Fish Like Aquatic Robot Demonstrates Characteristics of a Linear System

In the recent past the design of many aquatic robots has been inspired by the motion of fish. In some recent work the authors described an underactuated planar swimming robot, that is propelled via the motion of an internal rotor. This robot is inspired by a simplified model of the fluid-body interaction mediated by singular distributions of vorticity. Such a model is a significant simplification of the fluid-structure interaction that can be understood using resource intensive numerical computations of the Navier Stokes equation that are unwieldy from a controls perspective. At the same time the simplified model incorporates the creation of vorticity and interaction of the body with the vorticity which many control theoretical models ignore. In this paper we show that despite the complexity of the interaction between the aquatic robot and the ambient vorticity in a fluid, the response of the robot is a nearly linear function of the control input. This surprisingly simple feature emerges in our theoretical model and is validated by our experimental data of the motion of the robot. This simplifying observation is an important step towards developing control algorithms for aquatic robots.