacturing industry, driven by Industry 4.0, is experiencing a paradigm shift with the integration of collaborative robots (cobots). These cobots are essential for safe human-robot collaboration, requiring predictable trajectories in the task space. To address the complexity of interpolating key poses, this research introduces a novel \(\mathcal {C}^2\) -continuous interpolation scheme with unit dual quaternion pose representation. This scheme facilitates smooth, synchronized motion along a given set of key poses. Leveraging the algebraic efficiency and double cover property of unit dual quaternions, the proposed method provides improved computational efficiency and a user-friendly trajectory definition interface, which is particularly beneficial for non-expert users.