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Figure 11. The following robot fish saves energy by vortex phase matching. (A) Relative power coefficient: Positive and negative values,
respectively, represent energy saving and energy cost relative to swimming alone. The dashed line represents the function between
phase difference and front-back distance, as shown in (B). (B) Location of energy saving: The size and darkness of the dots represent the
number of times that the energy saving state occurs [50] .

adjusting the tail-beat phase difference as they swim. This suggested that individuals in swimming schools
might engage in competitive games.

The discussion of various planar formations aids in determining the best formation. The average swimming
efficiency of robot fish formations formed in tandem, square, diamond, and rectangular shapes was
investigated by Li et al. . It was found that the average swimming efficiency of the tandem formation was
[52]
highest when the spacing of robot fishes was less than 1.25 BL. The average swimming efficiency of the
rectangular formation was highest when the spacing was greater than 1.25 BL. In addition, the wake and
pressure generated by the oscillation of the robot fish had an important effect on the Froude efficiency. The
wake primarily influenced propulsive force, while pressure primarily influenced the lateral power loss. In
this study, the phase difference of each robot fish’s oscillation was constant, and the situation when the
phase difference changed was not discussed.

The 3D formation is closer to a natural school of fish, and therefore it has more practical application. 3D is
mainly reflected by having the height difference as a variable. The energy consumption of two robot fishes
when they formed a 3D formation was studied by Li et al. . The results show that the following robot fish
[53]
could save energy consumption when there was a linear relationship between the height difference and
phase difference of the two robot fishes. This research result is significant because it provided ideas for the
future 3D formation of robot fishes.

4.2. Communication of multiple robot fishes
When multiple robot fishes form a formation, they must communicate with others in order to maintain the
formation and avoid a collision. Since the distance between each robot fish is short, this is a problem for
underwater close communication. Relevant studies have been conducted to date, and some solutions have
been proposed. Among them, Xie Guangming’s team from Peking University conducted extensive research
and produced impressive results.