Fast Inverse Kinematics Based on Pseudo-Forward Dynamics Computation: Application to Musculoskeletal Inverse Kinematics

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 letter 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 ${\mathrm{O}(N)}$ forward dynamics algorithm is utilized by introducing a virtual dynamical system derived from damping or weighing factors used in the LM method. The letter 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.