Analytical Solution for Inverse Kinematics Using Dual Quaternions

Abstract

This paper presents a new solution for inverse kinematics (IK) by using dual quaternions (DQ) as operators and combining them with the Paden-Kahan subproblem to determine the analytical solution. Kinematics under the structure of screw theory makes the process mathematically efficient and gives geometric meaning. Both derived results and simulation outgrowths, when compared with the generally used numerical solution and matrix-based analytical solution, show that our method is faster and does not suffer from the numerical instability caused by being near to a singular configuration. The method has been proven to have the advantages of reducing the computational load and promoting precision, and it can provide multiple choices for IK.

Keywords

• Analytical solution
• dual quaternions (DQ)
• inverse kinematics (IK)
• Paden–Kahan subproblems
• screw theory