Quantifying Joint Stiffness During Movement: A Quantitative Comparison of Time-Varying System Identification Methods

Careful control of joint impedance, or dynamic joint stiffness, is crucial for successful performance of movement. Time-varying system identification (TV-SysID) enables quantification of joint impedance during movement. Several TV-SysID methods exist, but have never been systematically compared. Here, we simulate time-varying joint behavior and propose three performance metrics that enable to quantify and compare TV-SysID methods. Time-varying joint stiffness is simulated using a square wave and subsequently estimated with three TV-SysID methods: the ensemble, short data segment, and basis impulse response function method. These methods were compared based on (1) bias with respect to the simulated joint stiffness, (2) random error across 100 simulation trials, and (3) maximum adaptation speed in joint stiffness that can be captured. This approach revealed that each TV-SysID method has its own unique properties. The simulation method and performance metrics pave the way for developing a framework to quantify the strengths and weaknesses of TV-SysID algorithms for estimating joint impedance.