Frequency Domain Analysis of Nonlinear Series Elastic Actuator via Describing Function

TL;DR

The paper addresses the lack of frequency-domain tools for nonlinear series elastic actuators in assistive robotics. It introduces a describing function approach to the nonlinear stiffness element (NSEE), derives a closed-form relation $N_{\tau}(A)$ between input deflection amplitude and output torque, and validates the method against a physical Simscape model. The work also casts NSEAs as a linear parameter-varying system $G(s,A)$ to enable LPV and $\mathcal{H}_{\infty}$ control design, outlining practical pathways to muscle-like, adaptive impedance in robots. The results demonstrate meaningful alignment between the describing function predictions and real-system behavior, supporting its use in actuator design and control for safer, more adaptable assistive devices.

Abstract

Nonlinear stiffness SEAs (NSEAs) inspired by biological muscles offer promise in achieving adaptable stiffness for assistive robots. While assistive robots are often designed and compared based on torque capability and control bandwidth, NSEAs have not been systematically designed in the frequency domain due to their nonlinearity. The describing function, an analytical concept for nonlinear systems, offers a means to understand their behavior in the frequency domain. This paper introduces a frequency domain analysis of nonlinear series elastic actuators using the describing function method. This framework aims to equip researchers and engineers with tools for improved design and control in assistive robotics.

Figures (9)

• Figure 1: The Schematic of the simplified series elastic actuator.
• Figure 2: The Schematic of Nonlinear Stiffness Elastic Element.
• Figure 3: Feedback system representation of NSEA.
• Figure 4: Physical Simulation Model
• Figure 5: Stiffness Characteristic of NSEE