Conditions for energetically-optimal elasticity and their implications for biomimetic propulsion systems

TL;DR

This paper investigates how both linear and nonlinear elasticities can be optimally introduced into oscillating systems to minimize energy consumption, challenging previous assumptions and offering new design principles for biomimetic propulsion.

Contribution

It demonstrates that nonlinear elasticities can be as optimal as linear ones, providing a method to construct such elasticities and revealing new principles for energy-efficient system design.

Findings

Nonlinear elasticities can be equivalently optimal as linear resonant elasticity.

A method to construct nonlinear elasticities for optimal energy efficiency.

Insights into structural elasticity roles in biological organisms.

Abstract

Minimising the energy consumption associated with periodic motion is a priority common to a wide range of technologies and organisms - among them, many species of flying insect, for which flapping-wing flight is a life-essential mode of locomotion. In pursuit of this priority, the following problem often manifests: how to introduce elasticity into an actuated, oscillating, system in order to minimise actuator power consumption? Here, we explore this question in a range of general systems, and find some surprising answers. For instance, it is widely assumed that, if the system dynamics are linear, then linear resonant elasticity is the only optimal choice. We show, to the contrary, that there exist nonlinear elasticities with equivalent optimality, and provide an elegant method for constructing these elasticities in general systems. This is a new principle of linear and nonlinear dynamics, fundamentally altering how questions of energetic optimality in a wide range of dynamical systems must be approached. Furthermore, we show how this principle enables new forms of optimal system design, including optimal unidirectional actuation in nonlinear systems; new tools for the design of optimal biomimetic propulsion systems; and new insights into the role of structural elasticity in a range of different organisms.