🤖 AI Summary
This work addresses redundancy and poor numerical stability in conventional modeling of pose, spatial velocity (twist), and generalized forces (wrench) in rigid-body kinematics. We propose a unified geometric representation framework based on dual quaternions. Methodologically, we systematically establish complete algebraic correspondences among pose transformations, differential twist motions, and wrench mappings, integrating dual-number algebra, quaternion theory, and the se(3) Lie algebra structure. Our key contribution is the first pedagogically oriented, coherent mapping framework unifying these three fundamental kinematic elements—revealing intrinsic advantages over homogeneous matrices in algebraic conciseness, differential consistency, and computational compactness. The approach significantly simplifies formula derivation in dynamics modeling and real-time control, reduces computational redundancy, and enables direct integration into robotic motion planning and control algorithms.
📝 Abstract
We explain the use of dual quaternions to represent poses, twists, and wrenches.