Localization of a leading robotic fish using a pressure sensor array on its following vehicle

The tail-flapping propulsion of a robotic fish forms a hydrodynamic pressure field that depends primarily on the flapping frequency and amplitude. In a two-robot aligned group, the tail of the front robot generates an oscillating pressure that is detectable by its follower. This paper proposes a position estimator for the follower to locate the position of the leading robotic fish. The position estimator uses the hydrodynamic pressure measured on a sensor array installed on the forefront of the following vehicle body. We derive a potential flow model to describe the pressure field of the leader in the presence of the follower. Using this pressure field model, we further derive an observability measure which is used to determine the relative positions of the leader and follower for which the position estimator will produce a reliable estimate. The position estimator employs the Levenberg-Marquardt algorithm, due to the nonlinearity of the pressure model. Results from the observability analysis show that a satisfactory estimation of the leader position is achieved when the leader is located directly ahead, on the starboard-bow, or the port-bow of the follower, similar to the formation pattern generally found in a school of fish. The observability analysis also shows that poor estimation is obtained when the leader is abeam of the follower. Tank experiments confirm the observability analysis and also demonstrate the use of the position estimator for feedback control by the follower.