In the murky waters of the Amazon Basin, a fish glides effortlessly—forward, backward, and in place—without bending its body. The black ghost knifefish (Apteronotus albifrons) performs these feats using only a single, ribbon-like fin running along its underside. Now, a team of researchers has decoded the biomechanical principles behind this remarkable agility, offering a roadmap for building more capable and maneuverable underwater robots.
Published in the journal Ocean, the study led by Ze-Jun Liang and colleagues from Northwestern Polytechnical University's Ocean Institute in China provides the most detailed analysis to date of the knifefish's anal fin morphology and kinematics. Their findings challenge conventional assumptions about fish locomotion and lay the groundwork for a new generation of bio-inspired propulsion systems.
"Traditional propeller-based systems struggle with low-speed maneuverability and stability in complex environments," said corresponding author Peng Xu. "By contrast, the knifefish achieves precise control using undulations of its anal fin—a flexible, elongated structure that generates traveling waves to produce thrust without body bending. Understanding this mechanism is key to overcoming the limitations of current underwater vehicles."
The researchers studied 18 live specimens, capturing nearly 2,000 instantaneous motion cases with high-speed cameras. They found that the anal fin follows an arched, streamlined profile, with a maximum fin height-to-body height ratio of approximately 0.24—a design that minimizes body drag. More importantly, the fish achieves its signature agility by dynamically controlling the direction of wave propagation and the undulation mode.
Unlike most fish that rely on a single wave traveling from head to tail, the knifefish can generate waves that move forward, backward, or even in opposite directions simultaneously. When two counter-propagating waves meet, they create a "node" where forces cancel, allowing the fish to hover or make rapid direction changes without turning its body.
"What's striking is that the fish can maintain a rigid body posture while swimming, which reduces drag and simplifies the engineering challenge of building robotic systems," said co-author Yi-Wei Fan. "This ability to independently control wave parameters offers a new paradigm for propulsion—one that decouples thrust generation from body bending."
Using spatiotemporal Fourier transform analysis, the team extracted key kinematic parameters, including wave frequency, speed, wavelength, and amplitude. Their results show that wave frequency is the primary control variable for cruising speed, while wave speed, wavelength, and wave number form an interrelated operational range that collectively governs propulsion performance.
"We observed a clear functional relationship between swimming speed and undulation parameters," explained co-author Dong-Yang Chen. "Wave frequency emerged as the most reliable predictor of speed, while amplitude and wave number remained relatively stable across different swimming conditions. This suggests that the fish modulates its motion by fine-tuning frequency, much like a musician adjusting tempo."
The study also revealed that the undulation amplitude along the fin follows an asymmetric, arched distribution—smaller at both ends and larger in the middle—which contributes to efficient thrust generation. This non-uniform pattern contrasts sharply with the simplified constant-amplitude models used in most existing robotic prototypes.
"Most bio-inspired undulating fin designs to date have relied on idealized rectangular fins and constant-amplitude undulations," said lead author Ze-Jun Liang. "Our findings show that real biological systems are far more sophisticated. By incorporating the morphological and kinematic synergies we've identified, we believe robotic propulsion efficiency and maneuverability can be significantly improved."
The researchers note that the black ghost knifefish is an ideal model not only for its hydrodynamic prowess but also for its neurobiological significance. As a weakly electric fish, it relies on a rigid body to minimize electric field distortion during electrolocation. Its propulsion system must therefore generate thrust without compromising sensory capabilities—a constraint that aligns closely with the needs of sensor-laden autonomous underwater vehicles.
Looking ahead, the team plans to apply these insights to the development of a new class of undulating-fin robots. Their next steps include translating the kinematic database into control algorithms and testing prototype designs in real-world aquatic environments, including turbulent flows and confined spaces.
"Our ultimate goal is to create underwater vehicles that can operate with the same efficiency and agility as the knifefish," said Xu. "This would open up new possibilities for inspection, exploration, and search-and-rescue missions in complex underwater environments where traditional propellers fall short."
The study was supported by the Postdoctoral Innovation Fund of Northwestern Polytechnical University Taicang Yangtze River Delta Research Institute, the National Natural Science Foundation of China, and other research programs.
