Sparse Machine Learning Discovery of Dynamic Differential Equation of an Esophageal Swallowing Robot

Considering the limitation of conventional rheometry measurements and the relevance of the study of food viscosity in the study of dysphagia, we commenced developing a soft-bodied esophageal swallowing robot (ESR). Using experimental data, this paper aims to discover the differential equations (DEs) of the ESR that governs the peristaltic deformation in the esophageal conduit at the given time-varying pressure. The deformation data of the conduit are collected from a quarter version of the ESR due to the inaccessibility to the esophageal occlusion. The three-dimensional displacements of the markers placed on the interior surface of the conduit are measured using a Vicon optical motion capturing system. The dimension of the dataset is first reduced using the principal orthogonal decomposition (POD) method, which is then used to discover the ESR's DEs by the sparse identification of nonlinear dynamics (SINDy). The marker displacements are considered as the ESR's states. The ESR's states are reduced from 27 to 2 by initially applying power spectral density (PSD), and then the POD. The identified states essential to the DEs capture 95$ \%$ of the total variance of the deformation dataset. Finally, the conduit deformation simulated from the DEs are validated by the experimental measurements in the full version of the ESR.