View source for Geometric Control of Particle Manipulation in a Two-Dimensional Fluid

{{HTDB paper
| authors = Yizhar Or, Joris Vankerschaver, Scott D Kelly, Richard M Murray, Jerrold E Marsden
| title = Geometric Control of Particle Manipulation in a Two-Dimensional Fluid
| source = Conference on Decision and Control (CDC)
| year = 2009
| type = Preprint
| funding = 
| url = http://www.cds.caltech.edu/~murray/preprints/or+09-cdc.pdf
| abstract = 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.
| flags = 
| tag = or+09-cdc
| id = 2009c
}}