Article ID: 25-00257
Undulatory motion is an effective propulsion mechanism widely observed in nature, offering advantages in environments where traditional propulsion systems struggle, such as highly viscous fluids. This study systematically investigates how the number of links and fluid viscosity influence the propulsion characteristics of a multi-link swimmer. A fluid force model incorporating pressure and viscous drag, valid across a wide range of Reynolds numbers, was utilized. Multi-objective optimization was then performed to identify Pareto-optimal solutions for swimming speed and average power by varying the number of links and control inputs across three distinct fluid viscosities. The results reveal several key findings. First, a greater number of links enables higher speeds and more efficient propulsion, with the most significant improvement seen when increasing from four to eight links, after which the gains diminish, a phenomenon potentially linked to the uniform control strategy employed. Second, while a larger tail beat amplitude increases stride length, its effectiveness is reduced in highly viscous fluids where viscous drag becomes the dominant resistive force. Consequently, undulatory motion becomes an inefficient strategy in very low Reynolds number regimes (Re ~ 10−2). Finally, the robot’s optimal motion aligns with established scaling laws for aquatic animals, although the constant Strouhal number at high Reynolds numbers (~ 1.0) differs from typical biological values (~ 0.3). This discrepancy suggests that body shape and surface material, in addition to motion patterns, are critical factors for achieving high efficiency. These findings provide design guidelines for bio-inspired robots operating in diverse viscous environments.
