Elastic-bound conditions for energetically optimal elasticity and their implications for biomimetic propulsion systems

Minimising the energy consumption associated with periodic motion is a priority common to wide range of technologies and organisms. These include many forms biological biomimetic propulsion system, such as flying insects. Linear nonlinear elasticity can play an important role in optimising energetic behaviour these systems, via linear or resonance. However, existing methods for computing energetically optimal elasticities struggle when actuator regeneration imperfect: system cannot reuse work performed on actuator, occurs realistic systems. Here, we develop new analytical method that overcomes limitations. Our provides exact minimising mechanical power required generate target response, under conditions imperfect regeneration. We demonstrate how, general parallel- series-elastic actuation lead set non-unique elasticities. This solution space generalises properties resonance, described completely bounds loop: elastic-bound conditions. The choice from within leads tools systems design, particular relevance systems: controlling trade-off between peak duty cycle; using unidirectional actuators oscillations; further. More broadly, results perspectives organisms, insights into fundamental relationship elasticity, optimality.