Solution of an inverse kinematics problem using dual quaternions

Abstract

The paper proposes a solution to an inverse kinematics problem based on dual quaternions algebra. The method, relying on screw theory, requires less calculation effort compared with commonly used approaches. The obtained kinematic description is very concise, and the singularity problem is avoided. The dual quaternions formalism is applied to the problem decomposition and description. As an example, the kinematics problem of a multi-DOF serial manipulator is considered. Direct and inverse kinematics problems are solved using division into sub-problems. Each new sub-problem proposed is concerned with rotation about two subsequent axes by a given amount. The presented example verifies the correctness and feasibility of the proposed approach.

Dual quaternions for the kinematic description of a fish-like propulsion system

“…In recent years quaternions have become popular in computer graphics (Leclercq et al, 2013) for body motion analysis (Pennestrì and Valentini, 2010), robot manipulators (Grzadziela et al, 2020) as well as for neuroscience (Ling et al, 2022). Numerical precision and efficiency of real-time calculations are critical for robot control systems (Chen et al, 2020), particularly for autonomous vehicles (Morawski et al, 2020;Hożyń and Zalewski, 2020;Wawrzyński et al, 2022).…”