System Identification of Robotic Fish Swimming Reveals Roles of Reactive and Resistive Fluid Force in Two Distinct Swimming Gaits

Understanding how fish generate thrust across diverse swimming gaits is central to bio-inspired robotics. Here, we combine particle image velocimetry (PIV), system identification, and simulation to uncover the hydrodynamic mechanisms underlying swimming of a modular robotic fish (µBot). By modulating motor frequency, µBot exhibited two distinct gaits: a low–medium frequency traveling-wave “fish-like” gait shedding two pairs of vortices per cycle, and a high-frequency standing-wave “resonant” gait shedding double rows of single vortices of opposite sign per cycle. PIV revealed that thrust in the resonant gait is dominated by tail pressure (reactive), whereas such pressure contributions are negligible in the traveling-wave gait with thrust primarily generated by drag forces (resistive). We developed an analytical model incorporating reactive and resistive force components and identified its parameters using genetic algorithms to fit experimental data. The fitted model reproduced swimming speed and body kinematics with high accuracy and revealed gait-dependent variations in hydrodynamic parameters. Sensitivity analyses confirmed that only a subset of force components influenced swimming performance. Finally, energetic analyses showed resonance behavior in standing-wave gait but not in traveling-wave gait. This integrative framework highlights the distinct roles of reactive versus resistive forces across gaits, advancing the design and control of efficient fish-inspired robots.