LPOE-UDQ: An Efficient Kinematic Calibration Method for Robot

Reducing parameter redundancy in kinematic error models can enhance identification robustness while exerting negligible influence on error compensation efficiency - a process predominantly governed by pose representation architecture. Compared to homogeneous transformation matrices (HTM), the unit dual quaternion (UDQ) achieves efficient kinematic computation through its compact eight-element vector structure. This study formalizes UDQ's exponential/logarithmic mappings to bridge finite and instantaneous motions in exponential coordinates. By developing UDQ's adjoint operator for cross-frame twist transformation, we derive linearized error models through product-of-exponentials (POE) formula, effectively simplifying parameter identification and compensation workflows. Quantitative analysis reveals substantial arithmetic operation reductions relative to HTM-based POE approaches, with UDQ's single-dimensional array architecture further accelerating data processing during adjoint transformations. Experimental validation demonstrates these computational advantages particularly benefit robot calibration involving extensive trajectory sequences.