A Simple Physical Model for Control of a Propellerless Aquatic Robot

Abstract

This paper is concerned with the motion of an aquatic robot whose body has the form of a sharp-edged foil. The robot is propelled by rotating the internal rotor without shell deformation. The motion of the robot is described by a finitedimensional mathematical model derived from physical considerations. This model takes into account the effect of added masses and viscous friction. The parameters of the model are calculated from comparison of experimental data and numerical solution to the equations of rigid body motion and the Navier – Stokes equations. The proposed mathematical model is used to define controls implementing straight-line motion, motion in a circle and motion along a complex trajectory. Experiments for estimation of the efficiency of the model have been conducted.

Serpentine motion of a trimaran robot

“…The value of frequency, for which the maximum speed is reached (1.8 s 21 ), is relatively close to that obtained in calculations (1.5 s 21 ). Thus, the model (10), in spite of its simplicity, reveals steady propulsion mode, provides qualitative agreement with the experiment. Hence, the further development of this model is promising and worth the effort.…”

“…x(0) = V 0 , where V 0 is a small positive value. A periodic solution is sought for by direct numerical integration of (10). A rather long time interval is taken to ensure that the trajectory gets into a small enough vicinity of this periodic solution.…”

“…Note that Golovanov et al 33 discusses a system which can be obtained from (10) if h = 0 (the capsule is not submerged in water), c 2 = 0 (the counterelectromotive force of the motor is not taken into account), the control is given by (11), and it is shown that there exists a trajectory corresponding to directional propulsion of the robot along the OX axis. The values of parameters used for simulation in Golovanov et al 33 differ considerably from (12), and no parametric analysis is performed.…”

“…In some works, [9][10][11] an airfoil-shaped vibrational robot controlled by one internal flywheel is considered. Oscillations of the flywheel result in oscillations of the robot body, which produce the thrust force sufficient to maintain the directional motion.…”

“…They are based, in particular, on calculation of circulation, and taking into account trailing vortices and/or added masses. 9,10 There exists a modification of an airfoilshaped robot with a passive movable element 15,16 that demonstrates quite good characteristics in maneuverability as compared to many other autonomous swimming devices. 17 All above mentioned papers consider the swimming motion of objects with a cross-section representing a single-connected domain.…”