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

Abstract

Fish-inspired aquatic robots are gaining increasing attention in marine robot communities due to their high swimming speeds and efficient propulsion enabled by flexible bodies that generate undulatory motions. To support the design optimization 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 motor-actuated robotic fish, 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. Preliminary open-loop simulations examine how actuation frequency and body stiffness influence the swimming speed and energy efficiency of the robotic fish. Closed-loop simulations further assess how stiffness distribution impacts the controller's velocity-tracking performance and energy efficiency. The results demonstrate the model's potential for performance evaluation and control optimization of soft robotic swimmers when stiffness is treated as a design variable.

Figures (6)

• Figure 1: Configuration and coordinate systems of the fish model; (a) top view and (b) side view of the fish.
• Figure 2: Differential control volume and its momentum flux of the water added mass around the fish's body.
• Figure 3: (a) Comparisons of the fish head's COM trajectories over 3 full tail-beats, with the number of Ritz basis functions $N$ increasing from 1 to 6; (b) times consumed by the numerical simulations as $N$ increases.
• Figure 4: Simulation results of the tail-beat frequency sweep. Time-lapse plot of the fish from $t = 4s$ to $t = 5s$ with a tail-beat frequency of (a) 3Hz and (b) 1Hz (blue-red-green sequence); (c) $X$-direction velocity plots and (d) plots of steady-state average speed and COT at different tail-beat frequencies.
• Figure 5: Simulation results of the baseline Young's modulus sweep. Time-lapse plot of the fish from $t = 4s$ to $t = 5s$ with a baseline Young's modulus of (a) 0.2MPa and (b) 0.35MPa (blue-red-green-black sequence); (c) $X$-direction velocity plots and (d) plots of steady-state average speed and COT at different baseline Young's moduli.