Energy conservation analysis and formation control of multi-tadpoles based on lattice Boltzmann method

Tadpole swimming is a common swimming form in nature, but there are only few studies on the swimming properties of tadpoles and tadpole groups. This paper focuses on the control and energy consumption during tadpole swimming and studies the swimming formation suitable for the tadpole group based on their hydrodynamic properties. First, based on the immersed boundary-lattice Boltzmann method and tadpole model proposed in our previous studies, the swimming control strategy of tadpoles based on incremental proportional–integral–derivative control is proposed. Then, the influence of control quantity on tadpole swimming is analyzed, and the control thresholds are set to realize the stable swimming control of tadpoles. Furthermore, through energy analysis of the pairs of tadpoles at different lateral distances, phase differences, and horizontal distances, we found the reduction of tadpole lateral distance has a slight effect on energy-savings. It is the energy-efficient mode for swimming pairs of adjacent tadpoles, when the longitudinal distance is one body length and the phase difference is 5π/3. In addition, under different longitudinal distances, the phase difference for energy efficiency of tadpoles is also different, but it shows a periodicity. Finally, the study results were extended to a formation of three or four tadpoles for verification. Our research will provide a mechanical reference for studying tadpole swarm swimming and for the design and control of tadpole-like robots.