Geometric control of particle manipulation in a two-dimensional fluid

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-con...

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Bibliographic Details
Main Authors: Or, Y., Vankerschaver, J., Kelly, S.D., Murray, R.M., Marsden, J.E.
Format: Conference Proceeding
Language:English
Subjects:
Chemical processes
Context modeling
Control systems
Fluid dynamics
Fluid flow control
Machining
Microorganisms
Motion control
Nonlinear control systems
Probes
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Summary: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.
ISSN:0191-2216
DOI:10.1109/CDC.2009.5399499