Locally Periodic Kernel-Based Regression to Identify Time-Varying Ankle Impedance during Locomotion: A Simulation Study

Human joint impedance is a fundamental property of the neuromuscular system and describes the mechanical behavior of a joint. The identification of the lower limbs' joints impedance during locomotion is a key element to improve the design and control of active prostheses, orthoses, and exoskeletons. Joint impedance changes during locomotion and can be described by a linear time-varying (LTV) model. Several system identification techniques have been developed to retrieve LTV joint impedance, but these methods often require joint impedance to be consistent over multiple gait cycles. Given the inherent variability of neuromuscular control actions, this requirement is not realistic for the identification of human data. Here we propose the kernel-based regression (KBR) method with a locally periodic kernel for the identification of LTV ankle joint impedance. The proposed method considers joint impedance to be periodic yet allows for variability over the gait cycles. The method is evaluated on a simulation of joint impedance during locomotion. The simulation lasts for 10 gait cycles of 1.4 s each and has an output SNR of 15 dB. Two conditions were simulated: one in which the profile of joint impedance is periodic, and one in which the amplitude and the shape of the profile slightly vary over the periods. A Monte Carlo analysis is performed and, for both conditions, the proposed method can reconstruct the noiseless simulation output signal and the profiles of the time-varying joint impedance parameters with high accuracy (mean VAF ~ 99.9% and mean normalized RMSE of the parameters 1.33-4.06%).The proposed KBR method with a locally periodic kernel allows for the identification of periodic time-varying joint impedance with cycle-to-cycle variability.