Modeling Elastic-Body Dynamics of Fish Swimming Using a Variational Framework

Fish-inspired aquatic robots are gaining increasing attention in research communities due to their high swimming speeds and efficient propulsion enabled by flexible bodies that generate undulatory motions. To support the design optimizations and control of such systems, accurate, interpretable, and computationally tractable modeling of the underlying swimming dynamics is indispensable. In this letter, we present a full-body dynamics model for fish swimming, rigorously derived from Hamilton's principle. The model captures the continuously distributed elasticity of a deformable fish body undergoing large deformations and incorporates fluid-structure coupling effects, enabling self-propelled motion without prescribing kinematics. A preliminary parameter study explores the influence of actuation frequency and body stiffness on swimming speed and cost of transport (COT). Simulation results indicate that swimming speed and energy efficiency exhibit opposing trends with tail-beat frequency and that both body stiffness and body length have distinct optimal values. These findings provide insights into biological swimming mechanisms and inform the design of high-performance soft robotic swimmers.