Symmetries and Gaits for Purcell's Three-Link Microswimmer Model
Symmetries and Gaits for Purcell's Three-Link Microswimmer Model
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DOI：
10.1109/tro.2015.2500442
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发表时间：
2016-02-01
影响因子：
7.8
通讯作者：
Or, Yizhar
中科院分区：
文献类型：
--
作者：
Gutman, Emiliya;Or, Yizhar
机器人运动通常涉及使用步态 - 运动学形状的周期性变化，这会引起身体沿所需方向的净运动。一个例子是机器人微型游泳器，其灵感来自于游泳微生物的运动。最著名的微型游泳器理论模型之一是 Purcell 的平面三连杆游泳器，其结构具有两个对称轴。几项工作分析了基于身体固定速度积分的机器人三连杆系统的步态。使用这种方法，只能近似地获得所需方向上的有限运动。在本研究中，我们提出了基于系统结构对称性分析的步态，并沿主方向生成精确运动而无需净旋转。提出了另一种产生几乎纯旋转的步态，并通过使用扰动展开获得了小幅度残差平移的界限。接下来，该理论被扩展到只有一个对称轴的更现实的游泳者。提出了此类产生净平移的游泳者的步态，并使用扰动展开分析了它们的小幅度运动。通过数值模拟和在高粘性流体中使用机器人大型游泳器原型进行受控运动实验来证明理论结果。
Robotic locomotion typically involves using gaits-periodic changes of kinematic shape, which induce net motion of the body in a desired direction. An example is robotic microswimmers, which are inspired by motion of swimming microorganisms. One of the most famous theoretical models of a microswimmer is Purcell's planar three-link swimmer, whose structure possesses two axes of symmetry. Several works analyzed gaits for robotic three-link systems based on body-fixed velocity integrals. Using this approach, finite motion in desired directions can only be obtained approximately. In this study, we propose gaits which are based on analysis of the system's structural symmetries, and generate exact motion along principal directions without net rotation. Another gait that produces almost pure rotation is presented, and bounds on the small-amplitude residual translation are obtained by using perturbation expansion. Next, the theory is extended to more realistic swimmers which have only one symmetry axis. Gaits for such swimmers which generate net translation are proposed, and their small-amplitude motion is analyzed using perturbation expansion. The theoretical results are demonstrated by using numerical simulations and conducting controlled motion experiments with a robotic macroswimmer prototype in a highly viscous fluid.