Fish-inspired segment models for undulatory steady swimming

Many aquatic animals swim by undulatory body movements and understanding the diversity of these movements could unlock the potential for designing better underwater robots. Here, we analyzed the steady swimming kinematics of a diverse group of fish species to investigate whether their undulatory movements can be represented using a series of interconnected multi-segment models, and if so, to identify the key factors driving the segment configuration of the models. Our results show that the steady swimming kinematics of fishes can be described successfully using parsimonious models, 83% of which had fewer than five segments. In these models, the anterior segments were significantly longer than the posterior segments, and there was a direct link between segment configuration and swimming kinematics, body shape, and Reynolds number. The models representing eel-like fishes with elongated bodies and fishes swimming at high Reynolds numbers had more segments and less segment length variability along the body than the models representing other fishes. These fishes recruited their anterior bodies to a greater extent, initiating the undulatory wave more anteriorly. Two shape parameters, related to axial and overall body thickness, predicted segment configuration with moderate to high success rate. We found that head morphology was a good predictor of its segment length. While there was a large variation in head segments, the length of tail segments was similar across all models. Given that fishes exhibited variable caudal fin shapes, the consistency of tail segments could be a result of an evolutionary constraint tuned for high propulsive efficiency. The bio-inspired multi-segment models presented in this study highlight the key bending points along the body and can be used to decide on the placement of actuators in fish-inspired robots, to model hydrodynamic forces in theoretical and computational studies, or for predicting muscle activation patterns during swimming.