The traditional propeller-based propulsion of underwater robots is inefficient and poorly adapted to practice. By contrast, underwater biomimetic robots show better stability and maneuverability in harsh marine environments. This is particularly true of undulating propulsion biomimetic robots. This paper classifies the existing underwater biomimetic robots and outlines their main contributions to the field. The propulsion mechanisms of underwater biomimetic undulating robots are summarized based on theoretical, numerical and experimental studies. Future perspectives on underwater biomimetic undulating robots are also presented, filling the gaps in the existing literature.

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