A Nonlinear Autoencoder for Kinematic Synergy Extraction from Movement Data Acquired with HTC Vive Trackers

How the human central nervous system (CNS) copes with the several degrees of freedom (DoF) of the muscle-skeletal system for the generation of complex movements has not been fully understood yet. Many studies in literature have stated that likely the CNS does not independently control DoF but combines few building blocks that consider the synergistic actuation of each DoF. Such building blocks are called synergies. Synergies have been defined both at muscle level, i.e. muscle synergies, and kinematic level, i.e. kinematic synergies. Kinematic synergies consider the synergistic movement of several human articulations during the performance of a complex task, e.g. a reaching-grasping task. The principal component analyses (PCA) is the most used approach in literature for the kinematic synergy extraction. However, the PCA only considers linear correlations among DoFs which can be considered as the most-simple model of inter-joint coupling. In this work, we have extracted synergies from kinematics data (five upper limb angles) acquired during 12 different reaching movements with a tracking system based on the HTC Vive Trackers. After the extraction of the upper-limb joint angles with the OpenSim software, the kinematic synergies have been extracted using nonlinear under-complete autoencoders. Different models of nonlinear autoencoders were investigated and evaluated with R2 index and normalized reconstruction error. The results showed that 4 synergies were enough for describing the 0.973 ± 0.005 (R2 index of log sigmoid model) and 0.979 ± 0.004 (R2 index of tan sigmoid model) of the movement variance for the entire experiment with respectively a Normalized Reconstruction Error (ERMS) of 0.03 ± 0.005 and 0.034 ± 0.004. Comparing the non-linear autoencoders (AE) with the standard linear PCA it emerged that the AE performance are comparable with the PCA results. However, more experiments are needed to perform a deep comparison on a dataset including more joint angles.