A Computational Study on the Hydrodynamics of Bio-Inspired Quadrupedal Paddling.

Due to its exceptional terrain mobility, quadrupedal locomotion has been used in the design of many amphibious robots for broad applications including resource exploration, disaster rescue, and reconnaissance. In this work, swimming of a quadrupedal paddling model is considered, and the effects of the legs' initial swing angle, swing amplitude, and power phase duration are numerically investigated through three paddling gaits, namely, the trotting gait, the diagonal, and the lateral sequence gaits. Three different modes for drag-based thrust generation, the "Trotting Mode", the "Hindering Mode", and the "Separate Mode", are identified. In the "Trotting Mode", each pair of diagonal legs contributes equally and alternately to the thrust within the paddling cycle, and its contribution is impaired by the other pair of diagonal legs. In the "Hindering Mode", the thrust contribution of an individual leg is significantly undermined by the drag resulting from the preceding leg leaving its current power phase and entering the following recovery phase. In the "Separate Mode", the four legs independently contribute to the total thrust by forming a compact four-peak waveform equally distributed within one paddling cycle. At a given swing amplitude, the leg configuration at peak thrust moment is identical, regardless of initial swing angle and power phase ratio. Meanwhile, a forward-tilted leg configuration with flatter upper- and lower-limb alignment at peak thrust moment consistently indicates a lower thrust generation. Hydrodynamic moments in the diagonal and lateral sequence gaits are much larger than those in the trotting gait. In addition, enhanced thrust is typically accompanied by larger hydrodynamic moments and a higher energy expenditure.