Modeling and frequency domain analysis of nonlinear compliant joints for a passive dynamic swimmer

TL;DR

This paper models a nonlinear compliant joint in an underwater robotic fish using D"uffing's equation and compares analytical harmonic solutions with Volterra series, aiding the design of bio-inspired robots for energy harvesting.

Contribution

It introduces a simplified fluid-structure interaction model for underwater joints and compares solution methods, enhancing understanding of nonlinear resonance in bio-inspired robotics.

Findings

Trade-off between accuracy and flexibility of solution methods

Analytical harmonic solutions compared with Volterra series

Potential for energy extraction from flow-induced vortex shedding

Abstract

In this paper we present the study of the mathematical model of a real life joint used in an underwater robotic fish. Fluid-structure interaction is utterly simplified and the motion of the joint is approximated by D\"uffing's equation. We compare the quality of analytical harmonic solutions previously reported, with the input-output relation obtained via truncated Volterra series expansion. Comparisons show a trade-off between accuracy and flexibility of the methods. The methods are discussed in detail in order to facilitate reproduction of our results. The approach presented herein can be used to verify results in nonlinear resonance applications and in the design of bio-inspired compliant robots that exploit passive properties of their dynamics. We focus on the potential use of this type of joint for energy extraction from environmental sources, in this case a K\'arm\'an vortex street shed by an obstacle in a flow. Open challenges and questions are mentioned throughout the document.