KINEMATIC ANALYSIS AND EVALUATION OF WHEELCHAIR MOUNTED ROBOTIC ARMS

Transcription

1 FCRAR 2004 Florda Conference on Recent Advances n Robotcs May 6-7, 2004, Orlando, Florda KINEMATIC ANALYSIS AND EVALUATION OF WHEELCHAIR MOUNTED ROBOTIC ARMS Edward J. McCaffrey Ed.tracker@gte.net Redwan M. Alqasem alqasem@eng.usf.edu Rajv V. Dubey dubey@eng.usf.edu Unversty of South Florda Department of Mechancal Engneerng 4202 E. Fowler Avenue, ENB 118 Tampa, Florda 33620, USA Phone: (813) Fax: (813) ABSTRACT There has been sgnfcant progress n brngng commercally-vable wheelchar mounted robotc arms (WMRA) nto the marketplace n the past 30 years. Ths paper focuses on knematc analyss and evaluaton of such robotc arms. It addresses the knematcs of the WMRA wth respect to ts ablty to reach common postons whle performng actvtes of daly lvng (ADL). A procedure s developed for the knematc analyss and evaluaton of a wheelchar mounted robotc arm. In addton to developng the analytcal procedure, the manpulator s evaluated, and desgn recommendatons and nsghts are obtaned. Current commercally-avalable wheelchar mountable robotc manpulators have been desgned specfcally for use n rehabltaton robotcs. In an effort to evaluate two commercal manpulators, the procedure for knematc analyss s appled to each manpulator. Desgn recommendatons wth regard to each devce are obtaned. Ths method wll beneft the researchers by provdng a standardzed procedure for knematc analyss of WMRAs that s capable of evaluatng ndependent desgns. Keywords: Rehab, Robotc, Arm, Analyss, Wheelchar INTRODUCTION A wheelchar mounted robotc arm can enhance the manpulaton functons of people wth dsabltes. To better understand the effectveness of a robotc arm, t must be analyzed wth respect to ts knematcs and the workspace n whch t operates. Data from the US Census Bureau Statstcal Bref of 1993 showed that over 34 mllon Amercans had dffculty performng functonal actvtes [1]. The prmary focus of Rehabltaton Engneerng [2] and robotcs s to ncrease the qualty of lfe of ndvduals through ncreasng functonal ndependence and decreasng the costs assocated wth the assstance requred by the ndvdual. In the case of spnal njury or dysfuncton, robotc arm ads are most approprate for ndvduals wth spnal defcences rangng from cervcal spne vertebrae [3] through cervcal spne vertebrae [4]. Indvduals that requre moblty assst devces such as a power wheelchar can beneft from varous robotc devces because the power wheelchar provdes a platform wth whch to mount the devce as well as a power supply, usng the wheelchar s batteres. There are several desgns of workstaton-based robotc arm systems such as Handy-1 [5], whch s a 5 DOF robotc arm mounted to a non-powered wheeled base to assst n very specfc actvtes of daly lvng (ADL) such as eatng, drnkng, and make-up applcaton. In the feedng mode the operator controls the robot through an nterface that uses lghts whch move across the avalable food trays, and a button that selects the tem desred. An advancement of the technology of Handy-1 s beng explored wth the Robotc Ad to Independent Lvng [6] (RAIL) project. RAIL mproves upon the Handy-1 desgn by ncorporatng a new controller for better manpulator control, a 3D smulaton tool for modelng vrtual scenaros and attachment of sensors to assst set up and poston error determnaton. The ProVAR [8] s a system desgned to operate n a vocatonal envronment usng a web-based vrtual envronment to model the functonalty of the manpulator. In ths way the operator can examne potental arm movements for a gven task, and f the smulaton s successful, the acton can be ntated. 1

2 WMRA combnes the dea of a workstaton and a moblebase robot to mount a manpulator arm onto a power wheelchar. The most mportant desgn consderaton of where to mount a robotc arm n a power wheelchar s the safety of the operator [9]. WMRA can be mounted n the front, sde or rear of the wheelchar [10]. There have been several attempts n the past to create commercally-vable wheelchar mounted robotc arms, ncludng the two commercal WMRAs avalable, the Manus and the Raptor. The Manus utlzes a front mountng locaton to the left of the operator s left knee, whch makes the manpulator arm obtrusve [11]. The Manus manpulator s controlled by a joystck and a keypad. The joystck s used to manually operate the manpulator, and the 16- button keypad can be used to perform coordnated control of multple jonts wth preprogrammed gestures that can be taught to the Manus and stored for future use. A closed loop system s used to allow further ntegraton of the arm nto more complcated and ntellgent systems whch can assst the operator. Another producton of WMRA s the Raptor, whch mounts to the rght sde of the wheelchar. Ths ncreases the wdth of the power wheelchar and makes t more dffcult for the operator to maneuver through doorways and tght hallways [7]. Ths manpulator has four degrees of freedom and a planar grpper. The arm s drectly controlled by the user by ether a joystck or 10-button controller. Because the Raptor does not have encoders to provde feedback to the controller, the manpulator cannot be pre-programmed n the fashon of ndustral robots. An open loop controller places a human drectly n the loop of controllng the arm. The operator contnuously drects the arm one jont at a tme nto ts fnal poston, whch requres hgher levels of concentraton and eyehand coordnaton from the operator. The focus of ths paper s to analyze and evaluate WMRAs and develop an analytcal procedure to systematcally study the effectveness of WMRAs. The procedure s executed and the manpulator s then evaluated usng crtera specfc to rehabltaton applcatons. Desgn recommendatons are stated to better fulfll the specfc needs of a rehabltaton robotc manpulator. KINEMATIC ANALYSIS A workspace has been chosen whch reflects specfc requrements of ndvduals wth dsabltes [12]. Horzontal planes (x-y) were chosen wth respect to the floor as the vertcal axs z = 0. The orgn of the usercoordnate system s 31.8 above the floor and all values gven are referenced above the floor. A value of 2 above a gven plane was requred n order to gve room for the manpulator to reach an object. The value n parenthess s the z-axs heght wth respect to the user coordnate system Fgure 1: Workspace Horzontal Planes (farthest forward-most pont between the armrests) can be seen n Fgure 1, and they are as follows: Small objects on the floor: 2 (-29.8 ), Larger lght objects on the floor: 9 (-22.8 ), Heght of electrc socket: 18 (-13.8 ), Low coffee table: 26 ( ), Heght of standard table and door knob: 31 (-0.8 ), Ktchen counter top: 38 (6.18 ), Wall-mounted lght swtch: 50 (18.2 ), Low shelf above ktchen counter top 56 (24.18 ). The dstances n the x axs of the user coordnate system (farthest forward-most pont between the armrests) can be seen n Fgure 2. Startng from the farthest pont and workng toward the operator s descrbed as follows: 2 n front of the footrest of the power wheelchar (Ths s the prmary reference x-z plane), n front of the operator (Ths s 13.5 behnd the frst x-z plane), 6.75 n front of the operator (Ths s half the dstance of the 13.5 grd), 0.54 s front of the operator (Ths s 13.5 behnd the second x-z plane), The x-z plane at the orgn of the user reference plane, The x-z plane that reflects the mouth of the operator (4 behnd the orgn). To create the ndvdual ponts, a thrd plane (x-z) s defned. The plane located at the orgn separates the char nto two lateral halves and s shown n Fgure 2. The wheelchar used for the analyss s 27 wde ncludng the wdth of the drve wheels. The y axs n the user frame of reference s postve movng from the body to the rght hand extended out along the arm, these planes are: The plane ntersectng the orgn, 13.5 from the orgn toward the mounted arm, 23.5 from the orgn toward the mounted arm (10 from the outermost edge of the wheels). The Denavt-Hartenberg (D-H) parameters [13] are a method of analyzng robotc manpulators that was frst ntroduced n Each jont angle s analyzed separately wth lnks separatng each jont. When analyzng a jont of n dmensons, the jont s broken nto n jonts wth one degree of freedom connected to (n-1) lnks. Wthn the nomenclature varable refer to the lnk number. Fgure 3 shows the relatonshps between lnk number Fgure 2: Workspace Vertcal Planes Fgure 3: D-H Lnk Parameters (), lnk length (a -1), lnk twst (α ι 1), lnk offset (d), and jont angle (θ). 2

3 The lnk transformaton equaton relates all of the D-H parameters together can be wrtten as: T = R α ) D ( a ) R ( θ ) D ( d ), Or : x ( x cθ sθ 0 α sθ cα cθ cα sα sα d = T sθ sα cθ sα cα cα d Where c stands for Cos, s stands for Sn. The Jacoban s a multdmensonal form of the dervatve that relates jont veloctes to Cartesan velocty at the tp of the grpper. The relatonshp between jont velocty and Cartesan manpulator tp veloctes reles on the requrement that the Jacoban velocty be nvertble (not sngular), and that governs the workspace of the robotc arm. Θ & = J 1 ( Θ)ν A concept known as the manpulablty ellpsod s ntroduced as well as the volume of the ellpsod as the manpulablty measure. The manpulablty measure s the absolute value of the determnate of the Jacoban matrx (J) of the postonal sub-matrx of the fnal transformaton matrx of the manpulators arm reference frame. Both manpulators beng studed have three degrees of freedom. The relaton between the velocty vector v and the jont velocty s: v = J ( q) q& If we consder the set of all possble jont veloctes and the resultant end effector veloctes, we can get the manpulablty ellpsod as: q & = ( q& + q& + q& Whch must be less than or equal to unty. In the case beng analyzed the manpulablty ellpsod wll have three axes as shown n Fgure 4. In the specal case where all the ellpsod axes are equal, the ellpsod wll actually be sphercal, where the end effector can move n any drecton wth the same maxmum velocty. The larger the sze of the ellpsod the faster the end effector can move. One possble method of analyss s to determne the volume of the ellpsod. Ths s computatonally straght forward and s defned as follows: C m 2π ( 2(2 π) /2 m = m 1)/2 /[2 4 6 ( m 2) m] /[2 3 5 ( m 2) m] 1 W = σ z 2 1σ 2σ 3 Fgure 4: Manpulablty Ellpsod 3 f z f m m s s odd even The value of Cm s constant when m s fxed, whch s the case when m = 3. In ths case, we can see that the volume of the ellpsod s proportonal to the value of w. We refer to w as the manpulablty measure, whch has specfc propertes that allow us to defne t readly from the Jacoban and known jont angles. Frst n the broadest sense the manpulablty measure shown s defned as: W = det J ( q) J T ( q) For our specfc case, the manpulator s non-redundant, the prevous equaton reduces to: W = det J ( q) Ths shows that at a sngular confguraton, the value of w approaches or equals to zero. Hence the value of the manpulablty measure, whch s the volume of the manpulablty ellpsod, wll be equal to the determnate of the Jacoban. PROCEDURE FOR ANALYSIS Sold Works s used to determne the jont angles of each robot arm n order to fnd the manpulablty measure and to verfy t wthn the sold model. The Jacoban matrx s derved from the 1x3 postonal matrx wthn the fnal transformaton matrx of the arm. The transformaton matrx s created through the Judcous applcaton of the D-H parameters usng the approprate formulae. The reverse knematcs of the robotc arms was determned wth a program n MatLAB to determne the jont angles of the robotc arm for a gven pont n 3-D space. The program uses the Jacoban matrx n a numercal methods approach subdvdng the postonal dfference from the start poston of the grpper and the desred goal poston nto several dscrete goals. These dscrete goal postons were entered sequentally nto the Jacoban. The output of the Jacoban s a matrx contanng the ncremental change of jont angles requred to obtan the new poston. The jont angle change s added to the prevous jont angle and ths new value s nput nto the forward knematcs of the transformaton matrx. The actual poston s compared to the desred dscrete poston and f t s below an error value than the next poston s computed. If the error s too great the fnal error poston s subtracted from the desred poston and recomputed nto the Jacoban and the process repeats the loop. In the nverse knematc soluton there are four subroutnes along wth the man program. The subroutnes are called by the man program to execute addtonal steps. In order to create a procedure for the knematc analyss of WMRAs t s necessary to separate the process nto a seres of steps as follows: After creatng a D-H parameter table and transformaton matrces for the manpulator to be measured, lnk transformatons for the manpulator are calculated, and hence, the Jacoban matrx s developed. Then, the manpulator and a generc power wheelchar were modeled n Sold Works so that angle and jont relatonshps can be shown graphcally. A seres of ponts (grds) surroundng the wheelchar / arm assembly are specfed accordng to specfc applcatons n rehabltaton engneerng. A computer program s created usng numercal methods approach to determne the jont angles of the arm for a gven pont n the workspace. The jont angles are then used to determne the manpulablty of the arm for the gven pont. The normalzed manpulablty measures for each arm s beng plotted and compare to verfy that the jont angle provded by the nverse knematcs program correspond to postons n the model space. 3

4 MANUS ANALYSIS RESULTS AND DISCUSSION Fgure 5 below shows the frames of reference for the power wheelchar and the Manus n ts fully lowered poston. The D-H Parameters for the Manus wth 3 DOF are outlned n Table 1. From these parameters, each respectve frame transformaton s calculated. The transformaton matrx whch relates: T1wrt0: frame 1 to frame 0, T2wrt1: frame 2 to frame 1, T3wrt2: frame 3 to frame 2, TGwrt3: frame G (the frame of the grpper) to frame 3, and T0wrtU: frame 0 to the user frame U. These transformaton matrces are multpled together to gve the fnal transform relatng the end grpper poston wth respect to the user frame as follows: Table 1: MANUS D-H Parameters TGwrtU = T0wrtU*T1wrt0*T2wrt1*T3wrt2*TGwrt3 The poston vector s the frst three rows of column 4 of the fnal transformatonal matrx (forward knematc matrx). When the three jont angles are computed, the result s the poston of the grpper n space wth respect to the user frame {U}. From the forward knematc matrx, we can compute the Jacoban Matrx of the Manus, whch s the partal dervatve of the postonal matrx. Values for the manpulablty measure are plotted n both horzontal and vertcal planes. The grd densty n the analyzed workspace s greater n the z axs, whch gves a greater number of ponts wth whch to observe trends and changes of the manpulablty measure. In order for a pont n the workspace to be Fgure 5: MANUS Reference Frames α -1 a -1 d ( 2-90) defned as Fgure 6: Manpulablty Measure Representaton accessble, t must have a manpulablty measure of at least 100. The maxmum value of the manpulablty measure n the data set was at pont [-4, -6.75, 13.5]. A method for representng the relatve value of the manpulablty measure and a qualtatve determnaton are shown n Fgure 6. The sze and color of the spheres are used to represent the manpulablty measure as a percentage of the maxmum manpulablty measure computed. Fgure 7 shows the manpulablty measures of the Manus for vertcal planes wthn the defned workspace. The Manus arm offered very good access to low cabnets and shelves n front of and to the far left corner of the workspace that has been defned. In Fgure 7a, manpulablty measure remaned very good throughout the z-axs n ths far left corner of the operator s workspace. A sgnfcant lmtaton was the very lmted ablty to grab objects from the floor drectly n front of the operator s feet. The area of hghest aglty would be at least Fgure 7: Manpulablty Measure for MANUS n the y-z Plane partally obscured by the robot base. As the y-z plane approaches the manpulator base, a sngularty creates a lmtaton of movement near the frst rotatonal axs as shown n Fgure 7b, and the manpulablty measure becomes very low at the lne of data ponts that satsfy y = 13.5 and y-z plane x = Wth the threshold that was used for the program, these ponts were defned as unobtanable. The Manus arm as shown n Fgure 7c has very good access to objects along the sde of the char at the vertcal plane of x = The only lmtaton to ths sde reach s approachng low objects on the floor. It should also be noted that the effect of the sngularty has not been completely elmnated. At the vertcal lne on the y-z plane at y = 13.5, the manpulablty measure s very low from coffee table (z= ) to ktchen countertop (z = 6.18 ). Access to hgh shelves and counters ncreased as the operator approached them from the left sde. Values of the manpulablty measure n Fgure 7d were near optmum for reachng objects when the operator algned the goal parallel to the seat of the char at the y-z plane of x = Access to the mouth was at maxmum values and actually ncreased as the arm moved past the mouth poston [-4, 0, 13.5] n Fgure 7e toward the opposte sde of the char. The arm has very good access to the area drectly n front of the chest of the operator. It s nterestng to note that the Manus arm s capable of reachng across the centerlne of the wheelchar to manpulate objects. In fact, n regons drectly around the operator, the manpulablty 4

5 measure actually rses to a maxmum value 6.75 past the centerlne of the wheelchar. The maxmum manpulablty measure for the Manus manpulator was found at [-4, -6.75, 13.5] n Fgure 7f. These values were determned through dscrete analyss and are not necessarly a global maxmum. The measure s ncreasng, movng from x = 0 through x = -4 to x = -6.75, where the last data pont was on the z = 13.5 heght. The Manus has excellent manpulablty measures at the vertcal plane (x = -4 ) at or near the heght of the mouth (z = 13.5 to 16.5 ) of the operator. The Manus provdes excellent manpulator use when feedng and completng tasks that are at or about the mouth of the operator. Approachng the analyss from horzontal slces better ft the requrements for desgnng a manpulator as an assstve devce. Most objects rest on horzontal surfaces that have standard heghts above ground level. Startng at the top or hghest defned plane, Fgure 8a shows that for access to low ktchen cabnet shelves, the Manus has very good manpulablty measures drectly to the front and to the sde of the char. The overall average of normalzed manpulablty s good at The closer the goal s to the frst rotatonal axs, the lower the manpulablty measure wll be. Ths remans constant throughout all of the horzontal planes. Fgure 8: Manpulablty Measure for MANUS n the x-y Plane In Fgure 8b, the horzontal plane of a lght swtch (z=18.2 ) can be seen. When attemptng to operate a lght swtch, the optmum approach s from the sde because the n value drectly to the sde of the operator s excellent (0.83). The manpulablty measure s stll very good n the far front of the operator and to the far left corner of the workspace. The average n-value for ths plane s good at At the ktchen countertop level, Fgure 8c, the manpulator s effectveness drops sgnfcantly. Ths s due n part to the plane beng observed havng very lttle vertcal separaton from the plane that the frst lnk rotates along. Ths would make the manpulablty measure reach low values n the horzontal plane of z = Because the planes of the countertop (z = 6.16 Fgure 8c) and desktop / door handle (z = Fgure 8d) are close to ths plane, they have very smlar values for the manpulablty measure. The average n-value for the plane s good at The hghest n-value on ths plane s to the left of the operator. Accessblty of objects wthn the workspace are best when attempted close to the operator, such as at x = 0.54 compared to any other y-z plane. The Manus arm manpulablty at the heght of a table or door knob s shown n Fgure 8d. At ths plane the nteror regons of the plane have very lmted accessblty. At the outer corners of the workspace the arm has good or better access to objects wth the maxmum manpulablty, for ths plane, to the left of the operator. The average n-value for the plane s 0.41 and s the poorest average plane value wth the excepton of lowest plane. Ths plane s margnally good on the qualtatve scale. Manus arm at the heght of a coffee table s shown n Fgure 8e. Access to an object to the sde of the operator s good and has ts hghest value of n (0.79) left of the operator s hand (0.54, 23.5, -5.82). The average n-value for ths plane s good at The arm has lower accessblty near the centerlne of the wheelchar (y = 0) compared wth the outer edge of the workspace (y = 23.5). Closer to the ground, the measure begns to rse and access to an electrc socket (z = n Fgure 8f) s excellent to the sde of the char and stll very hgh n front of the wheelchar. It can be noted here that ths s the lowest plane that stll has good or better qualtatve ratng. The average n-value for ths plane s good at 0.52 but the range of manpulablty measures wthn ths plane s larger than other planes. The lowest reachable n- value s 0.27 and the hghest s Fgure 8g shows that accessblty of tall objects on the ground s very good drectly to the front of and to the sdes of the wheelchar. Reachng ths plane s best from the sde of the wheelchar wth the average value along the rght sde of the plane beng Overall, the plane has a good average n-value of Objects low to the ground, shown n Fgure 8h, are at the lower lmt of the reach of the Manus manpulator. The arm s not capable of reachng objects n the far corners of the workspace on the horzontal plane at z = The average n- value for all the ponts on the plane s Ths means that the manpulator has very lmted access to the plane. It s nterestng to note that regons where the arm tradtonally has lower manpulablty measures are the areas that have the hghest measures at z = These zones are the vertcal lnes that share the ponts (27.54, 13.5, z) and (14.04, 23.5, z). A summary of effectveness n reachng areas common to actvtes of daly lvng (ADL) s shown n Table 2. The qualtatve assessment s based on the average of the normalzed manpulablty measure of all possble wheelchar 5

6 orentatons possble to accomplsh the task. Sx possble qualtatve assessments could be gven for each task. For example, an object can be pcked off the ground from n front of the wheelchar as well as along the sde. The average of all the recorded values for the normalzed manpulablty measure (n) along the entre permeter of the wheelchar at the plane of the specfc actvty of daly lvng s shown n the second column of Table 2. Each row nvolved only one horzontal plane Table 2: Summary of MANUS Effectveness except for pckng up objects on the ground and access to mouth. For the ADL Pckup off Ground the average value for the permeter of the char was taken for the two lowest planes (z = and z = ). The ADL Access to mouth took the average of three ponts on two vertcal planes x = 0 and x = -4. Because head poston may not be perfectly n the centerlne of the wheelchar ponts, y = 4, 0, -4 were averaged at both head heghts (z = 13.5 and z = 16.5 ). The Manus manpulator provded excellent (0.81) access to the mouth of the operator. The ablty to do tasks above the ktchen countertop heght such as reach a lght swtch and reach a low ktchen shelf was very good. Reachng from the sde of the operator would yeld the hghest manpulablty measures from the arm. Access to a coffee table and the operator s lap were close to very good and had a qualtatve ratng of good (0.57). The ablty to reach a doorknob and a ktchen countertop were both good (0.53 and 0.54 respectvely). Fnally, the lowest value for the actvtes lsted n Table 2 was reachng the floor. Access to the floor was lmted wth a value of RAPTOR ANALYSIS RESULTS AND DISCUSSION Fgure 9 represents the Raptor mounted to a generc power wheelchar along wth the correspondng frames of reference (frames 0 to G). Table 3 shows the D- H parameter table for the Raptor wth 3DOF. From ths table, transformaton matrx s created the same way as n the case of MANUS. There s also a row for the fourth lnk that connects the grpper to the thrd jont, and t s purely a translatonal relaton, so the coordnate system for Fgure 9: RAPTOR Reference Frames the thrd jont and the grpper have the same orentaton. Wth the Raptor manpulator mounted securely, a sgnfcant amount (1-2 ) of play could be felt at the end effector. The same procedure s used n the case of RAPTOR to fnd the transformaton matrx of each lnk, and then fnd the fnal transformaton matrx. From the forward knematc matrx, we can compute the Jacoban Matrx of the Raptor, whch s the partal dervatve of the postonal matrx. Fgure 10 shows the manpulablty measures for the Raptor arm as mounted on the Arrow Storm Seres power α -1 a -1 d Table 3: RAPTOR D-H Parameters wheelchar. After all data ponts were collected, the maxmum manpulablty measure for the Raptor was found to be at the pont [-4,-3.5,16.5]. As shown n Fgure 10a, the Raptor s ncapable of reachng objects on a hgh shelf. At ths dstance of n front of the user frame, operatng a lght swtch s only possble when drectly n lne wth the plane of the frst lnk s rotaton (x-z plane where y = ), whch also s the Fgure 10: Manpulablty Measure for RAPTOR n the y-z Plane plane that has maxmum manpulablty measure values. The Raptor has very good manpulablty from the ground to the heght of a low coffee table (z = ) and stll has good manpulablty at the heght of a standard table (z = ). At ths dstance from the user frame, the arm s not capable of reachng objects on a low shelf (z = 24.18). A lght swtch can only be manpulated drectly along a lateral lne of y = From Fgure 10b, t can be seen that the ablty of the Raptor manpulator to reach low ktchen cabnet shelves s very lmted. At ths dstance (x = ) the operator would have to poston hs/her feet approxmately 20 under a countertop. Ths s not possble wth some ktchen desgns [2]. At ths dstance, accessblty of objects on tables and countertops s excellent from the front. Access to all levels except for the low shelf s very good from the sde. At the y-z plane where x = 6.75, shown n Fgure 10c, the Raptor s fnally able to reach objects on low shelves wth more than a mnmal value. The ablty to reach objects to the sde of the char begns to drop off, although t stll can reach the ground wth a good manpulablty measure. Access to the sde at ths plane s good but all eght horzontal planes can be reached at ths dstance from the operator. Ths s the only vertcal plane that offers ths ablty to reach all horzontal planes wth the Raptor. 6

7 In order to gan the hghest manpulablty measure n the low cabnets, the operator wll have to approach the cabnet shelf from the sde. Ths y-z plane s represented n Fgure 10d. The measure at ths pont s only moderate but ths s the hghest value avalable. Access to objects lower than a ktchen counter begns to dmnsh due to a sngularty of the arm at the heght of an electrc socket (z = ). The Raptor has ts hghest manpulablty measure at the pont [0,-13.5, 16.5] whch s shown n Fgure 10e. The ablty to manpulate objects s excellent toward the operator s rght sde but rapdly dmnshes once the centerlne of the arm s reached. Objects slghtly above the lap of the operator have a lmted manpulablty measure. The manpulator s unable to access an object to the left of the centerlne (y = 0) of the wheelchar. Fgures 10e,f show that the manpulablty measure s very hgh toward the outer edge of the defned workspace to both heghts (z = 13.5 and z = 16.5 ) and s stll very good at the operator s mouth. Fgure 11: Manpulablty Measure for RAPTOR n the x-y Plane Startng from the plane of a low ktchen shelf, Fgure 11a shows that the Raptor s able to reach objects from the sde of the wheelchar drectly to the rght of the operator. Although these ponts can be reached, the access to them s mnmal. The average n-value of the horzontal plane s very lmted at At the level of a wall-mounted lght swtch, the manpulablty measure ncreases compared to the hghest plane. The grpper s able to reach a lght swtch both from drectly n front of the arm and to the sde of the char. Access to objects to the sde of the operator s good. Ths would be the preferred wheelchar orentaton when attemptng to actuate a lght swtch. Fgure 11b shows that access to the lght swtch drectly n front of the arm s lmted, whle along the sde of the char the manpulablty measures are very good. The average n-value for ths plane s good at At ktchen countertop level, the Raptor has very good to excellent access to the sdes of the char, whle access to the front of the char s moderate as shown n Fgure 11c. At ths pont, the grpper s unable to reach drectly n front of the operator. Access to objects to the sde of the wheelchar s very good to excellent. Ths s the hghest plane that the manpulator can reach an object n the far rght corner of the workspace. Overall the plane has the hghest average manpulablty measures of all the horzontal planes analyzed at 0.64 wth a very good qualtatve assessment. Ths s the maxmum average n-value for any horzontal plane. The Raptor s able to reach objects drectly n front of the operator at the heght of a standard table as shown n Fgure 11d. At ths elevaton and below, the manpulator has lmted access to objects drectly n front of the operator and the manpulator s able to access all twelve ponts n the workspace. Ths s the only plane above the seat of the wheelchar that ths occurs. To open a door, the operator would have a greatest chance for success by approachng the door drectly n front of the manpulator (y = ). The average n value for ths plane s good at Manpulablty s at ts hghest level on ths plane at x = and decreases steadly as you approach x = 0.54 except for the x-z plane at y = 0. At the heght of a coffee table (Fgure 11e), access to all ponts n front of the operator s good to excellent. The ablty to reach objects to the sde of the operator contnues to decrease. The average n-value of the plane s good at From Fgure 11f, access to objects to the sde of the char s at ts lowest pont value at z = Ths s due prmarly to the lnk geometry, the frst lnk s 27 long and the second s 17.5 long, ther dfference of 9.5 means that the Raptor s ncapable reachng objects that are closer than 9.5 to the frame 0 [-6.26, -13.5, ]. The average n-value (0.36) for ths plane s lmted whch s the lowest of all the horzontal planes evaluated. Near the ground, the manpulablty measure does not change sgnfcantly for hgh and low objects on the floor (Fgure 11g,h). Low objects on the floor can be accessed from the front as well as the sde of the char. Along the sde of the wheelchar, the manpulablty measure drops the farther back the object s and objects drectly to the rght of the operator s very lmted. The average n-value for ths plane s lmted at An nterestng note s that there s an apparent horzontal lne of symmetry approxmately between z = and z = The true plane of symmetry would be the horzontal plane that the frst Table 4: Summary of RAPTOR Effectveness rotatonal axs rests (z = ). The average n-value for ths plane s good at 0.50 wth the hghest pont wthn the workspace s at (27.54, -13.5). 7

8 A summary of the Raptor s effectveness n reachng areas common n actvtes of daly lvng (ADL) s shown n Table 4. Ths table shows the task, the average manpulablty measure of all possble wheelchar orentatons that could acheve the task, and the qualtatve assessment. Overall, the average normalzed manpulablty measure (n) for all the eght tasks n Table 4 s good (0.44). For the tasks that nvolved reachng onto planes lower than a ktchen countertop orented from the front or sde, the Raptor was close to very good on the qualtatve scale (0.54 ~ 0.59). Access to the lap of the operator was lmted (0.31) and the values dmnshed as the goal moved closer to the operator. Addtonally, the nablty of the grpper to reach areas to the opposte of the centerlne of the wheelchar lmted the effectveness of the arm n the operator s lap. Reachng a lght swtch had lmted access (0.35). Ths was due to the low normalzed manpulablty measures n front of the wheelchar. Access to the sde of the operator was very good and as long as ths wheelchar orentaton was possble, the qualtatve accessblty would be very good (0.62). The area least able to be reached s a low ktchen shelf. The Raptor has very lmted access and was only able to reach the shelf n two of the sx possble outer permeter data ponts. CONCLUSIONS AND RECOMMENDATIONS There has been sgnfcant progress n brngng commercally-vable WMRAs nto the marketplace n the past 30 years. Of these devces, the Manus arm has seen the most development, though mostly n Europe. There s stll much progress to be made n order to mnmze user effort and reduce operator fatgue. Over the operatonal lfe of WMRAs they are cost-effectve yet ther hgh ntal cost has been a prohbtve barrer for many users. Lnk lengths need to be kept as short as possble to reduce dynamc loads. Whle longer lnks allow for greater values of manpulablty measure, they requre greater encoder precson to acheve the same level of precson as a shorter lnk. Mountng the arm closer to the ground bases the arm s ablty to manpulatng objects close to the ground, desks and countertops. Whle a rear mount would solve the problems of ncreased char wdth and vsual obstructon, t can cause further dffcultes wth lnk geometres. Whle Raptor desgn s very good at manpulatng objects n front of the wheelchar, t was challenged to reach nto the lower cabnet at almost any orentaton. The Raptor lnk geometres could be slghtly modfed to allow access to low cabnets and provde better access across the centerlne of the wheelchar. The mountng locaton of the Manus allowed for excellent access to low shelves and desks but suffered from nternal sngulartes whch lmted ts ablty to manpulate objects close to ts base. Often the start pont of the arm had to be changed several tmes n order for the grpper frame to reach the goal. Future work ncludes both software and hardware-based methods to further the work done n ths paper. The software development would further the nverse knematc program, and the hardware advancement would create vrtual manpulators usng track mount and modular lnks. These hardware models would use both the Manus and Raptor as a baselne for comparson. A better study of the entre workspace would be acheved wth a denser map of the manpulablty measures. For each arm, the smallest grd analyzed was 6.21 by 10 by 5.02 wth a total number of 131 data ponts. Although only gven a cursory look n ths paper, the use of modular lnks and jonts n a reconfgurable desgn would make a WMRA more versatle so that t could be used n a varety of applcatons. Ths flexblty would allow a producton arm to fll more nches and ncrease the number of unt sales, further decreasng unt cost and ncreasng avalablty of the unt. Controller desgn s a vtal consderaton when desgnng a complete robotc manpulator system. The greatest gans for robotc manpulators n rehabltaton applcatons wll come from advanced controllers that are easly programmed and operated. REFERENCES [1] US Census Bureau (1993). Amercans wth Dsabltes. Statstcal Bref SB/94-1, January. [2] R. Cooper: Rehabltaton Engneerng Appled to Moblty and Manpulaton, Insttute of Physcs Publshng, ISBN: [3] J.B.Reswck, "The Moon over Dubrovnk -- A Tale of Worldwde Impact on Persons wth Dsabltes," Advances n External Control of Human Extremtes, [4] T. Rahman, S. Stroud, R. Ramanathan, M. Alexander, R. Alexander, R. Selktar, W. Harwn: Consumer Crtera for an Arm Orthoss, Appled Scence and Engneerng Laboratores, www95.homepage.vllanova.edu/rungun.ramanathan/publc atons/t_and_d.pdf. [5] M.J. Toppng. The Development of Handy-1, A Robotc System to Assst the severely Dsabled, Proc ICORR 99, [6] M. Toppng, H. Heck, G. Bolmsjo, D. Weghtman: The Development of RAIL (Robotc Ad to Independent Lvng) Proceedngs of the thrd TIDE Congress. (1998). [7] M. Hllman, A. Gamme. The Bath Insttute of Medcal Engneerng Assstve Robot. Proc. ICORR 94, [8] N. Katevas (Ed): Moble Robotcs n Health Care Servces IOS Press Amsterdam, 2000, pp [9] H.A. Yanco: "Integratng Robotc Research: A Survey of Robotc Wheelchar Development" AAAI Sprng Symposum on Integratng Robotc Research, Stanford, Calforna, March, [10] P.R. Warner, S.D. Pror: "Investgatons nto the Desgn of a Wheelchar-Mounted Rehabltaton Robotc Manpulator", Proceedngs of the 3rd Cambrdge Workshop on Rehabltaton Robotcs, Cambrdge Unversty, England, Aprl [11] H. Eftrng, K. Boschan: Techncal Results from Manus User Trals, Proc. ICORR 99, [12] M. Hllman, K. Hagan, S. Hagan, J. Jepson, R. Orppwood: A Wheelchar Mounted Assstve Robot, Proc. ICORR 99, [13] J. Crag: Introducton to Robotcs Mechancs and Control, Second Edton, Addson- Wesley Publshng, ISBN