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-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 rob...

• Type: Conference
• Year: 2009
• Where: CDC
• Authors: Yizhar Or, Joris Vankerschaver, Scott D. Kelly, Richard M. Murray, Jerrold E. Marsden
• Keywords: CDC 2009, Circular Rigid Body, Control Systems, Cyclic Motion, Rigid Body