  Walking is a common bipedal and quadrupedal gait and is often associated with
terrestrial and aquatic organisms. Inspired by recent evidence of the neural
underpinnings of primitive aquatic walking in the little skate Leucoraja
erinacea, we introduce a theoretical model of aquatic walking that reveals
robust and efficient gaits with modest requirements for body morphology and
control. The model predicts undulatory behavior of the system body with a
regular foot placement pattern which is also observed in the animal, and
additionally predicts the existence of gait bistability between two states, one
with a large energetic cost for locomotion and another associated with almost
no energetic cost. We show that these can be discovered using a simple
reinforcement learning scheme. To test these theoretical frameworks, we built a
bipedal robot and show that its behaviors are similar to those of our minimal
model: its gait is also periodic and exhibits bistability, with a low
efficiency gait separated from a high efficiency gait by a "jump" transition.
Overall, our study highlights the physical constraints on the evolution of
walking and provides a guide for the design of efficient biomimetic robots.
