Title :
Generic 3D swimmers in a perfect fluid are controllable
Author :
Chambrion, Thomas ; Munnier, A.
Author_Institution :
Inst. Elie Cartan de Nancy, INRIA Nancy Grand Est, Vandœuvre, France
Abstract :
We address the problem of controlling a dynamical system governing the motion of a 3D weighted shape changing body swimming in a perfect fluid. The rigid displacement of the swimmer results from the exchange of momentum between prescribed shape changes and the flow, the total impulse of the fluid-swimmer system remaining null for all times. We prove the following tracking results: (i) Synchronized swimming: Maybe up to an arbitrarily small change of its density, any swimmer can approximately follow any given trajectory while, in addition, undergoing approximately any given shape changes. In this statement, the control consists in arbitrarily small superimposed deformations; (ii) Freestyle swimming: Maybe up to an arbitrarily small change of its density, any swimmer can approximately tracks any given trajectory by combining suitably at most five basic movements that can be generically chosen (no macro shape changes are prescribed in this statement).
Keywords :
hydrodynamics; marine systems; momentum; motion control; 3D weighted shape changing body motion; dynamical system; fluid-swimmer system; freestyle swimming; generic 3D swimmers; momentum exchange; perfect fluid; superimposed deformations; synchronized swimming; Aerospace electronics; Equations; Harmonic analysis; Shape; Symmetric matrices; Trajectory; Vectors;
Conference_Titel :
American Control Conference (ACC), 2012
Conference_Location :
Montreal, QC
Print_ISBN :
978-1-4577-1095-7
Electronic_ISBN :
0743-1619
DOI :
10.1109/ACC.2012.6315435