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

2025-09-19

AI Summary

Modeling the flexible-body dynamics of fish-like underwater robots faces a fundamental trade-off among accuracy, interpretability, and computational tractability. Method: Leveraging Hamilton’s variational principle, this work rigorously derives, for the first time, a whole-body dynamic model that fully couples distributed elasticity with fluid–structure interaction—enabling self-propelled simulation without prescribed kinematics. The approach integrates Lagrangian mechanics, variational modeling, and parametric numerical simulation. Contribution/Results: The model systematically uncovers non-monotonic effects of caudal fin actuation frequency, body stiffness, and body length on swimming speed and energy cost. Specifically, speed and efficiency exhibit opposing trends with respect to frequency; optimal stiffness and body length exist, enhancing propulsion efficiency by up to 32% and reducing cost of transport by 18%. This framework establishes a new paradigm for both bio-inspired soft underwater robot design optimization and mechanistic studies of aquatic locomotion.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Low Level & Physics-based Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

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.

Problem

• Modeling fish swimming dynamics using variational framework
• Capturing elastic body deformations and fluid-structure coupling
• Optimizing swimming performance through parameter analysis

Innovation

• Variational framework derived from Hamilton's principle
• Model captures distributed elasticity and fluid coupling
• Enables self-propelled motion without prescribed kinematics