A Preliminary Study on The Linearity Assumption of the Upper Limb for Stochastic Estimation: Spring Array Experiment

Abstract

It is crucial to quantify upper limb mechanical impedance because it provides a wealth of information ranging from basic muscle properties to assessing the stages of neurological impairment like stroke. The recent stochastic estimation method of the mechanical impedance has advantages over other methods and needs one assumption to be met: the upper limb behaves linearly. However, a previous study using a low friction robot (i.e., MIT-MANUS) showed low partial coherence (<0.8), indicating that the upper limb may behave nonlinearly. A recent study elucidated that the low coherence could be due to nonlinear joint friction in the robot rather than the upper limb using a robot with large friction due to the use of harmonic drive with a large velocity reduction ratio. Thus, there is a strong need to investigate further if the low coherence is due to the nonlinearity in the upper limb or the robot. To clarify the effect of uncompensated robot friction, the experiment was carried out using a direct-drive robot almost identical to the MIT-MANUS, and the spring arrays, the second-order linear system. The finding revealed that if the friction is not compensated, it lowers the coherence functions. This is indirect but significant proof that the cause of low reliability stemmed from the friction of the robot, not the human arm.