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Updated: Sep 30, 2025
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Preparation and 3D Tracking of Catalytic Swimming Devices
Published on: July 1, 2016
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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
Summary
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.
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.
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