Hybrid undulatory kinematics of a robotic Mackerel (Scomber scombrus): Theoretical modeling and experimental investigation

Fishes that use undulatory locomotion occasionally change their inherent kinematics in terms of some natural behavior. This special locomotion pattern was vividly dubbed "hybrid kinematics" by biologists recently. In this paper, we employed a physical model with body shape of a Mackerel (Scomber scombrus), to use the three most typical undulatory kinematics: Anguillform, carangiform and thunniform, to investigate the hydrodynamic performance of the so-called "hybrid kinematics" biological issue. Theoretical models of both kinematics and hydrodynamics of the physical model swimming were developed. Base on this model, the instantaneous force produced by fish undulatory body and flapping tail were calculated separately. We also quantitatively measured the hydrodynamic variables of the robotic model swimming with the three undulatory kinematics on an experimental apparatus. The results of both theoretical model and experiment showed that the robot with thunniform kinematics not only reaches a higher speed but also is more efficient during steady swimming mode. However, anguilliform kinematics won the speed race during the initial acceleration. Additionally, the digital particle image velocimetry (DPIV) results showed some difference of the wake flow generated by the robotic swimmer among the three undulatory kinematics. Our findings may possibly shed light on the motion control of a biomimetic robotic fish and provide certain evidence of why the "hybrid kinematics" exists within the typical undulatory locomotion patterns.