A comparative study of planar waveforms for propulsion of a joined artificial bacterial flagella swimming robot

Artificial bacterial flagella (ABF) is one of the more interesting alternatives for the design of swimming nano and microrobots moving in life environments. In this paper the propulsion of an ABF swimming robot is studied by considering four different travelling waves: harmonic (from Eukaryotic cells), linear and quadratic amplitude modulation (from Carangiform swimmers), and a novel fractional order amplitude growing. The last one, proposed in this paper, allows to preserve, in a different way, two important propulsion properties: 1) the flagellum head is always maintained at zero amplitude (boundary condition), and 2) the wave amplitude along the flagellum can be modulated. A comparison of the propulsion performance obtained with each wave, in terms of the mechanical power developed by the robot and the electrical power supplied to actuators, is given in order to demonstrate that the fractional travelling wave seems to be the most effective for propulsion. For simulation purposes, the robot is modeled by using Simscape, a physical modeling tool included in the Matlab/Simulink package.