Exact Isoholonomic Motion of the Planar Purcell's Swimmer

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 o...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2022-01, Vol.67 (1), p.429-435
Main Authors: Kadam, Sudin, Phogat, Karmvir Singh, Banavar, Ravi N., Chatterjee, Debasish
Format: Article
Language:English
Subjects:
Aerospace electronics
Algorithms
Boundary value problems
Discrete optimal control
Fluid flow
Kinematics
Lie groups
Locomotion
low Reynolds number swimming
Manifolds
Maximum principle
Optimal control
Optimization
principal fiber bundle
Purcell's swimmer
Reynolds number
Shape
Sports
Trajectory
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Summary: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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2021.3059693