平面Purcell游泳者精确等效运动学运动
Exact isoholonomic motion of the planar Purcell's swimmer
AI总结：
本文提出并解决了平面Purcell游泳者的离散时间等效运动学问题，通过离散时间庞特里亚金极大值原理求解，建立了保持结构的离散时间运动学模型，并通过数值方法求解最优状态转移的必要条件。
摘要：
在本文中，我们提出了平面Purcell游泳者的离散时间等效运动学问题，并利用离散时间庞特里亚金极大值原理对其进行求解。3连杆Purcell游泳者是一种在低雷诺数环境中运动的运动系统。该系统的运动学在主纤维丛上演化。通过离散连接的局部形式，获得了该系统的结构保持的离散时间运动学模型。随后，采用矩阵李群上的离散极大值原理的改编版本，得出最优状态转移时最小化控制努力的必要最优条件。这些必要条件表现为一个两点边界值问题，并通过数值技术进行求解。数值实验的结果用于说明该算法。
英文摘要：
In this article we present the discrete-time isoholonomic problem of the planar Purcell's swimmer and solve it using the Discrete-time Pontryagin maximum principle. The 3-link Purcell's swimmer is a locomotion system moving in a low Reynolds number environment. The kinematics of the system evolves on a principal fiber bundle. A structure preserving discrete-time kinematic model of the system is obtained in terms of the local form of a discrete connection. An adapted version of the Discrete Maximum Principle on matrix Lie groups is then employed to come up with the necessary optimality conditions for an optimal state transfer while minimizing the control effort. These necessary conditions appear as a two-point boundary value problem and are solved using a numerical technique. Results from numerical experiments are presented to illustrate the algorithm.
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