Robust and efficient forward, differential, and inverse kinematics using dual quaternions. (September 2021)

• Record Type: Journal Article
• Authors: Dantam, Neil T
• Other Names: Morales Marco guest-editor.; Tapia Lydia guest-editor.; Sánchez-Ante Gildardo guest-editor.; Hutchinson Seth guest-editor.
• Is Part Of: International journal of robotics research. Volume 40:Number 10/11(2021)
• Page Start: 1087
• Page End: 1105
• Publication Date: 2021-09
• Subjects: Kinematics -- manipulation -- control architectures and programming; Robots -- Periodicals; Robots, Industrial -- Periodicals; 629.89205
• DOI: 10.1177/0278364920931948
• Languages: English
• ISSNs: 0278-3649

Abstract

Modern approaches for robot kinematics employ the product of exponentials formulation, represented using homogeneous transformation matrices. Quaternions over dual numbers are an established alternative representation; however, their use presents certain challenges: the dual quaternion exponential and logarithm contain a zero-angle singularity, and many common operations are less efficient using dual quaternions than with matrices. We present a new derivation of the dual quaternion exponential and logarithm that removes the singularity, we show an implicit representation of dual quaternions offers analytical and empirical efficiency advantages compared with both matrices and explicit dual quaternions, and we derive efficient dual quaternion forms of differential and inverse position kinematics. Analytically, implicit dual quaternions are more compact and require fewer arithmetic instructions for common operations, including chaining and exponentials. Empirically, we demonstrate a 30–40% speedup on forward kinematics and a 300–500% speedup on inverse position kinematics. This work relates dual quaternions with modern exponential coordinates and demonstrates that dual quaternions are a robust and efficient representation for robot kinematics.