Research Article A Driving Behaviour Model of Electrical ...downloads.hindawi.com/journals/cin/2016/7189267.pdf · Research Article A Driving Behaviour Model of Electrical Wheelchair

Research ArticleA Driving Behaviour Model of Electrical Wheelchair Users

S O Onyango1 Y Hamam1 K Djouani1 B Daachi2 and N Steyn1

1FrsquoSATI Tshwane University of Technology Private Bag Box X680 Staatsartillerie Road Pretoria West Pretoria 0001 South Africa2Laboratoire drsquoInformatique Avancee de Saint de Denis (LIASD) University of Paris 8 France

Correspondence should be addressed to S O Onyango oburastevinegmailcom

Received 24 November 2015 Revised 9 March 2016 Accepted 20 March 2016

Academic Editor Jianjun Ni

Copyright copy 2016 S O Onyango et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In spite of the presence of powered wheelchairs some of the users still experience steering challenges and manoeuvring difficultiesthat limit their capacity of navigating effectively For such users steering support and assistive systems may be very necessary Toappreciate the assistance there is need that the assistive control is adaptable to the userrsquos steering behaviourThis paper contributes towheelchair steering improvement bymodelling the steering behaviour of powered wheelchair users for integration into the controlsystemMore precisely the modelling is based on the improved Directed Potential Field (DPF)method for trajectory planningThemethod has facilitated the formulation of a simple behaviour model that is also linear in parameters To obtain the steering datafor parameter identification seven individuals participated in driving the wheelchair in different virtual worlds on the augmentedplatformThe obtained data facilitated the estimation of user parameters using the ordinary least square method with satisfactoryregression analysis results

1 Introduction

(1) Motivation The manoeuvring difficulty experienced bywheelchair users with Parkinsonrsquos disease multiple sclero-sis and related handicaps is the main motivation for thisstudy Such handicaps complicate the ability to effectivelymanipulate the conventional joystick even within fairlysimple environments [1] According to Fehr et al [2] about40 of the users struggle to steer the standard poweredwheelchair with ordinary user interfaces Fehr et al observethat close to 50 of the affected user group can be assistedif better control methods with supplemented user interfacesandor support systems capable of accommodating theirneeds and preferences were employed Huge research onjoysticks and related interfaces including haptic systemshas emerged [3ndash7] and new control models [8 9] arecontinuing to develop The available driver models howeversuffer lack of individuality [10] focusing mostly on thecommon user attributes and assume that all users respond toparticular navigational situations by similar general patternsSuch driver models employ general parameters that barelycorrespond to measurements obtained from extreme usersand hardly take into consideration the contextual nature of

human response to stimuli Besides the available control andassistive techniques rarely consider the fact that the steeringcapability of users with degenerative conditions like ageingdeteriorates progressively over time Adapting the wheelchairto the userrsquos best steering behaviour may simplify the generalsteering task and limit the steering troubles attributable to theworsening disability condition of the user This necessitatesmodelling and a priori identification of the driverrsquos steeringbehaviour

(2) Background Although extensive information regardingmodelling and control of powered wheelchairs exists [11ndash17] behaviour modelling for assistance and rehabilitation isstill limited In fact apart from [18ndash23] the authors failed tolocate more behaviour models related to wheelchair driversStudies in the vast area of behaviour modelling have beenapproached mainly from the field of automotives aviationsimulators and robotic intelligence [24 25] The existingformulations in these areas have been modified progressivelyfrom linear to empirical models with the hope of findinggeneral models that represent the operatorsrsquo behaviour [26ndash28] According to [29ndash32]most of the available drivermodelsare qualitative with elaborate explanations of the driversrsquo

Hindawi Publishing CorporationComputational Intelligence and NeuroscienceVolume 2016 Article ID 7189267 20 pageshttpdxdoiorg10115520167189267

2 Computational Intelligence and Neuroscience

perception and vehicle handling techniques while othersentail detailed reports of the driversrsquo actions during normaldriving situationsThe commonquantitativemodels availablein the literature represent specific driving tasks [33ndash36] Theadaptive and comprehensive control models of the drivingbehaviour are however very few [37 38]

According to Michon [39] the entire driving task hasthree demand levels consisting of the strategic level thetactical level and the control level Each level encompassesthe driver the wheelchair and the environment The threeelements interact continuously and every state of the vehiclecan be linked to this interaction [18] The driving taskslike risk avoidance and steering velocity determination aretherefore entirely dependent upon the three elements How-ever the adaptive behaviours executed within the drivingenvironment are greatly controlled by preferences of thedriver which makes the driver a very important element inthe driving task

In the literature hierarchical structures of car drivingmodels have been presented in terms of skill based rulebased and knowledge based behaviours [40] However it ishard to verify the contributions of such qualitative modelsof perceptual processes and neural activities in the actualexecution of the driving task Pilutti and Galip Ulsoy [41]therefore considered the system identification approachusingthe back-box model with autoregressive exogenous structure(ARX) to identify the driver modelrsquos parameters Chen andUlsoy [42] also presented the same formulation approach forboth driver model and model uncertainties using the actualdriving data captured from a fixed-base driving simulatorThe model however employed the autoregression movingaverage with exogenous inputs (ARMAX) to improve onaccuracy based on the consideration that ARMAX can yieldresiduals closer to white noise with fewer parameters giventhe same model order The system identification approach isalso considered in [10] nevertheless the authors do not takeinto account exogenous inputs in their affine autoregressivesystem but instead derive a multistep model output errorcriterion and present an algorithm to identify the parametersof the subsystemusingmeasurablemotion data Although theconsideration of black-box method of system identificationis straight forward and common with availability of dataauthors believe that sufficient information can be foundto relate the driverrsquos actions to the perceivable contextualenvironment

The study contributes to wheelchair driver behaviourmodelling by formulating a simple steering model that isalso linear in parameters The complexity of the steeringmodel is very instrumental in determining whether themodel is applicable on-line for real-time adaptation or off-line for periodic or permanent adaptation Derivation ofthe presented model is based on deductive reasoning fromthe known steering operations and systematic relationshipsbetween the observable behaviours taking into considerationthe environmental situation It however shuns the consider-ation of social events occurring within the driverrsquos mind Inorder to capture the adaptable demands of the driver at thecontrol and tactical levels the driver-specific parameters areidentified The steering data obtained from the augmented

virtual-reality wheelchair platform known as Virtual-Space1 (VS-1) at FSATI (FSATI is an acronym for French South-African Institute of Technology) in TUT (TUT is an acronymfor Tshwane University of Technology) [43] is utilised inthe identification of the model parameters The identifiedparameters are then used to curve-fit and compare the modelagainst the observed data

The presented steering model can be used to adapt thewheelchair to the userrsquos steering behaviour according toFigure 1 Due to its simplicity and linearity the proposedmodel is applicable to wheelchair self-tuning adaptive con-trol to observe the preceding behaviour and self-tune theparameters to fit the observation

This paper is organised as follows Section 1 has presentedthe introduction in terms of the motivation and backgroundof behaviour modelling taking into consideration the inter-active elements involved in the accomplishment of steeringtasks Section 2 presents some of the approaches that havepreviously been considered in the derivation of specificdriver control models including the available wheelchairdriver behaviour models In Section 3 simulator evaluationand summary of the experiments conducted to obtain thenecessary steering data for driver identification are presentedThe driver behaviour model is presented in Section 4 whilethe statistical analysis of the model and its comparison toobserved data are discussed in Section 5 Finally conclusionsand future recommendation are presented in Sections 6 and7 respectively

2 Related Path Planning Models andDriver Adaptation Literature

Driving begins when an optimal path to the destinationis conceived This involves careful consideration of theentire workspace Based on the associated constraints theconception is accomplished either fully in advance beforesetting out the journey or in parts within conceptuallysubdivided sections of the workspace during the drivingprocess Path planning for robotic automation has beenachieved by deliberate and reactive planners Deliberateplanners including cell decomposition road-maps and evo-lutionary algorithms ensure prior plan of the whole journeyHowever they entail expensive computations that limit theirpractical application in higher dimensional configurationsDeliberate planners are therefore commonly applied tounmanned ground vehicle in confined environments On thecontrary local planners provide cheap trajectory planningalgorithms based on sensor information captured from thelocal surrounding Local planners ensure both faster and real-time update of the environmental information as well asreactive response to stimuli As a result they are commonlyaimed at ensuring safety and stability of both the driverand the vehicle Nonetheless the paths obtained from theseapproaches may not be optimal and the vehicle could betrapped into localminimaThismakes the application of localplanners to unmanned mobile systems inefficient withoutdeliberate planners Both deliberate and reactive planners stillcommand significant influence in the literature However the

Computational Intelligence and Neuroscience 3

Joystick Driver behaviour

model Controller Wheelchair

Environment

User Position

User parameters

Intentiondetection model

0

x

y

zlfloorlceil

rfloorrceil

][

Figure 1 The control diagram of a wheelchair with integrated driver behaviour model and intention detection model

current focus is aimed mainly at integrating deliberate andreactive planners into unified structures to overcome thedrawback of individual planners This explains the currentincrease in hybrid planners [44]

Although wheelchair steering also involves both delib-erate and local planning the actual control or steeringbehaviour of the users can be considered local This ischaracterised by reactive adaptations that the user performsin response to perceived risks and undesired situations Localplanners can therefore be considered in the formulation ofwheelchair driversrsquo steering behaviour Besides the driverrsquospresence eliminates the common limitations of local plan-ners as heshe is personally available to solve the nonop-timality and the global (local minima and trap situations)problems The common local planners in literature includenearness diagram dynamic window velocity obstacle andpotential field methods The strength of nearness diagramsis based on the situation analysis performed by the system toselect the new direction ofmotion that reduces the local min-ima Both dynamic window and velocity obstacle approachesoperate in the systemrsquos velocity space by admitting allvelocities that allow stopping without collision Howeverthey are computationally intensive and only up to 10ms hasbeen achieved with dynamic window approach according to[45] The velocity obstacle approach also requires completeknowledge of other agents in the environment includingtheir future dynamics Besides the implementation of theiranalytical solutions is more difficult with environmentaluncertainties and noisy data from the agents [46] On theother hand the potential field method is known to beldquoelegantrdquo and compatible to most real-time problem solvingtools with minimal computational demands

21 The Potential Field Method The Artificial Potential Field(APF)method is therefore considered in this studyTheAPFmethods allocate the potential function in (1) in the config-uration space by representing the goal as an attractor andobstacles as repellers The potential field function denotedas Uart is defined as sum of the attractive potential Uatt andrepulsive potential Urep The force function can be obtainedby computing the negative integral of Uart

Uart = Uatt + Urep (1)

211 Attractive Potential The attractive force is commonlysimply represented to attain itsminimumat the intended goal[47ndash49] However because the driver is always available inwheelchair steering to provide the motivating force to the

goal the conventional Khatibrsquos [47] attractive potential maybe unnecessary in the wheelchair steering behaviour model

212 Repulsive Potential The repulsive potential is oftenconsidered to have an inverse relationship with the squareof obstacles distance 1205882obst In the literature the followingrepresentations are commonly used to express the repulsivepotential

MinimumDistance RepresentationHere the repulsive force iscomputed out of the minimum distance between the obstacleand the vehicle at time instant 119896

Frep119896 = 1198961199001

min (1205882obst119896) (2)

where 119896119900is a positive constant that scales the repulsive

potential while 120588obst(q qobst) is the distance between thevehicle at position q and the obstacle at position qobst

Multiple Distance Representation Here several 119894 equidistantpoints on the obstacle are selected and the repulsive forcedirected to the vehicle is computed at every time instant 119896according to the following expression

Frep119896 =119873

sum

119894=1

119896119900

1

120588

2

obst119894119896

(3)

Representation with Restricted Radius of Influence Latombe[50] proposed an adjustment to the conventional repulsivepotential by limiting the radius of influence 120588

0obstof the

obstacle This eliminates unnecessary obstacle effects on thevehicle when 120588obst119894 is large enough to allow safe passage

Urep =

1

2

119896119900(

1

120588obstminus

1

1205880obst

) 120588obst le 1205880obst

0 120588obst gt 1205880obst

(4)

Directed Potential Field (DPF) The approach proposed byTaychouri et al [51] is of special interest Apart from usingdistance representation and taking into account the positionof the obstacle and its direction of motion it also allocatesmaximal repulsive potential whenever the vehicle is movingdirectly towards the obstacle and negligible potential when-ever the obstacle is at right angle to the direction of motionDue to its strength and ingenious simplicity this formulation


is considered to represent the subjective risk function of thedriverrsquos behaviour during steering

Frep119896 =119873

sum

119894

119896119900

(cos120572119894)

119898

120588

2

obst119894119896

(5)

In (5) 120572119894is the angle between point 119894 of the obstacle and the

direction of motion of the vehicle while119898 is a gain constantThe main causes of discontents that have seen several

modifications in the potential field approach [52 53] includethe availability of local minima and trap situations [54]the nonoptimality problem and the goals nonreachablewith obstacles nearby (GNRON) Some of the recent APFmodifications that have been proposed include the Evo-lutionary Artificial Potential Field (EAPF) method [55]which integrates the APF method with genetic algorithmsto derive an optimal potential field function that ensuresglobal planning without local minima The EAPF modeluses both Multiobjective Evolutionary Algorithm (MOEA)to identify the most optimal potential field function andthe escape force algorithm to avoid the local minima In[53] the concept of Parallel Evolutionary Artificial PotentialField (PEAPF) is introduced as a new path planning methodin mobile robot navigation PEAPF improves the earlierEAPF method by making the controllability of the vehiclein real-world scenarios with dynamic obstacles possibleThe recent Bacterial Evolutionary Algorithm (BEA) [56]also compares closely with PEAPF introducing an enhancedflexible planner to improve the EAPF method While thesealways solve the APF drawbacks the logical consideration ofthese modifications with regard to real-time applications inmost cases turns out to be unrealistic because the resultingmodels involve expensive computational steps [57]

The important considerations in the approach of choicefor wheelchair drivers include the features that enhance theiradaptational behaviours within the local environment Thisis because unlike in robotics the driver is always availablein wheelchair steering to solve the globality problems Theauthors therefore believe that global planning at the expenseof computational simplicity may constitute a worthless trade-off especially for real-time applications The features ofconsideration regarded in this study include computationalcomplexity path smoothness context scalability directional-ity and handling capability in complex environments

Computational Complexity The implementation of a controlmodel in a real-time application is strongly influenced bythe amount time it takes to compute the control signal thatgenerates both feasible path and desired speed Accordingto [57] it is more suitable to have a very fast path plannerfor real-time applications than to perceive a vehicle that onlylearns its workspace to memorise a variety of standard pathsA finite control behaviour encompassing only the perceivableworkspace can be considered to increase plannerrsquos computa-tional speed

Path SmoothnessThis regards the capability of the planner tointerpret the dynamic and static behaviours of other agentswithin the workspace in order to execute the adaptive control

Table 1 Comparison of the potential field modifications based ontheir applicability in the formulation steering behaviour of wheel-chair users

APF EAPF PEAPF BPF DPFSmooth planning

Local planning

Global planning

Complex environments

Highly scalable

Directionality

Min computational time

without jerks The response speed of the planner and thecomputedmagnitude of the steering signal are very crucial indetermining the quality of the resulting path A driver modelwith smooth planning capability could be instrumental inthe assistance of wheelchair users with disabilities like handtremors and cognitive disorders

Context Scalability It is important that only behaviours ofthe agents that influence the driverrsquos subjective risk are takeninto consideration Scaling down the entire workspace forinstance to the area enclosed by the look-ahead radius andfurther to a smaller area encompassing the driverrsquos field ofview may reduce the complexity of analysis and enhance thequality of control

Directivity This concerns the amount of influence imposedon the driver by virtue of the agentrsquos position and the directionof motion of the vehicle Directed models enhance smoothervariations in the sensor signals and therefore influence thequality of the generated path

Handling Capability in Complex Environments The handlingcapability regards the computational speed of the planner andits ability to take into consideration the dynamic behaviour ofother agents in the configuration space

Table 1 compares the features of some recent potentialfield methods with the proposed DPF

22 The Available Wheelchair Driver Models in LiteratureMost of the wheelchair driver models in the literature areconcerned with detection of the userrsquos intention in termsof the direction of travel rather than adaptation of thewheelchair to the userrsquos steering behaviour In [58 59] forinstance an intelligent decisionmaking agent is presented fordriverrsquos intention detection in uncertain local environmentsbased on the Partially Observable Markov Decision Process(POMDP) Using the same methodology a global intentionrecognition model is also presented in [60] for autonomouswheelchair navigation Besides a multihypothesis approachis considered in [61 62] to predict the driverrsquos intentionand provide collaborative control by adjusting the steeringsignal to avoid observable risks during navigation Theuse of Bayesian networks for user intention recognitionand estimation of uncertainty on the userrsquos intent has also


plusmn120596w

120575

rx

Nx

rp120596r

minusr

+r Fx

Tc1

Tc2

120596r = 120596s

120596a 120591a

(a)

Front roller

Front roller

Right roller position encoder

(b)

Figure 2The roller system on the motion platform that enables both rotational motion of the wheels and the mapping of the wheelrsquos motioninto the virtual world

been considered [19 20 63 64] These Bayesian networkapproaches formulate the intended direction of the user on-line during navigation Although the uncertainty involved istaken into consideration suchmodels do not incorporate theadaptable demand of the driver into the wheelchair

Apart from the intention detection models a filteringapproach that presumes an experienced reference driver toeliminate the user handicap is considered in [22] while thetask oriented models that generate autonomous behavioursat different levels are proposed in [65ndash70] The task ori-ented models may allocate the driver more or less controldepending on the contextual need at one level and enable thewheelchair to perform autonomous tasks without the driverrsquosinput at another level In both cases however the resultingbehaviour may not represent the actual steering preference ofthe user

The reactive model of wheelchair driver behaviour thatcan be used to adapt wheelchair steering to the userrsquosbehaviour is proposed by [18] The model is derived in termsof two force components the driving force F

119889(6) and the

environmental or obstacle force F119896(7)

F119889=

119870

120591

[119881max (1 minus119883saf119883act

) e minus 119881act] (6)

F119896= 119896119900exp(minus

120588obst119861

)n119863V (7)

where 119870 is the weight constant 120591 is the driverrsquos relaxationor reaction time 119881max is the maximum limit of wheelchairvelocity 119883saf is the safe distance e is a unit vector in thedirection of motion and 119883act is the current wheelchairposition Additionally 119861 is a constant that represents therange of the repulsive force n is a unit vector in the directionof the moving obstacle and119863V is the directivity factor

Although this model is good it is nonlinear and does notrepresent in a simple way the diminishing influence of therisks positioned behind or perpendicular to the direction ofthe wheelchairrsquos motion In addition it is not tested to realdata

3 Experiments and Acquisition ofSteering Data

31 Evaluation of the VS-1 Simulator The experiments toobtain the required steering data have been conducted onthe VS-1 simulator [71] depicted in Figure 3 The platformrsquosbasic components include the visual interface the motionplatform and the controller The virtual interface presentsto the user the synchronised virtual world either throughstereoscopic Head Mounted Display (HMD) or through thefour-connected screens display The motion platform thatconsists of a user ramp and a stage can either host anelectrical or a manual wheelchair whereas the controllerinterlinks the motion platform and the display unit Theroller system in Figure 2 on the motion platform enablesboth rotational motion of the wheels and the mapping of thewheelsrsquo motion into the virtual world This is facilitated bythe force exerted on the rollers as a result of the wheelchairrsquosand the userrsquos weight The pulse generating rotary encodersmounted on the rollers enable determination of positionvelocity and acceleration of the wheelchair in the virtualspace and facilitate themeasuring of differential drivemotionas the driving wheels in direct contact with the rollers rotateThis generates forward or backward translations in the virtualworld with equal angular velocities 120596

119877and 120596

119871for the right

and left rear wheels respectively and rotational translationswith 120596

119877= 120596119871

In Figure 2 the actuated force feedback roller (119903119909)rotates at a velocity of plusmn120596 119865

119909represents the frictional force

between one single roller and the wheel while the variables120596119898

and 120591119898

represent the actuatorrsquos angular velocity andtransferred torque respectively Slip dynamics at the pointof contact between the driving wheels and the rollers couldbe the major source of simulator error that may contributeto inaccurate representation of the wheelchairrsquos dynamicsin the simulator According to [72] slip is defined as thedifference between the rotational velocity of the wheels andthe actual or absolute velocity of the wheelchair Howeversince the actual linear velocity of the wheelchair on the


Multiple virtual world displays

Main system controller

Motion platform actuators

Wheeled mobility motion platform

Platform ramp

Users wheeled mobility

Useroperator stage

Figure 3 Virtual-Reality System 1 (VS-1) the augmented virtual and motion simulator at FSATI for wheelchair simulations

motion platform is zero the theoretical difference betweenthe rotational velocity of the driving wheel and the rollersis used to account for the possible wheel slip errors in thesimulator A comparison between the wheelrsquos velocity and themotorrsquos current in relation to the torque 120591

119908of the driving

wheel is also made to determine the wheelchairrsquos instabilityThis involves examining the basic properties of the dc motorrequired in the theoretical determination of the output torque120591119898 Instability is considered if 120591

119898= 120591119908 In this case a

method for automobile traction control [73] is used in thestabilisation However to avoid the tipping-over instability ofthe wheelchair on the simulator fastening straps have beenused to hold the wheelchair in position

Regarding the data collection experiments an electricalwheelchair is used with the original embedded joystick as themain interface To effectively evaluate the steering behavioursof the participants in relation to the general environmentthe virtual worlds attempted as much as possible to representthe areas encountered frequently by the participants Sevenindividuals participated in the data collection A few of thedata collection experiments are elaborated in Sections 33ndash35 The seven participants include a female and six malesaged between 26 and 74 Although none of the participantshad a degenerative disability condition or tremors three wereregular wheelchair users while the rest had not used thewheelchair before The first time users had to familiarisethemselves with the steering of wheelchair in both virtual andreal environments before the capturing of their steering datacould start Table 2 presents the participantsrsquo information

Five desirable characteristics of the VS-1 platform regard-ing this study are noted (1) it guarantees safety of theparticipant (2) it eliminates the need for sensor installation(3) it enables the user to feel the synchronised pitch androll rotational driving motions on flat and inclined surfaces

Table 2 Information about the seven participants who took part inthe steering task for data collection

Age Sex UsageParticipant 1 50 Male NeverParticipant 2 26 Male NeverParticipant 3 52 Male RegularParticipant 4 60 Male NeverParticipant 5 74 Male RegularParticipant 6 30 Female RegularParticipant 7 46 Male Never

reducing the possibility of simulator sickness (4) experi-ments can be performed using real manual or electricalwheelchairs the electrical wheelchair can be steered usingthe standard embedded joystick or any other available userinterface and finally (5) the virtual world (examples inFigures 4 and 8) provides the user with a close representationof a real environment and a feeling of collision sound

Notwithstanding the above advantages the potentialusefulness of the motion platform in user evaluation canonly be acceptable if the virtual world and the impressionof motion in the simulated environment conform to the realworld to a certain extent A study evaluating participantsrsquoperception of degree of presence and comparing the usabilityof the simulated world of VS-1 with the reality world isconducted in [71] The degree of presence compared to thereal world is evaluated in terms of spatial presence involve-ment realism and system value a portion of evaluationoutcome is presented in Figure 5 Spatial presence indicatesthe extent to which participants acknowledge their existencein the environment in the actual sense while involvement


Figure 4 A user steering the wheelchair in a living room setup inboth virtual and reality environments

concerns system response to user inputs and the resultingmotion feedback Realism is expressed by the use of a realwheelchair and the rotational motion of VS-1 platformwhile system value represents the degree to which usersrecognise the motion platform in general as an evaluationaid According to the study the participants experienced 75disorientation with regard to steering tasks and platformusage at the beginning of evaluation in both reality andsimulated world However adaptation was much faster inboth cases with 81 adaptation rate in the reality world and69 in the virtual world Considering the presented tasks theparticipants observed 73 and 75 challengesuncertaintiesin the reality and simulated worlds respectively The studythus demonstrates a fair similarity between the steeringexperience observed within the virtual world and within thereality world Figure 4 for instance shows the user capturedwhile steering the wheelchair in a living room environmentin both virtual and reality worlds during the evaluation

As in most simulators the existence of cue conflictsbetween the motion platform and the virtual world dueto lack of the platformrsquos linear motion and the sensorysimulation artefacts (such as reduced field of view in thevirtual world)must be acknowledgedMoreover in themindsof participants however important it is a simulation task willalways be perceived as a simulation exercise with few risksfor careless actions and few rewards for desired behavioursNevertheless studies have demonstrated the feasibility ofsimulation techniques and have shown that simulation resultsapproximate those obtained by other methods [74] Authorstherefore trust the relative validity of VS-1 as sufficient fordriver behaviour assessment

32 Experimental Data Captured for Behaviour ModellingWhile it is apparent that complete success inmodelling driverbehaviour requires vast information that may not be fullycaptured by experiments alone the platform provides thefollowing sensor information for utilisation

(1) Range or distance between the wheelchair and otherobjects (120588obst)

(2) Range rate or velocity of the wheelchair relative toother objects (]obst)

(3) Direction of an object from the position of wheelchair(120601obst)

(4) Absolute velocity of the wheelchair (]119896)

(5) Yaw angle of the wheelchair (120601119896)

Besides VS-1 also avails yaw rate pitch angle and roll angle

33 Experiment 1 Experiment 1 is conducted in a ldquoriskrdquofree environment The word ldquoriskrdquo is used in this studyto represent the objects or agents that the driver wouldnot wish to steer over or closer to or collide onto Goalpositions 119866

1to 1198665are set 4m away from the starting point

119878 at angles 90∘ 60∘ 30∘ 0∘ and minus30∘ respectively In eachtrip the participant is directed to drive five times fromposition 119878 (with wheelchair initially oriented towards 119866

1) to

all the goals Trajectories and speeds observed during theexperiment are shown in Figure 6 It is noticeable that steeringtowards 119866

1involved a steeper rise in steering speed as

compared to the restMore skewed directions of the goal fromthe initial wheelchair orientation at position 119878 result in slowerinitial accelerations Explanation regarding this behaviouris considered common knowledge that drivers constantlyperceive an instantaneous or look-ahead goal whose positionfrom the vehicle is a function of the available steering spaceand path curvature According to Figure 6 highly skewedglobal goals involve highly curved paths at the beginningof the journey implying closer initial instantaneous goalsand slower initial accelerations Desired steering velocityis therefore related to position of the instantaneous goalBesides participants prefer aligning themselves to the globalgoal (if possible) at the initial phases of the journey Oncealigned the position of the instantaneous goal rapidly shiftstowards the global goal and steeper rise in speeds is realisedThis is the observable pattern however the amount of shiftwith regard to the environmental situation is subjective Itmay be concluded therefore that the local driving velocity ina risk free environment is related directly to the position of theinstantaneous goal and is influencedmajorly by the curvatureof the path

34 Experiment 2 The second experiment is conducted ina configuration with an object placed 4m 8m and 12maway from the starting point in the first second and thirdtrip respectively In each trip the participant is advised todrive from the starting point close to (0 0) in Figure 7to the goal approximately 15m away Figure 7 depicts thetrajectories and the speeds captured fromone participant It isobservable that although the participants deviate away fromthe observed risk the availability of sufficient space withinthe configuration enables them to choose the paths with littleeffect on the desired steering speed

35 Experiment 3 The third experiment observes the steer-ing behaviour of the participants in the living room envi-ronment depicted in Figures 4 and 8 In this experimentparticipants are advised to drive five times to the goals 119866

1

1198662 and 119866

3from the starting point 119878 without speed or path

restrictions Interestingly most participants considered thepaths and speeds depicted in Figure 9 allocating additionallocal priority to the local risk compared to the global goalIt may be important also to note that participants preferredlonger safer paths as opposed to shorter risky paths theldquomagnitude of riskrdquo in this case is determined by the amountsteering accuracy required to avoid collision At positions


Spatial presence Involvement Realism System value0

10

20

30

40

50

60

70

80

90

100

573

638

63 68

3

VS-1

rate

d pr

esen

ce (

)

(a) Degree of presence

Real world Simulated world0

20

40

60

80

100

120

75

7581

6973

75

Rate

d (

)

Disorientation at the beginning of the taskAdaptation to steering taskGeneral challagesuncertainities

(b) Comparative participantsrsquo experience in real and simulated worlds

Figure 5 Virtual-Reality System 1 (VS-1) the augmented virtual and motion platform at FSATI for wheelchair simulations

minus05 0 05 1 15 2 25 3 35 4minus2

minus1

0

1

2

3

4

x (m)

y (m

)

Wheelchair trajectory

Path 1Path 2Path 3

Path 4Path 5

S

G1

G2

G3

G4

G5

(a)

Path 1Path 2Path 3

Path 4Path 5

0 1 2 3 4 5 6 7 8 9minus02

0

02

04

06

08

1

12

14

16

t (s)

Spee

d (m

s)

Wheelchair speed

(b)

Figure 6 Wheelchair trajectories and speeds observed during experiment 1

A B C and D the apparent possibility of collision withfurniture and reduction in the immediate forward spacealong the perceived curved path compels participants toobserve closer instantaneous goals this accordingly resultedin the reduction of the steering speed at the respective pointsas depicted in Figure 10

4 Driver Behaviour Modelling

According to the intentional stance strategy Dennett [75]treats an entity (an organism or artefact) as a rational agenthaving the ability to regulate its choice of action by itsdesires and beliefs Dennett then defines ldquobehaviourrdquo as a


minus2 minus15 minus1 minus05 0 05 1 15 2

0

2

4

6

8

10

12

14

16

x (m)

y (m

)Wheelchair trajectory

Path 1Path 2Path 3

TableP1

P2

P3

(a)

Path 1Path 2Path 3

0 2 4 6 8 10 12 14

0

05

1

15

2

t (s)

Spee

d (m

s)

Wheelchair speed

(b)

Figure 7 Trajectories and speeds of wheelchair observed during experiment 2

Figure 8 The virtual living room environment considered forexperiment for experiment 3 perimeter wall not shown for clarityreason

goal oriented activity of an agent that can only be understoodby assigning intentions or goals to the agent Modelling thedriving behaviour of an individual thus involves definingone of the numerous goals that a driver may be requiredto reach Generally different drivers demonstrate differentsteering actions and reactions within the same environmentto achieve the same objective These subjective behavioursare commonly related to the driverrsquos capability in termsof decision making (choice) and risk taking (desires) andare affected by personality experience state of driver taskdemand and environment Adapting an artefact to exhibitthe desired characteristics of an individual and to take intoaccount the evolving and dynamic behaviour of users maythus be approached in two ways namely

(1) System TrainingHere the model learns by observingover time the way human drivers execute particular

minus4 minus2 0 2 4 6 8

minus7

minus6

minus5

minus4

minus3

minus2

minus1

0

1

2

x (m)

y (m

)

Wheelchair trajectory in a living room environment

WallObstacles

Path 1Path 2Path 3

G1

G2

B

AS

C

D G3

Figure 9 Wheelchair trajectories observed during experiment 3The rectangular shapes in the configuration space represent theliving room furniture

tasks Once a task is perfectly learned the modelcan proceed to learn other tasks This approachcould be applicable to motor-vehicle driving tasksbecause of the regular nature of the motor-vehicledriving and the fact that most vehicle-driving tasksare well defined and easily representable by heuristicsIn the wheelchair however the workspace is very


0 2 4 6 8 10 12minus05

0

05

1

15Speed observed in path 1

t (s)

A

B

Spee

d (m

s)

(a)

t (s)0 2 4 6 8

minus05

0

05

1

15 Speed observed in path 2

BA

Spee

d (m

s)

(b)

t (s)0 1 2 3 4 5 6 7

minus05

0

05


DC

Spee

d (m

s)

(c)

Figure 10 Wheelchair speeds observed during experiment 3 in the living room experiment

complex andundefinedwith various tasks lacking thechronological rules of execution

(2) Representing the Entire Driving Behaviour Theoreti-callyThis approach has been considered in this paperAll local tasks performed by the driver are consideredtogether to realise the driving behaviour Theoreticaldriver behaviour models of this nature are initiallylimited in scope and may not perfectly representthe behaviours considered specific or specialised innature However they can be advanced over time toclosely predict the actual driving behaviour Thesetheoretical driving models may be validated by com-paring their outputs against some real data fromhuman drivers

41 Dynamic Representation of Driving Behaviour Fourmajor factors are therefore considered to influencewheelchair driving as follows The first prompts the user toexert some force to begin or continue in motion pertains tothe difference between the actual wheelchair position andthe target position (in this case the instantaneous goal) Thisfactor is the primary motivational element that instigatesthe driver to move as long as it exists the wheelchair driveris understood to apply and continue applying the drivingforce The second factor influences the amount of forceexerted in ldquoattemptrdquo to minimise the positional differenceThis factor the desired velocity is related to the urgency oraverage time required by the user to accomplish the drivingtask at hand and it is usually a function of disposition and

the prevailing personal desire and priority of the driver Thethird factor concerns risk assessment and involves both thedriving capability of the user and the driverrsquos safety opinionof the environment All these factors contribute concurrentlyleading to variations in wheelchair velocity while in motiontowards the goal Besides there exists an interrelationshipbetween the three factors in that the users establish asubjective constant risk level and when this is exceeded acompensation mechanism is activated For instance thismay involve altering the position of the instantaneous goalwhich then alters the direction and speed of driving Finallyit is important to observe that the amount of force exertedis constrained by physical limits of the wheelchair The localdriving velocity ] limited by maximum wheelchair velocity]max is therefore considered to be a function of goal ]des(119892119894)and environmental situation ]env(env) as presented in

] = 1003816100381610038161003816

]des (119892119894) + ]env (env)1003816100381610038161003816

le ]max (8)

42 Desired Steering Velocity Drivers are generally believedto prefer some constant driving speeds in environments withminimal risk factors Desired speed is a personality factorthat varies from one individual to the other It is affected notonly by composition of the workspace but also by the impliedsteering complexity and user experience The composition ofthe workspace introduces an aspect of risk and safety whichcompels a driver to take on some adaptation mechanisms inorder to limit the perceived risk to an acceptable subjectivethreshold Such mechanisms generally confine the localdriving speed to a safe minimum A discussion in this regard


is presented in Section 43 The steering complexity on theother hand pertains to influence of complex orientationalmanoeuvres involved in the steering task including effectspath curvature Disassociating the influence of risks resultingfrom environmental configuration from the desired speedand considering desired speed as a function of the steeringcomplexity alone result in (9) where the desired velocity isconsidered to be a function of path curvature in the directionof the instantaneous goal As presented in (9) desired velocityonly takes the observable variables having a systematicrelationship with the steering behaviour into considerationand avoids the effects of nonquantifiable subjective factorsincluding user experience and task urgencies

]des = 119904descos119901(120601119896minus 120601119896minus1) e (9)

where 119901 is a constant 119904des is the desired driving speed 120601119896is

the direction of thewheelchair at time instant 119896 and cos119901(120601119896minus

120601119896minus1) is the influence of path curvature on desired velocity e

as expressed by (10) is the direction of desired velocity

e =q119871119896minus q119896

10038161003816100381610038161003816

q119871119896minus q119896

10038161003816100381610038161003816

(10)

In (10) q119871119896

is the position of the instantaneous goal while q119896

is the instantaneous position of the wheelchair

43 Influence of Risk and User Adaptation Mechanism Colli-sion or threat avoidance and goal-seeking reactions constitutethe driverrsquos fundamental behaviours In fact in most casesthe capability of a wheelchair driver is evaluated based on theability to avoid threats and collisions during steering Besidescommon wheelchair accidents that have resulted in severewheelchair damages and injuries to the driver can be relatedto collision Collision avoidance is therefore elemental to thesafety of both the wheelchair and the user Drivers generallypresume some constant risk thresholds and safety marginsthat they seek to observe in the vicinity of danger duringsteering When such thresholds are exceeded certain risk-compensating mechanisms are initiated to minimise the risklevel In the Taylorrsquos risk-speed compensation model [76]it is observed that drivers regulate their driving speeds inaccordance with the magnitude of the perceived risk in sucha way that larger magnitudes result in slower speeds In orderto adapt the wheelchair to such behaviours and eliminate thecommon variations in the driversrsquo level of attention properrisk detection systems need to be instituted on thewheelchairThe following two hypotheses are proposed in this paper asthe main adaptation references commonly presumed by thedrivers to confine wheelchair within the limits of safety

(1) Time-to-risk (TTR)(2) Distance-to-risk (DTR)

The time-to-contact with a risk is a function of both thewheelchairrsquos distance from the risk and speed of traveltowards the risk The consideration of TTR naturally impliesthat the wheelchair can reach or get very close to risky objectsat very low velocities On the other hand DTR means that

minus002 minus001 0 001 002 003 004 005 006 007minus003minus002minus001

0001002003

Influence of risky situations on wheelchair steering

x

y

drisk = 4

drisk = 5

drisk = 6

Figure 11 Influence of risky situations on wheelchair steering with119898 and 119899 = 2 and with distance-to-risk 119889risk considered as the mainuser adaptation reference

the driver will maintain a comfortable distance from therisk Expression (11) is considered to represent the driversrsquoavoidance behaviour in the vicinity of risks

]env119896 = minus119896env119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(11)

where 119896env 119898 119899 and 119873 are constants 120601obst119894 is the instan-taneous direction of point 119894 of the risk from the positionof wheelchair 120601

119896is wheelchair direction at time instant 119896

and 119860 is the adaptation mechanism presumed by the userFigure 11 depicts the variation of (11) with respect to differentpositions and directions of risks in the workspace with DTRpresumed as the main adaptation reference The strength of(11) is based on the aspect that only risks within the fieldof view affect steering behaviour Risks considered closerand directed to the viewer have greater influence comparedto those viewed as skewed and further away It thereforescales down the workspace to a smaller workable field ofconsideration Taking both (9) and (11) into account themodel considered to represent the driverrsquos behaviour in thelocal context is represented by

]119896+1

= ]119896+ 119896] (]des minus ]

119896) minus 119896env

119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(12)

5 Simulation Results and Discussion

51 Parameter Identification and AdaptationMechanism Thelinearity in parameters of the proposed driver behaviourmodel enabled the consideration of ordinary least squaresmethod in the identification of parameters In addition themoving average filter with a span of 20 is used in smoothingthe captured data The result of regression analysis of themodel is presented first in Table 3 where the DTR criteriapresented in (13) are considered as the primary adaptationmechanism adopted by the participants to avoid collision


Table 3 Statistical analysis of the model with DTR being the adaptation mechanism Indicated constants represent a pair that resulted in thehighest coefficient of determination

119901 Parameters Std error 1119905stat Max Dev 119877

2

Participant 1

2119896] 00023296 00000493 212 0021145

00066778 09998727119896env 00000607 00000042 692 0069456]des 21620485 00000664 0003 0000031

Participant 2

1119896] 00013058 00000457 350 0034998

00044821 09998751119896env 00000168 00000050 298 0297619]des 31936471 00000572 0002 1791e minus 5

Participant 3

2119896] 00016111 00000638 396 0039600

00282700 09998215119896env 00001812 00000042 232 0023179]des 29748170 00000809 0003 2720e minus 5

Participant 4

1119896] 00022988 00000481 210 0020924

00096421 09998336119896env 00001566 00000041 262 0026181]des 15590495 00000483 0003 3098e minus 5

Participant 5

1119896] 00011705 00000330 282 0028193

00048858 09999171119896env 00000525 00000024 457 0045714]des 23263703 00000322 0001 1384e minus 5

Participant 6

2119896] 00033319 00003469 104 0104115

00288915 09992932119896env 00002114 00000097 459 0045885]des 20650043 00003439 0017 1665e minus 4

Participant 7

2119896] 00007837 00000496 633 0063290

00108345 09998355119896env 00001583 00000048 303 0030322]des 55191529 00000688 0001 1247e minus 5

risks and also in Table 4 where TTR in (14) is the primaryadaptation mechanism

DTR119896= 120588obst119896119894

q119894+ 120588obst119896119895

q119895 (13)

TTR119896=

120588obst119896119894]119896119894

q119894+

120588obst119896119895

]119896119895

q119895 (14)

In (13) and (14) 120588obst119896 = qobst minus q119896is the instantaneous

distance between the risk at position qobst and the wheelchairat position q

119896 while ]

119896is the instantaneous velocity of the

wheelchairTable 3 contains the model constant 119901 the identified

parameter values standard error in value and percentage119905-statistics maximum deviation between the fitted and theobserved data and coefficients of determination of the anal-ysis for each of the seven participants The optimised valuesof constants 119898 and 119899 used in the identification process are 4and 2 respectivelyThese values represent a pair that resultedin the highest coefficient of determination with regards tomost participants In Figure 11 the value of constant119898 definesthe shape of the contours along which risks possess the samemagnitude of influence a higher value indicates that the

driver is less bothered about skewed risks as compared to risksperceived along or closer to the direction of the wheelchairReferring to (11) 119898 = 1 results in a circular contour whilehigher values (119898 gt 1) produce oval contour shapes Thehigh value of constant 119898 considered in the identificationprocess thus represents the reduced influence of side riskson the participantrsquos steering behaviour Constant 119899 on theother hand determines the magnitude of risk influencebased on the presumed adaptationmechanismHigher valuesimply that the magnitude of influence of the observed riskis considerably high within the close neighbourhood butnegligible outside the neighbourhood

In parameter identification navigation data exceeding80000 data sets per participant obtained from the previoussteering experiments were collected and utilised Out ofthe captured data 85 are used in parameter identificationto ensure that the observed parameters represent well thenatural behaviour of the participant while only 15 areused in curve fitting validation The observed values of 1198772in Table 3 demonstrate how well the model replicates thecollected data Besides the resulting large absolute valuesof 119905-statistics established the significance of the identified


Table 4 Statistical analysis of the model with TTR being the adaptation mechanism and for the same constants as those in Table 3


2

Participant 1

2119896] 00022305 00000508 228 0022775

00051076 09998726119896env 00000116 00000024 207 0206897]des 21419324 00000642 0003 2997e minus 5

Participant 2

1119896] 00012839 00000472 368 0036763

00042400 09998751119896env 00000059 00000018 3051 0305085]des 32207044 00000570 0002 1770e minus 5

Participant 3

2119896] 00011325 00000646 570 0057042

00077142 09998197119896env 00000370 00000027 730 0072973]des 33136044 00000776 0002 2342e minus 5

Participant 4

1119896] 00017910 00000473 264 0026410

00053594 09998327119896env 00000718 00000043 599 0059889]des 15635212 00000435 0003 2782e minus 5

Participant 5

1119896] 00010542 00000339 322 0032157

00042527 09999171119896env 00000403 00000018 447 0044665]des 24670341 00000319 0001 1293e minus 05

Participant 6

2119896] minus0001482 00004203 minus284 minus028360

00274354 09992838119896env 00002261 00000146 646 0064573]des minus1513273 00002957 minus002 minus195e minus 4

Participant 7



0 5 10 15minus4minus2

024

Participant 1Model response and observed data curve

t (s)

v (m

s)

1235 124 1245 125minus006minus004minus002

0002004

Model responseObserved data

times105

times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus4minus2

024



1275 128 1285 129times105

times104

minus004minus002

0002004

(b)

Figure 12 Captured linear velocity and model response for participants 1 and 7

coefficients in the behaviour model It is noticeable thathigher values of 119905-statistics corresponding to 119896] as comparedto 119896env are obtained which indicates the stronger impactof desired velocity as compared to risks avoidance whichcould be influenced by the driversrsquo subjective goal reachingurgencies during the steering experiments The variability of

]des from one participant to the other also demonstrates theimportance of identifying the individual driverrsquos behaviourbecause different drivers prefer particular driving speeds

Similar results are presented in Table 4 The same con-stants in Table 3 are also considered in comparing the rele-vance of the two hypothesised risk adaptation mechanisms


t (s)

v (m

s)

0 5 10 15minus01

minus0050

00501

Participant 1Regression error

times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus015minus01

minus0050

00501


times104

(b)


minus4 minus2 0 2 4 6 8minus8

minus6

minus4

minus2

0

2

x (m)

y (m

)

The 1st trajectory of participant 1

WallObstacles

CapturedModel

x (m)

y (m

)


minus6

minus4

minus2

0

2

The 2nd trajectory of participant 1

WallObstacles

CapturedModel

0 2 4 6 8 10 120

05

1

15

2

25

3

Linear velocitycorresponding to the 1st trajectory

CapturedModel

t (s)

v (m

s)

CapturedModel

0 10 20 30 40 50 60 70 800

1

2

3

4

5

Linear velocitycorresponding to the 2nd trajectory

t (s)

v (m

s)

Figure 14 Observed trajectories and linear velocities of participant 1

TTR is adopted and the observed results are found to bevery close to those in Table 3 Nonetheless one can quicklyrealise the slightly lower coefficient of determination and 119905-statistics obtained with the consideration of TTR Besidesthe parameters obtained with respect to participants 6 and

7 may not represent the actual behaviour because ]des and119896] are negative Moreover the desired velocity obtained forparticipant 7 seems unreasonable These may have resultedfrom the driversrsquo preference and their choice of adaptationcriteria Because of the slow wheelchair speed driver with



minus6

minus4

minus2

0

2

x (m)

y (m

)

WallObstacles

CapturedModel



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

0 5 10 150

05

1

15

2

25


CapturedModel

t (s)

v (m

s)

0 10 20 30 40 50 600

1

2

3

4


CapturedModel

t (s)

v (m

s)


confidence on the braking system may for instance onlyobserve the distance to the risk and apply an instant brake atsufficient distance just before collision It may be consideredthat TTR is not observed if there is no progressive reductionin the speed as the driver approaches the threat the use ofTTR in this case may produce the observed invalid results Itmay therefore be concluded that the consideration of DTR asthe principal adaptation criteria that wheelchair drivers adoptin the vicinity of risks corresponds well with most wheelchairdrivers

52 Trajectory Fitting Because of the space limitation onlytwo randomly chosen participantsrsquo results are presented inthis section to validate the behaviour model The presentedcurves include a comparison between the model and cap-tured data observed error between the model and captured

data and wheelchair trajectory and steering velocity for thetwo participants Figure 12 depicts the relationship betweenthe observed data and model response it shows the largeamount of data used in the least squares estimation of themodel parameters presented in Table 3 for each participantWith these constants and parameters it is interesting toobserve how the model closely represents captured dataThe observed difference between the model and captureddata as presented in Figure 13 basically represents whitenoise The observed and generated trajectories and linearvelocities of participant 1 and participant 7 are depicted inFigures 14 and 15 respectively The depicted comparison ofthe ldquomodel generatedrdquo trajectories and linear velocities withthe corresponding trajectories and linear velocities observedfrom real data in Figures 14 and 15 demonstrate the goodcorrespondence between themodel and the actual behaviour



minus6

minus4

minus2

0

2

x (m)

y (m

)


minus6

minus4

minus2

0

2

x (m)

y (m

)

The trajectory of the presented model The trajectory of Emam et al (2010) model

0 10 20 30 40 50 60 70 80minus005

0

005 Linear velocity error of the presented model

t (s) t (s)

Error Error

0 10 20 30 40 50 60 70 80minus01

minus008

minus006

minus004

minus002

0

002

004

006Linear velocity error of Emam et al (2010) model

WallObstacles

CapturedModel

WallObstacles

CapturedModel

(m

s)

(m

s)

Figure 16 The curve fitting comparison between the presented model and Emam et al [18]rsquos model

53 A Comparison with Emam et al [18]rsquos Driver BehaviourModel A curve fitting comparison between the presentedmodel and Emam et alrsquos model [18] is also presented inFigure 16 The second trajectory of participant 1 (presentedin Figure 14) is used in the comparison with DTR asthe adaptation criteria It is noticeable that the presentedmodel performs better with a very close fitting comparedto Emam et alrsquos model In addition Table 5 also presentsthe estimated parameter values standard error 119905-statisticsmaximum deviation and 119903-squared for Emam et alrsquos modelwith respect to the seven participants Comparing the regres-sion analysis in Table 3 with the analysis in Table 5 itis apparent with comparatively higher standard errors andmaximum deviation that the presented linear model stillperforms better Besides some negative parameters valuewere obtained during the identification

6 Conclusion

The primary objective of this study was to develop a modelthat represents the local steering behaviour of a wheelchairdriver This paper has presented a good driver behaviourmodel that is also linear in parameters The model assumesexplicit knowledge of subsequent intentions of the driver inorder to generate the adaptation signals that may be requiredto adapt the wheelchair to the driverrsquos steering behaviour Itis observable from the identified parameters that althoughparticipants exhibited similar driving behaviours there isalways an implied uniqueness with each participant whichvalidates the need for modelling and identification of thedriverrsquos behaviour This is more important especially for theageing users whose steering capabilities deterioratewith timeDue to simplicity and linearity of the model the ordinaryleast square method has been used in the determination of


Table 5 The regression parameters obtained with Emam et alrsquos model

Param value Std error 1119905stat Max Dev 119877

2

Participant 1119870(1) minus000097 000033 minus34184 minus03418

039777 099258119870(2) minus099680 000074 minus00744 minus744e minus 4119870(3) 0002372 000132 554434 055443119870(4) 2666837 047865 179482 017948

Participant 2119870(1) 0000822 000169 2062e2 206227


Participant 3119870(1) 0007529 000099 131842 013184


Participant 4119870(1) 54794e minus 5 2577e minus 5 470383 047038


Participant 5119870(1) 0001279 000086 671672 067167


Participant 6119870(1) 0003097 000096 309182 030918

001506 099205119870(2) minus099582 000063 minus00633 minus633e minus 4119870(3) minus000016 000123 minus782e2 minus78198119870(4) 0645253 119476 1851e3 185161

Participant 7119870(1) 0002894 000192 662751 066275


model parameters The regression analysis of the model withidentified parameter values have demonstrated acceptableperformance results for all participants

7 Recommendation for Future Works

In this study explicit driver intention is assumed to beknown However not all wheelchair users have the capabilityof communicating properly all the navigational commandsrequired to make the wheelchair move stop or turn withthe available user interface Complete assistance demands amodel that can utilise the available information to predictthe driverrsquos intention to assist a disadvantaged driver to steerin the right direction Incorporating an intention detectionmodel in the driver behaviour model may therefore be

considered if the model is to be used as a codriver to providereal-time assistance to the driver

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors of this paper gratefully appreciate the contri-bution of South African National Research Fund (NRF)Tshwane University of Technology (TUT) and the FrenchSouth African Institute of Technology (FrsquoSATI) for providingall the relevant and necessary support for this research


References

[1] G Eizmendi JM Azkoitia andGM CraddockChallenges forAssistive Technology AAATE 07 IOS Press 2007

[2] L Fehr W E Langbein and S B Skaar ldquoAdequacy of powerwheelchair control interfaces for persons with severe disabil-ities a clinical surveyrdquo Journal of Rehabilitation Research andDevelopment vol 37 no 3 pp 353ndash360 2000

[3] L Wei H Hu and Y Zhang ldquoFusing EMG and visual data forhands-free control of an intelligent wheelchairrdquo InternationalJournal of Humanoid Robotics vol 8 no 4 pp 707ndash724 2011

[4] B E Dicianno R A Cooper and J Coltellaro ldquoJoystickcontrol for powered mobility current state of technology andfuture directionsrdquo Physical Medicine and Rehabilitation Clinicsof North America vol 21 no 1 pp 79ndash86 2010

[5] A Trujillo-Leon and F Vidal-Verdu ldquoDriving interface basedon tactile sensors for electric wheelchairs or trolleysrdquo Sensorsvol 14 no 2 pp 2644ndash2662 2014

[6] G U Sorrento P S Archambault F Routhier D Dessureaultand P Boissy ldquoAssessment of Joystick control during theperformance of powered wheelchair driving tasksrdquo Journal ofNeuroengineering and Rehabilitation vol 8 article 31 2011

[7] A Bauer D Wollherr and M Buss ldquoHuman-robot collabora-tion a surveyrdquo International Journal of Humanoid Robotics vol5 no 1 pp 47ndash66 2008

[8] J S Ju Y Shin and E Y Kim ldquoVision based interface systemfor hands free control of an intelligent wheelchairrdquo Journal ofNeuroEngineering and Rehabilitation vol 6 article 33 2009

[9] G Vanacker J D R Millan E Lew et al ldquoContext-basedfiltering for assisted brain-actuated wheelchair drivingrdquo Com-putational Intelligence and Neuroscience vol 2007 Article ID25130 12 pages 2007

[10] G Diehm S Maier M Flad and S Hohmann ldquoAn identifica-tion method for individual driver steering behaviour modelledby switched affine systemsrdquo in Proceedings of the 52nd IEEEConference on Decision and Control (CDC rsquo13) pp 3547ndash3553Firenze Italy December 2013

[11] F Chenier P Bigras and R Aissaoui ldquoAn orientation estimatorfor thewheelchairrsquos caster wheelsrdquo IEEETransactions onControlSystems Technology vol 19 no 6 pp 1317ndash1326 2011

[12] T N Nguyen S Su and H T Nguyen ldquoNeural network baseddiagonal decoupling control of powered wheelchair systemsrdquoIEEE Transactions on Neural Systems and Rehabilitation Engi-neering vol 22 no 2 pp 371ndash378 2014

[13] R J K Vegter S de Groot C J Lamoth D H Veeger andL H V van der Woude ldquoInitial skill acquisition of handrimwheelchair propulsion a new perspectiverdquo IEEE Transactionson Neural Systems and Rehabilitation Engineering vol 22 no 1pp 104ndash113 2014

[14] R Becher P Steinhaus and R Dillmann ldquoThe collaborativeresearch center 588 lsquohumanoid robotsmdashlearning and cooper-ating multimodal robotsrsquordquo International Journal of HumanoidRobotics vol 1 no 3 pp 429ndash448 2004

[15] S O Onyango Y Hamam and K Djouani ldquoVelocity andorientation control in an electrical wheelchair on an inclinedand slippery surfacerdquo in Proceedings of the 8th InternationalConference on Informatics in Control Automation and Roboticspp 112ndash119 IEEE July 2011

[16] S O Onyango Y Hamam M Dabo K Djouani and G QildquoDynamic control of an electrical wheelchair on an inclinerdquo inProceedings of the Conference in Africa (AFRICON rsquo09) pp 1ndash6IEEE Nairobi Kenya September 2009

[17] S O Onyango Y Hamam K Djouani and G Qi ldquoDynamiccontrol of powered wheelchair with slip on an inclinerdquo inProceedings of the 2nd International Conference on AdaptiveScience and Technology (ICAST rsquo09) pp 278ndash283 IEEE AccraGhana December 2009

[18] H Emam Y Hamam E Monacelli and K Djouani ldquoPowerwheelchair driver behaviour modellingrdquo in Proceedings of the7th International Multi-Conference on Systems Signals andDevices (SSD rsquo10) pp 1ndash7 Amman Jordan June 2010

[19] A Huntemann E Demeester M Nuttin and H Van BrusselldquoOnline user modeling with Gaussian Processes for Bayesianplan recognition during power-wheelchair steeringrdquo in Pro-ceedings of the IEEERSJ International Conference on IntelligentRobots and Systems (IROS 08) pp 285ndash292 IEEE Nice FranceSeptember 2008

[20] EDemeester AHuntemannDVanhooydonck et al ldquoBayesianestimation of wheelchair driver intents modeling intents asgeometric paths tracked by the driverrdquo in Proceedings of theIEEERSJ International Conference on Intelligent Robots andSystems (IROS rsquo06) pp 5775ndash5780 Beijing China October2006

[21] E Demeester M Nuttin D Vanhooydonck and H Van Brus-sel ldquoA model-based probabilistic framework for plan recogni-tion in shared wheelchair control experiments and evaluationrdquoin Proceedings of the IEEERSJ International Conference onIntelligent Robots and Systems (IROS rsquo03) vol 2 pp 1456ndash1461IEEE October 2003

[22] G Vanacker D Vanhooydonck E Demeester et al ldquoAdaptivefiltering approach to improve wheelchair driving performancerdquoin Proceedings of the 15th IEEE International Symposium onRobot and Human Interactive Communication (ROMAN rsquo06)pp 527ndash532 IEEE Hatfield UK September 2006

[23] S O Onyango Y Hamam K Djouani and B Daachi ldquoIden-tification of wheelchair user steering behaviour within indoorenvironmentsrdquo in Proceedings of the IEEE International Confer-ence on Robotics and Biomimetics (ROBIO rsquo15) IEEE ZhuhaiChina December 2015

[24] P C Cacciabue and O Carsten ldquoA simple model of driverbehaviour to sustain design and safety assessment of automatedsystems in automotive environmentsrdquo Applied Ergonomics vol41 no 2 pp 187ndash197 2010

[25] J Boril R Jalovecky and R Ali ldquoHuman-machine interactionand simulation models used in aviationrdquo in Proceedings of the15th International Conference on Mechatronics (MECHATRON-IKA rsquo12) Prague Czech Republic December 2012

[26] J-H Kim S Hayakawa T Suzuki et al ldquoModeling of driverrsquoscollision avoidance behavior based on piecewise linear modelrdquoin Proceedings of the 43rd IEEE Conference on Decision andControl (CDC rsquo04) vol 3 pp 2310ndash2315 December 2004

[27] S D Keen and D J Cole ldquoBias-free identification of a linearmodel-predictive steering controller from measured driversteering behaviorrdquo IEEE Transactions on Systems Man andCybernetics Part B Cybernetics vol 42 no 2 pp 434ndash443 2012

[28] P Angkititrakul C Miyajima and K Takeda ldquoModeling andadaptation of stochastic driver-behaviormodel with applicationto car followingrdquo in Proceedings of the IEEE Intelligent VehiclesSymposium (IV rsquo11) pp 814ndash819 IEEE Baden-Baden GermanyJune 2011

[29] J Engstrom and E Hollnagel ldquoA general conceptual frameworkfor modelling behavioural effects of driver support functionsrdquoinModelling Driver Behaviour in Automotive Environments pp61ndash84 Springer London UK 2007


[30] B Peters and L Nilsson ldquoModelling the driver in controlrdquo inModelling Driver Behaviour in Automotive Environments pp85ndash104 Springer London UK 2007

[31] O Carsten ldquoFrom driver models to modelling the driver whatdowe really need to knowabout the driverrdquo inModellingDriverBehaviour in Automotive Environments pp 105ndash120 SpringerLondon UK 2007

[32] K Bengler ldquoSubject testing for evaluation of driver informationsystems and driver assistance systems learning effects andmethodological solutionsrdquo in Modelling Driver Behaviour inAutomotive Environments pp 123ndash134 Springer US 2007

[33] M Brackstone and M McDonald ldquoCar-following a historicalreviewrdquo Transportation Research Part F Traffic Psychology andBehaviour vol 2 no 4 pp 181ndash196 1999

[34] P Ranjitkar T Nakatsuji and M Asano ldquoPerformance evalu-ation of microscopic traffic flow models with test track datardquoTransportation Research Record vol 1876 pp 90ndash100 2004

[35] J L Blanco J A Fernandez-Madrigal and J Gonzalez ldquoA novelmeasure of uncertainty for mobile robot SLAM with rao black-wellized particle filtersrdquo The International Journal of RoboticsResearch vol 27 no 1 pp 73ndash89 2008

[36] T Okada W T Botelho and T Shimizu ldquoMotion analysis withexperimental verification of the hybrid robot PEOPLER-II forreversible switch between walk and roll on demandrdquoThe Inter-national Journal of Robotics Research vol 29 no 9 pp 1199ndash1221 2010

[37] A James McKnight and B B Adams ldquoDriver education taskanalysis Volume I task descriptions Final report (August1969ndashJuly 1970)rdquo Tech Rep Human Resources Research Orga-nization Alexandria Va USA 1970

[38] T A Ranney ldquoModels of driving behavior a review of theirevolutionrdquo Accident Analysis amp Prevention vol 26 no 6 pp733ndash750 1994

[39] J AMichon ldquoA critical view of driver behaviormodels what dowe know what should we dordquo in Human Behavior and TrafficSafety L Evans and R C Schwing Eds pp 485ndash524 SpringerNew York NY USA 1985

[40] J Rasmussen Information Processing and Human-MachineInteraction An Approach to Cognitive Engineering North-Holland New York NY USA 1986

[41] T Pilutti and A Galip Ulsoy ldquoIdentification of driver state forlane-keeping tasksrdquo IEEE Transactions on Systems Man andCybernetics Part A Systems andHumans vol 29 no 5 pp 486ndash502 1999

[42] L-K Chen and A G Ulsoy ldquoIdentification of a driver steeringmodel and model uncertainty from driving simulator datardquoJournal of Dynamic Systems Measurement and Control vol 123no 4 pp 623ndash629 2001

[43] N Steyn E Monacelli and Y Hamam ldquoDifferential DrivenMobility Aidrdquo Green Gazette South Africa 2013 httpswwwgreengazettecozapagespatent-journal-9-of-25-september-2013-vol-46-part-2-of-2 20130925-PAT-00009-018pdf

[44] E Masehian and D Sedighizadeh ldquoClassic and heuristicapproaches in robotmotion planningmdasha chronological reviewrdquoWorld Academy of Science Engineering and Technology vol 29no 5 pp 101ndash106 2007

[45] T Fraichard ldquoA short paper aboutmotion safetyrdquo in Proceedingsof the IEEE International Conference on Robotics and Automa-tion (ICRA rsquo07) pp 1140ndash1145 IEEE Roma Italy April 2007

[46] T Kruse A K Pandey R Alami and A Kirsch ldquoHuman-awarerobot navigation a surveyrdquo Robotics and Autonomous Systemsvol 61 no 12 pp 1726ndash1743 2013

[47] O Khatib ldquoReal-time obstacle avoidance for manipulators andmobile robotsrdquo in Proceedings of the IEEE International Confer-ence on Robotics and Automation vol 2 pp 500ndash505 St LouisMo USA March 1985

[48] S S Ge and Y J Cui ldquoNew potential functions for mobile robotpath planningrdquo IEEE Transactions on Robotics and Automationvol 16 no 5 pp 615ndash620 2000

[49] S S Ge and Y J Cui ldquoDynamic motion planning for mobilerobots using potential field methodrdquo Autonomous Robots vol13 no 3 pp 207ndash222 2002

[50] J-C Latombe Robot Motion Planning Kluwer Academic Pub-lishers 1991

[51] F Taychouri Y Hamam E Monacelli and N Chebbo ldquoPathplanning for electrical wheelchair accessibility and comfort fordisabled peoplerdquo in Proceedings of the 6th EUROSIM Congresson Modelling and Simulation pp 9ndash13 Ljubljana SloveniaSeptember 2007

[52] R Raja A Dutta and K S Venkatesh ldquoNew potential fieldmethod for rough terrain path planning using genetic algorithmfor a 6-wheel roverrdquo Robotics and Autonomous Systems vol 72pp 295ndash306 2015

[53] O Montiel R Sepulveda and U Orozco-Rosas ldquoOptimal pathplanning generation for mobile robots using parallel evolution-ary artificial potential fieldrdquo Journal of Intelligent amp RoboticSystems vol 79 no 2 pp 237ndash257 2014

[54] F Ahmed and K Deb ldquoMulti-objective optimal path planningusing elitist non-dominated sorting genetic algorithmsrdquo SoftComputing vol 17 no 7 pp 1283ndash1299 2013

[55] P Vadakkepat K C Tan and W Ming-Liang ldquoEvolutionaryartificial potential fields and their application in real time robotpath planningrdquo in Proceedings of the Congress on EvolutionaryComputation (CEC 00) vol 1 pp 256ndash263 July 2000

[56] OMontiel U Orozco-Rosas and R Sepulveda ldquoPath planningfor mobile robots using bacterial potential field for avoidingstatic and dynamic obstaclesrdquo Expert Systems with Applicationsvol 42 no 12 pp 5177ndash5191 2015

[57] J Barraquand B Langlois and J-C Latombe ldquoNumericalpotential field techniques for robot path planningrdquo IEEE Trans-actions on SystemsMan and Cybernetics vol 22 no 2 pp 224ndash241 1992

[58] T Yong W Tianmiao W Hongxing and C Diansheng ldquoAbehavior control method based on hierarchical POMDP forintelligent wheelchairrdquo in Proceedings of the IEEEASME Inter-national Conference on Advanced Intelligent Mechatronics (AIMrsquo09) pp 893ndash898 IEEE Singapore July 2009

[59] T Taha J V Miro and G Dissanayake ldquoPOMDP-based long-term user intention prediction for wheelchair navigationrdquo inProceedings of the IEEE International Conference onRobotics andAutomation (ICRA rsquo08) pp 3920ndash3925 IEEE Pasadena CalifUSA May 2008

[60] T Taha J V Miro and G Dissanayake ldquoWheelchair driverassistance and intention prediction using POMDPsrdquo inProceed-ings of the International Conference on Intelligent Sensors SensorNetworks and Information Processing (ISSNIP rsquo07) pp 449ndash454IEEE Melbourne Australia December 2007

[61] T Carlson and Y Demiris ldquoCollaborative control in humanwheelchair interaction reduces the need for dexterity in precisemanoeuvresrdquo in Proceedings of the ldquoRobotic Helpers UserInteraction Interfaces and Companions in Assistive andTherapyRoboticsrdquo aWorkshop at ACMIEEEHRI pp 59ndash66 Universityof Hertfordshire Hatfield UK 2008


[62] T Carlson and Y Demiris ldquoCollaborative control for a roboticwheelchair evaluation of performance attention and work-loadrdquo IEEE Transactions on Systems Man and Cybernetics PartB Cybernetics vol 42 no 3 pp 876ndash888 2012

[63] D Vanhooydonck E Demeester A Huntemann et al ldquoAdapt-able navigational assistance for intelligent wheelchairs bymeans of an implicit personalized user modelrdquo Robotics andAutonomous Systems vol 58 no 8 pp 963ndash977 2010

[64] E Demeester M Nuttin D Vanhooydonck and H VanBrussel ldquoFine motion planning for shared wheelchair controlrequirements and preliminary experimentsrdquo in Proceedings ofthe 11th International Conference on Advanced Robotics (ICARrsquo03) pp 1278ndash1283 Coimbra Portugal June-July 2003

[65] S P Parikh V Grassi Jr V Kumar and J Okamoto JrldquoIncorporating user inputs in motion planning for a smartwheelchairrdquo in Proceedings of the IEEE International Conferenceon Robotics and Automation (ICRA rsquo04) vol 2 pp 2043ndash2048IEEE May 2004

[66] S P Parikh V Grassi Jr V Kumar and J Okamoto Jr ldquoInte-grating human inputs with autonomous behaviors on an intel-ligent wheelchair platformrdquo IEEE Intelligent Systems vol 22no 2 pp 33ndash41 2007

[67] Q Li W Chen and J Wang ldquoDynamic shared control forhuman-wheelchair cooperationrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo11) pp 4278ndash4283 Shanghai China May 2011

[68] CUrdiales E J Perez G Peinado et al ldquoOn the construction ofa skill-based wheelchair navigation profilerdquo IEEE Transactionson Neural Systems and Rehabilitation Engineering vol 21 no 6pp 917ndash927 2013

[69] S Simon Levine D David Bell L Lincoln Jaros R RichardSimpson Y Koren and J Borenstein ldquoThe NavChair assistivewheelchair navigation systemrdquo IEEE Transactions on Rehabili-tation Engineering vol 7 no 4 pp 443ndash451 1999

[70] LMontesanoMDıaz S Bhaskar and JMinguez ldquoTowards anintelligentwheelchair system for userswith cerebral palsyrdquo IEEETransactions on Neural Systems and Rehabilitation Engineeringvol 18 no 2 pp 193ndash202 2010

[71] N Steyn Virtual reality platform modelling and design for ver-satile electric wheelchair simulation in an enabled environment[PhD thesis] Tshwane University of Technology 2014

[72] H Emam Y Hamam E Monacelli and I MougharbelldquoDynamicmodel of an electrical wheelchairwith slipping detec-tionrdquo in Proceedings of the 6th EUROSIMCongress onModellingand Simulation (EUROSIM rsquo07) pp 9ndash13 EUROSIMSLOSIMLjubljana Slovenia September 2007

[73] YHori Y Toyoda andY Tsuruoka ldquoTraction control of electricvehicle basic experimental results using the test EV UOTelectric marchrdquo IEEE Transactions on Industry Applications vol34 no 5 pp 1131ndash1138 1998

[74] AN Beare andR EDorris ldquoA simulator-based study of humanerrors in nuclear power plant control room tasksrdquo Proceedingsof the Human Factors and Ergonomics Society Annual Meetingvol 27 no 2 pp 170ndash174 1983

[75] D Dennett The Intentional Stance MIT Press CambridgeMass USA 1989

[76] D H Taylor ldquoDriversrsquo galvanic skin response and the risk ofaccidentrdquo Ergonomics vol 7 no 4 pp 439ndash451 1964

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


RoboticsJournal of



Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



perception and vehicle handling techniques while othersentail detailed reports of the driversrsquo actions during normaldriving situationsThe commonquantitativemodels availablein the literature represent specific driving tasks [33ndash36] Theadaptive and comprehensive control models of the drivingbehaviour are however very few [37 38]

According to Michon [39] the entire driving task hasthree demand levels consisting of the strategic level thetactical level and the control level Each level encompassesthe driver the wheelchair and the environment The threeelements interact continuously and every state of the vehiclecan be linked to this interaction [18] The driving taskslike risk avoidance and steering velocity determination aretherefore entirely dependent upon the three elements How-ever the adaptive behaviours executed within the drivingenvironment are greatly controlled by preferences of thedriver which makes the driver a very important element inthe driving task

In the literature hierarchical structures of car drivingmodels have been presented in terms of skill based rulebased and knowledge based behaviours [40] However it ishard to verify the contributions of such qualitative modelsof perceptual processes and neural activities in the actualexecution of the driving task Pilutti and Galip Ulsoy [41]therefore considered the system identification approachusingthe back-box model with autoregressive exogenous structure(ARX) to identify the driver modelrsquos parameters Chen andUlsoy [42] also presented the same formulation approach forboth driver model and model uncertainties using the actualdriving data captured from a fixed-base driving simulatorThe model however employed the autoregression movingaverage with exogenous inputs (ARMAX) to improve onaccuracy based on the consideration that ARMAX can yieldresiduals closer to white noise with fewer parameters giventhe same model order The system identification approach isalso considered in [10] nevertheless the authors do not takeinto account exogenous inputs in their affine autoregressivesystem but instead derive a multistep model output errorcriterion and present an algorithm to identify the parametersof the subsystemusingmeasurablemotion data Although theconsideration of black-box method of system identificationis straight forward and common with availability of dataauthors believe that sufficient information can be foundto relate the driverrsquos actions to the perceivable contextualenvironment

The study contributes to wheelchair driver behaviourmodelling by formulating a simple steering model that isalso linear in parameters The complexity of the steeringmodel is very instrumental in determining whether themodel is applicable on-line for real-time adaptation or off-line for periodic or permanent adaptation Derivation ofthe presented model is based on deductive reasoning fromthe known steering operations and systematic relationshipsbetween the observable behaviours taking into considerationthe environmental situation It however shuns the consider-ation of social events occurring within the driverrsquos mind Inorder to capture the adaptable demands of the driver at thecontrol and tactical levels the driver-specific parameters areidentified The steering data obtained from the augmented

virtual-reality wheelchair platform known as Virtual-Space1 (VS-1) at FSATI (FSATI is an acronym for French South-African Institute of Technology) in TUT (TUT is an acronymfor Tshwane University of Technology) [43] is utilised inthe identification of the model parameters The identifiedparameters are then used to curve-fit and compare the modelagainst the observed data

The presented steering model can be used to adapt thewheelchair to the userrsquos steering behaviour according toFigure 1 Due to its simplicity and linearity the proposedmodel is applicable to wheelchair self-tuning adaptive con-trol to observe the preceding behaviour and self-tune theparameters to fit the observation

This paper is organised as follows Section 1 has presentedthe introduction in terms of the motivation and backgroundof behaviour modelling taking into consideration the inter-active elements involved in the accomplishment of steeringtasks Section 2 presents some of the approaches that havepreviously been considered in the derivation of specificdriver control models including the available wheelchairdriver behaviour models In Section 3 simulator evaluationand summary of the experiments conducted to obtain thenecessary steering data for driver identification are presentedThe driver behaviour model is presented in Section 4 whilethe statistical analysis of the model and its comparison toobserved data are discussed in Section 5 Finally conclusionsand future recommendation are presented in Sections 6 and7 respectively

2 Related Path Planning Models andDriver Adaptation Literature

Driving begins when an optimal path to the destinationis conceived This involves careful consideration of theentire workspace Based on the associated constraints theconception is accomplished either fully in advance beforesetting out the journey or in parts within conceptuallysubdivided sections of the workspace during the drivingprocess Path planning for robotic automation has beenachieved by deliberate and reactive planners Deliberateplanners including cell decomposition road-maps and evo-lutionary algorithms ensure prior plan of the whole journeyHowever they entail expensive computations that limit theirpractical application in higher dimensional configurationsDeliberate planners are therefore commonly applied tounmanned ground vehicle in confined environments On thecontrary local planners provide cheap trajectory planningalgorithms based on sensor information captured from thelocal surrounding Local planners ensure both faster and real-time update of the environmental information as well asreactive response to stimuli As a result they are commonlyaimed at ensuring safety and stability of both the driverand the vehicle Nonetheless the paths obtained from theseapproaches may not be optimal and the vehicle could betrapped into localminimaThismakes the application of localplanners to unmanned mobile systems inefficient withoutdeliberate planners Both deliberate and reactive planners stillcommand significant influence in the literature However the




Environment

User Position

User parameters


0

x

y

zlfloorlceil

rfloorrceil

][










Frep119896 = 1198961199001

min (1205882obst119896) (2)




Frep119896 =119873

sum

119894=1

119896119900

1

120588

2

obst119894119896

(3)


0obstof the


Urep =

1

2

119896119900(

1

120588obstminus

1

1205880obst

) 120588obst le 1205880obst

0 120588obst gt 1205880obst

(4)




Frep119896 =119873

sum

119894

119896119900

(cos120572119894)

119898

120588

2

obst119894119896

(5)









Local planning

Global planning


Highly scalable

Directionality









plusmn120596w

120575

rx

Nx

rp120596r

minusr

+r Fx

Tc1

Tc2

120596r = 120596s

120596a 120591a

(a)

Front roller

Front roller


(b)





119889(6) and the


F119889=

119870

120591

[119881max (1 minus119883saf119883act

) e minus 119881act] (6)

F119896= 119896119900exp(minus

120588obst119861

)n119863V (7)





119877and 120596

119871for the right


119877= 120596119871




and 120591119898







Platform ramp


Useroperator stage





119898= 120591119908 In this case a






















1) to






1

1198662 and 119866





10

20

30

40

50

60

70

80

90

100

573

638

63 68

3

VS-1

rate

d pr

esen

ce (

)



20

40

60

80

100

120

75

7581

6973

75

Rate

d (

)




minus05 0 05 1 15 2 25 3 35 4minus2

minus1

0

1

2

3

4

x (m)

y (m

)


Path 1Path 2Path 3

Path 4Path 5

S

G1

G2

G3

G4

G5

(a)

Path 1Path 2Path 3

Path 4Path 5

0 1 2 3 4 5 6 7 8 9minus02

0

02

04

06

08

1

12

14

16

t (s)

Spee

d (m

s)

Wheelchair speed

(b)







0

2

4

6

8

10

12

14

16

x (m)

y (m


Path 1Path 2Path 3

TableP1

P2

P3

(a)

Path 1Path 2Path 3

0 2 4 6 8 10 12 14

0

05

1

15

2

t (s)

Spee

d (m

s)

Wheelchair speed

(b)






minus7

minus6

minus5

minus4

minus3

minus2

minus1

0

1

2

x (m)

y (m

)


WallObstacles

Path 1Path 2Path 3

G1

G2

B

AS

C

D G3




0 2 4 6 8 10 12minus05

0

05

1


t (s)

A

B

Spee

d (m

s)

(a)

t (s)0 2 4 6 8

minus05

0

05

1


BA

Spee

d (m

s)

(b)

t (s)0 1 2 3 4 5 6 7

minus05

0

05


DC

Spee

d (m

s)

(c)






] = 1003816100381610038161003816

]des (119892119894) + ]env (env)1003816100381610038161003816

le ]max (8)









e =q119871119896minus q119896

10038161003816100381610038161003816

q119871119896minus q119896

10038161003816100381610038161003816

(10)

In (10) q119871119896







0001002003


x

y

drisk = 4

drisk = 5

drisk = 6



]env119896 = minus119896env119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(11)




]119896+1

= ]119896+ 119896] (]des minus ]

119896) minus 119896env

119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(12)






2

Participant 1

2119896] 00023296 00000493 212 0021145

00066778 09998727119896env 00000607 00000042 692 0069456]des 21620485 00000664 0003 0000031

Participant 2

1119896] 00013058 00000457 350 0034998

00044821 09998751119896env 00000168 00000050 298 0297619]des 31936471 00000572 0002 1791e minus 5

Participant 3

2119896] 00016111 00000638 396 0039600

00282700 09998215119896env 00001812 00000042 232 0023179]des 29748170 00000809 0003 2720e minus 5

Participant 4

1119896] 00022988 00000481 210 0020924

00096421 09998336119896env 00001566 00000041 262 0026181]des 15590495 00000483 0003 3098e minus 5

Participant 5

1119896] 00011705 00000330 282 0028193

00048858 09999171119896env 00000525 00000024 457 0045714]des 23263703 00000322 0001 1384e minus 5

Participant 6

2119896] 00033319 00003469 104 0104115

00288915 09992932119896env 00002114 00000097 459 0045885]des 20650043 00003439 0017 1665e minus 4

Participant 7

2119896] 00007837 00000496 633 0063290

00108345 09998355119896env 00001583 00000048 303 0030322]des 55191529 00000688 0001 1247e minus 5


DTR119896= 120588obst119896119894

q119894+ 120588obst119896119895

q119895 (13)

TTR119896=

120588obst119896119894]119896119894

q119894+

120588obst119896119895

]119896119895

q119895 (14)



119896 while ]









2

Participant 1

2119896] 00022305 00000508 228 0022775

00051076 09998726119896env 00000116 00000024 207 0206897]des 21419324 00000642 0003 2997e minus 5

Participant 2

1119896] 00012839 00000472 368 0036763

00042400 09998751119896env 00000059 00000018 3051 0305085]des 32207044 00000570 0002 1770e minus 5

Participant 3

2119896] 00011325 00000646 570 0057042

00077142 09998197119896env 00000370 00000027 730 0072973]des 33136044 00000776 0002 2342e minus 5

Participant 4

1119896] 00017910 00000473 264 0026410

00053594 09998327119896env 00000718 00000043 599 0059889]des 15635212 00000435 0003 2782e minus 5

Participant 5

1119896] 00010542 00000339 322 0032157

00042527 09999171119896env 00000403 00000018 447 0044665]des 24670341 00000319 0001 1293e minus 05

Participant 6



Participant 7




024


t (s)

v (m

s)


0002004


times105

times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus4minus2

024



1275 128 1285 129times105

times104

minus004minus002

0002004

(b)






t (s)

v (m

s)

0 5 10 15minus01

minus0050

00501


times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus015minus01

minus0050

00501


times104

(b)



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

x (m)

y (m

)


minus6

minus4

minus2

0

2


WallObstacles

CapturedModel

0 2 4 6 8 10 120

05

1

15

2

25

3


CapturedModel

t (s)

v (m

s)

CapturedModel

0 10 20 30 40 50 60 70 800

1

2

3

4

5


t (s)

v (m

s)






minus6

minus4

minus2

0

2

x (m)

y (m

)

WallObstacles

CapturedModel



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

0 5 10 150

05

1

15

2

25


CapturedModel

t (s)

v (m

s)

0 10 20 30 40 50 600

1

2

3

4


CapturedModel

t (s)

v (m

s)







minus6

minus4

minus2

0

2

x (m)

y (m

)


minus6

minus4

minus2

0

2

x (m)

y (m

)


0 10 20 30 40 50 60 70 80minus005

0


t (s) t (s)

Error Error

0 10 20 30 40 50 60 70 80minus01

minus008

minus006

minus004

minus002

0

002

004


WallObstacles

CapturedModel

WallObstacles

CapturedModel

(m

s)

(m

s)



6 Conclusion





2



Participant 2119870(1) 0000822 000169 2062e2 206227


Participant 3119870(1) 0007529 000099 131842 013184




Participant 5119870(1) 0001279 000086 671672 067167


Participant 6119870(1) 0003097 000096 309182 030918


Participant 7119870(1) 0002894 000192 662751 066275






Competing Interests


Acknowledgments



References






















































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






Environment

User Position

User parameters


0

x

y

zlfloorlceil

rfloorrceil

][










Frep119896 = 1198961199001

min (1205882obst119896) (2)




Frep119896 =119873

sum

119894=1

119896119900

1

120588

2

obst119894119896

(3)


0obstof the


Urep =

1

2

119896119900(

1

120588obstminus

1

1205880obst

) 120588obst le 1205880obst

0 120588obst gt 1205880obst

(4)




Frep119896 =119873

sum

119894

119896119900

(cos120572119894)

119898

120588

2

obst119894119896

(5)









Local planning

Global planning


Highly scalable

Directionality









plusmn120596w

120575

rx

Nx

rp120596r

minusr

+r Fx

Tc1

Tc2

120596r = 120596s

120596a 120591a

(a)

Front roller

Front roller


(b)





119889(6) and the


F119889=

119870

120591

[119881max (1 minus119883saf119883act

) e minus 119881act] (6)

F119896= 119896119900exp(minus

120588obst119861

)n119863V (7)





119877and 120596

119871for the right


119877= 120596119871




and 120591119898







Platform ramp


Useroperator stage





119898= 120591119908 In this case a






















1) to






1

1198662 and 119866





10

20

30

40

50

60

70

80

90

100

573

638

63 68

3

VS-1

rate

d pr

esen

ce (

)



20

40

60

80

100

120

75

7581

6973

75

Rate

d (

)




minus05 0 05 1 15 2 25 3 35 4minus2

minus1

0

1

2

3

4

x (m)

y (m

)


Path 1Path 2Path 3

Path 4Path 5

S

G1

G2

G3

G4

G5

(a)

Path 1Path 2Path 3

Path 4Path 5

0 1 2 3 4 5 6 7 8 9minus02

0

02

04

06

08

1

12

14

16

t (s)

Spee

d (m

s)

Wheelchair speed

(b)







0

2

4

6

8

10

12

14

16

x (m)

y (m


Path 1Path 2Path 3

TableP1

P2

P3

(a)

Path 1Path 2Path 3

0 2 4 6 8 10 12 14

0

05

1

15

2

t (s)

Spee

d (m

s)

Wheelchair speed

(b)






minus7

minus6

minus5

minus4

minus3

minus2

minus1

0

1

2

x (m)

y (m

)


WallObstacles

Path 1Path 2Path 3

G1

G2

B

AS

C

D G3




0 2 4 6 8 10 12minus05

0

05

1


t (s)

A

B

Spee

d (m

s)

(a)

t (s)0 2 4 6 8

minus05

0

05

1


BA

Spee

d (m

s)

(b)

t (s)0 1 2 3 4 5 6 7

minus05

0

05


DC

Spee

d (m

s)

(c)






] = 1003816100381610038161003816

]des (119892119894) + ]env (env)1003816100381610038161003816

le ]max (8)









e =q119871119896minus q119896

10038161003816100381610038161003816

q119871119896minus q119896

10038161003816100381610038161003816

(10)

In (10) q119871119896







0001002003


x

y

drisk = 4

drisk = 5

drisk = 6



]env119896 = minus119896env119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(11)




]119896+1

= ]119896+ 119896] (]des minus ]

119896) minus 119896env

119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(12)






2

Participant 1

2119896] 00023296 00000493 212 0021145

00066778 09998727119896env 00000607 00000042 692 0069456]des 21620485 00000664 0003 0000031

Participant 2

1119896] 00013058 00000457 350 0034998

00044821 09998751119896env 00000168 00000050 298 0297619]des 31936471 00000572 0002 1791e minus 5

Participant 3

2119896] 00016111 00000638 396 0039600

00282700 09998215119896env 00001812 00000042 232 0023179]des 29748170 00000809 0003 2720e minus 5

Participant 4

1119896] 00022988 00000481 210 0020924

00096421 09998336119896env 00001566 00000041 262 0026181]des 15590495 00000483 0003 3098e minus 5

Participant 5

1119896] 00011705 00000330 282 0028193

00048858 09999171119896env 00000525 00000024 457 0045714]des 23263703 00000322 0001 1384e minus 5

Participant 6

2119896] 00033319 00003469 104 0104115

00288915 09992932119896env 00002114 00000097 459 0045885]des 20650043 00003439 0017 1665e minus 4

Participant 7

2119896] 00007837 00000496 633 0063290

00108345 09998355119896env 00001583 00000048 303 0030322]des 55191529 00000688 0001 1247e minus 5


DTR119896= 120588obst119896119894

q119894+ 120588obst119896119895

q119895 (13)

TTR119896=

120588obst119896119894]119896119894

q119894+

120588obst119896119895

]119896119895

q119895 (14)



119896 while ]









2

Participant 1

2119896] 00022305 00000508 228 0022775

00051076 09998726119896env 00000116 00000024 207 0206897]des 21419324 00000642 0003 2997e minus 5

Participant 2

1119896] 00012839 00000472 368 0036763

00042400 09998751119896env 00000059 00000018 3051 0305085]des 32207044 00000570 0002 1770e minus 5

Participant 3

2119896] 00011325 00000646 570 0057042

00077142 09998197119896env 00000370 00000027 730 0072973]des 33136044 00000776 0002 2342e minus 5

Participant 4

1119896] 00017910 00000473 264 0026410

00053594 09998327119896env 00000718 00000043 599 0059889]des 15635212 00000435 0003 2782e minus 5

Participant 5

1119896] 00010542 00000339 322 0032157

00042527 09999171119896env 00000403 00000018 447 0044665]des 24670341 00000319 0001 1293e minus 05

Participant 6



Participant 7




024


t (s)

v (m

s)


0002004


times105

times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus4minus2

024



1275 128 1285 129times105

times104

minus004minus002

0002004

(b)






t (s)

v (m

s)

0 5 10 15minus01

minus0050

00501


times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus015minus01

minus0050

00501


times104

(b)



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

x (m)

y (m

)


minus6

minus4

minus2

0

2


WallObstacles

CapturedModel

0 2 4 6 8 10 120

05

1

15

2

25

3


CapturedModel

t (s)

v (m

s)

CapturedModel

0 10 20 30 40 50 60 70 800

1

2

3

4

5


t (s)

v (m

s)






minus6

minus4

minus2

0

2

x (m)

y (m

)

WallObstacles

CapturedModel



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

0 5 10 150

05

1

15

2

25


CapturedModel

t (s)

v (m

s)

0 10 20 30 40 50 600

1

2

3

4


CapturedModel

t (s)

v (m

s)







minus6

minus4

minus2

0

2

x (m)

y (m

)


minus6

minus4

minus2

0

2

x (m)

y (m

)


0 10 20 30 40 50 60 70 80minus005

0


t (s) t (s)

Error Error

0 10 20 30 40 50 60 70 80minus01

minus008

minus006

minus004

minus002

0

002

004


WallObstacles

CapturedModel

WallObstacles

CapturedModel

(m

s)

(m

s)



6 Conclusion





2



Participant 2119870(1) 0000822 000169 2062e2 206227


Participant 3119870(1) 0007529 000099 131842 013184




Participant 5119870(1) 0001279 000086 671672 067167


Participant 6119870(1) 0003097 000096 309182 030918


Participant 7119870(1) 0002894 000192 662751 066275






Competing Interests


Acknowledgments



References






















































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





Frep119896 =119873

sum

119894

119896119900

(cos120572119894)

119898

120588

2

obst119894119896

(5)









Local planning

Global planning


Highly scalable

Directionality









plusmn120596w

120575

rx

Nx

rp120596r

minusr

+r Fx

Tc1

Tc2

120596r = 120596s

120596a 120591a

(a)

Front roller

Front roller


(b)





119889(6) and the


F119889=

119870

120591

[119881max (1 minus119883saf119883act

) e minus 119881act] (6)

F119896= 119896119900exp(minus

120588obst119861

)n119863V (7)





119877and 120596

119871for the right


119877= 120596119871




and 120591119898







Platform ramp


Useroperator stage





119898= 120591119908 In this case a






















1) to






1

1198662 and 119866





10

20

30

40

50

60

70

80

90

100

573

638

63 68

3

VS-1

rate

d pr

esen

ce (

)



20

40

60

80

100

120

75

7581

6973

75

Rate

d (

)




minus05 0 05 1 15 2 25 3 35 4minus2

minus1

0

1

2

3

4

x (m)

y (m

)


Path 1Path 2Path 3

Path 4Path 5

S

G1

G2

G3

G4

G5

(a)

Path 1Path 2Path 3

Path 4Path 5

0 1 2 3 4 5 6 7 8 9minus02

0

02

04

06

08

1

12

14

16

t (s)

Spee

d (m

s)

Wheelchair speed

(b)







0

2

4

6

8

10

12

14

16

x (m)

y (m


Path 1Path 2Path 3

TableP1

P2

P3

(a)

Path 1Path 2Path 3

0 2 4 6 8 10 12 14

0

05

1

15

2

t (s)

Spee

d (m

s)

Wheelchair speed

(b)






minus7

minus6

minus5

minus4

minus3

minus2

minus1

0

1

2

x (m)

y (m

)


WallObstacles

Path 1Path 2Path 3

G1

G2

B

AS

C

D G3




0 2 4 6 8 10 12minus05

0

05

1


t (s)

A

B

Spee

d (m

s)

(a)

t (s)0 2 4 6 8

minus05

0

05

1


BA

Spee

d (m

s)

(b)

t (s)0 1 2 3 4 5 6 7

minus05

0

05


DC

Spee

d (m

s)

(c)






] = 1003816100381610038161003816

]des (119892119894) + ]env (env)1003816100381610038161003816

le ]max (8)









e =q119871119896minus q119896

10038161003816100381610038161003816

q119871119896minus q119896

10038161003816100381610038161003816

(10)

In (10) q119871119896







0001002003


x

y

drisk = 4

drisk = 5

drisk = 6



]env119896 = minus119896env119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(11)




]119896+1

= ]119896+ 119896] (]des minus ]

119896) minus 119896env

119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(12)






2

Participant 1

2119896] 00023296 00000493 212 0021145

00066778 09998727119896env 00000607 00000042 692 0069456]des 21620485 00000664 0003 0000031

Participant 2

1119896] 00013058 00000457 350 0034998

00044821 09998751119896env 00000168 00000050 298 0297619]des 31936471 00000572 0002 1791e minus 5

Participant 3

2119896] 00016111 00000638 396 0039600

00282700 09998215119896env 00001812 00000042 232 0023179]des 29748170 00000809 0003 2720e minus 5

Participant 4

1119896] 00022988 00000481 210 0020924

00096421 09998336119896env 00001566 00000041 262 0026181]des 15590495 00000483 0003 3098e minus 5

Participant 5

1119896] 00011705 00000330 282 0028193

00048858 09999171119896env 00000525 00000024 457 0045714]des 23263703 00000322 0001 1384e minus 5

Participant 6

2119896] 00033319 00003469 104 0104115

00288915 09992932119896env 00002114 00000097 459 0045885]des 20650043 00003439 0017 1665e minus 4

Participant 7

2119896] 00007837 00000496 633 0063290

00108345 09998355119896env 00001583 00000048 303 0030322]des 55191529 00000688 0001 1247e minus 5


DTR119896= 120588obst119896119894

q119894+ 120588obst119896119895

q119895 (13)

TTR119896=

120588obst119896119894]119896119894

q119894+

120588obst119896119895

]119896119895

q119895 (14)



119896 while ]









2

Participant 1

2119896] 00022305 00000508 228 0022775

00051076 09998726119896env 00000116 00000024 207 0206897]des 21419324 00000642 0003 2997e minus 5

Participant 2

1119896] 00012839 00000472 368 0036763

00042400 09998751119896env 00000059 00000018 3051 0305085]des 32207044 00000570 0002 1770e minus 5

Participant 3

2119896] 00011325 00000646 570 0057042

00077142 09998197119896env 00000370 00000027 730 0072973]des 33136044 00000776 0002 2342e minus 5

Participant 4

1119896] 00017910 00000473 264 0026410

00053594 09998327119896env 00000718 00000043 599 0059889]des 15635212 00000435 0003 2782e minus 5

Participant 5

1119896] 00010542 00000339 322 0032157

00042527 09999171119896env 00000403 00000018 447 0044665]des 24670341 00000319 0001 1293e minus 05

Participant 6



Participant 7




024


t (s)

v (m

s)


0002004


times105

times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus4minus2

024



1275 128 1285 129times105

times104

minus004minus002

0002004

(b)






t (s)

v (m

s)

0 5 10 15minus01

minus0050

00501


times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus015minus01

minus0050

00501


times104

(b)



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

x (m)

y (m

)


minus6

minus4

minus2

0

2


WallObstacles

CapturedModel

0 2 4 6 8 10 120

05

1

15

2

25

3


CapturedModel

t (s)

v (m

s)

CapturedModel

0 10 20 30 40 50 60 70 800

1

2

3

4

5


t (s)

v (m

s)






minus6

minus4

minus2

0

2

x (m)

y (m

)

WallObstacles

CapturedModel



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

0 5 10 150

05

1

15

2

25


CapturedModel

t (s)

v (m

s)

0 10 20 30 40 50 600

1

2

3

4


CapturedModel

t (s)

v (m

s)







minus6

minus4

minus2

0

2

x (m)

y (m

)


minus6

minus4

minus2

0

2

x (m)

y (m

)


0 10 20 30 40 50 60 70 80minus005

0


t (s) t (s)

Error Error

0 10 20 30 40 50 60 70 80minus01

minus008

minus006

minus004

minus002

0

002

004


WallObstacles

CapturedModel

WallObstacles

CapturedModel

(m

s)

(m

s)



6 Conclusion





2



Participant 2119870(1) 0000822 000169 2062e2 206227


Participant 3119870(1) 0007529 000099 131842 013184




Participant 5119870(1) 0001279 000086 671672 067167


Participant 6119870(1) 0003097 000096 309182 030918


Participant 7119870(1) 0002894 000192 662751 066275






Competing Interests


Acknowledgments



References






















































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




plusmn120596w

120575

rx

Nx

rp120596r

minusr

+r Fx

Tc1

Tc2

120596r = 120596s

120596a 120591a

(a)

Front roller

Front roller


(b)





119889(6) and the


F119889=

119870

120591

[119881max (1 minus119883saf119883act

) e minus 119881act] (6)

F119896= 119896119900exp(minus

120588obst119861

)n119863V (7)





119877and 120596

119871for the right


119877= 120596119871




and 120591119898







Platform ramp


Useroperator stage





119898= 120591119908 In this case a






















1) to






1

1198662 and 119866





10

20

30

40

50

60

70

80

90

100

573

638

63 68

3

VS-1

rate

d pr

esen

ce (

)



20

40

60

80

100

120

75

7581

6973

75

Rate

d (

)




minus05 0 05 1 15 2 25 3 35 4minus2

minus1

0

1

2

3

4

x (m)

y (m

)


Path 1Path 2Path 3

Path 4Path 5

S

G1

G2

G3

G4

G5

(a)

Path 1Path 2Path 3

Path 4Path 5

0 1 2 3 4 5 6 7 8 9minus02

0

02

04

06

08

1

12

14

16

t (s)

Spee

d (m

s)

Wheelchair speed

(b)







0

2

4

6

8

10

12

14

16

x (m)

y (m


Path 1Path 2Path 3

TableP1

P2

P3

(a)

Path 1Path 2Path 3

0 2 4 6 8 10 12 14

0

05

1

15

2

t (s)

Spee

d (m

s)

Wheelchair speed

(b)






minus7

minus6

minus5

minus4

minus3

minus2

minus1

0

1

2

x (m)

y (m

)


WallObstacles

Path 1Path 2Path 3

G1

G2

B

AS

C

D G3




0 2 4 6 8 10 12minus05

0

05

1


t (s)

A

B

Spee

d (m

s)

(a)

t (s)0 2 4 6 8

minus05

0

05

1


BA

Spee

d (m

s)

(b)

t (s)0 1 2 3 4 5 6 7

minus05

0

05


DC

Spee

d (m

s)

(c)






] = 1003816100381610038161003816

]des (119892119894) + ]env (env)1003816100381610038161003816

le ]max (8)









e =q119871119896minus q119896

10038161003816100381610038161003816

q119871119896minus q119896

10038161003816100381610038161003816

(10)

In (10) q119871119896







0001002003


x

y

drisk = 4

drisk = 5

drisk = 6



]env119896 = minus119896env119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(11)




]119896+1

= ]119896+ 119896] (]des minus ]

119896) minus 119896env

119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(12)






2

Participant 1

2119896] 00023296 00000493 212 0021145

00066778 09998727119896env 00000607 00000042 692 0069456]des 21620485 00000664 0003 0000031

Participant 2

1119896] 00013058 00000457 350 0034998

00044821 09998751119896env 00000168 00000050 298 0297619]des 31936471 00000572 0002 1791e minus 5

Participant 3

2119896] 00016111 00000638 396 0039600

00282700 09998215119896env 00001812 00000042 232 0023179]des 29748170 00000809 0003 2720e minus 5

Participant 4

1119896] 00022988 00000481 210 0020924

00096421 09998336119896env 00001566 00000041 262 0026181]des 15590495 00000483 0003 3098e minus 5

Participant 5

1119896] 00011705 00000330 282 0028193

00048858 09999171119896env 00000525 00000024 457 0045714]des 23263703 00000322 0001 1384e minus 5

Participant 6

2119896] 00033319 00003469 104 0104115

00288915 09992932119896env 00002114 00000097 459 0045885]des 20650043 00003439 0017 1665e minus 4

Participant 7

2119896] 00007837 00000496 633 0063290

00108345 09998355119896env 00001583 00000048 303 0030322]des 55191529 00000688 0001 1247e minus 5


DTR119896= 120588obst119896119894

q119894+ 120588obst119896119895

q119895 (13)

TTR119896=

120588obst119896119894]119896119894

q119894+

120588obst119896119895

]119896119895

q119895 (14)



119896 while ]









2

Participant 1

2119896] 00022305 00000508 228 0022775

00051076 09998726119896env 00000116 00000024 207 0206897]des 21419324 00000642 0003 2997e minus 5

Participant 2

1119896] 00012839 00000472 368 0036763

00042400 09998751119896env 00000059 00000018 3051 0305085]des 32207044 00000570 0002 1770e minus 5

Participant 3

2119896] 00011325 00000646 570 0057042

00077142 09998197119896env 00000370 00000027 730 0072973]des 33136044 00000776 0002 2342e minus 5

Participant 4

1119896] 00017910 00000473 264 0026410

00053594 09998327119896env 00000718 00000043 599 0059889]des 15635212 00000435 0003 2782e minus 5

Participant 5

1119896] 00010542 00000339 322 0032157

00042527 09999171119896env 00000403 00000018 447 0044665]des 24670341 00000319 0001 1293e minus 05

Participant 6



Participant 7




024


t (s)

v (m

s)


0002004


times105

times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus4minus2

024



1275 128 1285 129times105

times104

minus004minus002

0002004

(b)






t (s)

v (m

s)

0 5 10 15minus01

minus0050

00501


times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus015minus01

minus0050

00501


times104

(b)



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

x (m)

y (m

)


minus6

minus4

minus2

0

2


WallObstacles

CapturedModel

0 2 4 6 8 10 120

05

1

15

2

25

3


CapturedModel

t (s)

v (m

s)

CapturedModel

0 10 20 30 40 50 60 70 800

1

2

3

4

5


t (s)

v (m

s)






minus6

minus4

minus2

0

2

x (m)

y (m

)

WallObstacles

CapturedModel



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

0 5 10 150

05

1

15

2

25


CapturedModel

t (s)

v (m

s)

0 10 20 30 40 50 600

1

2

3

4


CapturedModel

t (s)

v (m

s)







minus6

minus4

minus2

0

2

x (m)

y (m

)


minus6

minus4

minus2

0

2

x (m)

y (m

)


0 10 20 30 40 50 60 70 80minus005

0


t (s) t (s)

Error Error

0 10 20 30 40 50 60 70 80minus01

minus008

minus006

minus004

minus002

0

002

004


WallObstacles

CapturedModel

WallObstacles

CapturedModel

(m

s)

(m

s)



6 Conclusion





2



Participant 2119870(1) 0000822 000169 2062e2 206227


Participant 3119870(1) 0007529 000099 131842 013184




Participant 5119870(1) 0001279 000086 671672 067167


Participant 6119870(1) 0003097 000096 309182 030918


Participant 7119870(1) 0002894 000192 662751 066275






Competing Interests


Acknowledgments



References






















































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in








Platform ramp


Useroperator stage





119898= 120591119908 In this case a






















1) to






1

1198662 and 119866





10

20

30

40

50

60

70

80

90

100

573

638

63 68

3

VS-1

rate

d pr

esen

ce (

)



20

40

60

80

100

120

75

7581

6973

75

Rate

d (

)




minus05 0 05 1 15 2 25 3 35 4minus2

minus1

0

1

2

3

4

x (m)

y (m

)


Path 1Path 2Path 3

Path 4Path 5

S

G1

G2

G3

G4

G5

(a)

Path 1Path 2Path 3

Path 4Path 5

0 1 2 3 4 5 6 7 8 9minus02

0

02

04

06

08

1

12

14

16

t (s)

Spee

d (m

s)

Wheelchair speed

(b)







0

2

4

6

8

10

12

14

16

x (m)

y (m


Path 1Path 2Path 3

TableP1

P2

P3

(a)

Path 1Path 2Path 3

0 2 4 6 8 10 12 14

0

05

1

15

2

t (s)

Spee

d (m

s)

Wheelchair speed

(b)






minus7

minus6

minus5

minus4

minus3

minus2

minus1

0

1

2

x (m)

y (m

)


WallObstacles

Path 1Path 2Path 3

G1

G2

B

AS

C

D G3




0 2 4 6 8 10 12minus05

0

05

1


t (s)

A

B

Spee

d (m

s)

(a)

t (s)0 2 4 6 8

minus05

0

05

1


BA

Spee

d (m

s)

(b)

t (s)0 1 2 3 4 5 6 7

minus05

0

05


DC

Spee

d (m

s)

(c)






] = 1003816100381610038161003816

]des (119892119894) + ]env (env)1003816100381610038161003816

le ]max (8)









e =q119871119896minus q119896

10038161003816100381610038161003816

q119871119896minus q119896

10038161003816100381610038161003816

(10)

In (10) q119871119896







0001002003


x

y

drisk = 4

drisk = 5

drisk = 6



]env119896 = minus119896env119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(11)




]119896+1

= ]119896+ 119896] (]des minus ]

119896) minus 119896env

119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(12)






2

Participant 1

2119896] 00023296 00000493 212 0021145

00066778 09998727119896env 00000607 00000042 692 0069456]des 21620485 00000664 0003 0000031

Participant 2

1119896] 00013058 00000457 350 0034998

00044821 09998751119896env 00000168 00000050 298 0297619]des 31936471 00000572 0002 1791e minus 5

Participant 3

2119896] 00016111 00000638 396 0039600

00282700 09998215119896env 00001812 00000042 232 0023179]des 29748170 00000809 0003 2720e minus 5

Participant 4

1119896] 00022988 00000481 210 0020924

00096421 09998336119896env 00001566 00000041 262 0026181]des 15590495 00000483 0003 3098e minus 5

Participant 5

1119896] 00011705 00000330 282 0028193

00048858 09999171119896env 00000525 00000024 457 0045714]des 23263703 00000322 0001 1384e minus 5

Participant 6

2119896] 00033319 00003469 104 0104115

00288915 09992932119896env 00002114 00000097 459 0045885]des 20650043 00003439 0017 1665e minus 4

Participant 7

2119896] 00007837 00000496 633 0063290

00108345 09998355119896env 00001583 00000048 303 0030322]des 55191529 00000688 0001 1247e minus 5


DTR119896= 120588obst119896119894

q119894+ 120588obst119896119895

q119895 (13)

TTR119896=

120588obst119896119894]119896119894

q119894+

120588obst119896119895

]119896119895

q119895 (14)



119896 while ]









2

Participant 1

2119896] 00022305 00000508 228 0022775

00051076 09998726119896env 00000116 00000024 207 0206897]des 21419324 00000642 0003 2997e minus 5

Participant 2

1119896] 00012839 00000472 368 0036763

00042400 09998751119896env 00000059 00000018 3051 0305085]des 32207044 00000570 0002 1770e minus 5

Participant 3

2119896] 00011325 00000646 570 0057042

00077142 09998197119896env 00000370 00000027 730 0072973]des 33136044 00000776 0002 2342e minus 5

Participant 4

1119896] 00017910 00000473 264 0026410

00053594 09998327119896env 00000718 00000043 599 0059889]des 15635212 00000435 0003 2782e minus 5

Participant 5

1119896] 00010542 00000339 322 0032157

00042527 09999171119896env 00000403 00000018 447 0044665]des 24670341 00000319 0001 1293e minus 05

Participant 6



Participant 7




024


t (s)

v (m

s)


0002004


times105

times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus4minus2

024



1275 128 1285 129times105

times104

minus004minus002

0002004

(b)






t (s)

v (m

s)

0 5 10 15minus01

minus0050

00501


times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus015minus01

minus0050

00501


times104

(b)



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

x (m)

y (m

)


minus6

minus4

minus2

0

2


WallObstacles

CapturedModel

0 2 4 6 8 10 120

05

1

15

2

25

3


CapturedModel

t (s)

v (m

s)

CapturedModel

0 10 20 30 40 50 60 70 800

1

2

3

4

5


t (s)

v (m

s)






minus6

minus4

minus2

0

2

x (m)

y (m

)

WallObstacles

CapturedModel



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

0 5 10 150

05

1

15

2

25


CapturedModel

t (s)

v (m

s)

0 10 20 30 40 50 600

1

2

3

4


CapturedModel

t (s)

v (m

s)







minus6

minus4

minus2

0

2

x (m)

y (m

)


minus6

minus4

minus2

0

2

x (m)

y (m

)


0 10 20 30 40 50 60 70 80minus005

0


t (s) t (s)

Error Error

0 10 20 30 40 50 60 70 80minus01

minus008

minus006

minus004

minus002

0

002

004


WallObstacles

CapturedModel

WallObstacles

CapturedModel

(m

s)

(m

s)



6 Conclusion





2



Participant 2119870(1) 0000822 000169 2062e2 206227


Participant 3119870(1) 0007529 000099 131842 013184




Participant 5119870(1) 0001279 000086 671672 067167


Participant 6119870(1) 0003097 000096 309182 030918


Participant 7119870(1) 0002894 000192 662751 066275






Competing Interests


Acknowledgments



References






















































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in

















1) to






1

1198662 and 119866





10

20

30

40

50

60

70

80

90

100

573

638

63 68

3

VS-1

rate

d pr

esen

ce (

)



20

40

60

80

100

120

75

7581

6973

75

Rate

d (

)




minus05 0 05 1 15 2 25 3 35 4minus2

minus1

0

1

2

3

4

x (m)

y (m

)


Path 1Path 2Path 3

Path 4Path 5

S

G1

G2

G3

G4

G5

(a)

Path 1Path 2Path 3

Path 4Path 5

0 1 2 3 4 5 6 7 8 9minus02

0

02

04

06

08

1

12

14

16

t (s)

Spee

d (m

s)

Wheelchair speed

(b)







0

2

4

6

8

10

12

14

16

x (m)

y (m


Path 1Path 2Path 3

TableP1

P2

P3

(a)

Path 1Path 2Path 3

0 2 4 6 8 10 12 14

0

05

1

15

2

t (s)

Spee

d (m

s)

Wheelchair speed

(b)






minus7

minus6

minus5

minus4

minus3

minus2

minus1

0

1

2

x (m)

y (m

)


WallObstacles

Path 1Path 2Path 3

G1

G2

B

AS

C

D G3




0 2 4 6 8 10 12minus05

0

05

1


t (s)

A

B

Spee

d (m

s)

(a)

t (s)0 2 4 6 8

minus05

0

05

1


BA

Spee

d (m

s)

(b)

t (s)0 1 2 3 4 5 6 7

minus05

0

05


DC

Spee

d (m

s)

(c)






] = 1003816100381610038161003816

]des (119892119894) + ]env (env)1003816100381610038161003816

le ]max (8)









e =q119871119896minus q119896

10038161003816100381610038161003816

q119871119896minus q119896

10038161003816100381610038161003816

(10)

In (10) q119871119896







0001002003


x

y

drisk = 4

drisk = 5

drisk = 6



]env119896 = minus119896env119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(11)




]119896+1

= ]119896+ 119896] (]des minus ]

119896) minus 119896env

119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(12)






2

Participant 1

2119896] 00023296 00000493 212 0021145

00066778 09998727119896env 00000607 00000042 692 0069456]des 21620485 00000664 0003 0000031

Participant 2

1119896] 00013058 00000457 350 0034998

00044821 09998751119896env 00000168 00000050 298 0297619]des 31936471 00000572 0002 1791e minus 5

Participant 3

2119896] 00016111 00000638 396 0039600

00282700 09998215119896env 00001812 00000042 232 0023179]des 29748170 00000809 0003 2720e minus 5

Participant 4

1119896] 00022988 00000481 210 0020924

00096421 09998336119896env 00001566 00000041 262 0026181]des 15590495 00000483 0003 3098e minus 5

Participant 5

1119896] 00011705 00000330 282 0028193

00048858 09999171119896env 00000525 00000024 457 0045714]des 23263703 00000322 0001 1384e minus 5

Participant 6

2119896] 00033319 00003469 104 0104115

00288915 09992932119896env 00002114 00000097 459 0045885]des 20650043 00003439 0017 1665e minus 4

Participant 7

2119896] 00007837 00000496 633 0063290

00108345 09998355119896env 00001583 00000048 303 0030322]des 55191529 00000688 0001 1247e minus 5


DTR119896= 120588obst119896119894

q119894+ 120588obst119896119895

q119895 (13)

TTR119896=

120588obst119896119894]119896119894

q119894+

120588obst119896119895

]119896119895

q119895 (14)



119896 while ]









2

Participant 1

2119896] 00022305 00000508 228 0022775

00051076 09998726119896env 00000116 00000024 207 0206897]des 21419324 00000642 0003 2997e minus 5

Participant 2

1119896] 00012839 00000472 368 0036763

00042400 09998751119896env 00000059 00000018 3051 0305085]des 32207044 00000570 0002 1770e minus 5

Participant 3

2119896] 00011325 00000646 570 0057042

00077142 09998197119896env 00000370 00000027 730 0072973]des 33136044 00000776 0002 2342e minus 5

Participant 4

1119896] 00017910 00000473 264 0026410

00053594 09998327119896env 00000718 00000043 599 0059889]des 15635212 00000435 0003 2782e minus 5

Participant 5

1119896] 00010542 00000339 322 0032157

00042527 09999171119896env 00000403 00000018 447 0044665]des 24670341 00000319 0001 1293e minus 05

Participant 6



Participant 7




024


t (s)

v (m

s)


0002004


times105

times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus4minus2

024



1275 128 1285 129times105

times104

minus004minus002

0002004

(b)






t (s)

v (m

s)

0 5 10 15minus01

minus0050

00501


times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus015minus01

minus0050

00501


times104

(b)



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

x (m)

y (m

)


minus6

minus4

minus2

0

2


WallObstacles

CapturedModel

0 2 4 6 8 10 120

05

1

15

2

25

3


CapturedModel

t (s)

v (m

s)

CapturedModel

0 10 20 30 40 50 60 70 800

1

2

3

4

5


t (s)

v (m

s)






minus6

minus4

minus2

0

2

x (m)

y (m

)

WallObstacles

CapturedModel



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

0 5 10 150

05

1

15

2

25


CapturedModel

t (s)

v (m

s)

0 10 20 30 40 50 600

1

2

3

4


CapturedModel

t (s)

v (m

s)







minus6

minus4

minus2

0

2

x (m)

y (m

)


minus6

minus4

minus2

0

2

x (m)

y (m

)


0 10 20 30 40 50 60 70 80minus005

0


t (s) t (s)

Error Error

0 10 20 30 40 50 60 70 80minus01

minus008

minus006

minus004

minus002

0

002

004


WallObstacles

CapturedModel

WallObstacles

CapturedModel

(m

s)

(m

s)



6 Conclusion





2



Participant 2119870(1) 0000822 000169 2062e2 206227


Participant 3119870(1) 0007529 000099 131842 013184




Participant 5119870(1) 0001279 000086 671672 067167


Participant 6119870(1) 0003097 000096 309182 030918


Participant 7119870(1) 0002894 000192 662751 066275






Competing Interests


Acknowledgments



References






















































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





10

20

30

40

50

60

70

80

90

100

573

638

63 68

3

VS-1

rate

d pr

esen

ce (

)



20

40

60

80

100

120

75

7581

6973

75

Rate

d (

)




minus05 0 05 1 15 2 25 3 35 4minus2

minus1

0

1

2

3

4

x (m)

y (m

)


Path 1Path 2Path 3

Path 4Path 5

S

G1

G2

G3

G4

G5

(a)

Path 1Path 2Path 3

Path 4Path 5

0 1 2 3 4 5 6 7 8 9minus02

0

02

04

06

08

1

12

14

16

t (s)

Spee

d (m

s)

Wheelchair speed

(b)







0

2

4

6

8

10

12

14

16

x (m)

y (m


Path 1Path 2Path 3

TableP1

P2

P3

(a)

Path 1Path 2Path 3

0 2 4 6 8 10 12 14

0

05

1

15

2

t (s)

Spee

d (m

s)

Wheelchair speed

(b)






minus7

minus6

minus5

minus4

minus3

minus2

minus1

0

1

2

x (m)

y (m

)


WallObstacles

Path 1Path 2Path 3

G1

G2

B

AS

C

D G3




0 2 4 6 8 10 12minus05

0

05

1


t (s)

A

B

Spee

d (m

s)

(a)

t (s)0 2 4 6 8

minus05

0

05

1


BA

Spee

d (m

s)

(b)

t (s)0 1 2 3 4 5 6 7

minus05

0

05


DC

Spee

d (m

s)

(c)






] = 1003816100381610038161003816

]des (119892119894) + ]env (env)1003816100381610038161003816

le ]max (8)









e =q119871119896minus q119896

10038161003816100381610038161003816

q119871119896minus q119896

10038161003816100381610038161003816

(10)

In (10) q119871119896







0001002003


x

y

drisk = 4

drisk = 5

drisk = 6



]env119896 = minus119896env119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(11)




]119896+1

= ]119896+ 119896] (]des minus ]

119896) minus 119896env

119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(12)






2

Participant 1

2119896] 00023296 00000493 212 0021145

00066778 09998727119896env 00000607 00000042 692 0069456]des 21620485 00000664 0003 0000031

Participant 2

1119896] 00013058 00000457 350 0034998

00044821 09998751119896env 00000168 00000050 298 0297619]des 31936471 00000572 0002 1791e minus 5

Participant 3

2119896] 00016111 00000638 396 0039600

00282700 09998215119896env 00001812 00000042 232 0023179]des 29748170 00000809 0003 2720e minus 5

Participant 4

1119896] 00022988 00000481 210 0020924

00096421 09998336119896env 00001566 00000041 262 0026181]des 15590495 00000483 0003 3098e minus 5

Participant 5

1119896] 00011705 00000330 282 0028193

00048858 09999171119896env 00000525 00000024 457 0045714]des 23263703 00000322 0001 1384e minus 5

Participant 6

2119896] 00033319 00003469 104 0104115

00288915 09992932119896env 00002114 00000097 459 0045885]des 20650043 00003439 0017 1665e minus 4

Participant 7

2119896] 00007837 00000496 633 0063290

00108345 09998355119896env 00001583 00000048 303 0030322]des 55191529 00000688 0001 1247e minus 5


DTR119896= 120588obst119896119894

q119894+ 120588obst119896119895

q119895 (13)

TTR119896=

120588obst119896119894]119896119894

q119894+

120588obst119896119895

]119896119895

q119895 (14)



119896 while ]









2

Participant 1

2119896] 00022305 00000508 228 0022775

00051076 09998726119896env 00000116 00000024 207 0206897]des 21419324 00000642 0003 2997e minus 5

Participant 2

1119896] 00012839 00000472 368 0036763

00042400 09998751119896env 00000059 00000018 3051 0305085]des 32207044 00000570 0002 1770e minus 5

Participant 3

2119896] 00011325 00000646 570 0057042

00077142 09998197119896env 00000370 00000027 730 0072973]des 33136044 00000776 0002 2342e minus 5

Participant 4

1119896] 00017910 00000473 264 0026410

00053594 09998327119896env 00000718 00000043 599 0059889]des 15635212 00000435 0003 2782e minus 5

Participant 5

1119896] 00010542 00000339 322 0032157

00042527 09999171119896env 00000403 00000018 447 0044665]des 24670341 00000319 0001 1293e minus 05

Participant 6



Participant 7




024


t (s)

v (m

s)


0002004


times105

times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus4minus2

024



1275 128 1285 129times105

times104

minus004minus002

0002004

(b)






t (s)

v (m

s)

0 5 10 15minus01

minus0050

00501


times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus015minus01

minus0050

00501


times104

(b)



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

x (m)

y (m

)


minus6

minus4

minus2

0

2


WallObstacles

CapturedModel

0 2 4 6 8 10 120

05

1

15

2

25

3


CapturedModel

t (s)

v (m

s)

CapturedModel

0 10 20 30 40 50 60 70 800

1

2

3

4

5


t (s)

v (m

s)






minus6

minus4

minus2

0

2

x (m)

y (m

)

WallObstacles

CapturedModel



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

0 5 10 150

05

1

15

2

25


CapturedModel

t (s)

v (m

s)

0 10 20 30 40 50 600

1

2

3

4


CapturedModel

t (s)

v (m

s)







minus6

minus4

minus2

0

2

x (m)

y (m

)


minus6

minus4

minus2

0

2

x (m)

y (m

)


0 10 20 30 40 50 60 70 80minus005

0


t (s) t (s)

Error Error

0 10 20 30 40 50 60 70 80minus01

minus008

minus006

minus004

minus002

0

002

004


WallObstacles

CapturedModel

WallObstacles

CapturedModel

(m

s)

(m

s)



6 Conclusion





2



Participant 2119870(1) 0000822 000169 2062e2 206227


Participant 3119870(1) 0007529 000099 131842 013184




Participant 5119870(1) 0001279 000086 671672 067167


Participant 6119870(1) 0003097 000096 309182 030918


Participant 7119870(1) 0002894 000192 662751 066275






Competing Interests


Acknowledgments



References






















































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





0

2

4

6

8

10

12

14

16

x (m)

y (m


Path 1Path 2Path 3

TableP1

P2

P3

(a)

Path 1Path 2Path 3

0 2 4 6 8 10 12 14

0

05

1

15

2

t (s)

Spee

d (m

s)

Wheelchair speed

(b)






minus7

minus6

minus5

minus4

minus3

minus2

minus1

0

1

2

x (m)

y (m

)


WallObstacles

Path 1Path 2Path 3

G1

G2

B

AS

C

D G3




0 2 4 6 8 10 12minus05

0

05

1


t (s)

A

B

Spee

d (m

s)

(a)

t (s)0 2 4 6 8

minus05

0

05

1


BA

Spee

d (m

s)

(b)

t (s)0 1 2 3 4 5 6 7

minus05

0

05


DC

Spee

d (m

s)

(c)






] = 1003816100381610038161003816

]des (119892119894) + ]env (env)1003816100381610038161003816

le ]max (8)









e =q119871119896minus q119896

10038161003816100381610038161003816

q119871119896minus q119896

10038161003816100381610038161003816

(10)

In (10) q119871119896







0001002003


x

y

drisk = 4

drisk = 5

drisk = 6



]env119896 = minus119896env119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(11)




]119896+1

= ]119896+ 119896] (]des minus ]

119896) minus 119896env

119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(12)






2

Participant 1

2119896] 00023296 00000493 212 0021145

00066778 09998727119896env 00000607 00000042 692 0069456]des 21620485 00000664 0003 0000031

Participant 2

1119896] 00013058 00000457 350 0034998

00044821 09998751119896env 00000168 00000050 298 0297619]des 31936471 00000572 0002 1791e minus 5

Participant 3

2119896] 00016111 00000638 396 0039600

00282700 09998215119896env 00001812 00000042 232 0023179]des 29748170 00000809 0003 2720e minus 5

Participant 4

1119896] 00022988 00000481 210 0020924

00096421 09998336119896env 00001566 00000041 262 0026181]des 15590495 00000483 0003 3098e minus 5

Participant 5

1119896] 00011705 00000330 282 0028193

00048858 09999171119896env 00000525 00000024 457 0045714]des 23263703 00000322 0001 1384e minus 5

Participant 6

2119896] 00033319 00003469 104 0104115

00288915 09992932119896env 00002114 00000097 459 0045885]des 20650043 00003439 0017 1665e minus 4

Participant 7

2119896] 00007837 00000496 633 0063290

00108345 09998355119896env 00001583 00000048 303 0030322]des 55191529 00000688 0001 1247e minus 5


DTR119896= 120588obst119896119894

q119894+ 120588obst119896119895

q119895 (13)

TTR119896=

120588obst119896119894]119896119894

q119894+

120588obst119896119895

]119896119895

q119895 (14)



119896 while ]









2

Participant 1

2119896] 00022305 00000508 228 0022775

00051076 09998726119896env 00000116 00000024 207 0206897]des 21419324 00000642 0003 2997e minus 5

Participant 2

1119896] 00012839 00000472 368 0036763

00042400 09998751119896env 00000059 00000018 3051 0305085]des 32207044 00000570 0002 1770e minus 5

Participant 3

2119896] 00011325 00000646 570 0057042

00077142 09998197119896env 00000370 00000027 730 0072973]des 33136044 00000776 0002 2342e minus 5

Participant 4

1119896] 00017910 00000473 264 0026410

00053594 09998327119896env 00000718 00000043 599 0059889]des 15635212 00000435 0003 2782e minus 5

Participant 5

1119896] 00010542 00000339 322 0032157

00042527 09999171119896env 00000403 00000018 447 0044665]des 24670341 00000319 0001 1293e minus 05

Participant 6



Participant 7




024


t (s)

v (m

s)


0002004


times105

times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus4minus2

024



1275 128 1285 129times105

times104

minus004minus002

0002004

(b)






t (s)

v (m

s)

0 5 10 15minus01

minus0050

00501


times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus015minus01

minus0050

00501


times104

(b)



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

x (m)

y (m

)


minus6

minus4

minus2

0

2


WallObstacles

CapturedModel

0 2 4 6 8 10 120

05

1

15

2

25

3


CapturedModel

t (s)

v (m

s)

CapturedModel

0 10 20 30 40 50 60 70 800

1

2

3

4

5


t (s)

v (m

s)






minus6

minus4

minus2

0

2

x (m)

y (m

)

WallObstacles

CapturedModel



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

0 5 10 150

05

1

15

2

25


CapturedModel

t (s)

v (m

s)

0 10 20 30 40 50 600

1

2

3

4


CapturedModel

t (s)

v (m

s)







minus6

minus4

minus2

0

2

x (m)

y (m

)


minus6

minus4

minus2

0

2

x (m)

y (m

)


0 10 20 30 40 50 60 70 80minus005

0


t (s) t (s)

Error Error

0 10 20 30 40 50 60 70 80minus01

minus008

minus006

minus004

minus002

0

002

004


WallObstacles

CapturedModel

WallObstacles

CapturedModel

(m

s)

(m

s)



6 Conclusion





2



Participant 2119870(1) 0000822 000169 2062e2 206227


Participant 3119870(1) 0007529 000099 131842 013184




Participant 5119870(1) 0001279 000086 671672 067167


Participant 6119870(1) 0003097 000096 309182 030918


Participant 7119870(1) 0002894 000192 662751 066275






Competing Interests


Acknowledgments



References






















































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0 2 4 6 8 10 12minus05

0

05

1


t (s)

A

B

Spee

d (m

s)

(a)

t (s)0 2 4 6 8

minus05

0

05

1


BA

Spee

d (m

s)

(b)

t (s)0 1 2 3 4 5 6 7

minus05

0

05


DC

Spee

d (m

s)

(c)






] = 1003816100381610038161003816

]des (119892119894) + ]env (env)1003816100381610038161003816

le ]max (8)









e =q119871119896minus q119896

10038161003816100381610038161003816

q119871119896minus q119896

10038161003816100381610038161003816

(10)

In (10) q119871119896







0001002003


x

y

drisk = 4

drisk = 5

drisk = 6



]env119896 = minus119896env119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(11)




]119896+1

= ]119896+ 119896] (]des minus ]

119896) minus 119896env

119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(12)






2

Participant 1

2119896] 00023296 00000493 212 0021145

00066778 09998727119896env 00000607 00000042 692 0069456]des 21620485 00000664 0003 0000031

Participant 2

1119896] 00013058 00000457 350 0034998

00044821 09998751119896env 00000168 00000050 298 0297619]des 31936471 00000572 0002 1791e minus 5

Participant 3

2119896] 00016111 00000638 396 0039600

00282700 09998215119896env 00001812 00000042 232 0023179]des 29748170 00000809 0003 2720e minus 5

Participant 4

1119896] 00022988 00000481 210 0020924

00096421 09998336119896env 00001566 00000041 262 0026181]des 15590495 00000483 0003 3098e minus 5

Participant 5

1119896] 00011705 00000330 282 0028193

00048858 09999171119896env 00000525 00000024 457 0045714]des 23263703 00000322 0001 1384e minus 5

Participant 6

2119896] 00033319 00003469 104 0104115

00288915 09992932119896env 00002114 00000097 459 0045885]des 20650043 00003439 0017 1665e minus 4

Participant 7

2119896] 00007837 00000496 633 0063290

00108345 09998355119896env 00001583 00000048 303 0030322]des 55191529 00000688 0001 1247e minus 5


DTR119896= 120588obst119896119894

q119894+ 120588obst119896119895

q119895 (13)

TTR119896=

120588obst119896119894]119896119894

q119894+

120588obst119896119895

]119896119895

q119895 (14)



119896 while ]









2

Participant 1

2119896] 00022305 00000508 228 0022775

00051076 09998726119896env 00000116 00000024 207 0206897]des 21419324 00000642 0003 2997e minus 5

Participant 2

1119896] 00012839 00000472 368 0036763

00042400 09998751119896env 00000059 00000018 3051 0305085]des 32207044 00000570 0002 1770e minus 5

Participant 3

2119896] 00011325 00000646 570 0057042

00077142 09998197119896env 00000370 00000027 730 0072973]des 33136044 00000776 0002 2342e minus 5

Participant 4

1119896] 00017910 00000473 264 0026410

00053594 09998327119896env 00000718 00000043 599 0059889]des 15635212 00000435 0003 2782e minus 5

Participant 5

1119896] 00010542 00000339 322 0032157

00042527 09999171119896env 00000403 00000018 447 0044665]des 24670341 00000319 0001 1293e minus 05

Participant 6



Participant 7




024


t (s)

v (m

s)


0002004


times105

times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus4minus2

024



1275 128 1285 129times105

times104

minus004minus002

0002004

(b)






t (s)

v (m

s)

0 5 10 15minus01

minus0050

00501


times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus015minus01

minus0050

00501


times104

(b)



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

x (m)

y (m

)


minus6

minus4

minus2

0

2


WallObstacles

CapturedModel

0 2 4 6 8 10 120

05

1

15

2

25

3


CapturedModel

t (s)

v (m

s)

CapturedModel

0 10 20 30 40 50 60 70 800

1

2

3

4

5


t (s)

v (m

s)






minus6

minus4

minus2

0

2

x (m)

y (m

)

WallObstacles

CapturedModel



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

0 5 10 150

05

1

15

2

25


CapturedModel

t (s)

v (m

s)

0 10 20 30 40 50 600

1

2

3

4


CapturedModel

t (s)

v (m

s)







minus6

minus4

minus2

0

2

x (m)

y (m

)


minus6

minus4

minus2

0

2

x (m)

y (m

)


0 10 20 30 40 50 60 70 80minus005

0


t (s) t (s)

Error Error

0 10 20 30 40 50 60 70 80minus01

minus008

minus006

minus004

minus002

0

002

004


WallObstacles

CapturedModel

WallObstacles

CapturedModel

(m

s)

(m

s)



6 Conclusion





2



Participant 2119870(1) 0000822 000169 2062e2 206227


Participant 3119870(1) 0007529 000099 131842 013184




Participant 5119870(1) 0001279 000086 671672 067167


Participant 6119870(1) 0003097 000096 309182 030918


Participant 7119870(1) 0002894 000192 662751 066275






Competing Interests


Acknowledgments



References






















































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










e =q119871119896minus q119896

10038161003816100381610038161003816

q119871119896minus q119896

10038161003816100381610038161003816

(10)

In (10) q119871119896







0001002003


x

y

drisk = 4

drisk = 5

drisk = 6



]env119896 = minus119896env119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(11)




]119896+1

= ]119896+ 119896] (]des minus ]

119896) minus 119896env

119873

sum

119894=1

cos119898 (120601obst119894 minus 120601119896)119860

119899

119894

(12)






2

Participant 1

2119896] 00023296 00000493 212 0021145

00066778 09998727119896env 00000607 00000042 692 0069456]des 21620485 00000664 0003 0000031

Participant 2

1119896] 00013058 00000457 350 0034998

00044821 09998751119896env 00000168 00000050 298 0297619]des 31936471 00000572 0002 1791e minus 5

Participant 3

2119896] 00016111 00000638 396 0039600

00282700 09998215119896env 00001812 00000042 232 0023179]des 29748170 00000809 0003 2720e minus 5

Participant 4

1119896] 00022988 00000481 210 0020924

00096421 09998336119896env 00001566 00000041 262 0026181]des 15590495 00000483 0003 3098e minus 5

Participant 5

1119896] 00011705 00000330 282 0028193

00048858 09999171119896env 00000525 00000024 457 0045714]des 23263703 00000322 0001 1384e minus 5

Participant 6

2119896] 00033319 00003469 104 0104115

00288915 09992932119896env 00002114 00000097 459 0045885]des 20650043 00003439 0017 1665e minus 4

Participant 7

2119896] 00007837 00000496 633 0063290

00108345 09998355119896env 00001583 00000048 303 0030322]des 55191529 00000688 0001 1247e minus 5


DTR119896= 120588obst119896119894

q119894+ 120588obst119896119895

q119895 (13)

TTR119896=

120588obst119896119894]119896119894

q119894+

120588obst119896119895

]119896119895

q119895 (14)



119896 while ]









2

Participant 1

2119896] 00022305 00000508 228 0022775

00051076 09998726119896env 00000116 00000024 207 0206897]des 21419324 00000642 0003 2997e minus 5

Participant 2

1119896] 00012839 00000472 368 0036763

00042400 09998751119896env 00000059 00000018 3051 0305085]des 32207044 00000570 0002 1770e minus 5

Participant 3

2119896] 00011325 00000646 570 0057042

00077142 09998197119896env 00000370 00000027 730 0072973]des 33136044 00000776 0002 2342e minus 5

Participant 4

1119896] 00017910 00000473 264 0026410

00053594 09998327119896env 00000718 00000043 599 0059889]des 15635212 00000435 0003 2782e minus 5

Participant 5

1119896] 00010542 00000339 322 0032157

00042527 09999171119896env 00000403 00000018 447 0044665]des 24670341 00000319 0001 1293e minus 05

Participant 6



Participant 7




024


t (s)

v (m

s)


0002004


times105

times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus4minus2

024



1275 128 1285 129times105

times104

minus004minus002

0002004

(b)






t (s)

v (m

s)

0 5 10 15minus01

minus0050

00501


times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus015minus01

minus0050

00501


times104

(b)



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

x (m)

y (m

)


minus6

minus4

minus2

0

2


WallObstacles

CapturedModel

0 2 4 6 8 10 120

05

1

15

2

25

3


CapturedModel

t (s)

v (m

s)

CapturedModel

0 10 20 30 40 50 60 70 800

1

2

3

4

5


t (s)

v (m

s)






minus6

minus4

minus2

0

2

x (m)

y (m

)

WallObstacles

CapturedModel



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

0 5 10 150

05

1

15

2

25


CapturedModel

t (s)

v (m

s)

0 10 20 30 40 50 600

1

2

3

4


CapturedModel

t (s)

v (m

s)







minus6

minus4

minus2

0

2

x (m)

y (m

)


minus6

minus4

minus2

0

2

x (m)

y (m

)


0 10 20 30 40 50 60 70 80minus005

0


t (s) t (s)

Error Error

0 10 20 30 40 50 60 70 80minus01

minus008

minus006

minus004

minus002

0

002

004


WallObstacles

CapturedModel

WallObstacles

CapturedModel

(m

s)

(m

s)



6 Conclusion





2



Participant 2119870(1) 0000822 000169 2062e2 206227


Participant 3119870(1) 0007529 000099 131842 013184




Participant 5119870(1) 0001279 000086 671672 067167


Participant 6119870(1) 0003097 000096 309182 030918


Participant 7119870(1) 0002894 000192 662751 066275






Competing Interests


Acknowledgments



References






















































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






2

Participant 1

2119896] 00023296 00000493 212 0021145

00066778 09998727119896env 00000607 00000042 692 0069456]des 21620485 00000664 0003 0000031

Participant 2

1119896] 00013058 00000457 350 0034998

00044821 09998751119896env 00000168 00000050 298 0297619]des 31936471 00000572 0002 1791e minus 5

Participant 3

2119896] 00016111 00000638 396 0039600

00282700 09998215119896env 00001812 00000042 232 0023179]des 29748170 00000809 0003 2720e minus 5

Participant 4

1119896] 00022988 00000481 210 0020924

00096421 09998336119896env 00001566 00000041 262 0026181]des 15590495 00000483 0003 3098e minus 5

Participant 5

1119896] 00011705 00000330 282 0028193

00048858 09999171119896env 00000525 00000024 457 0045714]des 23263703 00000322 0001 1384e minus 5

Participant 6

2119896] 00033319 00003469 104 0104115

00288915 09992932119896env 00002114 00000097 459 0045885]des 20650043 00003439 0017 1665e minus 4

Participant 7

2119896] 00007837 00000496 633 0063290

00108345 09998355119896env 00001583 00000048 303 0030322]des 55191529 00000688 0001 1247e minus 5


DTR119896= 120588obst119896119894

q119894+ 120588obst119896119895

q119895 (13)

TTR119896=

120588obst119896119894]119896119894

q119894+

120588obst119896119895

]119896119895

q119895 (14)



119896 while ]









2

Participant 1

2119896] 00022305 00000508 228 0022775

00051076 09998726119896env 00000116 00000024 207 0206897]des 21419324 00000642 0003 2997e minus 5

Participant 2

1119896] 00012839 00000472 368 0036763

00042400 09998751119896env 00000059 00000018 3051 0305085]des 32207044 00000570 0002 1770e minus 5

Participant 3

2119896] 00011325 00000646 570 0057042

00077142 09998197119896env 00000370 00000027 730 0072973]des 33136044 00000776 0002 2342e minus 5

Participant 4

1119896] 00017910 00000473 264 0026410

00053594 09998327119896env 00000718 00000043 599 0059889]des 15635212 00000435 0003 2782e minus 5

Participant 5

1119896] 00010542 00000339 322 0032157

00042527 09999171119896env 00000403 00000018 447 0044665]des 24670341 00000319 0001 1293e minus 05

Participant 6



Participant 7




024


t (s)

v (m

s)


0002004


times105

times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus4minus2

024



1275 128 1285 129times105

times104

minus004minus002

0002004

(b)






t (s)

v (m

s)

0 5 10 15minus01

minus0050

00501


times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus015minus01

minus0050

00501


times104

(b)



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

x (m)

y (m

)


minus6

minus4

minus2

0

2


WallObstacles

CapturedModel

0 2 4 6 8 10 120

05

1

15

2

25

3


CapturedModel

t (s)

v (m

s)

CapturedModel

0 10 20 30 40 50 60 70 800

1

2

3

4

5


t (s)

v (m

s)






minus6

minus4

minus2

0

2

x (m)

y (m

)

WallObstacles

CapturedModel



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

0 5 10 150

05

1

15

2

25


CapturedModel

t (s)

v (m

s)

0 10 20 30 40 50 600

1

2

3

4


CapturedModel

t (s)

v (m

s)







minus6

minus4

minus2

0

2

x (m)

y (m

)


minus6

minus4

minus2

0

2

x (m)

y (m

)


0 10 20 30 40 50 60 70 80minus005

0


t (s) t (s)

Error Error

0 10 20 30 40 50 60 70 80minus01

minus008

minus006

minus004

minus002

0

002

004


WallObstacles

CapturedModel

WallObstacles

CapturedModel

(m

s)

(m

s)



6 Conclusion





2



Participant 2119870(1) 0000822 000169 2062e2 206227


Participant 3119870(1) 0007529 000099 131842 013184




Participant 5119870(1) 0001279 000086 671672 067167


Participant 6119870(1) 0003097 000096 309182 030918


Participant 7119870(1) 0002894 000192 662751 066275






Competing Interests


Acknowledgments



References






















































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






2

Participant 1

2119896] 00022305 00000508 228 0022775

00051076 09998726119896env 00000116 00000024 207 0206897]des 21419324 00000642 0003 2997e minus 5

Participant 2

1119896] 00012839 00000472 368 0036763

00042400 09998751119896env 00000059 00000018 3051 0305085]des 32207044 00000570 0002 1770e minus 5

Participant 3

2119896] 00011325 00000646 570 0057042

00077142 09998197119896env 00000370 00000027 730 0072973]des 33136044 00000776 0002 2342e minus 5

Participant 4

1119896] 00017910 00000473 264 0026410

00053594 09998327119896env 00000718 00000043 599 0059889]des 15635212 00000435 0003 2782e minus 5

Participant 5

1119896] 00010542 00000339 322 0032157

00042527 09999171119896env 00000403 00000018 447 0044665]des 24670341 00000319 0001 1293e minus 05

Participant 6



Participant 7




024


t (s)

v (m

s)


0002004


times105

times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus4minus2

024



1275 128 1285 129times105

times104

minus004minus002

0002004

(b)






t (s)

v (m

s)

0 5 10 15minus01

minus0050

00501


times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus015minus01

minus0050

00501


times104

(b)



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

x (m)

y (m

)


minus6

minus4

minus2

0

2


WallObstacles

CapturedModel

0 2 4 6 8 10 120

05

1

15

2

25

3


CapturedModel

t (s)

v (m

s)

CapturedModel

0 10 20 30 40 50 60 70 800

1

2

3

4

5


t (s)

v (m

s)






minus6

minus4

minus2

0

2

x (m)

y (m

)

WallObstacles

CapturedModel



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

0 5 10 150

05

1

15

2

25


CapturedModel

t (s)

v (m

s)

0 10 20 30 40 50 600

1

2

3

4


CapturedModel

t (s)

v (m

s)







minus6

minus4

minus2

0

2

x (m)

y (m

)


minus6

minus4

minus2

0

2

x (m)

y (m

)


0 10 20 30 40 50 60 70 80minus005

0


t (s) t (s)

Error Error

0 10 20 30 40 50 60 70 80minus01

minus008

minus006

minus004

minus002

0

002

004


WallObstacles

CapturedModel

WallObstacles

CapturedModel

(m

s)

(m

s)



6 Conclusion





2



Participant 2119870(1) 0000822 000169 2062e2 206227


Participant 3119870(1) 0007529 000099 131842 013184




Participant 5119870(1) 0001279 000086 671672 067167


Participant 6119870(1) 0003097 000096 309182 030918


Participant 7119870(1) 0002894 000192 662751 066275






Competing Interests


Acknowledgments



References






















































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




t (s)

v (m

s)

0 5 10 15minus01

minus0050

00501


times104

(a)

t (s)

v (m

s)

0 2 4 6 8 10 12 14 16minus015minus01

minus0050

00501


times104

(b)



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

x (m)

y (m

)


minus6

minus4

minus2

0

2


WallObstacles

CapturedModel

0 2 4 6 8 10 120

05

1

15

2

25

3


CapturedModel

t (s)

v (m

s)

CapturedModel

0 10 20 30 40 50 60 70 800

1

2

3

4

5


t (s)

v (m

s)






minus6

minus4

minus2

0

2

x (m)

y (m

)

WallObstacles

CapturedModel



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

0 5 10 150

05

1

15

2

25


CapturedModel

t (s)

v (m

s)

0 10 20 30 40 50 600

1

2

3

4


CapturedModel

t (s)

v (m

s)







minus6

minus4

minus2

0

2

x (m)

y (m

)


minus6

minus4

minus2

0

2

x (m)

y (m

)


0 10 20 30 40 50 60 70 80minus005

0


t (s) t (s)

Error Error

0 10 20 30 40 50 60 70 80minus01

minus008

minus006

minus004

minus002

0

002

004


WallObstacles

CapturedModel

WallObstacles

CapturedModel

(m

s)

(m

s)



6 Conclusion





2



Participant 2119870(1) 0000822 000169 2062e2 206227


Participant 3119870(1) 0007529 000099 131842 013184




Participant 5119870(1) 0001279 000086 671672 067167


Participant 6119870(1) 0003097 000096 309182 030918


Participant 7119870(1) 0002894 000192 662751 066275






Competing Interests


Acknowledgments



References






















































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





minus6

minus4

minus2

0

2

x (m)

y (m

)

WallObstacles

CapturedModel



minus6

minus4

minus2

0

2

x (m)

y (m

)


WallObstacles

CapturedModel

0 5 10 150

05

1

15

2

25


CapturedModel

t (s)

v (m

s)

0 10 20 30 40 50 600

1

2

3

4


CapturedModel

t (s)

v (m

s)







minus6

minus4

minus2

0

2

x (m)

y (m

)


minus6

minus4

minus2

0

2

x (m)

y (m

)


0 10 20 30 40 50 60 70 80minus005

0


t (s) t (s)

Error Error

0 10 20 30 40 50 60 70 80minus01

minus008

minus006

minus004

minus002

0

002

004


WallObstacles

CapturedModel

WallObstacles

CapturedModel

(m

s)

(m

s)



6 Conclusion





2



Participant 2119870(1) 0000822 000169 2062e2 206227


Participant 3119870(1) 0007529 000099 131842 013184




Participant 5119870(1) 0001279 000086 671672 067167


Participant 6119870(1) 0003097 000096 309182 030918


Participant 7119870(1) 0002894 000192 662751 066275






Competing Interests


Acknowledgments



References






















































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





minus6

minus4

minus2

0

2

x (m)

y (m

)


minus6

minus4

minus2

0

2

x (m)

y (m

)


0 10 20 30 40 50 60 70 80minus005

0


t (s) t (s)

Error Error

0 10 20 30 40 50 60 70 80minus01

minus008

minus006

minus004

minus002

0

002

004


WallObstacles

CapturedModel

WallObstacles

CapturedModel

(m

s)

(m

s)



6 Conclusion





2



Participant 2119870(1) 0000822 000169 2062e2 206227


Participant 3119870(1) 0007529 000099 131842 013184




Participant 5119870(1) 0001279 000086 671672 067167


Participant 6119870(1) 0003097 000096 309182 030918


Participant 7119870(1) 0002894 000192 662751 066275






Competing Interests


Acknowledgments



References






















































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






2



Participant 2119870(1) 0000822 000169 2062e2 206227


Participant 3119870(1) 0007529 000099 131842 013184




Participant 5119870(1) 0001279 000086 671672 067167


Participant 6119870(1) 0003097 000096 309182 030918


Participant 7119870(1) 0002894 000192 662751 066275






Competing Interests


Acknowledgments



References






















































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




References






















































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



























































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in


























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



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