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Medical Engineering & Physics 31 (2009) 1244–1254

Contents lists available at ScienceDirect

Medical Engineering & Physics

journa l homepage: www.e lsev ier .com/ locate /medengphy

eal-time model based electrical powered wheelchair control�

ongwu Wanga,b, Benjamin Salatina,b, Garrett G. Grindlea,b, Dan Dinga,b,c, Rory A. Coopera,b,c,∗

Human Engineering Research Laboratories, VA Pittsburgh Healthcare System, Pittsburgh, PA 15206, USADepartment of Rehabilitation Science and Technology, University of Pittsburgh, Pittsburgh, PA 15261 USADepartment of Bioengineering, University of Pittsburgh, Pittsburgh, PA 15261, USA

r t i c l e i n f o

rticle history:eceived 3 June 2009eceived in revised form 3 August 2009

a b s t r a c t

The purpose of this study was to evaluate the effects of three different control methods on driving speedvariation and wheel slip of an electric-powered wheelchair (EPW). A kinematic model as well as 3Ddynamic model was developed to control the velocity and traction of the wheelchair. A smart wheelchair

ccepted 5 August 2009

eywords:lectric-powered wheelchairD dynamic modelodel based control

platform was designed and built with a computerized controller and encoders to record wheel speeds andto detect the slip. A model based, a proportional-integral-derivative (PID) and an open-loop controllerwere applied with the EPW driving on four different surfaces at three specified speeds. The speed errors,variation, rise time, settling time and slip coefficient were calculated and compared for a speed step-response input. Experimental results showed that model based control performed best on all surfaces

IDedical rehabilitation

across the speeds.

. Introduction

Over 200,000 people in the United States use electric-poweredheelchairs (EPWs) as their primary means of mobility [1,2]. EPWsrovide functional mobility for people with both lower and upperxtremity impairments. Great advances have been made in theesign of electric-powered wheelchairs over the past 20 years, yethe control algorithms for these wheelchairs have improved com-aratively little since the early 1980s. Electric-powered wheelchairriving could become safer, more effective in a broader array ofnvironments, and functional for more people with the applicationf advanced control systems [3,4].

Control systems research has achieved broad application inther areas, such as telecommunications, robotics, automation, andedicine. The simple proportional-integral (PI) controller used onost EPWs today for velocity control does not perform well when

ubjected to disturbances, sensor uncertainties and load varia-ion [5,6]. In addition, wheelchair users may encounter different

nvironments and road conditions when driving indoors or out-oors. Incidence of loss of control and injury are far too frequentmong EPW users [3,5]. A substantial fraction of EPW accidentsan be directly attributed to the control system and design fea-

� This article is being submitted as a Full Paper for publication in Med. Eng. andhys.∗ Corresponding author at: Human Engineering Research Laboratories (151R-1),A Pittsburgh Healthcare System, 7180 Highland Dr., Building 4 Room 243e 151R-1,ittsburgh, PA 15206, United States. Tel.: +1 412 365 4850; fax: +1 412 365 4858.

E-mail address: rcooper+@pitt.edu (R.A. Cooper).

350-4533/$ – see front matter. Published by Elsevier Ltd on behalf of IPEM.oi:10.1016/j.medengphy.2009.08.002

Published by Elsevier Ltd on behalf of IPEM.

tures of EPWs [3–6]. Persons with severe and complex disabilitiesmight find it difficult to steer an EPW in a confined environmentor under adverse conditions such as slippery or uneven terrain orobstacles. Sometimes, even experienced users may lose control oftheir chairs under such driving conditions. Especially problematicare the actions of negotiating a slope-transition and crossing thethreshold of a doorway. These complex actions require hand–eyecoordination and fine motor control that for some individuals withhigh-level spinal cord injury, multiple sclerosis or brain injury thatmay be exceedingly challenging. For some of these people, learninghow to safely and effectively use an EPW can take hours or weeks.Fehr et al. reported that 18–26% of their patients who used a manualwheelchair could not safely operate an EPW. Their study concludedthat no independent mobility options for these patients existed atthe time of assessment [7]. Furthermore, a report using data fromthe United States emergency departments stated that in 2003 over100,000 wheelchairs related accidents were treated with 65–80%of the accidents being tips and falls [8].

Some research has been conducted on simulation and controlof EPWs. Brown et al. [9] applied optimal control theory to thedesign and development of a control system for an EPW. Theydeveloped a PID controller with self-adaptive gains. The controllerdid not consider robustness in terms of external disturbance rejec-tion. Shung et al. [10] described a computer model of an EPW andits motor control circuitry. In their later work [11], they presented

an EPW velocity feedback controller based on the rear wheel driveEPW model and motor control circuitry developed in Ref. [10].A computer simulation study showed that the velocity controllermade the EPW easier to drive under varying surface conditions.No driving experiments were reported to verify the practical use

ring & Physics 31 (2009) 1244–1254 1245

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H. Wang et al. / Medical Enginee

f the proposed controller. Another issue identified by EPW user’ss wheel slip, which frequently occurs when driving over low-raction terrain, deformable terrain, steep hills, or during collisionsith obstacles, and can frequently result in wheelchair loss of con-

rol or immobilization. The wheelchair should quickly detect thetalled state in order to let the user or control system take appro-riate action, such as planning an alternate route away from the

ow-traction terrain region or implementing a traction control algo-ithm [12]. For most automobiles, wheel slip can be accuratelystimated through the use of encoders by comparing the speed ofriven wheels to that of the coasting wheels [13]; however, thisoes not apply for all-wheel drive vehicles or those without redun-ant encoders such as most EPWs. Ding and Cooper reviewed theast researches on EPW and stated that “control algorithms forhese [EPW] wheelchairs have not improved substantially since thearly 1980s.” [5].

The goal of this research is to provide EPW users expandedndependent mobility that is safe, to eventually provide more peo-le independent mobility. The controller for this study is basedn the Versalogic EBX-12 COBRA industrial single board com-uter installed with VxWorks 6.3 real-time operating system thateplaces the Original Equipment Manufacturer (OEM) control elec-ronics on an EPW as well as wheel encoders and inertia sensorso provide the researcher with control of the driving algorithmsnd the ability to read state data. The system is semiautonomous,hich takes advantage of the intelligence of the wheelchair user

y allowing the user to plan the general route while taking overower level functions such as speed and anti-slip control. [14] Thisaper describes the evaluation of three different control methodsn driving speed variation and wheel slip of an electric-poweredheelchair (EPW): a 3D hybrid advanced control system (3D-HACS)

ased on the model of EPW that includes robust velocity controlRVC) and robust traction control (RTC) to reject external distur-ances and compensate for parameter and sensor variations, PIDontrol and open-loop control.

. Development of a 3D hybrid advanced control system

Our initial findings using a robust velocity control (RVC) algo-ithm based on a 2D EPW model are described in Refs. [15,16]. Theimulation results showed that the RVC suppressed disturbancesetter than a PI controller. In this study, we further refined the pre-

ious EPW dynamic model by considering EPW motion in 3D onnclined surfaces with cross-slopes (Fig. 1). We have incorporatedtri-axial gyroscope for providing real-time feedback of the inclinend cross-slope angles.

Fig. 1. Conceptual model of a wheelchair on an inclined surface with cross-slope.

Fig. 2. Wheelchair axis systems on a slope showing OAP as the slope surface, Crepresents the wheelchair, ˛ (up/downhill slope of surface) and ˇ (side slope ofsurface) associated with the surface, � (slope along line of EPW motion) and � (cross-slope to EPW motion) associated with the wheelchair, and the EPW direction �.

2.1. Robust velocity control

2.1.1. Modeling the EPWAn EPW is a coupled electro-mechanical system in which two

independent electrical motors produce torque to cause rotation ofthe two rear drive wheels. Fig. 1 shows the coordinate systems.The wheelchair is composed of a rigid platform and non-deformingwheels, and it moves on inclines of varying slope and cross-slope.Our 3D models is based upon the coordinate system illustrated inFig. 2, x′y′z′are fixed to the earth, xyz describe the wheelchair withthe z-axis perpendicular to the earth. The coordinate axes, x′′y′′z′′

are affixed to the wheelchair with z-axis perpendicular to the slopesurface. Referring to Fig. 2, the following relations can be obtainedamong angles in these three coordinate systems.

sin � = sin ˛ · cos � − sin ˇ · sin � (1)

sin � = sin ˛ · sin � + sin ˇ · cos � (2)

We define the traction force provided by the drive wheels asFL, FR which are dependent upon the torque the motors provide toeach wheel.

From Fig. 3, we can derive the force balance equations:

FL + FR − �(F3 + F4 + F5 + F6) − FX = M · v̇x (3)

F1 + F2 − �(F3 + F4 + F5 + F6) + FY = M · v̇y (4)

F3 + F4 + F5 + F6 − FZ = M · v̇z = 0 (5)

where

v̇x = v̇R + v̇L

2− l · (vR − vL)2

W2(6)

v̇y = (v̇R − v̇L) · l

W+ (v2

R − v2L )

2 · W(7)

FX = M · g · tan �

1 + tan2 � + tan2 ˇ(8)

FY = M · g · tan ˇ

1 + tan2 � + tan2 ˇ(9)

FZ = 11 + tan2 � + tan2 ˇ

(10)

1246 H. Wang et al. / Medical Engineering & Physics 31 (2009) 1244–1254

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oment balance about the center of mass of the system in Fig. 3ields the equations:

FR − FL) · W

2− (F1 + F2) · l = IZ · � · ω̇z

180(11)

F3 + F5) · W

2+ (F1 + F2) · H − (F4 + F6) · W

2= 0 (12)

F5 + F6) · (L − l) + (FR + FL) · H − (F3 + F4) · l = 0 (13)

here H is the height of center of mass (m), l is the distance that theenter of mass is forward of rear axle (m), IZ is moment of inertiabout z′′-axis (kg m2), L is the EPW length measured from frontxle to rear axle (m), M is total mass of EPW and driver (kg), W isidth of EPW measured between rear wheel footprints (m), � is

he friction coefficient of the surface of the slope, FX, FY, FZ are x′′,′′, z′′ component of total weight (N), FR, FL are the traction forcerovided by the motor (N), F1–F6 are the other forces acting onront or rear wheels (N), v̇x, v̇y are x′′, y′′ component of velocity ofenter of mass (m/s), vR, vL are right/left wheel velocity (m/s), ωz isPW angular velocity about z′′-axis (degree/s).

From Eqs. (3) through (13), it can be found that

˙ R = A + B

2(14)

˙ L = A − B

2(15)

z = d�

dt= 180 · (vR − vL)

� · W(16)

here A and B are given by:

= 2(FL + FR − �FZ − FX )M

+ 2 · l · (vR − vL)2

W2(17)

= (2 · (FY − �FZ ) · l + (FR − FL) · W/(2 · M · l)) − (v2R − v2

L /2 · W)(l/W) + (IZ/M · l · W)

(18)

pplying Euler’s method, we find that

R(k) = (A + B) · �t

2+ vR(k − 1) (19)

L(k) = (A − B) · �t

2+ vL(k − 1) (20)

(k) = 180 · (vR − vL) · �t

� · W+ �(k − 1) (21)

rent views of a wheelchair on a slope.

2.1.2. Model based robust velocity control systemThe models described above are essential parts of simulation

models to control the motion of the wheelchair. However, no mat-ter how detailed the analysis, these models will have uncertainparameters, such as the coefficient of rolling resistance, coefficientof friction and surface of the terrains.

The models of open-loop and closed-loop control systems thatcan be utilized to control the velocity are shown in Fig. 4 foreach driving wheel of the wheelchair. Since the open-loop sys-tem is highly sensitive to these uncertainties and hence can yieldpoor velocity control, while the feedback system can dramaticallyreduce the effects of the model uncertainty. In the experimen-tal test described in the following session, the closed-loop modelbased control system is employed as the RVC algorithm. The wholedynamic models of the chair and wheelchair-terrain interactionswere described as above. In our study, a modified PID controllerwas adopted from [17] where the input to the derivative term ofthe PID is the reference signal instead of error signal.

For motor, the moment of inertia and viscous friction of themotor are assumed small enough compared with inertia and fric-tion associated with the wheelchair thus could be ignored. Thespeed and current curve for the DC motor [18], which is of the formωw = −Im + b(Vm), where ωw and Im are respectively the angularvelocity and current of the motor, when > 0 such that the slope isnegative, and b(Vm) changes monotonically with the motor voltageVm. The motor must be constrained such that I < Im, where repre-sents the maximum current allowable before the motor is in dangerof overheating and burning out. The motor control could be treatedas an electrical drive system for the motor. In this study the AdvanceMotion Control 50A8DDE motor controller had been utilized.

2.2. Traction control

The wheel slip is usually defined by a nonlinear function of thewheel velocity ωw, wheel radius rw, and the wheelchair velocity Vas follows:

= ωwrw − V

ωwrw(22)

The wheel slip can be monitored via the above equation, whichalso functions as a switch between the RTC algorithm and RVC

algorithm, i.e.,

Controller ={

RTC, >= limit

RVC, < limit

H. Wang et al. / Medical Engineering & Physics 31 (2009) 1244–1254 1247

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3.3. Experimental protocol

The experimental protocol consisted of driving the EPW witheach of the control algorithms in-turn on five different surfaces

Fig. 4. Open-loop and closed-loop control sy

These algorithms serve as the basis for our hybrid robust con-roller that was compared to open-loop and PID classical methods.n our research, the data from the caster encoder which is theaster velocity represents the velocity of the wheelchair, and fromncoder data of the driving wheel we collect the wheel velocity.f a wheel slip was detected, there would be a difference between

heelchair velocity and wheel velocity. The threshold of slip coeffi-ient limit for whether the traction controller will be chosen basedn the experimental results.

If a slip is detected, while the driving wheel velocity is big-er than wheelchair velocity, in order to get enough traction, theontroller will slow down the driving wheel velocity until theheelchair begins moving. In case that the wheelchair does notove before it completely stops, user input may be required to

ither turn the wheelchair or backup the wheelchair to exit fromhe slippery situation.

. Experimental methods

.1. Test wheelchair

The controller hardware and sensors were mounted on a Goldenlante wheelchair frame. The core electronic systems were divided

nto high and low power components. The high current compo-ents consist of two 12 V batteries, two 420 W motors with brakes,wo industrial amplifiers, a brake release circuit, a DC–DC con-erter, and fuses. The motors and batteries are original equipmentetained from the Golden Alante EPW that was chosen as thease. The Alante base was chosen for its simplicity and abilityo operate as a front wheel or rear wheel drive EPW. The powermplifiers used were the Advance Motion Control 50A8DDE, whichre power rated for 25 A continuous and 50 A for 2 s and accept20–28 V input. The output for the 50A8DDE is controlled bypulse-width-modulation (PWM) signal and a digital direction

in. The joystick was from the wheelchair OEM from which twooltage outputs representing speed (vertical axis) and directionhorizontal axis) and are within 1–4 V ranges, with 3.5 V rep-esenting the neutral position voltage. The sensors on the EPWmployed in this study were three digital incremental encodersttached to both of the driving wheel and one of the casters asell as a six degree of freedom Micro-Electro-Mechanical Systems

MEMS) based inertia sensor amounted on the seat post of thePW (Fig. 5) which provides the linear acceleration and angularelocity of the EPW. The data collected were recorded at 200 HZn an onboard 32 Gb solid state hard drive. Control algorithmsere written in C language implemented on a VxWorks Operating

ystem.

for the model based control of a wheelchair.

3.2. Software algorithms

All control algorithms were embedded within the VxWorks real-time operating system. For open-loop control, no feedback wasapplied to the controller and the EPW actual speed was directlyproportional to the joystick output. The control output frequencyand sample frequency for data collection were set at 200 HZ.

For PID control, the instantaneous wheels speeds were used asfeedback to the controller which adjusted the error signal betweenthe desired speed (set by the joystick) and the actual wheel speedto track the desired speed.

The model based controller was based on our 3D EPW model.The physical parameters for the model were measured within thelaboratory with the inertia of the EPW was measured using themethod stated in Ref. [19]. The traction forces provided by themotor FR, FL were estimated from the current of the motor whichwas measured from sensors within the amplifiers. The anti-slipcontrol algorithm compares the speeds of the driving wheels andthe caster. The caster wheels are not powered, and therefore casterspeed provides an estimate of the EPW velocity. Loss of traction,wheel slip, was defined as a difference in the angular velocity ofthe each drive wheel with respect to the caster of greater than 20%.When loss of traction was detected, the driving wheel speed wasdecreased until the wheel slip was within tolerances, and the EPWcontinued forward progress albeit possibly at a reduced speed.

Fig. 5. The smart wheelchair platform used in this experiment.

1248 H. Wang et al. / Medical Engineering & Physics 31 (2009) 1244–1254

which

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Fig. 6. Five difference surfaces on

hich incorporated both indoor and outdoor environments (Fig. 6)nd collecting data about the wheelchair speeds. A 2.44 m Teflonheet attached to an adjustable slope ramp with maximum 5◦ wassed to simulate a slippery surface (e.g., ice, snow, wet grass). The

nitial set-up of the slope ramp is 3◦. For each of the surfaces, inrder to decrease the experimental error, the EPW was driven in theame manner for each trial. The control parameters were measurednd recorded during each trial. The driving test was carried outsing a step-response at three different desired speeds, fast 2 m/s,edium 1.5 m/s, and slow 1 m/s. All tests were conducted driving

traight forwards, turns and reverse driving tests will require fur-her development and are left for future studies. The order of testinghe driving surfaces was randomly chosen; however, for each sur-ace, the EPW was always driven with the fastest speed first, then

edium and then slow speed. Also tests on the next surface werenitiated after all the tests on the former surface were completed.he actual speeds of the two driving wheels and the caster wereollected by encoders incorporated on the EPW. For PID and modelased control, driving wheel encoder data were used as feedbacko the controller. The caster encoder data were compared with theverage of the driving wheel encoder data in the controller to detecthe slip then initiate traction control if slip was detected. Data forach trial were analyzed using Matlab 7 (R14) and normalized to0 s for comparison purposes.

In order to evaluate the performance of each control algo-ithm, the following variables were calculated and compared: riseime, settling time, speed error, speed variance and slip coefficient.ontrol algorithm performance was defined by lower errors andariances as well as faster response and shorter rise times. The riseime was measured as the time it took for the wheelchair outputpeed to rise beyond 90% of the desired speed for the first time. Theettling time was recorded as the time from beginning to the time itook for the system to converge to its steady-state. The steady-stateere was the desired speed for PID and model based control andhe stable speed for open-loop control since with open-loop con-

rol, the wheelchair could not be able to reach the desired speed.he system was considered to be steady-state while changing ofhe velocity within 95% of the desired speed. This variable showsow fast the wheelchair could settle down to the desired speed.he 10 s normalized root mean square error (NRMSE) between the

able 1hysical parameters for the test EPW and test surface, where ‘*’ means the parameters w

Result

Constant variablesH (height of COM) 23.23 cml (distance between COM and rear axle) 7.63 cmL (chair length between rear and front axle) 17.05 cmW (width of wheelchair between two rear footprints) 21.22 cmM (weight of wheelchair) 123.75 kgIZ (inertia of wheelchair to Z-axis) 5.00 kg m2

Surface variables Teflon� (friction coefficient)* 0.04˛ (up/downhill slope of road) 5◦

ˇ (side slope of road) 0◦

� (chair direction) 0◦

the experiment was conducted.

desired speed and real speed recorded by the encoders was used asthe speed error. Variance of the error between desired speed andactual speed at steady-state was used for representing the speedvariance to examine “bucking” of the control on different surfacesat different speeds. EPW drivers are sensitive the “bucking” andwill reject controllers with intolerable speed variance. The differ-ence between driving wheel speed and wheelchair speed (casterspeed) normalized to the driving wheel speed was used to definethe slip coefficient to evaluate traction control.

4. Results

The parameters for the PID controller were chosen based oncomputer simulation results. During the experimental tests the PIDparameters were Ki = 0.8, Kp = 1.5 and Kd = 1.25. Before the processof applying the model based control, physical parameters for thetest EPW system were measured (see Table 1). The mass parameterin the table includes the EPW and the test-pilot (146 lb).

Table 2 shows the overall mean, standard deviation of speederrors, speed variance, rise time, settling time and slip coefficient.For both left and right wheels, speed errors of PID (left wheel:1.46 ± 1.47 m/s; right wheel: 0.93 ± 1.03 m/s) and model based con-trol (left wheel: 1.47 ± 1.38 m/s; right wheel: 0.69 ± 0.44 m/s) weremuch smaller than open-loop control (left wheel: 2.56 + 1.99 m/s;right wheel: 1.91 + 1.58 m/s). As for the speed variance, model basedcontrol (left wheel: 1.35 ± 1.07 m/s; right wheel: 0.44 ± 0.28 m/s)was less than PID (left wheel: 1.47 ± 1.49 m/s; right wheel:1.03 ± 0.93 m/s) control while PID control was less than open-loopcontrol (left wheel: 1.99 ± 1.77 m/s; right wheel: 1.58 ± 1.39 m/s).For the rise time, both PID (3.08 ± 2.09 s) and model based(2.92 ± 1.69 s) control were slightly longer than open-loop control(2.15 ± 0.66 s), but the difference was less than 1 s. The settling timeof PID (8.59 ± 5.91 s) and model based control (8. 59 ± 5.26 s) weresimilar and less than half second longer than open-loop control(8.08 ± 5.09 s). The slip coefficient tracks the difference between the

wheelchair speed and the driving wheels speed. Table 2 shows thatmodel based control (0.04 ± 0.02) and PID control (0.06 ± 0.04) hadsmaller slip-coefficient values than open-loop control (0.11 ± 0.04).

Fig. 7a–f shows representative plots of the desired speeds andreal speeds at 1 m/s and 2 m/s for the three control algorithms on

ere found from other resources.

Tile Asphalt Slope Grass0.55 0.72 1.02 0.353◦ 1◦ 11◦ 0◦

1.2◦ 0.7◦ 8◦ 0◦

0◦ 0◦ 0◦ 0◦

H. Wang et al. / Medical Engineering & Physics 31 (2009) 1244–1254 1249

Table 2Test results of the mean, standard deviation and variance of the wheels speed NRMSE of all the three control methods.

Method Speed error (mean (std)) (m/s) Variance (m/s) Settling time (s) Rise time (s) Slip coefficient

Open loop Left: 2.56 (1.99) 1.99 (1.77) 8.08 (5.09) 2.15 (0.66) 0.11 (0.04)Right: 1.91 (1.58) 1.58 (1.39)

PID Left: 1.46 (1.47) 1.47 (1.49) 8.59 (5.91) 3.08 (2.69) 0.06 (0.04)

Fsc

Right: 0.93 (1.03) 1.03 (0.93)

Model based Left: 1.47 (1.38) 1.35 (1.07)Right: 0.69 (0.44) 0.44 (0.28)

ig. 7. A example figure of two driving wheels and caster speeds with different controlllow speed. (b) Open-loop control with high speed. (c) PID control with low speed. (d) PIontrol with high speed.

8.59 (5.26) 2.92 (1.69) 0.04 (0.02)

ers applied at low and high speeds on a grass surface. (a) Open-loop control withD control with low speed. (e) Model based control with low speed. (f) Model based

1250 H. Wang et al. / Medical Engineering &

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ig. 8. Slip coefficients of three controllers with the wheelchair driving on grass atm/s.

grass surface. From Fig. 7, one can observe that PID and modelased control methods track the desired speed better than open-

oop control.The slip coefficient of the wheelchair driving on 2 m/s on grass

urface is shown in Fig. 8, from which one can see that with modelased control, the slip coefficient was smaller than PID and open-

oop control, especially during the critical acceleration phase of thetep-response.

Fig. 9a–e shows box plots of the different variables betweenhe three control methods categorized by speed. From Fig. 9a and

one can see that for the same method, higher speeds inducedarger errors and variances than the low speed. For the rise time andettling time, the faster the speed, less time was needed. The slipoefficient, with open-loop and PID control, the faster the speed,he bigger the slip coefficient indicating greater slip was detected.owever, with model based control, the slip coefficient was visibly

ower at all desired speeds.Fig. 10a–e shows box plots of the different variables between

hree methods categorized by surface. From Fig. 10e one can seehat greater slip occurred for open-loop and PID control then modelased control. When examining the model based controller, thereas more slip on grass than any other surfaces. For the left and

ight wheel speed error (Fig. 10a and b), there was larger error onhe Teflon surface than any other surface. For the rise time andettling time (Fig. 10c and d), the tougher the surface (grass andlope), the more time was needed to obtain the desired speed ando reach a stable speed.

During the experimental tests, no slip could be seen by thenvestigators while observing the tests. However, our focus grouparticipants reported having seen there wheels slip. Therefore,uture studies should examine other surfaces or conditions. In ordero test whether the anti-slip control method was effective, we puthe Teflon on a ramp with 5◦ slope on which the wheelchair wasriven. The following Fig. 11a–c shows how the wheelchair per-ormed during this scenario. From Fig. 11a and b we observed thatith open-loop and PID control, when slip happened, the two driv-

ng wheels kept spinning while the speed of the EPW was almostero. In Fig. 11c, we could observe and recorded that the controller

ecreased the driving wheel speed in order to gain traction. How-ver, Teflon surface length was insufficient to have the EPW fullyeject slip, and regain the desired speed. Anti-slip control is an areahere further work is needed to overcome slip more rapidly and

ffectively.

Physics 31 (2009) 1244–1254

5. Discussion

The data collected indicated that both the PID controller andmodel based controller decreased the error between the desiredspeed and actual speed of the wheelchair as compared to open-loop control over all test conditions (terrain and speeds). The resultsalso showed that the model based control had smaller variances oferror than PID control and open-loop control (Table 2 and Fig. 7)showing that the speed performance of the model based control ismost consistent over different surfaces and speeds. The rise timeand settling time for the model based control were close to PID andopen-loop which indicates that the additional complexity of themodel based control did not significantly sacrifice response time todecrease speed error and variance. Furthermore, the slip coefficientfor model based control was smaller than PID and open-loop controldemonstrating that model based control has greater sensitivity andbetter control when loss of traction may occur (Table 2 and Fig. 8).Overall, model based control provided superior performance thanPID and open-loop control.

Examining the performance of the wheelchair while driving atdifferent speeds (Figs. 10a–e and 9a and b), it was observed thatfor each control algorithm higher speed had larger errors and vari-ances than the low speed. This is understandable since under higherspeed conditions, the distance traveled is longer between sam-pling periods for a fixed sampling rate. A more detailed model mayimprove the model based control at the fastest speed. Rise time andsettling time were lower at the faster speeds. The slip coefficient,with open-loop and PID control, the faster the speed the larger theslip coefficient indicating greater reduction in traction. However,with model based control, the slip coefficient was similar at differ-ent speeds because when slip exceeded the pre-defined thresholdthe algorithm decreased the driving wheel speed to increasing thetraction. Further investigation is needed to develop more effec-tive and rapid means of implementing anti-slip control. However,one challenge is to avoid introducing unnecessary complexity andmaintaining low-cost. Fortunately, sensor, computing, and memorycosts continue to decline.

Focusing on the performance of the wheelchair while driv-ing over different surfaces (Fig. 10a–e) there was greater speederror on the low-friction surface (Teflon) than with the othersurfaces for model based control. This was due to our anti-slip con-troller decreasing the driving wheel speed when slip was detected(Fig. 11), essentially trading-off speed for traction. The results ofthis study showed that our anti-slip control was ineffective if thewheelchair lost too much traction which requires further study.Future work on anti-slip control should examine control of wheeltorque as well as speed to reduce slip. This may have the desiredeffect of reducing speed error and increase effectiveness over awider variety of terrain (e.g., sand and gravel). From Fig. 10e, itcan be seen that the slip coefficient is larger for open-loop andPID control then model based control as a result of the anti-slipalgorithm. For the model based controller, the slip coefficient wasbetween the thresholds set in the algorithm resulting in higher val-ues than for the other surfaces. A rapid method for detecting terrainmay be helpful for setting terrain-specific slip coefficient controlthresholds or even entirely different control approaches.

A potential approach for detecting EPW driving terrain, slip andimmobilization is to add and analyze GPS measurements. However,nearby trees and buildings can cause signal loss and multi-patherrors and changing satellites can cause position and velocity jumps[20,21]. Additionally, GPS provides low frequency updates (e.g.,

typically near 1 Hz [22]) making GPS alone undesirable. Anotherapproach could rely on methods for detecting robot immobiliza-tion using a signal-recognition approach. Offline, a support vectormachine (SVM) classifier could be trained to recognize immobilizedconditions within a feature space formed using an inertial measure-

H. Wang et al. / Medical Engineering & Physics 31 (2009) 1244–1254 1251

F ) Left wt s.

mScq[

ig. 9. Wheelchair performances with three controllers at three different speeds. (aime with 3 speeds (d). Settling time with 3 speeds. (e) Slip coefficient with 3 speed

ent unit and optional wheel speed measurements. The trainedVM can then be used to quickly detect immobilization with littleomputation. Experimental results have shown the algorithm touickly and accurately detect immobilization in various scenarios23,24].

heel speed error with 3 speeds. (b) Right wheel speed error with 3 speeds. (c) Rise

The tougher surfaces (grass and slope) required more time to getthe desired speed and stabilize at the desired speed. These surfacesinduced more involuntary jostling of the test-pilot, which may havecaused deviation from the model based control parameters. Incor-poration of a more accurate human model within the algorithm

1252 H. Wang et al. / Medical Engineering & Physics 31 (2009) 1244–1254

F (a) LeR ve sur

mp

rm

ig. 10. Wheelchair performances with three controllers on five different surfaces.ise time on five surfaces. (d) Settling time on five surfaces. (e) Slip coefficient on fi

ay improve control. Further study should have both the humanilot and wheelchair in the 3D model.

From Table 2 and Figs. 8–10, it can be observed that the left andight drive wheels did not perform the same during the experi-ents despite no tasks requiring turns. The EPW model assumed

ft wheel speed error on five surfaces. (b) Left wheel speed error on five surfaces. (c)faces.

for simplicity that the two drive wheel motors of the EPW weresymmetric. In practice, EPW do not use matched motors, and theirparameters may vary notably resulting in differences between thespeeds of the driving wheels, especially with open-loop control.Future studies may benefit from using matched motors or a model

H. Wang et al. / Medical Engineering & Physics 31 (2009) 1244–1254 1253

F odelo

ta

pdmttaugu

ddtaiwoaaf

F

E0

ig. 11. Slip measurements with three different controllers: open-loop, PID and mpen loop. (c) Slip measurement with model based control.

hat does not assume symmetry during the further developmentnd testing.

This control system experiments could be expanded to incor-orate more driving scenarios. The results of this study may beependent on the test EPW set-up and test-pilot so further experi-entation may be necessary to generalize the results to other EPW

ypes. A wider variety of terrains should be tested such as differentypes of carpets, slippery surfaces and ramps. As more is learnedbout the challenges of driving an EPW, the information will besed to develop and refine our driving control algorithms with theoal of creating a higher level of safety and usability for all EPWsers.

In future studies, models based on front- and middle- wheelrive wheelchairs including caster dynamics will be tested; theynamics and performances of users will be included in the modelo provide better feedback from the wheelchair users; the stabilitynd safety of the users and wheelchairs should be considered dur-ng deciding the thresholds of control parameters; more sensors

ill be added and more effective control algorithms will be devel-ped to improve the performance of EPWs. At the same time, were working on to design a more compact, durable and economicffordable controller box which could be marketed and served asuture controller.

unding

This work was supported in part by Quality of Life Technologyngineering Research Center, National Science Foundation (EEC-540865), the National Institutes of Health (1R03HD048465-01A1),

based control. (b) Slip measurement with PID control. (a) Slip measurement with

and the VA Rehabilitation Research and Development Service(B3142C).

Conflict of interest

None of the authors has a financial or other relationship thatmight lead to conflict of interest concerning the publication of thismanuscript or the research described.

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