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The -Link Swimmer in Three Dimensions: Controllability and Optimality Results.

Roberto Marchello1, Marco Morandotti1, Henry Shum2

  • 1Dipartimento di Scienze Matematiche "G. L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy.

Acta Applicandae Mathematicae
|March 18, 2022
PubMed
Summary
This summary is machine-generated.

This study proves that a 3D multi-link swimmer is fully controllable in low Reynolds number fluids. Using geometric control theory, researchers demonstrate that the swimmer can reach any configuration by manipulating its shape parameters.

Keywords:
ControllabilityMicro-swimmersMotion in viscous fluidsOptimal control problemsResistive force theory

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Area of Science:

  • Robotics
  • Fluid Dynamics
  • Control Theory

Background:

  • Understanding the motion of micro-swimmers is crucial in fields like targeted drug delivery.
  • Previous studies often focused on simpler models or specific fluid environments.

Purpose of the Study:

  • To investigate the controllability of a fully three-dimensional (3D) multi-link swimmer in a low Reynolds number fluid.
  • To determine if such a swimmer can achieve any desired position and orientation.

Main Methods:

  • Derivation of equations of motion using Resistive Force Theory.
  • Application of Geometric Control Theory to analyze the swimmer's dynamics.
  • Utilizing Lie brackets to assess the generation of motion vectors.

Main Results:

  • The minimal 2-link swimmer was shown to be controllable, generating all necessary motion directions.
  • Controllability was extended to the general N-link swimmer.
  • Analysis of optimal control strategies for minimal time and power expenditure was performed.

Conclusions:

  • The 3D multi-link swimmer is demonstrated to be fully controllable in low Reynolds number fluids.
  • The findings provide a theoretical foundation for designing and controlling micro-robotic swimmers.
  • Optimal control strategies offer insights into efficient swimmer operation.