Bioinspir. Biomim. 11 (2016) 055001 doi:10.1088/1748-3190/11/5/055001

PAPER

Enhanced detection performance in electrosense through capacitivesensing

YangBai1, IzaakDNeveln2,Michael Peshkin1 andMalcolmAMacIver1,2,3,41 Department ofMechanical Engineering, NorthwesternUniversity, Evanston, IL, USA2 Department of Biomedical Engineering, NorthwesternUniversity, Evanston, IL, USA3 Department ofNeurobiology, NorthwesternUniversity, Evanston, IL, USA4 Author for correspondence.

E-mail:maciver@northwestern.edu

Keywords: artificial electrosense, capacitive sensing, object identification, underwater robotics

Supplementarymaterial for this article is available online

AbstractWeakly electricfish emit anAC electric field into thewater and use thousands of sensors on the skin todetect field perturbations due to surrounding objects. Thefish’s active electrosensory system allowsthem to navigate and hunt, using separate neural pathways and receptors for resistive and capacitiveperturbations.We have previously developed a sensingmethod inspired by theweakly electric fish todetect resistive perturbations and now report on an extension of this system to detect capacitiveperturbations as well. In ourmethod, an external object is probed by anACfield overmultiplefrequencies.We present a quantitative framework that relates the response of a capacitive object atmultiple frequencies to the object’s composition and internal structure, andwe validate thisframeworkwith an electrosense robot that implements our capacitive sensingmethod.Wedefine ametric for comparing the electrosensory range of different underwater electrosense systems. Fordetecting non-conductive objects, we show that capacitive sensing performs better than resistivesensing by almost an order ofmagnitude using thismeasure, while for conductive objects there is afour-fold increase in performance. Capacitive sensing could therefore provide electricfishwithextended sensing range for capacitive objects such as prey, and gives artificial electrolocation systemsenhanced range for targets that are capacitive.

1. Introduction

Sensory systems transduce the energy of their effectivestimulus along multiple dimensions of the stimulusenergy. These dimensions are sometimes indepen-dently analyzed by parallel processing pathways. Forexample, auditory stimuli have intensity (amplitude)and phase components that are independently pro-cessed by auditory systems (Takahashi et al 1984),while movement processing versus color processing ofvisual stimuli are streamed into different paralleldivisions of the visual system (Merigan and Maun-sell 1993). In electrosense, certain species of freshwaterfish are able to detect nearby objects through thealterations those objects cause to a self-generatedelectric field (Lissmann and Machin (1958); reviews:Turner et al (1999), Krahe and Fortune (2013)). Twokey aspects of the alterations objects can cause to a self-

generated field are, first, a change in amplitude of thevoltage detected at electroreceptors scattered over thebody surface, and second, a change in phase (withrespect to the emitted field’s phase) at electroreceptors(figure 1). These two aspects are analyzed by twoparallel pathways: ‘P-type’ afferents encode changes inamplitude, while ‘T-type’ afferents encode changes inphase (Scheich et al 1973), with some overlap (CarlsonandKawasaki 2008).

For example, nearby objects that are either lessconductive or more conductive than the surroundingwater cause large amplitude perturbations, resulting inlarge changes in voltage at electroreceptors, and largechanges in the corresponding P-type sensory afferent’sfiring rate, while far objects cause small amplitude per-turbations and correspondingly smaller changes in fir-ing rate. Objects similarly differ in how much theychange the phase of the emitted field. Objects without

RECEIVED

18May 2016

REVISED

29 June 2016

ACCEPTED FOR PUBLICATION

6 July 2016

PUBLISHED

8August 2016

© 2016 IOPPublishing Ltd

capacitance, such as water, or pure conductors orinsulators, cause only an amplitude perturbation andnot a phase perturbation. However, most living organ-isms, such as the prey eaten by electric fish, differ inconductivity compared to water but also have capaci-tance due to the presence of less conductive bodyexteriors and cellular membranes, and can thereforecause a perturbation in the amplitude and phase atelectroreceptors (von der Emde 1990, 1998, Nelsonet al 2002).

The neural pathways for processing amplitudeperturbations have been more extensively character-ized than those that process phase perturbations.Similarly, robots implementing electrosense havefocused on sensing amplitude perturbations (Solberget al 2008, Boyer et al 2012, 2013 Neveln et al 2013),although an algorithm based on capacitive electro-sense has been proposed (Ammari et al 2013, 2014).For this study, we devised a robotic electrosense plat-form that canmeasure the phase perturbations causedby capacitive objects. With this system we find thatphase perturbation measurements arising from

objects with capacitance have higher signal to noiseratios (SNR), resulting in enhanced detection andlocalization of capacitive objects (Ammari andWang 2016). Our results point to the possibility that inthe initial stages of prey capture, when targets arefurthest away (MacIver et al 2001), behavior may bemediated by the phase pathway. Enhanced detectiondue to the low noise of the phase component of per-turbations may help explain why prey can be detectedat distances that are beyond what measurements andmodeling of the amplitude pathway suggest should bepossible with that pathway alone (Maler 2009). Con-sistent with this hypothesis, a sensory structure calledthe dorsal filament on the dorsum of weakly electricfish (specifically Gymnotiforms) has been shown to bestudded with sensors that have the anatomical featuresof phase-encoding electroreceptors (Franchina andHopkins 1996). The dorsum of the body, which has ahigher density of electroreceptors than the rest of thetrunk (Carr et al 1982), has been shown to be impor-tant in detection of prey (MacIver et al 2001). Further-more, prior measurements of live prey indicate that

Figure 1.Howobjects differentially affect the amplitude and phase of afish’s electric organ discharge (EOD). On the left, a pebble withan unusual density of conductiveminerals causes an increased current density in the proximal patch of skin of the fish (typical pebblesare primarily silica, which is insulative). The two images show a snapshot of themoment (t = 0)when the objects reach theirmaximumcross-sectional profile as they pass through the horizontal plane of thefish,moving from above to below thefish. Thevoltage over time at the purple dot on the right side of thefish by the pectoralfin is shown in the signals below each case, with t = 0indicated by the vertical black line. For the conductive pebble, the voltage across thefish’s skin increases due to the concentration ofcurrent flow and causes an amplitudemodulation (AM, blue). For the prey (shown larger than real life so that themodulation is stillvisible), there is also an increase in amplitude because prey aremore conductive thanwater, but in addition, due to the prey’scapacitance, there is a phasemodulation (PM, red) as illustrated here. Adapted from figure 1 of Krahe andMaler (2014)withpermission fromElsevier.

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the phase shift they cause to an electric field ismaximalat typical field frequencies of electric fish (MacI-ver 2001,Nelson et al 2002).

A useful analogy for the enhanced performance ofthe phase pathway is to consider how different proper-ties of light are transduced in visual systems (Caputiand Budelli 2006). Sensors that detect only luminanceof light generate gray scale images. Adding the abilityto detect color (light wavelength) increases the con-trast of a colored object in a gray background of similarluminance. Analogously, phase detection in electro-sense should enable a capacitive object to pop out of abackground dominated by purely resistive sources,such as the water in which the fish swims. Prey couldthereby be detected further away than purely resistivedetritus of similar geometry and bulk conductivity.

2.Methods

We know from prior work described above thatelectric fish are sensitive to both the amplitude andphase of field perturbations caused by objects. Thesetwo components of a perturbation clearly exist inde-pendently of the biological details of the fish’s trans-duction system. Here we describe our technicalapproach to measuring these two aspects of voltageperturbations. Our approach does not attempt tomimic themanner in which fish accomplish transduc-tion of amplitude and phase, the biophysical details ofwhich are notwell understood.

In our robotic electrosense system (hereafter Sen-sorPod), the voltage perturbation caused by an

external object is measured by sending the signal froma voltage sensor on one side of the body, and a secondsensor on the opposite side of the robot (figure 2) to adifferential amplifier (Solberg et al 2008). The differ-entially amplified signal is then processed using a syn-chronous detector circuit (also referred to as a lock-inamplifier) to extract the very small changes that rideon top of the large emitted field.

In synchronous detection, the received signal ismultiplied with two reference signals as shown infigure 3. One of the reference signals is identical to theemitted field signal and in phase with it, and the otheris 90 out of phase. See Bai et al (2015) for additionalreferences on synchronous detection.

Intuitively, the in-phase measurement shown infigure 3 is sensitive to both resistive and capacitiveproperties of objects, whereas the out of phase mea-surement is sensitive only to the capacitance of objectsarising from non-zero phase shift f. By measuring therelative magnitude of the in-phase and out-of-phasecomponents, we can compute the phase angle fas f = ( )‐ ‐V Vatan out phase in phase .

2.1. Estimating object capacitance and internalstructureObject capacitance and internal structure are esti-mated when the objects are stationary relative to theSensorPod underwater. The analytical framework toestimate capacitance and internal structure is derivedfrom the framework established in our previous work(Bai et al 2015). Extensions to this framework arepresented in the supplementary material. We brieflydescribe the process here.

Figure 2.The SensorPod electrosensing robot. The robot is suspended from ahigh performance gantry system. Large electrodes ateach end of the robot are emitters, while the smaller circumferential electrodes are sensors. Interior of robot holds a series of customcircuit boards for on-board synchronous detection and other signal processing. Bottom color illustration shows thefive equatorialpairs of electrodes, of which one, S4, was used for themeasurements reported here. Each pair is connected tomeasure the differencebetween the left and right sides of the robot (differentialmode amplification).

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The capacitance of a sphere with a thin film oflayered conductive and dielectric materials can be cal-culated fromobject properties by

p= ( )� �C

R

d

4. 1film rel 0

2

film

�0 is the vacuum permittivity and is equal to´ - -8.85 10 F m12 1. �rel is the relative permittivity of

the dielectric material and is 3.1 for Mylar which wasused in this work to create capacitive spheres. R is thesphere radius and dfilm is the film thickness. Cfilm,which is based solely on object properties, can be com-pared to estimates of capacitance derived from electro-sensorymeasurements.

The key for estimation using the SensorPod is tosweep the frequency of the emitted field until the in-phase channel is zero with non-zero out-of-phasereading. Such a response corresponds to a 90 phaseshift and a purely imaginary point in the frequencyresponse. We call the corresponding frequency of theemitted field the critical frequency fcrit and its angularversion w p= f 2crit crit .

A simple relationship between wcrit and the bulkpermittivity of an object, �bulk, can be derived using afirst-order frequency response model of a sphericalobject in a uniform field (see supplementary materialfor the full derivation):

sw

= ( )� 2, 2bulk

water

crit

where swater is the water conductivity. By determiningwcrit from electrosensory data, we use equation (2) todetermine �bulk of the whole sphere. Assuming a

sphere made of homogeneous dielectric material, wecan express its capacitance as

pp= = ( )� � �C

R

RR

4

22 . 3obj bulk

2

objrel 0

The size of an object can also be estimated fromelectrosensory data (Bai et al 2015). We then compareCobj estimated from electrosensory measurements tothe thin film capacitance Cfilm calculated fromequation (1).

More complex objects may have multiple layers ofdifferent dielectric materials warranting a deeper ana-lysis of the full frequency response. With this addi-tional complexity, the response increases in order (i.e.the number of poles and zeros increases with eachlayer), adding additional features to the frequencyresponse as detailed in supplementarymaterial.

2.2. Analysis of electrosense performanceActive electrosensory system performance can beassessed with respect to two fundamental tasks: objectdetection and estimation of an object’s position. Wefirst define a metric called electrosense sensitivity toquantify the ability to detect objects. We then alsoprovide statistical measures to quantify the quality ofposition estimation.

2.2.1. DetectionSensitivity is the smallest change in signal that ameasurement system can detect. This change in thesignal must overcome baseline noise levels that arepresent in the absence of objects. Here, we investigatethe ability of our artificial electrosense device to detect

Figure 3. Illustration of the two channel weak-signal detectionmethod of synchronous detection used in the SensorPod. An emitted1 kHz sinusoidal voltage (green) at±2 V amplitude passes through thewater (amplitudes shownhere for illustration purposes only;actual voltages used differ). For prey (top row), there is a phase shift (here 32° for example) as well as an amplitude perturbation (here areduction in voltage by a factor of 1

2). Themeasurements (red line) in the in-phase (left) and out-of-phase channels (right) are

multiplied by the emitted signal (blue line) and low-pass filtered to obtain themean of the detected signal (black line). Themeasurements across the two channels enable the calculation of the phase angle by the equation shown on the right, and capacitanceof the object. For the pebble (bottom row), there is only the factor of 1

2decrement in the emitted voltage and reversal of polarity due to

it being a net insulator, but no out-of-phase component, leading to a reading of- 1

2the emitted voltage at =180 0 phase angle.

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the presence of an external object. Intuitively, thesmaller and further away an object, the harder it is todetect. In this work, for an object of a certain size, weexperimentally determine the maximum distance thatyields a detectable signal. We can also estimate thesmallest object that could be detected at a fixeddistance using scaling relationships between the volt-age perturbation and the size, composition, anddistance of the object. We use SensorPod’s excitationelectrode separation (approx. 46 cm) as the fixeddistance because it determines the electric field config-uration. Thus, we can define electrosense sensitivity aseither the detection range of certain sized objects orthe smallest detectable object volume given a fixeddistance.

In our experiments, we move the SensorPod at afixed velocity in a straight line by a stationary objectwhile continually collecting measurements. Such a setof voltage measurements is called a fly-by profile. Todetermine electrosense sensitivity, we first establish adetection threshold using statistical analysis betweenobject-present and object-absent fly-by profiles. Inorder to incorporate the sequential time domaininformation, we calculate the cumulative sum of thevoltage perturbations associated with each fly-by pro-file and examine the distributions of these sums. Wecall a distribution from an object-present fly-by a sig-nal distribution and a distribution from an object-absentfly-by a noise distribution.

We treat detection as a binary classification taskgiven the cumulative sum distribution of measure-ments. Due to noise and drift in measurements(seesection 4.5), the voltage measurements are stochastic.We examine the Jensen–Shannon Divergen-ce(JSD)(Lin 1991) between the signal and noise dis-tributions. JSD is a value between 0 and 1 that indicatesthe similarity between two distributions, with a smal-ler value associated with higher similarity. We obtainan average noise distribution by averaging the noisedistributions from all object-absent fly-by profiles.Having obtained the average noise distribution, we areable to assess detection by comparing the JSD betweenmeasurement and noise to a set threshold in JSD value.If the JSD is above the threshold, the object is con-sidered detected.

As is standard for binary classifiers, the choice ofthreshold(and in this case a JSD value) affects classifi-cation performance. We calculate the JSD betweenindividual signal distributions and the average noisedistribution. In order to account for the difference indistance, we examined the measurement voltage(V )fall-off with distance(d). Because of the nonlinearityof the electricfield,V is related to d as the following

µ ( )( )V d , 4f d

where f (d) is a negatively valued function. Simulationresults show f (d) is roughly constant at −4 but doesvary slightly with distance, consistent with priormeasurements and analyzes (Rasnow 1996, Nelson

and MacIver 2006). In this paper, we scale detectiondistance to the standard distance(electrode separa-tion) following µ -V d 4.

Equation (4) also presents a convenient way toscale measurement object distance to a fixed distanceof 46 cm as the following

µ µ - ( )V dvolume . 54

To summarize, we quantify sensitivity as the max-imum distance of a sphere of fixed size whose fly-byprofile (signal distribution) has a JSD (compared to theobject-absent noise distribution) above a threshold.Then, using scaling functions, we determine the mini-mum size sphere detectable at a fixed distance. Thedata and specific choice of JSD value will be covered inthe results.

2.2.2. Position estimationWhile detection concerns a sensor’s classificationability (object present or not), position estimationconcerns the sensor’s ability to measure a continuousvariable. Good performance in this context corre-sponds to a narrow distribution of estimates, acrossmultiple trials, around the true position of the object.We quantify the quality of our position estimationthrough the extraction of zero-crossings across multi-ple fly-bys of a spherical object. A zero-crossing iswhere the voltage reading transits between positiveand negative, and in ideal conditions should occurwhen the spherical object center crosses the lineconnecting the two electrodes of the sensing pair, inwhich both electrodeswouldmeasure the same voltagedue to the symmetry of the field (Bai et al 2015).

However, it is possible that a fly-by profile hasmultiple zero-crossings due to noise. Across ten trialsat one object distance, we combine all the zero-cross-ings from every trial fly-by profile and calculate themedian and interquartile range to quantify both theaccuracy (proximity of the median to the true loca-tion) and precision (narrowness of interquartile range)of our estimate.

2.3. Experiment2.3.1. ApparatusThe experimental platform is the same as described inour previous work (Bai et al 2015). We used two basicexperimental setups: one for ‘dry-dock’ experimentsin which water was simulated with discrete compo-nents and underwater experiments.

For the dry-dock experiments, the SensorPod wastaken out of water and connected to a network of resis-tor elements in series and parallel meant to modelwater. To model an object embedded within thisapproximation of water, we used a resistor-capacitorcombination that replaced a single resistor at thedesired object location. Dry-dock experiments are asimple proof-of-concept showing the efficacy of oursystem for measuring complex perturbations thatinclude amplitude and phase distortions. The dry-

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dock experiments also allow for characterization ofother effects not included in our models, such as theparasitic capacitance discussed in the supplementarymaterial.

The underwater setup has the SensorPod sub-merged underwater with objects nearby. Three typesof test objects are used. (1)Insulating PVC pylons(11 cm diameter, 0.6 cm shell, 60 cm length) wereused to calibrate the electronics’ frequency-depen-dent, circuit-induced gain attenuation and phaseshifts. For more information and results of experi-ments with these objects, see supplementary informa-tion. (2)Capacitive objects were created by wrappingmetalized Mylar foil (Mylar side out) over rubberspheres. MetalizedMylar films of different thicknessesand rubber spheres of different sizes are used to obtaindifferent capacitance values. These capacitive objectswere attached to a wooden rod with the bottom of theMylar sealed by a zip-tie and hot glue to prevent elec-trical current leaking through water. These objectswere used to verify that the detected phase shift isindeed caused by the capacitance of objects rather thanartifacts in the electronics or the underwater environ-ment. The capacitance values (Cobj) estimated usingthe critical frequency and bulk material equivalence(see supplementary material) are compared againstcapacitance values (Cfilm) calculated as thin film usingequation (1). (3)Three natural capacitive objects,tomatoes of two varieties and three sizes, were mea-sured to demonstrate the ability to detect and identifytheir internal structures. The tomatoes were placed inwater with varying conductivities, see table 2 in sup-plementarymaterial.

2.3.2. Fly-by experiments to assess detection andestimation performanceWedesigned experiments in order to compare sensoryreadings from an environment with an external objectto those without an external object. We collected fly-by profiles for pairs of identical trajectories with andwithout the object present. We used three objects ofthe same size but different electrical properties:capacitive, insulative, and conductive. The capacitiveobject was one of the rubber spheres wrapped inmetalized Mylar as described above. The insulativeobject was the unwrapped rubber sphere and theconductive object was ametal sphere.We first selectedthe emitted field frequency that yields the maximumresponse in the out-of-phase channel for the capacitiveobject (not to be confused with the critical frequencydescribed earlier). Then experiments are carried outfor each object, with fly-bys that proceed along a linearpath in the same plane as the object at lateral distancesranging from 30 to 90cm. For each scenario(withand without object) and distance configuration, tenfly-by trials(with identical SensorPod trajectories)were collected. These data were used to assess detec-tion and longitudinal position estimation quality asdescribed above.

3. Results

3.1. Estimating capacitance and internal structureTable 1 shows the Cobj, the estimated capacitancebased on the measure critical frequencies of fourcapacitive objects (the rubber spheres wrapped inmetalized Mylar foil of varying thickness). Theseestimated capacitances are compared to the capaci-tances calculated using the thin film equation(equation (1)). Note that while the magnitudes of thetwo estimates differ by a factor of about three, thatfactor is consistent across the various objects.

By analyzing the full frequency response of a targetobject, we can model the internal structure of objects.For results and discussion on internal structure esti-mation, please refer to the supplementarymaterial.

3.2. Electrosensory performanceHere we show the results of the performance ofcapacitive sensing in detection and localization.

3.2.1. Object detectionFigure 4 shows the JSD between individual noisedistributions and the averaged noise distribution forboth in-phase and out-of-phase channels. Most ofindividual noise trials have JSD(w.r.t. the averagednoise distribution) less than 0.4 for both resistive andcapacitive channels. We select 0.4 as the JSD thresholdfor determining detection.

In order to determine detection range, we plot theJSD between individual signal distributions and averagenoise distribution for different object and distance con-figurations in figure 5. Despite the high variance in JSD,we are able to estimate the electrosense sensitivity basedon themean values of JSD. In figure 5, the green dashedline representing detection threshold(JSD= 0.4) inter-cepts three curves at approximately 49 cm for the insu-lative object, 72 cm for the conductive object, and86 cm for the capacitive object. Discounting objectcomposition and using equation (5), this translates toelectrosense sensitivity of 180 cm3 (sphere of radius3.5 cm) for the insulative object at 46 cm distance,80 cm3 (sphere of radius 2.7 cm) for the conductiveobject at 46 cm distance, and 20 cm3 (sphere of radius1.7 cm) for the capacitive object at 46 cm distance.Thus, by this measure, capacitive sensing is better thanresistive sensing by nearly an order of magnitude for

Table 1.Capacitance comparison.

Item Obj 1 Obj 2 Obj 3 Obj 4

Thickness(μm) 6 12 12 6Diameter(cm) 3 3 2.5 2.5Cfilm (nF) 26.9 13.5 9.3 18.7Equi. Rel.Permittivity

4.17´104

1.86´104

1.67´104

3.16´104

Cobj (nF) 88.4 39.4 29.5 55.9

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Figure 4.Histogramof the Jensen ShannonDivergence (JSD) between individual trial noise distributions and average noisedistribution. Blue bars represent the in-phase channel, and red bars represent the out-of-phase channel. Data for both channelsincludemeasurements at different distances. Distance information is not explicitly shown. Thisfigure is used to select the JSDthreshold of 0.4, shown as red dashed line.

Figure 5.The Jensen–ShannonDivergence(JSD) betweenwith andwithout object trials plotted against distances. Three objects areinsulative(black)measuredwith the in-phase channel, conductive(red)measuredwith the in-phase channel and capacitive(blue)measuredwith the out-of-phase channel.

Figure 6. Fly-by profiles for different objects underwater. For each subplot the solid line is themean valuewhile the shaded region isone standard deviation above and below themean. The three objects are insulative(A), conductive(B) and capacitive(C). All threeobjects are placed at a distance of 70 cm and ten trials were analyzed for each object. The vertical dashed line indicates the ground truthposition of the objects. The quality of the position estimate versus distance is plotted infigure 7.

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insulative objects, and by a factor of four over resistivesensing of conductive objects.

3.2.2. Object position estimationFigure 6 illustrates the fly-by profiles of three objects at70 cm. In each subplot, the mean and standarddeviation of measurements are plotted as a solid lineand shaded regions. The position estimation for a trialis the average of all zero-crossing positions for a fly-byprofile. We also show the accuracy of estimation byplotting the inter-quartile range and median of theestimates over many trials as a function of objectdistance in figure 7. A lower inter-quartile range alongwith a median close to ground truth indicates higherprecision and accuracy and therefore better perfor-mance. The estimate of the longitudinal position ofthe non-capacitive objects starts to degrade at a lateraldistance of around 50 cm while the estimate for thecapacitive object only starts to degrade around 70 cm.

4.Discussion

By extending our artificial electrosensory system to besensitive to phase perturbations caused by capacitiveobjects, we have shown that SNR for detecting andlocalizing capacitive objects can be higher than fornon-capacitive objects. While the current biologicalliterature has extensively discussed a variety of rolesfor phase perception in electric fish (Heiligen-berg 1974, 1975, Matsubara and Heiligenberg 1978,Heiligenberg 1980, Bastian and Yuthas 1984), to ourknowledge this is the first time that a gain in distanceof object detection has been proposed as an advantageof capacitive sensing. The extended distance range of

capacitive electrolocation may underlie the gapbetween theoretical electrolocation distances esti-mated from amplitude encoders and measured detec-tion distance to live prey (MacIver et al 2001,Maler 2009).

4.1.High sensitivity in capacitive sensingAs shown in figure 6, the out-of-phase sensing channelgives lowermeasurement noise. For capacitive objects,the background effect, mostly from the tank walls andwater environment, is eliminated through out-of-phase demodulation. The capacitive channel allowsthe SensorPod to exclusively sense isolated capacitiveobjects. Such inherent lower noise floor is reflected inobject detection and position estimation. Fromfigures 5 and 7, we observe that the out-of-phasechannel has extended range in detection and betteraccuracy in position estimation compared to the in-phase sensing channel. Comparing figures 5 and 7, wecan observe that the distance at which objects reachour detection criterion of JSD>0.4 is larger than thedistance at which objects can be accurately localized.For example, insulative objects are at detection thresh-old at 50 cm in figure 5, whereas at this distance,localization accuracy is significantly degraded accord-ing to figure 7. It is intuitive that detection is an easiertask than estimation and can be achieved at greaterdistances.

4.2.Water conductivity adaptation inweaklyelectricfishWeakly electric fish work in habitats of widely varyingconductivity, from tens of microsiemens per centi-meter to three hundred or more microsiemens

Figure 7.The estimation of object longitudinal position versus lateral distance. The three objects are insulative(black),conductive(red) and capacitive(blue). The solid bars indicate the inter-quartile range of zero-crossings for all trials and represent theprecision of the estimate. Green squares indicate themedian of the zero-crossing as an indicator of the accuracy of the estimate.Grouped bars show trials for the same distance and are only separated for clarity. Estimation of position for insulative and conductiveobjects degrades starting at around 50 cm,whereas the estimate for the capacitive object starts to degrade 40% further out, at around70 cm. For insulative objects, we did not record data beyond 70 cmbecause the variance became too large, and similarly for conductiveobjects beyond 80 cm.

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(discussion and references in MacIver et al 2001, p552). Such a wide range in habitat conductivity willlead to non-negligible phase shift for prey due to theircapacitance. This has been shown in behavioralexperiments with fish (von der Emde 1993), and canbe appreciated from the prey (top row) case of figure 3,and equation (10) of the supplement. Thus, ratherthanmonitoring a unique phase shift associated with acertain type of prey, such as Daphnia with its real andcapacitive electrical aspects (Nelson et al 2002), theelectric fish may need to be able to detect anddistinguish a wide range of phase shifts. Without somemechanism of disambiguation, other living organismsthat the electric fish do not prey on may look like theirprey in terms of phase angle at different waterconductivities.

In contrast, water conductivity has no influence onthe electric image of insulative objects such as rocks, sothe in-phase channel of the fish experiences negligiblechange. Therefore, for a mixed scene of backgroundrocks with a foreground prey, as water conductivitychanges there will be negligible change in the in-phasechannel, and significant change in the out of phasechannel. The fish will sense this with its T-units, whichdetect the time difference between its own dischargeand the received field.

One hypothesis that could be tested is that the fishaccommodates changes in phase angle due to seasonalvariation in conductivity simply through associatingsensed water conductivities with different desired tar-get phase shifts (time delays).

4.3. The SensorPod can estimate the permittivityand capacitance of objectsWe first show the validity and accuracy of using theuniform field analytical models (equations 10 and 17in supplementary material) in permittivity estimation.Figure 1 in supplementary material shows goodagreement between Bode plots from the analytical

models and FEM simulation. For the homogeneousobject, the critical frequency method(equation (3))accurately estimates the relative permittivity to be30 000. For the shell structure object, the permittivityestimated with our critical frequency method(whichassumes one homogeneous material) is 82 000. Theeffective permittivity (real part of �mix in equation 17in supplementary material is frequency dependent,and the value is 38 000 at wcrit. The discrepancy is dueto that fact that the inside medium conductivity is onpar with the water and an in-depth analysis is includedin the supplementarymaterial.

Second, we show experimentally that the detectedcapacitance is indeed caused by the object rather thanartifacts like the object holder or the water-electrodeinterface. For metalized Mylar covered rubberspheres, we compare the calculated capacitance withcapacitance derived from experiments. In table 1, thecapacitance estimated with critical frequency method(equation (3))maintains a relatively constant propor-tion, around 3, to the capacitance computed withequation (1). Another perspective is to look at theBode plots, as shown in supplementary materialfigures 7 and 8. The critical frequency point shiftstowards lower frequencywith higher capacitance (blueand red) and shifts towards higher frequency withhigher conductivity of water (red and green). It isimportant to note that capacitance itself is an inherentproperty of the object, independent of waterconductivity.

Third, we are able to increase the permittivity esti-mation accuracy of our critical frequency method(equation (3)) by including harmonics from squarewave excitation and employing more measurementpoints. In figure 8, we fit the experimental Bode plot ofa metalized Mylar covered sphere with homogeneoussphere analytical model with added harmonics. Therelative permittivity from model fitting is 2.24´ 104,smaller than 3.16 ´ 104 from critical frequency

Figure 8.Experimental Bode plot (blue) of ametalizedMylar covered spherewith all 21 frequencymeasurement points(blue circles)fitted sinusoidal excitation(black) and square wave excitation(red).

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method. The discrepancy between the two values isdue to the shifted phase plot and therefore shifted cri-tical frequency. Note that such discrepancy is systema-tic across all capacitive objects. Therefore, for thepurpose of comparison among capacitive objects,equation (3) provides a convenient solution.

Lastly, we want to point out some interestingproperties of the thin shell model. A thin dielectricshell looks like an object with much higher permit-tivity (supplementary material equation 17). This factexplains why the small relative permittivity ofMylar(∼3) yields an equivalent bulk relative permit-tivity on the order of 10 000. It also provides insightinto why living animals, such as the water insects thatmany electric fish hunt, have high capacitance, as theircellmembranes providemany shells.

4.4. Noise and non-ideal effectsNoise in the system stems from three sources. Thecircuit has inherent noise from the electrical compo-nents. A dry-dock experiment was performed bypassing electrical signals from the SensorPod througha resistor network and measuring the voltage acrossone resistor. The gantry motor adds high frequencynoise when turned on. The most unpredictable sourceof noise is from the electrochemistry at the electrodewater interface. This source of noise appears mostly asdrift, long-term variation in voltage measurements.The electrochemistry induced noise is indirectlyobtained by subtracting circuit noise from total noisemeasured when the gantry motors are turned off. Thenoise in table 2 is rootmean square noise.

Limited tank space is a major non-ideal effect thatregisters as non-zero reading at the sensor pair withoutthe presence of an external object. This non-zero read-ing varies from sensor to sensor and also highlydepends on the pose of the SensorPod in the tank. Thein-phase sensing channel is highly sensitive to theeffects of the tank walls, while the out-of-phase chan-nel is insensitive to the same effects. In order to elim-inate the effect from the tank walls, we measure thereadings solely due to the tank and subtract them fromexperimental results.

Other non-ideal effects include gain degradationand stray capacitance. These effects attenuate themag-nitude by less than 10% at 100 KHz, the highest fre-quency used. Both subjects are discussed in detail insupplementarymaterial.

5. Conclusion

Our work extends artificial electrosense object identi-fication from conductive and insulative objects tocapacitive objects. By probing capacitive objects atmultiple frequencies, a quantitative frameworkenables decoding basic attributes of an object’s com-position and internal structure.Wefind that capacitivesensing has significantly higher performance thanresistive sensing, nearly an order of magnitude higherrange with respect to resistive sensing of insulativeobjects. We explored several implications for ourbiological model system, the weakly electric fish,including the sensitivity of capacitive sensing to habitatconductivity, which varies seasonally over awide rangein the rivers where thesefish are found.

Acknowledgments

The authors would like to thank HDT Robotics whocollaborated in the design of SensorPod and built it aswell as the robotic positioning system used in thisstudy. The work is funded by NSF PECASE IOB-0846032, Office of Naval Research Small BusinessTechnology Transfer grant N00014-09-M-0306, withpartial support fromNSFCMMI-0941674.

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