Source seeking for a three-link model of fish locomotion

We present a method of locomotion control for underwater vehicles which are propelled by a periodic deformation of the vehicle body, similar to the way a fish moves. The control law employs extremum seeking, which is a non-model based method that has been used recently in ldquosource seekingrdquo control for nonholonomic mobile robots. In this paper we present a design for a fish model consisting of three rigid body links and employing a two degree of freedom, non-reciprocal, movement which propels the fish through a perfect fluid without the use of a Kutta condition to shed vortices. In a companion paper we present results for a second fish model based on a Joukowski airfoil which has only one degree of freedom in its movement, and thus relies on vortex shedding to move through a perfect fluid. With the use of extremum seeking, we achieve the same results in each case: The fish is capable of performing dasiasource seekingpsila in GPS-denied underwater environments, and, if position measurement is available, it is capable of navigating from point A to point B, as well as along a predetermined path.