Assessing Linearity in Multi-Joint Upper Limb Dynamics Under Small Perturbations for Reliable Mechanical Impedance Estimation

Abstract

This study investigates the linear behavior of multi-joint upper limb dynamics under small perturbations, a prerequisite for stochastic estimation of upper limb mechanical impedance, which is crucial for understanding motor control and has the potential to assess neurological disorders. Conflicting reports exist on the linearity of upper limb dynamics under small perturbations, even for healthy individuals. We hypothesized that the multi-joint upper limb behaves linearly under small perturbations and that uncompensated nonlinear robot joint frictions degrade impedance estimation reliability. The upper limb multi-joint mechanical impedance of ten healthy individuals was estimated using a 2-degree-of-freedom direct-drive robot similar to MIT-MANUS, known for small joint frictions, under two conditions: without (using Cartesian proportional-derivative control) and with (using internal model based impedance control) friction compensation. Multiple and partial coherences were close to unity with friction compensation and significantly higher than without it, confirming that the upper limb behaves linearly under small perturbations and that previously reported nonlinearity detected by low coherences was due to small but significant robot joint frictions. It is expected that confirming the linearity of the upper limb under small perturbations allows for confident upper limb impedance estimation, thereby promoting motor control studies and complementing the diagnosis of the altered upper-limb dynamics post-stroke.