Distributed Flow Sensing Using Bayesian Estimation for a Flexible Fish Robot

Flexibility plays an important role in fish behaviors by enabling high maneuverability for predator avoidance and swimming in turbulence. In this paper, we present a novel, flexible fish robot equipped with distributed pressure sensors for flow sensing. The body of the robot is made of a soft, hyperelastic material that provides flexibility. The fish robot features a Joukowskifoil shape conducive to modeling the fluid analytically. A quasisteady potential-flow model is adopted for real-time flow estimation, whereas a discrete-time vortex-shedding flow model is used for higher-fidelity simulation. The dynamics for the flexible fish robot are presented, and a reduced model for one-dimensional swimming is derived. A recursive Bayesian filter assimilates pressure measurements for estimating the flow speed, angle of attack, and foil camber. Simulation and experimental results are presented to show the effectiveness of the flow estimation algorithm. INTRODUCTION Fish have attracted scientific attention for their graceful locomotion, high maneuverability, and high energy efficiency. Inspired by nature, engineering researchers have made great efforts in designing and developing fish robots [1–5] that mimic real fish in order to improve the performance of underwater vehicles. Fish robots are typically designed in two segments. The front segment holds the electronic components, including a bat∗Address all correspondence to this author. tery, a micro-controller, navigational sensors, etc., whereas the back segment serves as the fish tail, usually flapped by a servo motor to provide thrust [3–5]. Although the multi-segment design is able to realize fish-like swimming motion by flapping the tail segment, the maneuverability achieved is still far less than real fish. We know that flexibility plays an important role in fish behaviors by enabling high maneuverability for predator avoidance and swimming in turbulence. In this work, we describe a novel, flexible fish robot that deforms its body in a continuous way. The flexibility of the body is achieved by the property of the material of the robot, rather than the rotational links between rigid parts. In this paper, we choose silicone rubber for the material and select a Joukowski foil [6] for the shape. This choice of shape is conducive to modeling the fluid dynamics. Flow sensing is important for fish to navigate in unknown, murky, and cluttered environments [7]. However, traditional submarines do not have this capability. Sonar is unsuitable for a fish robot due to its large cost, power consumption, and size [8]. Additionally, sonar may not provide accurate measurements at low speeds. Inertial measurement units (IMUs) accumulate errors over time due to dead reckoning [8]. In addition, IMUs do not provide information pertaining to the flow environment. The lateral line is a flow-sensing organ that fish use to detect movement and vibration in the surrounding water [7]. The recent development of artificial lateral-line systems shows promise for the application of flow sensing to underwater robots [9, 10]. In our previous work, we studied rheotaxis (i.e., aligning up1 Copyright © 2015 by ASME stream [10]) with a steady, rigid Joukowski-shaped fish robot by estimating the flow field using an artificial lateral-line system made of distributed pressure sensors [9, 10]. In this work, we extend the previous research to a flexible Joukowski-shaped fish robot with one-dimensional, free-swimming dynamics. This paper presents two flow models of a flexible, foilshaped fish robot: a quasi-steady potential-flow model and a higher-fidelity vortex-shedding model. The quasi-steady potential-flow model is adopted for flow estimation due to its tractability, whereas the vortex-shedding model is used in simulation to generate the flow field as ground truth for testing the flow estimation algorithm. The deformation of the robot body is modeled using a time-varying parameter (the camber ratio) A recursive Bayesian filter assimilates the distributed pressuresensor measurements. A testbed consisting of a flow tank, gantry system, and air-bearing linear guide is used to demonstrate onedimensional swimming. The experimental results show the effectiveness of the flow-sensing algorithm during flapping motion of a flexible fish robot. FLOW MODEL FOR A JOUKOWSKI-SHAPED FLEXIBLE FISH ROBOT This paper adopts the shape of a Joukowski foil for the design of the fish robot in order to utilize potential-flow theory to model the flow field. In fluid dynamics, potential-flow theory [6] describes the velocity field of incompressible, irrotational flow as the gradient of a scalar function, the velocity potential. This section describes the two-dimensional flow past a cambered Joukowski foil, first using the quasi-steady potential-flow method and then using the unsteady vortex-shedding method. Quasi-steady Potential-flow Model The fish robot modeled as a Joukowski foil takes the shape of the output of the Joukowski transformation of a circle. The Joukowski transformation, which is essentially a conformal mapping, is expressed as [6]