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Geometric Control of Particle Manipulation in a Two-Dimensional Fluid
Abstract Manipulation of particles suspended in flu …
Manipulation of particles suspended in fluids is crucial for many applications, such as precision machining, chemical processes, bio-engineering, and self-feeding of microorganisms. In this paper, we study the problem of particle manipulation by cyclic fluid boundary excitations from a geometric-control viewpoint. We focus on the simplified problem of manipulating a single particle by generating controlled cyclic motion of a circular rigid body in a two-dimensional perfect fluid. We show that the drift in the particle location after one cyclic motion of the body can be interpreted as the geometric phase of a connection induced by the system's hydrodynamics. We then formulate the problem as a control system, and derive a geometric criterion for its nonlinear controllability. Moreover, by exploiting the geometric structure of the system, we explicitly construct a feedback-based gait that results in attraction of the particle towards the rigid body. We argue that our gait is robust and model-independent, and demonstrate it in both perfect fluid and Stokes fluid.
it in both perfect fluid and Stokes fluid.  +
Authors Yizhar Or, Joris Vankerschaver, Scott D Kelly, Richard M Murray, Jerrold E Marsden  +
ID 2009c  +
Source Conference on Decision and Control (CDC)  +
Tag or+09-cdc  +
Title Geometric Control of Particle Manipulation in a Two-Dimensional Fluid +
Type Preprint  +
Categories Papers
Modification date
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15 May 2016 06:16:40  +
URL
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http://www.cds.caltech.edu/~murray/preprints/or+09-cdc.pdf  +
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Geometric Control of Particle Manipulation in a Two-Dimensional Fluid + Title
 

 

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