Math & Kinematics

Dual Quaternion

Dual Quaternion is an eight-parameter algebraic representation of rigid-body transformations, formed as a quaternion with dual-number coefficients, encoding rotation and translation in a single object. Unit dual quaternions compose transformations by multiplication, interpolate smoothly along screw motions, and avoid the singularities of Euler angles. They are used in kinematic modeling, hand-eye calibration, pose-graph optimization, and skinning in graphics.

Why it matters for physical AI

Compact, singularity-free pose algebra matters wherever transforms are estimated or interpolated, from calibration routines to pose regression targets in learned perception, where representation choice measurably affects accuracy.