Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA 16802, United States of America.
Department of Material Science and Engineering, The Pennsylvania State University, University Park, PA 16802, United States of America.
Bioinspir Biomim. 2024 Mar 14;19(3). doi: 10.1088/1748-3190/ad2f42.
In animal and robot swimmers of body and caudal fin (BCF) form, hydrodynamic thrust is mainly produced by their caudal fins, the stiffness of which has profound effects on both thrust and efficiency of swimming. Caudal fin stiffness also affects the motor control and resulting swimming gaits that correspond to optimal swimming performance; however, their relationship remains scarcely explored. Here using magnetic, modular, undulatory robots (Bots), we tested the effects of caudal fin stiffness on both forward swimming and turning maneuver. We developed six caudal fins with stiffness of more than three orders of difference. For aBot equipped with each caudal fin (andBot absent of caudal fin), we applied reinforcement learning in experiments to optimize the motor control for maximizing forward swimming speed or final heading change. The motor control ofBot was generated by a central pattern generator for forward swimming or by a series of parameterized square waves for turning maneuver. In forward swimming, the variations in caudal fin stiffness gave rise to three modes of optimized motor frequencies and swimming gaits including no caudal fin (4.6 Hz), stiffness <10Pa m(∼10.6 Hz) and stiffness >10Pa m(∼8.4 Hz). Swimming speed, however, varied independently with the modes of swimming gaits, and reached maximal at stiffness of 0.23 × 10Pa m, with theBot without caudal fin achieving the lowest speed. In turning maneuver, caudal fin stiffness had considerable effects on the amplitudes of both initial head steering and subsequent recoil, as well as the final heading change. It had relatively minor effect on the turning motor program except for theBots without caudal fin. Optimized forward swimming and turning maneuver shared an identical caudal fin stiffness and similar patterns of peduncle and caudal fin motion, suggesting simplicity in the form and function relationship inBot swimming.
在具有身体和尾鳍（BCF）形式的动物和机器人游泳者中，水动力推力主要由它们的尾鳍产生，尾鳍的刚度对游泳的推力和效率都有深远的影响。尾鳍的刚度也会影响运动控制和由此产生的与最佳游泳性能相对应的游泳步态；然而，它们之间的关系仍然很少被探索。在这里，我们使用磁性、模块化、波动机器人（Bots），测试了尾鳍刚度对前进游泳和转弯机动的影响。我们开发了六个具有三个以上刚度级别的尾鳍。对于配备每个尾鳍的 Bot（以及没有尾鳍的 Bot），我们在实验中应用强化学习来优化电机控制，以最大限度地提高前进游泳速度或最终航向变化。Bot 的电机控制由中央模式发生器生成，用于前进游泳，或由一系列参数化的方波生成，用于转弯机动。在前进游泳中，尾鳍刚度的变化导致了三种优化电机频率和游泳步态的模式，包括没有尾鳍（4.6 Hz）、刚度<10Pa m（约 10.6 Hz）和刚度>10Pa m（约 8.4 Hz）。然而，游泳速度与游泳步态的模式独立变化，并在刚度为 0.23×10Pa m 时达到最大值，没有尾鳍的 Bot 达到最低速度。在转弯机动中，尾鳍刚度对初始头部转向和随后的反弹的幅度以及最终的航向变化有相当大的影响。除了没有尾鳍的 Bot 之外，它对转弯电机程序的影响相对较小。优化的前进游泳和转弯机动共享相同的尾鳍刚度和类似的中轴和尾鳍运动模式，这表明 Bot 游泳的形式和功能关系简单。
