Exact Isoholonomic Motion of the Planar Purcell's Swimmer

• 成果类型: Article
• 署名作者: Kadam, Sudin; Phogat, Karmvir Singh; Banavar, Ravi N.; Chatterjee, Debasish
• 署名单位: Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Bombay
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3059693
• 发表日期: 2022
• 页码: 429-435
• 关键词: Kinematics; Aerospace electronics; optimal control; trajectory; sports; shape; MANIFOLDS; Discrete optimal control; low Reynolds number swimming; principal fiber bundle; Purcell's swimmer

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's maximum principle. The three-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 transfer from a given initial state while minimizing the mechanical energy expended in the presence of constraints on the controls. 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 and compared with the existing results for a similar case in the literature.