Conditions for energetically-optimal elasticity and their implications for biomimetic propulsion systems
This work addresses energy efficiency in actuated oscillating systems, such as flapping-wing flight in insects, with implications for biomimetic technologies, though it is incremental in extending existing principles to nonlinear cases.
The paper tackled the problem of minimizing energy consumption in periodic motion systems by introducing optimal elasticity, revealing that nonlinear elasticities can be as optimal as linear ones in linear dynamics, and providing a method to construct these elasticities. This led to new design principles for biomimetic propulsion systems and insights into organismal elasticity.
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.