Design and Implementation of the Bionic Webbed Feet for Thrust Efficiency Improvement Based on Surrogate-assisted Kinematic Characterization

Despite advancements, amphibious robots still exhibit inadequate locomotion performance. As natatores demonstrate exceptional walking and swimming capabilities, they provide an ideal bionic prototype for structural enhancement. Consequently, this study designed a novel propulsion mechanism inspired by waterfowl, featuring a slider-four-bar linkage system that simultaneously enables foot folding and retracting. Static structural analysis was performed to identify and optimize weak components of the mechanism. The achievable workspace of the mechanism was calculated through kinematic analysis. Mathematical and numerical hydrodynamic models were established to evaluate the mechanism’s hydrodynamic performance using a defined thrust efficiency metric. To analyze the influence of kinematic parameters on the propulsion mechanism across full motion cycles, a surrogate model correlating kinematic parameters with the thrust efficiency metric was developed. Results demonstrate that the optimized propulsion mechanism satisfies the requirement of static performance under working conditions. Compared to the Waterfowl-inspired robot-I (WIR-I), the proposed mechanism achieves reduction in retraction stroke resistance for robotic webbed-foot propulsion systems. Surrogate model results show the following hierarchy of influence across kinematic parameters on the thrust efficiency metric: Paddling angle per cycle exceeds temporal baseline, which in turn exceeds temporal scaling factor of extension phase, power stroke, flexion phase, and retraction stroke. Flow field characterization indicates that flow attachment constitutes the dominant factor governing thrust efficiency. These findings could provide new design principles for future biomimetic webbed-foot robotic systems and establish a theoretical foundation for hydrodynamic optimization in amphibious robotics development and deployment.