Bioinspired undulating fin: Hydrodynamic performance under unconventional motion patterns

Most existing studies on bioinspired undulating propulsion robots focus on uniform amplitude waveforms, making it difficult to reproduce the vertical and hovering motion patterns of biological prototypes. To explore the propulsion mechanisms of unconventional undulating fin patterns and enhance the maneuverability of these robots, four typical unconventional motion patterns are categorized: increasing amplitude waveform, decreasing amplitude waveform, inward counter-propagating waves, and outward counter-propagating waves. A unified kinematic model is developed for these patterns, and a numerical framework based on the constrained immersed boundary method is established to evaluate their hydrodynamic performance. Parametric optimization analyses reveal the hydrodynamic performance and underlying propulsion mechanisms of these motion patterns, and corresponding comparative experiments are carried out. Results show that the propulsion performance of the undulating fin improves with increasing amplitude. At fixed amplitudes, increasing amplitude waveform enhance thrust by up to 5.32% at an amplitude of 30–40°, whereas decreasing amplitude waveform produce greater lift. Counter-propagating waves cancel thrust but generate substantial lift, with inward waves yielding higher lift than outward ones due to wake vortex interactions. This study advances the understanding of certain biological phenomena while offering theoretical guidance for the design and optimization of multimodal locomotion strategies in undulating fin robots, enabling better emulation of biological prototypes.