Energy Saving of Schooling Robotic Fish in Three-Dimensional Formations

It has long been proposed that animals flying in the air and swimming in the water could extract energy from neighbour-induced flows. A large number of mechanisms have been proposed to explain whether, and if so how, animals can save energy by moving in two-dimensional (2D) formations-individuals swim in the horizontal plane. Seldom studies explore the mechanisms in three-dimensional (3D) formations-individuals swim in both horizontal and vertical planes, even though most animals perform 3D behaviour. In this letter, taking a pair of bio-inspired robotic fish as experimental physical models, we explore the energy cost of the follower when swimming close to a neighbour in 3D formations (mainly in the vertical plane). We found the cost of the follower is mainly affected by how it spatiotemporally interacts with the 3D vortices shed by the neighbour in 3D formations. A simple linear correlation was found between the spatial factor (the height difference) and temporal factor (the body phase difference) when the follower saves most energy compared to swimming alone. Preliminary flow visualisations and 3D computational fluid dynamic simulations show this is due to the structure of vortices along the span of the caudal fin's trailing edge. Our studies shed new light on the energy saving control of multiple artificial underwater robots in 3D formations.