Fast Inverse Kinematics Based on Pseudo-Forward Dynamics Computation: Application to Musculoskeletal Inverse Kinematics
Ko Ayusawa, Akihiko Murai, Ryusuke Sagawa, Eiichi Yoshida
Abstract
Recently, fast and practical inverse kinematics (IK) methods for complicated human models have gained considerable interest owing to the spread of convenient motion-capture or human-augmentation technologies. Although the IK algorithms developed in robotics can also be applied to humans, they experience computational speed issues, especially in real-time applications. This paper presents a new IK algorithm based on the Levenberg–Marquardt (LM) method, LM-PFD (Pseudo-Forward Dynamics), which is remarkably effective particularly in systems with a large degree of freedom (DoF). In the proposed method, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathrm{O}(N)}$</tex-math></inline-formula> forward dynamics algorithm is utilized by introducing a virtual dynamical system derived from damping or weighing factors used in the LM method. The paper firstly introduces the basic implementation of LM-PFD for open kinematic chains. Subsequently, an enhanced implementation is presented to address closed kinematic chains, specifically focusing on wire-driven systems. The proposed method was tested on the IK of musculoskeletal models. The computational time of the model with approximately 150 DoF and 300 wires was within 5 ms.