Using optimal control to obtain maximum displacement gait for Purcell's three-link swimmer
Using optimal control to obtain maximum displacement gait for Purcell's three-link swimmer
复制标题
使用最优控制获得 Purcell 三连杆游泳者的最大位移步态
DOI：
--
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Y. Or
中科院分区：
文献类型：
--
作者：
O. Wiezel;Y. Or
Purcell的游泳者是一个简单的三连杆游泳者在高粘性流体中运动的经典模型，类似于微生物或微型游泳机器人的运动。这两个关节角通常被规定为称为步态的周期轨迹，因此Purcell游泳者的动力学可以被表述为无漂移的非线性控制系统。在Tam和Hosoi的一篇著名论文中，他们通过将时间周期关节角表示为截断的傅立叶级数，并对其系数的有限集进行数值优化，找到了在一个周期内使净位移最大化的最佳步态。在这项工作中，重新审视了步态优化，并将其解析为一个只有两个状态变量和单个输入的最优控制系统的优雅问题，该问题可以使用庞特里亚金极大值原理来解决。由于控制系统的输入没有任何物理约束，结果表明最优解必须遵循“奇异弧”。得到了边值问题的数值解，准确再现了Tam和Hosoi的最优步态。
Purcell's swimmer is a classical model of a simple three-link swimmer moving in a highly viscous fluid, similar to the motion of microscopic organisms or robotic microswimmers. The two joint angles are commonly prescribed as periodic trajectories called gaits, so that the dynamics of Purcell's swimmer can be formulated as a driftless nonlinear control system. In a famous paper by Tam and Hosoi, they have found the optimal gait that maximizes net displacement over a cycle by representing the time-periodic joint angles as truncated Fourier series and numerically optimizing a finite set of their coefficients. In this work, the gait optimization is revisited and analytically formulated as an elegant problem of optimal control system with only two state variables and a single input, which can be solved using Pontryagin's maximum principle. Due to absence of any physical constraints on the control system's input, it turns out that the optimal solution must follow a “singular arc”. Numerical solution of the boundary value problem is obtained, which exactly reproduces Tam and Hosoi's optimal gait.