Nozomu Araki

Abstract IIn electroencephalography (EEG) with dry electrodes, a trade-off between signal stability and user comfort is a critical barrier to long-term, wearable applications. While various approaches exist, the mechanical impact of electrode tip geometry has not been adequately quantified. Moreover, while existing evaluations utilize subjective feedback, which is an indispensable metric for assessing user comfort, quantitative, mechanics-based analyses that complement these findings have not yet been commonly established. The current study aimed to evaluate the mechanical influence of different electrode tip geometries under both vertical and tilted contact conditions. Finite element analysis was conducted using strain energy density (SED), a mechanical index known to correlate with neural impulse activity, as a quantitative indicator of the mechanical influence of tip geometry on the skin. Six types of electrode tip geometries, ranging from flat to hemispherical, were defined based on the ratio of fillet radius to prong radius. These geometries were analyzed under inclination angles from 0° to 5°, and their peak SED values were compared. Building on these initial trends, an iterative search algorithm was employed to identify the geometry ratio that tends to minimize peak SED across extended inclination angles up to 15°, evaluated as a design boundary. The findings indicate that intermediate fillet geometries tend to reduce peak SED under inclined conditions. While hemispherical tips appear favorable at inclination angles beyond 15°, intermediate geometries may offer improved load distribution within the inclination range of 0° to 10° evaluated in this study.

This paper considered a new implementation method for the stable manifold method, which is one of the nonlinear optimal control methods, using the state-dependent Riccati equation (SDRE) method. In the conventional stable manifold method, the optimal trajectory of the control object was generated by integrating the Euler-Lagrange equations corresponding to the Hamiltonian in the inverse time direction, and the state feedback control law was obtained by a polynomial approximation of the obtained solution. However, implementing this method using polynomial approximation is difficult due to problems such as determining the degree of the approximation formula, the computational cost of the approximation calculation itself, and the inability to perform polynomial approximation for complex trajectories. In contrast, the proposed method in this study aimed to achieve pseudo-nonlinear optimal control by using the SDRE method to track the optimal trajectory obtained by the stable manifold method. This method is easier to implement than the conventional stable manifold method because it does not use polynomial approximation, which is a barrier to applying it to actual systems, and instead uses a linear optimal control framework to track the optimal trajectory. The effectiveness of this method was demonstrated by swing-up and stabilization control experiments of a rotary inverted pendulum.