Incorporating Geometric Nonlinearity in Theoretical Modeling of Muscle-Powered Soft Robotic Bio-Actuators

Biohybrid actuators aim to leverage the various advantages of biological cells over artificial components to build novel compliant machines with high performance and autonomy. Significant advances have been made in bio-fabrication technologies, enabling the realization of muscle-powered bio-actuators. However, the mechanics of muscle-scaffold coupling has been relatively understudied, limiting the development of bio-actuators to intuitive or biomimetic designs. Here, we consider the case of implementing muscle-based actuation for soft robotic swimmers operating at low Reynolds number. We develop an analytical model to describe the elasto-hydrodynamic problem and identify key design parameters. Muscle contraction dynamics is characterized experimentally and the implications of nonlinear amplitude-frequency relationship of muscle-based actuation are discussed. We show that a novel bio-actuator with high performance can be developed by introducing compliant flexural mechanisms undergoing large deflection. Geometric nonlinearities are accounted for in the analysis of the force-deflection relationship for the flexural mechanism. Our results show that for expected muscle contraction forces, this novel bio-actuator can outperform previous muscle-powered swimmers by up to two orders of magnitude in swimming speed.