hysteresis compensation for ground contact force ......ira a.fulton schools of engineering arizona...

HYSTERESIS COMPENSATION FOR GROUND CONTACT FORCE MEASUREMENTWITH SHOE-EMBEDDED AIR PRESSURE SENSORS

Prudhvi Tej Chinimilli, Sean Wolfgang Wachtel, Panagiotis Polygerinos, Wenlong Zhang∗The Polytechnic School

Ira A.Fulton Schools of EngineeringArizona State University

Mesa, Arizona 85212Email: {pchinimi, sfwachte, polygerinos, wenlong.zhang}@asu.edu

ABSTRACTThis paper reviews the design of smart shoes, a wearable de-

vice that measures ground contact forces (GCFs) for gait anal-ysis. Smart shoes utilize four coils of silicone tubes adhered di-rectly underneath the shoe insole at key points of interest. Airpressure sensors connect to each tube coil to measure pressurechanges caused by compression. This paper presents static anddynamic calibration performed on each sensing coil to establisha model of internal pressure and the GCF. Based on the model,a phase lead filter is designed to account for the hysteresis effectand visco-elastic properties of the silicone tube in order to pro-vide accurate GCF measurements. To design this filter, the airbladder is modeled using a standard linear solid (SLS) model.The prediction error minimization (PEM) algorithm is then im-plemented to identify the continuous-time transfer function of thisSLS model, which is then transformed to discrete time domain toimplement in a digital processor. Mechanical characterizationand testing on a healthy subject are performed to validate themodel and its capability to compensate for hysteresis in GCFmeasurement.

I. INTRODUCTIONIn recent years, sensor embedded shoes attained great popu-

larity as mobile sensing devices to detect human ground contactforces (GCFs) [1, 2]. They provide necessary information to de-tect gait phases for applications such as rehabilitation and gait

∗Address all correspondence to this author.

analysis [3]. Various force sensors have been studied to mea-sure GCFs. Razian and Pepper developed a tri-axial pressuresensor based on piezoelectric copolymer film [4]. Kothari et al.proposed a capacitive sensor to measure the pressure betweenthe foot and ground [5]. Force sensitive resistors (FSRs) aremost commonly used sensors to measure GCFs [6, 7]. However,they exhibit considerable hysteresis, sensitivity to shear forceand changes in response characteristics with prolonged use [8].These characteristics, along with their nonlinearity and low dura-bility, make FSRs unsuitable for practical use in GCF measure-ment. Huang et al. used a ninth order polynomial to compen-sate for non-linearity of FSRs [9]. In other paper, Hall et al.used a fourth order polynomial function of voltage to calibratethe FSRs [10]. As an alternative to FSRs, Kong et al. mea-sured pressure in air bladders installed on a shoe insole for morereliable and stable GCF measurement [2]. Much like FSRs, hys-teresis is the most common problem faced in many pressure sen-sors [6,10]. This presents major issues in GCF measurement dueto the rapid fluctuation in GCFs during a step.

In this paper, the design of smart shoes is reviewed. Theseshoes are developed for applications including rehabilitation andother clinical monitoring where GCF measurement provides use-ful insight. Also, this method of GCF measurement using smartshoes does not require expensive equipment such as force platesand can operate outside lab settings. A sensing unit similar tothat introduced by Kong et al. is used [2]. Silicone tubing iscoiled and adhered underneath a shoe insole then connected to anair pressure sensor. GCFs are calculated by measuring changes

Proceedings of the ASME 2016 Dynamic Systems and Control Conference DSCC2016

October 12-14, 2016, Minneapolis, Minnesota, USA

DSCC2016-9920

1 Copyright © 2016 by ASME

Downloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/conferences/asmep/91112/ on 03/13/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use

in pressure created during compression, caused in walking by afoot. In order to achieve accurate GCF measurement, the sensingunit is calibrated with the help of an Instron 5944 series materialtesting machine [11]. To properly calibrate the unit, tube coilsare subjected to both static and dynamic loading.

The novelties of this paper include the application of pre-diction error minimization (PEM) system identification methodto estimate the parameters of sensor system, and the design ofphase lead filter based on the estimated parameters. The follow-ing topics are discussed in this paper:

1) The design of an GCF measurement system based on airpressure based force sensing.

2) The setup to perform static and dynamic calibration tests onthe air bladders using an Instron machine.

3) The design of an algorithm to identify the dynamic modelof the whole sensing unit and the construction of a filter toreduce hysteresis in the air bladder and pressure sensors.

The remainder of this paper is organized as follows: sectionII demonstrates the design of the sensing unit in smart shoes.Section III describes the methodology for static and calibrationtests performed on the sensing unit and discusses the calibrationresults. In section IV, the modelling of air bladder using SLSmodel is described. Section V details the PEM approach fol-lowed in the paper. Section VI discusses the implementation ofthe phase lead filter. Section VII gives the experimental resultsfrom a healthy subject. Conclusion and the future work are pre-sented in section VIII.

II. DESIGN OF SENSING UNIT IN SMART SHOESIn an effort to obtain accurate results, a new sensing unit

is made prior to smart shoe testing. This sensing unit is consti-tuted by coiled silicone tubes and an air pressure sensor. Takingsurvey of existing solutions, FSRs are commonly used for GCFmeasurement. However, FSRs perform poorly due to their non-linearity, lacking durability and capability to measure distributedloads common in most any gait. An alternative solution utilizingair pressure sensors proposed by Kong et al. offers better read-ings, increased durability and stable measurement of distributedloads [2].

Four tubes are coiled and adhered to the bottom side of ashoe insole under the toes, inner and outer metatarsals (Meta1and Meta4), and heel as shown in Figure 1(a). The coils func-tion as air bladders and connect to air pressure sensors. Whenloaded different, during a step for instance, the tube coils arecompressed, generating pressure which, in turn, is measured bythe air pressure sensors. In this system, GCF is calculated fromthe pressure in the tube coils. Certain assumptions are made, in-cluding the lack of radial deformation and dynamic effects withinthe air bladder. Based on these assumptions, pressure change isproportional to force applied i.e., P(t) = F(t)

A(t) .

Heel

Toe

Meta 1

Meta 4

(a) SHOE INSOLE WITH FOUR AIR BLADDERS

Battery Holder

Sensor Box

Silicone Tubes

(b) SMART SHOES WITH SENSING UNIT

FIGURE 1. WIRELESS SMART SHOES

Silicone tube and unidirectional gauge pressure sensors areused to construct the semsing unit. Silicone tube is selected foruse due to its minimal creep [2] and desirable stiffness, rigid-ity and toughness. Unidirectional gauge pressure sensors fromFirst Sensors HDI series are used. Pressure sensors with 200mbar measurement range are connected to tubes coiled under theheels and metatarsals. Toes sustain less load than the heels andmetatarsals. Therefore, 100 mbar pressure sensors are connectedto the tubes coiled underneath the toes for higher resolution.

The sensor box provides housing for the four air pressuresensors on each shoe as shown in Figure 1(b). The air pressuresensors connect to a microcontroller which reads their outputvoltage through analog port connect to computer with bluetooth.The computer then, processes and analyzes data. The samplingrate of the smart shoes can go up to 200 Hz with the bluetoothmodule. It is important to calibrate the sensing unit prior to ac-tual usage in order to achieve accurate GCF measurements. Toperform static and dynamic calibration tests on the sensing unit,an Instron 5944 mechanical testing machine capable of applyingcompressive and tensive loads is selected.

III. CALIBRATION TEST SETUPA. Testing apparatus and configuration

Calibration testing apparatus is comprised of the sensingunit itself, an Instron 5944 mechanical testing machine [11] and a



FIGURE 2. SETUP FOR CALIBRATION TESTS

FIGURE 3. STATIC TEST (LOADING RANGE:450-600N): VOLT-AGE OUTPUT FROM INSTRON AND AIR PRESSURE SENSOR

National Instruments myRIO. As shown in Figure 2, the sensingunit lays on an anvil, the Instron machine applies compressiveload to the tube coils, and the myRIO measures analog signalsfrom the air pressure sensors. Test instructions are sent to theInstron machine by Bluehill 3 software running on a computer.The myRIO receives analog signals from the Instron and air pres-sure sensors, and sends the information to the computer via Lab-VIEW. To accurately calculate GCFs from pressure readings inpractice, the relationship between pressure readings and load oneach sensing node must be established and the dynamic charac-

(a) STEPS FOR STATIC CALIBRATION TEST

(b) STEPS FOR DYNAMIC CALIBRATION TEST

FIGURE 4. CALIBRATION TEST PROCEDURE

teristics of each sensor must be determined. To achieve this, in-dividual calibration tests are performed with static and dynamicloading. Figure 3 displays one example of data received during astatic calibration test.

In static testing, the Instron machine applied a compressiveload to individual tube coils, maintained that load for five sec-onds, then removed load. The test performed this process forloads from 50N to 800N in 50N intervals. Static tests were con-ducted for all 8 sensing nodes. In static testing, load is applied intwo phases. The first phase begins unloaded, then load is appliedat 50N/s and halted 5N below the desired load. In the secondphase, the final 5N are applied over five seconds. With load ap-plied, the load cell is halted and kept stationary for another fiveseconds. Finally, the load cell is retracted, reducing load at 50N/suntil complete unloaded. The system then rests for five secondsbefore repeating the entire cycle for a new load. The static cali-bration procedure is described in Figure 4(a).

In dynamic testing, the Instron machine applied compressiveload at the various rates. In loading phase, load was applied ata specified rate in N/s. This phase continued until the systemreached a maximum load of 800N. Thereafter, in the unloadingphase, load is reduced at same rate until the system is unloadedagain. This cycle is repeated for loading rates of 50, 100, 200,400, 600 and 800N/s. The steps followed for dynamic calibrationis shown in Figure 4(b).



Loading

Unloading

Loading

Unloading

FIGURE 5. DYNAMIC TEST (RATE OF LOADING 50-800 N/S):VOLTAGE OUTPUT FROM a) INSTRON AND b) AIR PRESSURESENSOR. c) LOW SPEED (100N/S) (d) HIGH SPEED (800N/S))

B. Discussion on calibration test resultsAt the first stage of the process, calibrated weights were stat-

ically placed over tube coils in order to obtain the relationship be-tween applied force and the pressure change i.e., output voltageof the pressure sensor. The loading range of weights and incre-ment between each reading are selected to be within the limits ofthe sensor. Thus, by using test setup, loads are increased from0 to 800N with the waveform shown in Figure 3. Most impor-tantly, Figure 3 illustrates the similar waveform between appliedload and recorded pressure in static load conditions. Minor hys-teresis is observed during load changes as apparent in the bowedlines during bulk loading and unloading in Figure 3(b).

For the dynamic test, triangular waveform of loading and un-loading is generated by Instron machine at variable loading ratesfrom 50N/s to 800N/s as shown in the Figure 5(a). Hysteresis isobserved during loading and unloading. The sensor follows up-per side of the curve during loading and lower side of the curveduring unloading as shown in Figures 5(c) and 5(d). Hysteresiseffect increases with higher rate of loading.

IV. APPROACH FOR DESIGNING HYSTERESIS COM-PENSATOR

The objective is to design a model based hysteresis compen-sator capable of improving GCF measurement and performanceof the sensing unit especially during dynamic situations charac-terized by rapid changes in force. This makes sensing suitable fordynamic activities such as walking, jogging and running. Theapproach to design such a filter is explained in three steps: 1)

ff

k1k2c

P Patm

x0

a) b)

P Patm

x-x0

FIGURE 6. a) SILICONE TUBE MODEL b) STANDARD LINEARSOLID MODEL

Develop a dynamic model for the air bladder. 2) Identify thecontinuous time transfer function of the model based on the in-put and output data measured in time domain. 3) Transform thecontinuous time transfer function in to the discrete time domainfor implementation in a digital controller.

A. Dynamic model for air bladderIn order to accurately capture the dynamic characteristics of

the air bladder system, a standard linear solid (SLS) model is em-ployed, which is used for modelling visco-elastic materials suchas silicone tubing [2]. This model consists of one damper andtwo Hookean springs, one connected in parallel and the other inseries with the damper. The air bladder and equivalent standardlinear model are shown in Figure 6. It is assumed that there areno inertia and air leakage in the air bladder. Therefore, mass Mis assumed to be zero. The force balance equation for air bladdersystem is:

(P−Patm− f )A− k1(x− x0)+k2cs(x− x0)

k2 + cs= 0. (1)

Here P and Patm are the absolute and atmospheric pressurein the tube, A is the effective area of the air bladder which isassumed to be constant. x− x0 is the deformation in the tube.Here s in (1) refers to a derivative operator in the Laplace do-main. Gauge pressure PG is the difference between P and Patm.The governing transfer function between the force applied f overlarge area and gauge pressure PG is derived in [2]:

f = PG +[k1 +k2cs

k2 + cs]

x20

nRTPG ≡

b1 +b2sa1 +a2s

PG, (2)

where

a1 = k2,a2 = c, (3)



b1 = k2[1+ k1x2

0nRT

],b2 = c[1+(k1 + k2)x2

0nRT

]. (4)

Physical properties of the silicone tube are as follows: n =4.2075×10−9[mol],R = 8.3145[m3 pak−1mol−1],T = 300k andx0 is the inside diameter of the undeformed silicone tube whichis 2 mm in our case. Here, PG is available from the air pressuresensor. However, it is difficult to get load measurement directlyfrom PG as it is not easy to calculate effective area of cross sectionfor distributed loads. Thus, it becomes important to identify therelationship between applied force and pressure change in orderto estimate GCF from the pressure sensor readings. As a result,we will identify the coefficients a1, a2, b1 and b2 in (2) in a datadriven approach.

V. PREDICTION ERROR MINIMIZATION (PEM) ALGO-RITHM

.To identify the coefficients of the first order transfer function, aPEM approach is applied. The main objective of this algorithmis to minimize the weighted norm of the prediction error which isthe difference between measured and predicted output. This al-gorithm basically performs two steps to estimate the coefficients:1) initialize parameters, and 2) update parameters.

A. Initialization of coefficients for transfer functionTo initialize numerator and denominator of the first or-

der transfer function, Simplified Refined Instrumental Variablemethod for Continuous time systems (SRIVC) algorithm is em-ployed [12]. SRIVC is one of the successful stochastic identifica-tion method where the noise w(t) is assumed to be discrete-time,and of white noise process w(tk) ∼ N(0,σ2). True system con-tains input u(t) and output x(t), which are the load measurementdata collected from air pressure sensors and Instron. The mainaim of the SRIVC is to create an auxiliary model equivalent tothe true system which can approximate transfer function of thetrue system B(s,θ∗)

A(s,θ∗) as shown in Figure 7.

True system modelThe input u(t)and output x(t) sampled data are available in

the time domain from air pressure sensors and Instron respec-tively. The operator polynomial representation of the true systemfor input u(t) and output x(t) is

A(s,θ ∗)x(t) = B(s,θ ∗)u(t), (5)y(t) = x(t)+w(t). (6)

y(t) is the measured output contaminated with white noise w(t).The operator polynomial is in the Laplace domain and true pa-

FIGURE 7. TRUE AND AUXILIARY MODEL

rameter θ ∗ can be defined by

A(s,θ ∗) = sn +a∗1sn−1 + .........+a∗n, (7)B(s,θ ∗) = b∗0sm +b∗1sm−1 + .........+b∗m, (8)

θ∗ = [a∗1 ..... a∗n b∗0 ..... b∗m]

T . (9)

From (2), our system should consist of one zero and pole. There-fore, n=m=1 which gives

A(s,θ ∗) = s+a∗1, (10)B(s,θ ∗) = b∗0s+b∗1, (11)

θ∗ = [a∗1 b∗0 b∗1]

T . (12)

Transfer function T for the true system representing dynamicmodel with input u(t) and output x(t)is

T =x(t)u(t)

=b∗0s+b∗1s+a∗1

. (13)

By comparing (13) and (2)

a∗1 =a1

a2, b∗0 =

b2

a2and b∗1 =

b1

a2. (14)

Let us assume that the value of a2 = 1 which means the value ofc becomes equal to 1 from (3). Further, this assumption is validsince the coefficients k1, k2 and c are coupled, the value of c = 1results in one set of values for k1 and k2. The increment or decre-ment in c changes k1 and k2 values accordingly. For our case, cis assumed to be one. Thus, the problem of estimating three co-efficients automatically reduces to two i.e., to estimate k1 and k2only. Therefore, coefficients a∗1, b∗0 and b∗1 need to be estimatedin order to identify the continuous-time transfer function for thetrue system i.e., the dynamic model of air bladder and the sensor.



Auxilary modelTo estimate system parameter vector θ ∗ from sampled in-

put and output, SRIVC method creates an auxiliary model asshown in Figure 7. This is an approximation of the true sys-tem which takes the input u(t) and estimates the output x(t) withno noise. The auxiliary model approximating the true systemequations (10), (11) and (12) is:

y(t) =D(s,θ)C(s,θ)

u(t)+ e(t), (15)

e(t) = y(t)−φT (t)θ , (16)

φ(t) = [−dy(t)dt

du(t)dt

u(t)]T , (17)

θ = [a−1 b−0 b−1 ]T . (18)

Here, a−1 , b−0 and b−1 are the estimates for a∗1, b∗0 and b∗1 in (14).The single input, single output (SISO) model in the continuoustime domain is algebraically equivalent to the discrete time SISOmodel explained in [13]. The equation containing error functione(t) in (16) can be written as

e(t) =1

C(s,θ)[C(s,θ)y(t)−D(s,θ)u(t)], (19)

Z(s) =1

C(s,θ). (20)

where Z(s)is given by pre-filter. In SRIVC method, the state vari-able filter (SVF) proposed by young (1964) is used as a prefilter.The minimal order SVF has the form [14]:

Zsv f (s) = (β

s+λ)n, (21)

where n is the system order and filter time constant λ is aprioriand usually λ=β . Now, taking Z(s) in (20) inside the squarebracket (19), error function e(t) becomes

e(t) =C(s,θ)y f (t)−D(s,θ)u f (t), (22)

y f (t) =y(t)

C(s,θ), u f (t) =

u(t)C(s,θ)

. (23)

The derivative of y f (t)and u f (t) is given by:

y(i)f (t) = fi(t)∗ y(t) i = 0,1, (24)

u(i)f (t) = fi(t)∗u(t) i = 0,1. (25)

Here y(i)f (t), u(i)f (t) are the ith derivative of y f (t)and u f (t) respec-tively. i is 0 and 1 in our case. * is the convolution operator andfilters take the form,

fi(t) = L-1(si

C(s,θ)), (26)

where L-1is the inverse Laplace transform. Therefore, the auxil-iary model at the nth sampling instant t = tn can be written as

e(tn) = y f (tn)−φTf (tn)θ , (27)

φ f (tn) = [−dy f (tn)

dtn

du f (tn)dtn

u f (tn)]T . (28)

To obtain an initial estimate of θ for a data sample of length N,the following equations are used:

VN =1N

N

∑i=1

φ f (ti)φ fT(ti), (29)

θ =V−1N

1N

N

∑t=1

φ f (ti)y(ti). (30)

The prefilter in SRIVC method provides C(s,θ) from the userdefined λ . From equations (29) and (30), initial value of θ canbe estimated.

B. Updating coefficients of transfer functionNonlinear least square search method is employed to itera-

tively adjust the unknowns in true system (6), as well as estimateof the instrument variable at each iteration of the algorithm, untilthat converges. Instrument variable at each iteration is given by

x(t) =D(s,θ)C(s,θ)

u(t). (31)

Here, θ is the estimated vector obtained at the previous iteration.Estimating coefficients of θ , a−1 , b−1 and b−0 in (19) can identifythe values k1, k2 and c given in (2). However, we considered c isalways equal to 1.

To update the initialized parameters for the transfer func-tion, a set of non-linear least squares search methods Gauss New-ton [15], Levenberg Marquardt [16,17] and trust region reflectiveNewton [18] from the system identification toolbox MATLABR2015b were adopted. Trust region based search methods arechosen in our approach because they have better convergenceproperties than regular line search method [19]. The main ob-jective of these search methods is to reduce the error e(t) givenin (16) by minimizing weighted prediction error norm.



C. Algorithm summarya) Input: x(t) and u(t)

where x(t) and u(t) are the load measurement data availablefrom Instron and air pressure sensor in time domain sampledat 100 Hz.

b) Prediction error minimization :

1. Define a value for filter time constant λ and maximumtolerance value µ .

2. Apply SRIVC method to find the initial estimate of θ ,which is the estimate of the continuous system param-eter vector θ ∗ from sampled input-output data using(29) and (30).

3. Update the value of θ on the basis of cost function us-ing nonlinear least square search method. The costfunction is a positive function of prediction error e(t)given in (16). For a model with n number of outputs,the cost function has the following general form:

Cost(θ) =1N

N

∑t=1

eT(t,θ)We(t,θ), (32)

where N is the number of data samples, e(t,θ ) is ann-by-1 error vector at a given time t, parameterized bythe parameter vector θ . W is the weighting matrix andit is a constant independent of θ .

4. Repeat step 3 until the maximum relative percentageof the estimated parameter θ in successive iterations isless than the tolerance value µ defined in the first step.

c) Continuous to discrete time domain transform: continuoustime transfer function obtained from PEM method is dis-cretized using bi-linear transformation for the real-time im-plementation.

d) output: r(t) is the filtered signal obtained by filtering incom-ing air pressure signals u(t).

VI. IMPLEMENTATION OF PHASE LEAD FILTERTwo types of air pressure sensors with range 100 mbar and

200 mbar were used in smart shoes. The sensor with 100 mbarrange was used for toe sensing point and other with 200 mbarrange were used for all other sensing points. The dynamic cali-bration tests were performed on sensors at left toe, left heel, righttoe and right heel. The load measurement data were availablesimultaneously from the air pressure sensor and Instron at thesampling rate of 100 Hz. This collected time sampled data fromthe air pressure sensor and Instron were used as input and outputin our proposed algorithm to identify the transfer function.

Trust region reflective Newton (TN) search method showedbetter performance compared to Gauss Newton (GN) and Leven-berg Marquardt (LM) search methods in terms of fit percentage.

TABLE 1. THE TRANSFER FUNCTION EQUATION AND CO-EFFICIENTS OF THE PHYSICAL MODEL FOR FOUR SENSINGUNITS

Sensing unit k1 k2 c Transfer function

Right toe 1.873 0.119 1 2.269z−2.267z−0.9988

Right heel 2.045 0.159 1 2.284z−2.281z−0.9984

Left toe 1.341 0.215 1 2.224z−2.221z−0.9979

Left heel 2.025 0.316 1 2.355z−2.349z−0.9968

For instance, on the left toe data, TN method exhibited 90.23 %fit percentage while LM and GN showed 83.62 % and 78.76 %respectively. Therefore, trust region reflective Newton methodsearch method was employed to identify the transfer function.

The identified values for k1, k2 and c in (4) are displayedin Table 1 along with their transfer fuction equations for foursensing points separately. There are certain points that can beinferred from Table 1:

1. If k1= k2 = 0 or nearly equal to zero, this explains that thematerial exhibit weak visco-elastic effect and no signal pro-cessing is required. From Table 1, it is clear that the coef-ficients k1 and k2 of any sensing units are not zero or evenclose to zero. It means that the material exhibits consider-able visco-elastic effect. Therefore, it becomes necessary tocarry out signal processing on the raw data.

2. If k1�0, it means the material is stiff and the gain of thetransfer fuction in (2) is very large such that noise will beamplified. From Table 1, it is clear that the value of k1’s arein the range from 1.341 to 2.025. This implies that materialexhibits considerable stiffness and noise gets amplified overtime.

3. If the magnitude of the pole is greater than zero i.e., | a1a2| >

| b1b2|, the transfer function amplifies the high frequency range

of the measured signal. The magnitude of the poles aregreater than zeros which implies filter designed on the basisof this transfer function will show magnifying characteris-tics in the high frequency range with the phase lead.

The filter exhibits magnifying characteristics in the high fre-quency range with the phase lead. The performance of the hys-teresis compensator designed for left shoe sensing unit can beseen in Figure 8. Filtered signal shows improved linearity inmeasurements with reduced hysteresis compared to raw signal.A variance level of 2.23N in root mean square is observed in thefiltered signal which is nearly 0.3 percent of total load appliedi.e., 800N. The root mean square error (RMSE) metrics are usedto compare between the filtered and raw signal.



Loading

Unloading

Loading

Unloading

Low speed (100 N/s) High speed (800 N/s)

(a) Raw signal at low speed(100 N/s) and high speed (800 N/s)

Loading

Unloading

Loading

Unloading

Low speed (100 N/s) High speed (800 N/s)

(b) Filtered signal at low speed(100 N/s) and high speed (800 N/s)

FIGURE 8. LEFT TOE SENSING UNIT COMPENSATOR PER-FORMANCE

Root mean square error (RMSE) metrics: a) RMSE betweenload measurement from Instron x(t)and raw data measurementu(t) from air pressure sensors. b) RMSE between load measure-ment data from Instron x(t) and filtered signal r(t) after applyinghysteresis compensator. c) Improvement percentage P% can bedefined as RMSE(u)−RMSE(r)

RMSE(u) ×100.where

RMSE(u) =

√∑

Ni=1(xi−ui)2

N, (33)

RMSE(r) =

√∑

Ni=1(xi− fi)2

N. (34)

where N is the total number of data samples.Table 2 displays the calculated metrics for four sensing units

individually. Instron generated triangular waveform of loadingrange 0 to 800N with loading rates 100, 200, 400, 600 and800N/s. This table compares filtered and raw data in terms ofRMSE metrics. Improvement percentage (P%) reveals the im-provement seen in the filtered signal after designed filter is ap-plied. It is clear from the range of P% that filtered signal showsless RMSE value compared to raw signal. These filters pro-

TABLE 2. COMPARISON BETWEEN RAW SIGNAL AND FIL-TERED SIGNAL FOR DIFFERENT RATE OF LOADING

Sensing unit Metrics (N/N/%) Rate of loading (N/s)

100 200 400 800

Right toe

RMSE(u)

RMSE(r)

P%

137.059 140.291 144.217 144.514

43.992 47.883 54.123 56.205

67.9 65.87 62.47 61.11

Right heel

RMSE(u)

RMSE(r)

P%

103.999 108.437 111.274 113.595

31.421 33.076 35.625 38.2441

69.79 69.50 67.98 66.33

Left toe

RMSE(u)

RMSE(r)

P%

224.283 232.154 238.448 239.654

55.272 64.159 73.185 76.0494

75.36 72.36 69.31 68.27

Left heel

RMSE(u)

RMSE(r)

P%

158.164 196.177 250.127 283.381

37.435 54.354 74.259 88.221

76.33 72.29 70.31 68.87

vide better performance at lower rates of loading than at higherspeeds. For instance, considering left toe sensing unit, the P%is 75.36% at 100 N/s and reduces to 68.27% at 800 N/s. Eventhough P% decreased with an increase in loading rates, filter ex-hibited sufficient compensation in hysteresis for varying loads asshown in Figure 8(b). Filtered signal shows better linearity withless hysteresis at both low and high speed.

VII. EXPERIMENTAL RESULTSTo evaluate the performance of the proposed phase lead fil-

ter on the GCF measurements, Data were collected from varioustrails of walking and standing activities performed by a healthysubject. The healthy subject is male, weight 53 kg, and is 5 feet10 inch tall.

1) For the standing trail, subject initially did toe movementi.e., he stood on tiptoe. Then, he went back to the normalstanding position and remained still for the whole trail.This activity was performed for a period of 60 seconds.Figure 9 shows the raw and filtered GCF estimate fromsensing units during standing trail. Total GCF exerted bythe subject is calculated for both raw and filtered data. TotalGCF estimate i.e., sum of the GCF estimate of all the eightsensing units from raw data is 618N, where from filtereddata, it is 535.2N. Therefore, subject weighting 53kg cannormally exert 519.4N on the ground. Thus, the filteredsignal provides more accurate estimate.

2) For the walking trail, subject performed continuous walkingon treadmill for 2 minutes at a speed of 6 mph. Figures 10and 11 show the performance of the hysteresis compensatorfor the walking trail. The raw data collected during this trail



(a) Raw signal from left foot (b) Raw signal from right foot

(c) Filtered signal from left foot (d) Filtered signal from right foot

FIGURE 9. GCF SIGNALS FOR STANDING TRAIL

are processed using the designed filter and compared withraw data for the left shoe and right shoes. The plot is drawnbetween GCF estimate from all sensing units and time in-terval from 20 to 26 seconds. From Figures 10 and 11, itis observed that in each walking step, the subject initiallytouched the ground with the heel followed by Meta4, Meta1and finally toe. It can also be inferred from Figures 10 and11 that the subject applied more force on the right side thanleft, and more specifically, right heel compared to left. Al-though, raw and filtered signal show similar GCF patternduring walking, differences can be observed in terms of theamplitude. For instance, from Figure 11, it can be seen thatthe filtered signal provides a lower estimate of heel GCFthan the raw data.

VIII. CONCLUSION AND FUTURE WORKIn this paper, A design for smart shoes was reviewed. Each

shoe contained four sensing units to measure GCFs at the heel,Meta1, Meta4 and toe positions. Static and dynamic calibrationtests were performed on each sensing unit using Instron mate-rial testing machine. A digital filter was proposed which couldcompensate for the hysteresis effect in sensing unit and provideaccurate GCFs estimates. The approach followed in designingthis filter constituted of two parts: 1) dynamic modeling of theair bladder using standard linear solid (SLS) model, and 2) ThePEM approach to identify transfer function of the compensatemodel. The filtered signal and raw data were compared with thedata from Instron. In addition, standing and walking practicalexperiments were conducted on a healthy subject to verify theperformance of the proposed filter.

(a) Raw signal from left foot

(b) Filtered signal from left foot

FIGURE 10. GCF SIGNALS FROM LEFT FOOT FOR WALKING

In the future, we plan to develop an activity recognition sys-tem consisting of smart shoes and inertial measurement units(IMUs) which can recognize various activities such as standing,sitting, walking, jogging and running in real time. The long termplan is to design a new approach for exoskeleton control throughactivity recognition. As for smart shoe design, we intend to makesensor box smaller to make it more user friendly.

REFERENCES[1] Zhang, W., Tomizuka, M., and Byl, N., 2016. “A wireless

human motion monitoring system for smart rehabilitation”.Journal of Dynamic Systems, Measurement, and Control,138(11), pp. 111004–111004.

[2] Kong, K., and Tomizuka, M., 2009. “A gait monitor-ing system based on air pressure sensors embedded in ashoe”. Mechatronics, IEEE/ASME Transactions on, 14(3),pp. 358–370.

[3] Byl, N., Zhang, W., Coo, S., and Tomizuka, M., 2015.“Clinical impact of gait training enhanced with visualkinematic biofeedback: Patients with parkinsons disease



(a) Raw signal from right foot

(b) Filtered signal from right foot

FIGURE 11. GCF SIGNALS FROM RIGHT FOOT FOR WALK-ING

and patients stable post stroke”. Neuropsychologia, 79,pp. 332–343.

[4] Razian, M. A., and Pepper, M. G., 2003. “Design, devel-opment, and characteristics of an in-shoe triaxial pressuremeasurement transducer utilizing a single element of piezo-electric copolymer film”. Neural Systems and Rehabilita-tion Engineering, IEEE Transactions on, 11(3), pp. 288–293.

[5] Kothari, M., Webster, J., Tompkins, W., Wertsch, J., andBach-y Rita, P., 1988. “Capacitive sensors for measuringthe pressure between the foot and shoe”. In Proceedings ofthe Annual International Conference of the IEEE Engineer-ing in Medicine and Biology Society.

[6] Bamberg, S. J. M., Benbasat, A. Y., Scarborough, D. M.,Krebs, D. E., and Paradiso, J. A., 2008. “Gait analysis us-ing a shoe-integrated wireless sensor system”. InformationTechnology in Biomedicine, IEEE Transactions on, 12(4),pp. 413–423.

[7] Pappas, I. P., Popovic, M. R., Keller, T., Dietz, V., andMorari, M., 2001. “A reliable gait phase detection sys-

tem”. Neural Systems and Rehabilitation Engineering,IEEE Transactions on, 9(2), pp. 113–125.

[8] Dabling, J. G., Filatov, A., and Wheeler, J. W., 2012. “Staticand cyclic performance evaluation of sensors for human in-terface pressure measurement”. In 2012 Annual Interna-tional Conference of the IEEE Engineering in Medicine andBiology Society, IEEE, pp. 162–165.

[9] Huang, B., Chen, M., Shi, X., and Xu, Y., 2007. “Gait eventdetection with intelligent shoes”. In Information Acqui-sition, 2007. ICIA’07. International Conference on, IEEE,pp. 579–584.

[10] Hall, R. S., Desmoulin, G. T., and Milner, T. E., 2008. “Atechnique for conditioning and calibrating force-sensing re-sistors for repeatable and reliable measurement of compres-sive force”. Journal of biomechanics, 41(16), pp. 3492–3495.

[11] Instron 5944 machine. http://www.instron.us/.[12] Young, P., and Jakeman, A., 1980. “Refined instrumen-

tal variable methods of recursive time-series analysis partiii. extensions”. International Journal of Control, 31(4),pp. 741–764.

[13] Young, P., and Jakeman, A., 1979. “Refined instrumen-tal variable methods of recursive time-series analysis part i.single input, single output systems”. International Journalof Control, 29(1), pp. 1–30.

[14] Ljung, L., 2009. “Experiments with identification of con-tinuous time models”.

[15] Hartley, H. O., 1961. “The modified gauss-newton methodfor the fitting of non-linear regression functions by leastsquares”. Technometrics, 3(2), pp. 269–280.

[16] More, J. J., 1978. “The levenberg-marquardt algorithm: im-plementation and theory”. In Numerical analysis. Springer,pp. 105–116.

[17] Marquardt, D. W., 1963. “An algorithm for least-squaresestimation of nonlinear parameters”. Journal of the societyfor Industrial and Applied Mathematics, 11(2), pp. 431–441.

[18] Coleman, T. F., and Li, Y., 1996. “An interior trust regionapproach for nonlinear minimization subject to bounds”.SIAM Journal on optimization, 6(2), pp. 418–445.

[19] Shi, Z., and Zhang, X., 2005. “From line search method totrust region method”. In International Symposium on ORand Its Applications, Vol. 213, Citeseer, pp. 156–170.



hysteresis compensation for ground contact force ......ira a.fulton schools of engineering arizona...

Documents