Bio-Inspired Pressure Sensing for Active YawControl of Underwater Vehicles

Amy Gao, Michael TriantafyllouDepartment of Mechanical EngineeringMassachusetts Institute of Technology

Cambridge, Massachusetts 02139{arg, mistetri}@mit.edu

Abstract—A towed underwater vehicle equipped with a bio-inspired artificial lateral line (ALL) was constructed and testedwith the goal of active detection and correction of the vehicle’sangle of attack. Preliminary experiments demonstrate that a lownumber of sensors are sufficient to enable the discriminationbetween different orientations, and that a basic proportionalcontroller is capable of keeping the vehicle aligned with thedirection of flow. We propose that a model based controllercould be developed to improve system response. Toward this, wederive a vehicle model based on a first-order 3D Rankine SourcePanel Method, which is shown to be competent in estimating thepressure field in the region of interest during motion at constantangles of attack, and during execution of dynamic maneuvers.To solve the inverse problem of estimating the vehicle orientationgiven specific pressure measurements, an Unscented KalmanFilter is developed around the model. It is shown to provide aclose estimation of the vehicle state using experimentally collectedpressure measurements. This demonstrates that an artificiallateral line is a promising technology for dynamically mediatingthe angle of a body relative to the oncoming flow.

I. INTRODUCTION

Over millions of years, the bodies and brains of fishhave evolved in many ways to achieve the objectives whichrender them capable of survival in the diverse and hostileenvironments of the oceans, rivers and seas. A few of themost difficult objectives, which engineers and roboticists havestriven to achieve for underwater vehicles and robotic fish inrecent years, include station keeping under large perturbations,rapid maneuvering, power-efficient endurance swimming, andtrajectory planning and tracking [1]. These challenges must beaddressed through careful consideration and implementationof sensory capabilities, actuation, and control and planningmechanisms.

While research in actuation has yielded many underwatervehicles that are capable of high speeds and/or fast turns [2]–[5], considerably less research has pursued the developmentand application of the underwater sensory systems that wouldbe critical to the autonomy of such vehicles in oceanic orlittoral environments. The majority of autonomous underwatervehicles (AUVs) today use sonar and vision for imaging andnavigation. However, these sensing systems are limited byblind zones, dark and murky environments, and processingspeed. For this reason, they are very powerful when used onlarge vehicles for the illumination of a global environment,but they face the shortcomings of being difficult and time-

consuming to interpret, incapable of operating in all environ-ments, and occasionally too slow to sense dangers in time.

Among the sensors fish are equipped with, there are visual,olfactory, acoustic, and tactile sensors, as well as an inner earfor maintaining orientation. But perhaps the most intriguing isthe lateral line system common to all fish (Fig. 1). The lateralline consists of tens or even hundreds of hair cell sensors calledneuromasts distributed over the body of the fish, with someof them located on the surface of the skin and others withinsubdermal canals.

Fig. 1. A photograph of a blind cavefish, overlaid with the approximatelocation of the canal lateral line and neuromasts within it [6].

The lateral line has been shown to be fundamental to manyfish behaviors, including object detection [7], the localizationof moving prey and predators [7]–[9], schooling [10], rheo-taxis [11], analysis of surface waves [12], and environmentalmapping [13]. With this sensor, even blind fish, such asAstyanax mexicanus, are rendered capable of behaviors such asnavigating through complex environments (Fig. 2), respondingto dangers and foraging for prey [6], [14].

The development of an artificial lateral line (ALL) couldtransform underwater robotics, as it offers the advantages ofsmall size, low weight, competitive pricing, and low bandwidthrequirements. Supplementing traditionally used sensors withan ALL would tremendously enhance the capability of AUVsto operate in all environments, with improved speed andmaneuverability.

To this end, several past studies have centered on the devel-opment of microelectromechanical systems (MEMS) technol-ogy for the creation of an artificial lateral line [15]–[18], andthe ability of these developments to track a stimulus sourcesuch as a mechanical dipole [19], [20], or to navigate andidentify vortices or objects [21], [22]. They have demonstrated

the feasibility of the artificial lateral line, but also highlightedthe complexity of the inherent hydrodynamics, which mustbe mathematically defined, for development of appropriatecontrol systems.

The present research falls within the overarching goalof applying hydrodynamic theory in developing the controlalgorithms necessary for using an ALL effectively to navigateunderwater. We specifically focus on the application of thelateral line concept to mediating the angle of a body relativeto the oncoming flow.

Fig. 2. Blind cavefish in their natural environment (image source: OpenCagePhotography).

II. TESTBED CONSTRUCTION AND EXPERIMENTS

To address the goal of estimating and correcting a vehicle’sangle of attack, the testbed aims to act as a simplistic replicaof the fish’s cranial lateral line system. We choose to focuson the cranial system because its location imparts upon itexceptional sensitivity to pressure fluctuations resultant ofchanges in orientation. In fish, the cranial lateral line systemis elemental in anticipating dangers and changes in flow, andis postulated to be critical in activities such as shoaling, preydetection and obstacle avoidance [23].

A. Vehicle Design

The testbed consists of a towed underwater vehicle (mea-suring 0.7 m long by 0.15 m diameter) with five off-the-shelf pressure sensors (Freescale MPXV7007) mounted atthe head (Fig. 3). The MPXV7007 sensors are monolithicsilicon piezoresistive transducers in a thermoplastic (PPS)surface mount package. They feature a range of -7 to 7 kPaand 5% maximum error over 0◦ to 85◦C, and are internallyamplified to output a signal between 0.5 and 4.5 V. Since thesensing unit is not amenable to water exposure, the sensorsare mounted on a board within the vehicle, and the surfacepressures are transmitted from the surface ports via thin tubesfilled with air. The analog signals are read by an NI USB-6009 data acquisition unit, and processed using code writtenin LabVIEW (National Instruments, Austin, TX).

Fig. 3. A computer-generated rendering of the vehicle constructed forexperiments.

B. Experimental Setup

The experiments were carried out in the MIT Towing Tank,a 30 m long pool that is approximately 1.2 m deep (Fig.4). The testbed is mounted to a carriage with streamlined

Fig. 4. The towing tank facility in which the experiments were conducted.

aluminum tubing, and the carriage is towed at a fixed rateof 1 m/s for all experiments. A Copley STA2510 direct drivemotor mounted to the carriage actuates the vehicle in yaw,to achieve or maintain various angles of attack. A positionsensor within the motor allows for angular position feedback.A computer and other supporting hardware are also locatedon the carriage for vehicle control and data processing (Fig.5). Pressure measurements were logged at a sampling rate of1000 Hz.

C. Preliminary Experiments

The preliminary tests consisted of 33 quasi-static angleof attack experiments - 3 tests each at two degree intervalsbetween 0 and 20 degrees, in order to observe the relationshipbetween yaw angle and pressure at the five sensor locations.These experiments demonstrated the existence of a strong

Fig. 5. A diagram of the experimental setup.

relationship between the angle of the vehicle and the pressuredifference between the left and right sides of the vehicle(hereby referred to as the differential pressure). This in turnsuggested that a Braitenberg type controller [24] might beable to regulate the angle of the vehicle by simply applying aproportional gain to the differential pressure observed.

A second set of experiments was conducted to test thisconcept. A proportional controller was developed in LabVIEWand implemented on the system, with the goal of returningthe vehicle to zero degrees following any perturbations andmaintaining that orientation. With this controller implemented,the vehicle was found to accomplish this goal (Fig. 6), but witha varying time lag. Furthermore, at higher gains, the systembecame unstable. This demonstrated the shortcomings of theBraitenberg controller, and suggested that a more complex,model-based controller would be required for improved systemresponse.

Fig. 6. A Braitenberg controller aligns the vehicle with the flow followingthree large perturbations, which can be seen as variations of the dotted line,the actual angular position. The blue line represents the averaged differentialpressure, which the proportional gain is applied to.

To investigate the pressure fluctuation during dynamic ma-neuvers, a final set of experiments was conducted in whichthe vehicle was commanded to turn sharply from 0 to 20

Fig. 7. The NMP-like response seen in the sensor output when the vehicleturns. This results in initial angle correction in the wrong direction with theP controller, which is a cause of delayed response and possible instability.

degrees while being towed forward at 1 m/s. The differentialpressure measured in one experiment is shown in Fig. 7.These experiments revealed that when the vehicle turned fromone static angle to another, the differential pressure responseexhibited initial undershoot, a characteristic often seen innon-minimum phase (NMP) systems, which are generallychallenging to control due to additional phase lag and limitedachievable closed-loop bandwidth. The similarities in the re-sponse of this system suggest that while a generic controller iscapable of maintaining the vehicle at zero degrees, a nonlinearmodel-based controller would be ideal, allowing for fasterperformance, robustness, and the ability to control turning tospecific angles.

III. PANEL METHOD FORWARD MODELING

A model-based controller requires a good model, and a goodmodel of the system should be capable of outputting relevantpressures, provided the system state over time. The clearnonlinearities in the problem and the infinite-dimensionality ofthe water suggest that a computational fluid dynamics (CFD)approach would be necessary for accurate results.

Several different types of CFD were investigated, includingpanel methods, full potential codes, finite volume methods,and finite element methods. A panel method was ultimatelychosen for the model for its flexibility, speed, and simplicity.

A. 3D Rankine Source Panel Method

We assume in this work that the flow is incompressible,inviscid, irrotational, and can therefore be completely definedby a hydrodynamic potential φ. Furthermore, because theReynolds number in the region of concern is high (measured atapproximately 150,000), we assume that the flow at the frontof the vehicle is fully attached, so the inviscid assumption ishighly accurate.

The vehicle is modeled using a first-order 3D RankineSource Panel Method, a well-studied method of simulatingincompressible potential flow [25], [26]. With this method, a3D body is discretized into a number of panels, which aremodeled as constant strength singularities. The potential at

Fig. 8. The pressure field over the surface of the vehicle as it turns from 0 to 20 degrees, with the profile of the turn shown in the lower left hand plot. Inparticular, note how the high pressure region shifts first to one side and finally settles on the other side at the front of the vehicle. The diagonal lines in thebackground show the direction of the oncoming flow.

any point due to each panel is obtained by integrating overthe panel, and the final potential at some point ~x comes fromsumming the influences of each individual panel. In integralform, this is written:

φ(~x, t) =

∫S

σ(~ξ, t)G(~x, ~ξ, t)dS (1)

Where φ is the vehicle disturbance potential, σ represents thesource strength of some point on the body surface S, ~ξ is thevector to that point on the body, and G is Green’s Function (thevelocity potential of a point source). Constant strength sourcepanels were selected over dipole panels for their ability togenerate smoother simulation data, and the lack of necessityfor simulating vorticity.

For this, we choose a coordinate system which is fixed tothe rotational center of the vehicle, but which maintains afixed angular position with reference to the inertial frame. Theboundary value problem (BVP) is summarized as follows:

In the fluid, continuity yields:

∇2Φ = 0 and ∇2φ = 0 (2)

Where Φ is the total fluid potential, given as:

Φ(~x, t) = −Ux+ φ(~x, t) (3)

U is the vehicle velocity in the inertially fixed x direction. Onthe surface of the body, the no-flux condition yields:

∂Φ

∂n(~x, t) = ~v(~x, t) · ~n(~x, t) (4)

Where ~n is the vector normal to the surface of the body atsome point of interest, and ~v is the water velocity at somepoint of interest. Finally, substituting the boundary conditionsinto the source panel method formuation (1) gives the finalboundary value equation for the problem:∫

S

σ(~ξ, t)∂G

∂n(~x, ~ξ, t)dS

=∂φ

∂n(~x, t) = Unx(~x, t)− ~v(~x, t) · n(~x, t) (5)

This condition is solved numerically by discretizing thebody geometry into 620 panels, assuming constant singularitystrength over each panel, integrating over each panel to calcu-late its effect, and summing the contributions of each panel tosolve for the hydrodynamic potential at some point of interest.In effect, the right hand side of equation (5) is represented asthe matrix Bi, for i = 1, 2... N (where N = 620 panels), andthe BVP can be rewritten:

N∑j=1

σ(~ξ, t)

∫Sj

∂

∂n(~x, t)G(~x, ~ξ, t)dS(~ξ, t) = Bi (6)

The integral term in the left hand side of equation (6) rep-resents the influence of each panel j at each control pointi, and when discretized appropriately, it can be written asa matrix Pij , the influence coefficient matrix. Discretizationof this integral term is complex and time-consuming, but ananalytically correct expansion is given by Hess and Smith [26].This results in the final discretized matrix equation:

N∑j=1

σjPij = Bi (7)

which is solved to obtain the source strengths of each panel,σj . These values are subsquently substituted back into equa-tion (7) to solve for the fluid velocity over the surface ofthe vehicle, which can then be used in Bernoulli’s unsteadypressure law to solve for the surface pressure:

P = −ρ(∂φ

∂t+

1

2|∇φ|2 + gz

)(8)

In (8), ρ is the water density, g is the gravitational accelerationconstant, and z is the current water depth.

While this method is straightforward to implement, specialcare must be taken in the case of rotating bodies or flows.In these cases, regardless of the reference frame chosen, it isrequired to update the surface normal velocity at each instant,which is a function of the oncoming flow and the body motion.

Several simulations were performed to visualize the pressurefield over the surface of the vehicle during a high speed turn.

Fig. 9. Simulated (green) and experimentally measured (blue) pressure observed at 4 pressure sensors during a turn from 0 to 16 degrees and back to 0degrees. Pressure (Pa) is plotted against time (s). The blue arrow represents the direction of oncoming flow.

The pressure field throughout one of these turns is displayedin Fig. 8.

Furthermore, simulations were performed and comparedwith experimental data for model validation. Simulations con-ducted at static angles of attack and constant oncoming flowvelocity (1 m/s) matched experimental data very well. How-ever, the more interesting case is that of the vehicle executingdynamic maneuvers, and to validate the model for these cases,a set of experiments and simulations were conducted with thevehicle performing turns at varying rates. Fig. 9 shows thestrong consistency between the experimental and simulatedpressure measurements for a turn to 16 degrees and backto 0 degrees. The nonlinear pressure fluctuations during theturns are well captured by the simulation. The oscillationsseen in the measurements are a result of mechanical vibrationsduring the experiment. The full set of these simulations servedto sufficiently validate the accuracy of the system model, arequirement for good observer and controller performance.

IV. KALMAN FILTER INVERSE MODELING

The Kalman Filter is an optimal observer, which recursivelyestimates the state of a system or process in a way thatminimizes the mean squared error. It is unique among filters inbeing a purely time-domain filter, requiring only the previousstate estimate and the current measurement at each time step.The standard Kalman Filter requires the state transition andobservation models of the system, which must be representedin linear matrix form. Where the system is nonlinear, anExtended Kalman Filter (EKF) can still produce relativelyaccurate results, by using Jacobian matrices as a linearizedrepresentation of the non-linear functions around the currentestimate. Where the functions are highly nonlinear, or it is dif-ficult to calculate its partial derivatives, an Unscented KalmanFilter (UKF) can be used. The UKF uses a deterministicsampling technique known as the unscented transform, whichoperates on the idea that a probability distribution is easier toapproximate than an arbitrary nonlinear function [27]. Withinthis approach, a number of sigma points which encode themean and covariance are first selected around the estimatedstate. These sigma points are then propagated through the exactnonlinear state transition and observation functions, to yield

the new state estimate. This allows for the propagation of meanand covariance information, resulting in greater accuracy andease of implementation, with the same order of calculationsas the EKF.

Within this application, an Unscented Kalman Filter is usedto estimate the system states (yaw angle θ and yaw rate θ),given four pressure measurements from the surface of thevehicle. The generalized state transition model is written as:

~xk+1 = f [~xk, ~uk] + ~wk (9)

Where ~x is the vehicle state, k is a discrete timestep, f is thenonlinear state transition function, ~u is the control input, and~w is the process noise associated with the system. For thissystem, the explicit state transition model is:

x1,k+1 = x1,k + x2,k · dt (10)

x2,k+1 = x2,k +

(τ

J +m66− x2,kJ +m66

Um66 cosx1,k

− 1

2(J +m66)(m22 −m11) sin 2x1,k

)· dt (11)

Where x1 is the yaw angle θ, x2 is the yaw rate θ, τ is themodel abstraction representing the amount of torque output bydeliberate vehicle actuation, and dt is the time elapsed sincethe last measurement update. J , m66, m11, and m22 are theinertial and added mass vehicle parameters estimated as:

m11 = 0.927 kgm22 = 9.12 kgm66 = 7.17 · 10−2 kg ·m2

J = 0.627 kg ·m2

These are estimated from the vehicle geometry and the slenderbody approximation, as defined by Newman [28].

As such, this model accounts for motions resulting froma known control effort, as well as added mass effects fromknown vehicle motion, but it does not account for the unknowndisturbances to vehicle angle or external current. A slightlyimproved model which also takes into account the dynamicsof helical vortices that form at the back of the vehicle duringturns can be formulated as described by Hoerner [29].

The generalized observation equation is:

~zk = g[~xk] + ~vk (12)

Where ~z is the vector of the pressure measurements, g is somenonlinear transformation, and ~v is the vector of associatedmeasurement noises. The explicit observation model is morecomplex; it incorporates the panel method system model previ-ously derived, which produces a set of pressure measurements,given the system state and relevant parameters. Presently, theimportance of an accurate system model becomes apparent.Since the state transition model is incapable of modelingdisturbances to the system, the measurements will be fullyresponsible for capturing their effect, and the panel methodmodel must then accurately decipher the pressure measure-ments in producing a corrected estimate.

The full UKF description is provided by Julier [27], so onlyan outline of the process is reproduced here.

First, a symmetric set of 2N sigma points with equalweights is generated, and instantiated through the processmodel (9) and observation model (12), using the standardunscented transformation. This produces the a priori stateestimate xk and the estimated measurement zk.

The innovation covariance (covariance of predicted mea-surements) is calculated as:

P zk =

p∑i=0

W (i)(z(i)k − zk)(z

(i)k − zk)T (13)

Where p is the number of sigma points and W (i) representsthe weight of each. The a priori state covariance matrix is:

Pk =

p∑i=0

W (i)(x(i)k − xk)(x

(i)k − xk)T (14)

And the cross covariance matrix is given as:

P xzk =

p∑i=0

W (i)(x(i)k − xk)(z

(i)k − zk)T (15)

These are used to update the state using the normal Kalmanfilter update equation:

xk = xk +Kk(zk − zk) (16)

Where zk is the vector of actual measurements, and Kk is theKalman gain matrix, given by:

Kk = P xzk (P z

k )−1 (17)

The a posteriori covariance matrix is:

Pk = Pk −KkPzkK

Tk (18)

The state estimate (16) and the covariance (18) are updatedat each timestep, given the new set of pressure measurements.In applying this filter, we make the assumption that theoncoming flow velocity is a constant 1 m/s, to reduce theorder of the system at hand. However, the Kalman Filter couldeasily be extended to estimate flow velocity and accelerationas additional states.

Within the filter, the process (Q) and measurement (R) noise

covariance matrices for the system are estimated to be:

Q =

[0.5 00 0.25

]deg, deg/s (19)

R =

3 0 0 00 3 0 00 0 3 00 0 0 3

Pascals (20)

Changing these parameters affects the UKF performance tosome degree. Typically, overestimation of the measurementnoise results in less oscillation of the estimate, but moredelay in convergence. When the estimated process noise isinaccurate, the estimated angle experiences some delay orsimply does not converge to the actual angle.

The application of the UKF with the parameters shownyields a reasonably accurate estimate, with oscillations aboutthe actual state on the order of the measurement noise, aspredicted (Fig. 10). These oscillations could be filtered out tosome extent with an additional low-pass filter for a smootheroverall estimate. A smoother estimate would improve robust-ness and stability when the estimate is used in conjunctionwith a PID controller for system control.

Fig. 10. A comparison between the actual angle the vehicle is at during anexperiment, the estimated angle as produced by the Unscented Kalman Filter,and the estimated angle as produced by the proportional estimator.

Fig. 10 shows a comparison between the estimate the UKFis capable of producing and the estimate which was usedwith the Braitenberg controller described previously. Due tothe nonlinear nature of the system, the gain which must beapplied to the system at a static angle of attack varies with theangle. As the angle increases, the gain must increase as well.This results in higher deviations of the estimate as the angleof attack grows larger. Furthermore, with the proportionalestimator, the dynamic responses observed in the pressureduring sudden turns results in an estimate that initially movesin the direction opposite to which the vehicle is turning, ascan be seen. The UKF is able to resolve both of these issues.

Through additional simulations, we also demonstrate thatthe noise in the estimate can be reduced by the use ofadditional sensors, as is expected.

V. CONCLUDING REMARKS

This project serves to demonstrate the feasibility of using anartificial lateral line to mediate angle of attack in underwatervehicles. A 3D Rankine Source panel method model wasproduced which was shown to be capable of simulating theflow field around the head of an underwater vehicle accurately.This model was applied to the problem of state estimationthrough an Unscented Kalman Filter, and it was shown toproduce a far better estimate than a previously developedproportional estimator. The filter is limited by the intensityof the measurement noise, but this can be reduced by usinga greater number of sensors. In conjunction with a PIDcontroller, the UKF should be capable of reducing time delaysand improving stability within the system.

Further work remains to be done in optimization of thepanel method model. A less complex model which utilizes alower number of sensors would be less accurate but faster.Alternately, compilation of a detailed lookup table could beused to inform the UKF, eliminating the necessity of resolvingthe panel model at each instant in time. Furthermore, thespeed of the simulation can be improved by implementingfar field approximations within the panel method [25]. Testsalso remain to be performed to quantify and optimize theaccuracy and robustness of the system. Following these steps,the UKF could be incorporated into a real-time control systemfor implementation on the test vehicle.

This project has demonstrated the practicality of an ALL inone application - the detection and correction of a vehicle’sangle of attack. In particular, it has shown that an exceptionallysimplistic and low-cost sensing system inspired by a fish’scranial lateral line is capable of producing fast feedback,which can be used, with an understanding of hydrodynamics,to control an underwater vehicle. Additional research in thehydrodynamic theory surrounding fluid motion around objects,in wakes, and in dynamic environments can be used to informcontrol systems for a variety of tasks for future AUVs.

ACKNOWLEDGMENT

This project was supported by SeaGrant, the Singapore/MITAlliance for Research and Technology (SMART), the WilliamI. Koch Chair Funds, and the National Science FoundationGraduate Research Fellowship under Grant No. 0645960.

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