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 behaviour 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 behaviours are similar to those of our minimal model: its gait is also periodic and exhibits bistability, with a low efficiency mode separated from a high efficiency mode 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.

中文翻译：

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底栖双足动物模型

步行是一种常见的双足和四足步态，通常与陆生和水生生物有关。受到小冰鞋 Leucoraja erinacea 原始水上行走的神经基础的最新证据的启发，我们引入了一种水上行走的理论模型，该模型揭示了稳健高效的步态，对身体形态和控制的要求适中。该模型以规律的足部放置模式预测系统身体的波动行为，这也在动物中观察到，此外还预测了两种状态之间步态双稳定性的存在，一种具有较大的运动能量成本，另一种几乎没有精力成本。我们表明可以使用简单的强化学习方案发现这些。为了测试这些理论框架，我们构建了一个双足机器人，并表明它的行为与我们的最小模型的行为相似：它的步态也是周期性的并且表现出双稳态，通过“跳跃”过渡将低效率模式与高效率模式分开。总的来说，我们的研究强调了步行进化的物理限制，并为高效仿生机器人的设计提供了指导。