The 009 IEEE/RS International Conferene on Intelligent Robots and Systems Otober -5, 009 St. Louis, USA Mehanism and Control of a 4D Roboti Platform for Omnidiretional heelhairs Masayoshi ada, Member, IEEE Abstrat This paper presents mehanism and ontrol of a Four-heel-Drie (4D) roboti platform for wheelhairs. The 4D mehanism equips four wheels, two omni-wheels in front and two normal tires in rear. The normal wheel and the omni-wheel, mounted on the same side of the base, are interonneted by a synhro-drie transmission to rotate in unison with a drie motor. To ontrol hair orientation on the 4D platform, the third motor is installed on the platform. The hair with the proposed omnidiretional 4D system is apable of moing in any diretion whih is so-alled holonomi and omnidiretional mobility. The holonomi omnidiretional mobile apability enables a person to drie a mobile system with no knowledge about the drie mehanism or its onfiguration sine it an moe in any diretion and rotate from any onfiguration of the mehanism. This paper presents the mehanism and ontrol of 4D platform to whih powered-aster omnidiretional ontrol is applied. The rotations of two pairs of wheel and ertial axis of a hair are ontrolled in suh a way that it performs as a powered twin-aster to realize holonomi motions. The prototype wheelhair is designed and built to erify the mehanism design and ontrol method. The smooth and flexible onidiretional motions are presented by the experioments. T I. INTRODUCTION HE mobile systems realizing holonomi omnidiretional motion is one of the important researh area in mobile robots. It proide flexibility and high maneuerability to motion planners or human driers. In some pratial appliations, aurate positioning or ertain tration fores on irregular terrains are required for mobile mehanisms. On the other hand, the holonomi and omnidiretional mobile apability is also ery onenient for human driers sine they do not hae to understand drie mehanisms and its onfiguration at all. A human only ommands the diretion and eloity of motion he/her wants to perform sine a holonomi and omnidiretional mehanism an start to moe in any diretion withy any onfiguration of the mehanism suh as diretions of wheels. This harateristis is ary suitable for wheelhairs and personal mobiles whih is used for daily life for maneuering rowded area at home. In this paper, a new type of omnidiretional system is Manusript reeied Marh, 009. This projet was supported by the Industrial Tehnology Researh Grant Program in 006 from the New Energy and Industrial Tehnology Deelopment Organization (NEDO), apan, researh ID 05A0675a. Masayoshi ada is with the Department of Human-Robotis, Saitama Institute of Tehnology, Fukaya, Saitama 369-093 APAN (phone: +8-48-585-6884; fax: +8-48-585-6884; e-mail: mwada@ ieee.org). proposed. Design of 4D platform and its omnidiretional ontrol, powered-aster ontrol, is presented. The experiment using prototype wheelhair erifies the proposed omnidiretional system. II. CONVENTIONAL MOBILE MECHANISMS FOR HEELCHAIRS Standard wheelhairs annot moe sideways. It needs a omplex series of moements resembling parallel automobile parking when a wheelhair user wants to moe sideways. Omnidiretional dries used on eletri wheelhairs were deeloped to enhane standard wheelhair maneuerability by enabling them to moe sideways without hanging the hair orientation. In Fig., an omnidiretional wheelhair with Mehanum wheels [] uses barrel-shaped rollers on the large wheel's rim inlining the diretion of passie rolling 45 degrees from the main wheel shaft and enabling the wheel to slide in the diretion of rolling. The standard four-mehanum-wheel onfiguration assumes a ar-like layout. The inlination of rollers on the Mehanum wheel auses the ontat point to ary relatie to the main wheel, resulting in energy loss due to onflitions in motion among the four wheels. Beause four-point ontat is essential, a suspension mehanism is definitely needed to ensure 3-degrees-of-freedom (3DOF) moement. Fig. shows an omnidiretinal wheelhair with a ball wheel mehanism deeloped at MIT []. Eah ball wheel is drien by an indiidual motor whih proides atie tration fore in a speifi diretion while perpendiular to the atie diretion. ith this drie system, the point of ontat of a wheel is stable relatie to the wheelhair body and smooth motion is realized. Fig. Omnidiretional wheelhair, Fujian [] Fig. Ball wheel omnidiretional wheelhair, MIT [] 978--444-3804-4/09/$5.00 009 IEEE 4855
The other omnidiretional mehanism is VUTON rawler[3] whih onsists of many ylindrial free rollers. Sine VUTON mehanism allows the multiple rollers to touh the ground simultaneously, heay load an be applied on the platform. All of the aboe omnidiretional systems need one motor to drie one wheel mehanism therefore four motors are needed to drie a four-wheeled wheelhair, while a wheelhair has three degrees of freedoms (DOF) on the floor. Therefore, it inoles DOF redundany in atuation whih auses onflitions in motion among the four wheels. The inerse kinematis of two-wheeled mobile robot is represented as (). x& a y& a = 0 x& b y& b 0 0 0 osφ x& sinφ y& osφ & φ sinφ () III. POERED-CASTER OMNIDIRECTIONAL CONTROL e apply powered-aster ontrol to 4D mehanism to gie an omnidiretional mobile apability to a wheelhair. In this setion, The powered-aster omnidiretional ontrol for the original single type onfiguration[4] is mentioned. A. Powered-aster Mehanism Fig.3 shows a top iew of a powered-aster. The original design of the powered-aster is a single wheel type in whih normal wheel is off-entered from steering shaft. The wheel shaft and the steering shaft of the powered-aster is drien by independent motors. hen only the wheel shaft is rotated by the motor, the aster moes in forward diretion whih is denoted as x& w in Fig.3. hen only the steering shaft is rotated by the motor, the mehanism rotates about the point of ontat whih is also shown in the figure. By this rotational motion, the loation of the steering shaft is hanged whih eloity is y& w direting tangential diretion of the irle whih enter is at the point of ontat and the radius is s, aster-offset. These eloity etors are independently ontrolled and direting right angle for eah other. Therefore, to generate a eloity V in the diretion θ at the enter of the steering shaft, the wheel and the steering shaft rotations, ω w and ω s, are deried by the following kinematis. ω w / r 0 x& w = () ωs 0 / s y& w where x& w = V osθ, y& w = V sinθ. These omponents are determined by a funtion of θ, the orientation of the aster mehanism. B. Omnidiretional Mobile Robot with Powered-asters Fig.4 shows a shemati oeriew of an omnidiretional mobile robot with two powered-asters. The robot with a pair of powered-asters is ontrolled by four eletri motors whih inoles one redundant DOF in atuation. For this lass of omnidiretional robots, the powered-aster proides an atie tration fore in an arbitrary diretion for propelling the robot. To oordinate the multiple powered-asters, motors on a powered-aster are ontrolled based on the eloity based robot model. Fig.3 : Veloity ontrol of a powered-aster Fig.4 : A two-wheeled omnidiretional robot IV. 4D OMNIDIRECTIONAL MOBILE SYSTEM A. Four-heel-Drie Mehanism A 4D drie system was inented in 989 [5] for enhaning the tration and step limbing apability of the differential drie systems whih shemati is illustrated in Fig.5. This 4D mehanism has reently applied to a produt design by a apanese ompany [6]. The wheelhair equips four wheels, two omni-wheels in front and two normal tires in rear. A normal wheel and an omni-wheel, mounted on the same side of the hair, are interonneted by a hain or a belt transmission to rotate in unison with a drie motor. A ommon motor is installed to drie normal and omni wheel pair ia synhro-drie transmission on eah side of the mehanism. Then two motors proide deferent eloity on eah side with presents differential drie motion of 4D mehanism. Thus all four wheels on 4D an proide tration fores. Sine the enter of rotation shifts bakward, when it turns about a stedy point on the floor, it requires large spae when the wheelhair is ontrolled in a differential drie 4856
manner. The offset distane between drie wheels and a enter of a hair makes the maneuerability of the wheelhair worse. Normal wheel heel motor 4D and the three motor angular eloities of the drie wheels and the hair rotation axis. First, we onsider the fundamental motions of a twin-aster drie (TCD). Figure 9a shows the translational motion of the ehile in whih two wheels rotate in same angular eloity to trael in same diretion. In this ase, TCD traels also straight forward, therefore TCD eloity and its rotation are represented as follows. Omni-wheel Synhro-drie transmission Fig.5. Original 4D synhronized transmission B. Omnidiretional Control of 4D In our projet, it is a goal to deelop an omnidiretional wheelhair with high mobility and maneuerability in a single design whih an be used in multiple enironments inluding outdoor and indoor. For omnidiretional motion with a 4D mehanism, a new type of omnidiretional system is proposed. To enable a wheelhair to moe in any diretion instantaneously, omnidiretional ontrol method, alled "powered-aster ontrol" whih was introdued in preious setion, is extended and applied to the 4D mehanism[7]. Fig.6 shows a shemati of the 4D omnidiretional wheelhair. The wheelhair has two omniwheels in front and standard pneumati tires in rear whih form 4D onfiguration. A pair of an omniwheel and a pneumati tire mounted on the same side of the wheelhair are onneted by belt transmission for rotating unison and drien by a ommon motor whih onfiguration is ompletely idential to the original 4D system shown in Fig.5. In our design, an additional third motor is mounted on the onentional 4D platform for rotating a hair about the ertial axis whih is also illustrated in Fig.4. Those three motors inluding two wheel motors and the third motor enable the wheelhair to realize independent 3DOF omnidiretional motion by a oordinated motion ontrol[8],[9]. To ahiee oordinated ontrol for omnidiretional motion of a hair, the powered-aster omnidiretional ontrol for twin-aster onfiguration has been applied to the 4D system. Fig.7 illustrates a shemati top iew of a 4D mehanism. In Fig.7, it is found that rear two drie wheels and enter axis form a twin-aster onfiguration, i.e. parallel two wheels are loated on the off-entered position whih midpoint is distant from ertial steering axis, whih is emphasized by thik lines in the Fig.7 and a ehile with a twin aster drie mehanism is shown in Fig.8. The powered-aster omnidiretional ontrol enables the aster mehanism to emulate the aster motion by atuating wheel and steering axes. The powered-aster based oordinate ontrol of three motors needs a kinemati model of the 4D. The kinemati model represents the relationships between the motion of the Fig.6. A 4D omnidiretional wheelhair x& = ( + ) = R L (3) & φ = ( ) = 0 R L Figure 9b shows another motion in whih two wheels are rotated at same angular eloities but in opposite diretions resulting in spin of TCD about the midpoint of two wheels. This motion proides only rotation but no translation eloity whih is represented as, x& = & φ = ( + ) R ( ) R L L = 0 = Fig.7 Omnidiretional ehile with 4D mehanism Fig.8 Omnidiretional ehile with a twin-aster (4) 4857
(a) Motion in X-diretion (b) Motion in Y-diretion Fig. 9 Omnidiretional ontrol for twin-aster drie (TCD) Now we fous on the motion of the steering enter whose loation is idential to the rotation enter of a hair. hen TCD rotates about the midpoint of two wheels, the enter of the steering presents a irular motion whose enter is at the midpoint and the radius equals the aster offset, s. At eah moment, eloity at the enter is direting tangential diretion of the irle whih direts the lateral diretion of TCD at all times. The lateral eloity denoted by y& in Fig. b is represented by, s s y& s ( ) = & φ = R L =. (5) The translation eloities x& and y& are direted at right angles to eah other. Note here, the rotation of TCD is not independently ontrolled sine the rotation & φ is determined by reating the lateral eloity y& to satisfy Eq (5). From Eqs. (3)-(5), the relationships between the ehile translation eloity and wheel eloities are deried as, x& / = y& s / / s / Thus, translation eloities along the X- and Y-diretions are ompletely determined and independently ontrolled by wheel eloities. To generate the required eloity etor that direts in an arbitrary diretion with arbitrary magnitude, the referene etor is projeted in X- and Y-diretions of ehile oordinate system (Fig.7 or 8). The eloity omponent in eah diretion, x& or y&, an be independently ahieed by using kinematis of TCD in Eq. (6). Fig. 0 Projetion of a ommand eloity into ehile oordinate axes depending on the TCD orientation. hen the referene eloity is steady to the ground, the eloity omponents in X- and Y-diretions ary depending on the TCD orientation relatie to the ground. Therefore, R L (6) wheel eloities also ary whih results in straight motion of the TCD enter (see Fig. 0). TCD shows spontaneous flipping behaior during the motion, whih is often found in passie asters installed on legs of hairs and tables, et. It is said the powered-aster ontrol emulates aster motion by atiely atuating the wheel axis. Translation in arbitrary diretion is ahieed by TCD as presented aboe. Howeer, orientation of TCD an not be ontrolled independently. To ontrol 3DOF motion of a hair, the hair rotation axis must be also oordinated. The eloity ommand is gien based on the hair orientation sine a joystik is fixed on the hair. Then the ommand eloity is translated into TCD oordinate by the relatie orientation of the hair to the ehile, θ. as x& = x& osθ y& sinθ y& = x& sinθ + y& osθ & θ = & θ + ω s From Eqs. (6) and (7), an oerall kinemati model of the omnidiretional 4D wheelhair is represented as follows. where, x& 0 ω R y& = 0 ω L & θ r / r / ω S r osθ rs sinθ = r osθ rs sinθ = + r sinθ rs osθ = + r sinθ rs osθ = here r, and s are the wheel radius, tread and aster-offset, respetiely. A 3x3 matrix in the right side of eq.(8), alled as aobian, is a funtion of orientation of the 4D unit with relatie to the hair base, θ. All elements in the aobian an always be alulated and a determinant of the aobian may not be zero for any θ. Therefore there is no singular point on the mehanism and an inerse aobian always exits. The three motors are ontrolled to realize a 3DOF angular eloity ommands x&, y& and & θ by independent speed ontrollers for omnidiretional moements. Thus, holonomi 3DOF motion an be realized by the proposed mehanism. Fig. shows a one of the simulation results in whih an omnidiretional ontrol of the twin-aster mehanism are tested. In the simulation, twin-aster mehanism is ontrolled to trak a straight line with a enter of a mehanism loating on the line at all times. During the motion, the orientation of (7) (8) (9) 4858
the mehanism is rapidly flipped oer and orient to the diretion of motion. This flip motion is often seen on passie asters whih installed on the legs of offie hairs and tables. Thus the powered-aster ontrol ahiees the emulation of aster motions by oordinated ontrol of multiple atuators. ** heelhair Speifiations** Dimension idth 600mm Length 700mm Height 450mm eight Total 80kg(human+wheelhair) heelhair 00kg (inluding batteries) Speed 6km/h Surmountable step 00mm in height Fig.: Omnidiretional ontrol for twin-aster mehanism This lass of omnidiretional mobility, so alled holonomi mobility, is ery effetie to realize the high maneuerability of wheelhairs by an easy and simple operation. Chair Steering motor 3D joystik Right wheel motor V. PROTOTYPE DESIGN heelhair speifiations for prototype design are shown below. The wheelbase and tread of the 4D mehanism are 400mm and 535mm respetiely. Those dimensions are determined to satisfy the limitation of the standard wheelhair speifiation for the dimension, 600mm in width and 700mm in length as shown in the spe. The required step height whih an be surmounted by the wheelhair is approx. 00mm for aessing to a train ar from a station platform with no assistane. The maximum running speed for ontinuous drie is 6km/h whih is same as onentional standard wheelhairs in apan. Fig. illustrates a 3D drawing of a prototype designed by 3D CAD. Fig.3 shows an oeriew of the prototype wheelhair. Left wheel motor Fig.. Prototype bottom iew by 3D CAD Fig.3. 4D omnidiretional wheelhair prototype Fig.4 System onfiguration of the prototype wheelhair 4859
VI. EXPERIMENTS A. Omnidiretional motion To erify the omnidiretional mobility of the proposed system, lateral motion was presented by the prototype wheelhair while keeping the hair orientation onstant. A small ball was attahed to the hair to indiate the enter of the steering axis. A stereo amera system (Quik Mag IV from OKK In, apan) detets the ball loation in 3D oordinates. The prototype was ontrolled by a remote PC ia a LAN onnetion. Thus, a omplete linear trajetory in lateral diretion was ommanded to the prototype. Figure 5 shows a hair motion deteted by the stereo amera system. An atual and a referene path are plotted in the figure whih losely agree. Figure 6 shows traking errors between the atual and the referene. The error was suppressed to within ± 5 mm despite the flipping behaior that ourred. The amera system also proided real-time ideo images with oer-writing retangle window(s) and the path of the target(s) (in this experiment, a small ball). Figure 7(a)-(j) shows a series of ideo images. The prototype wheelhair moed from the right side of the piture frame to the left. The final piture, Fig. 7(j) shows a straight path whih was reated by the wheelhair moement. During the motion, the 4D presented a flipping behaior, Fig. 7(d), (e) and (f), whih is also shown in a omputer simulation in Fig.. B. Variable enter of rotation The proposed system realizes holonomi and omnidiretional motion of a hair by the oordinated ontrol of three motors. The holonomi mobile apability makes it possible to hange the loation of a enter of rotation at any point to fit to ustomer requests. In a normal setup, a hair rotates about its enter when the operator ommands a spin turn by twisting the joystik. Howeer, the loation of the enter is ariable in the ontrol program to any point inluding the out-of-footprint area of the wheelhair. Howeer, usual requests may be to shift it to the bak side to simulate a rear drie wheelhair, or to shift to the front side to simulate a front drie wheelhair. To present the flexibility of the proposed system, two patterns of spin turn motion were performed. Figure 8(a) and (b) shows the final image of eah test run for whih the stereo amera system was used. The path of the wheelhair are remained in those apture images. In Fig. 8(a), the wheelhair rotated about the front position whih was loated approx. 500 mm forward of the enter of the hair. In Fig. 8(b), the enter was shifted also approx. 500 mm towards the rear. From these results, the enter of rotation an be ustomized to an indiidual. C. Task example The holonomi and omnidiretional mobile systems are easy to maneuer beause 3D ommand in X- and Y- diretions and rotation are diretory ommanded and an operator does not hae to onsider the wheel motions and its onfigurations. Error mm To demonstrate maneuerability, a task example was performed by the prototype. The task of getting out of a room by pulling the door open is a diffiult task for a wheelhair user. A task of pulling the door is relatiely more diffiult than pushing the door. This task example inludes sub tasks suh as: ) approahing to the door to grasp the door knob, ) moing bakward to pull the door open, 3) going through the door and getting out of the room, and 4) driing to another loation. Figure 9(a)-(j) shows sreen shots of the experiment. In this test, the prototype wheelhair was operated using a 3D joystik by a human operator who was sitting on the hair. Sine the wheelhair has high maneuerability, the task was suessfully ahieed with no ollision with the door or a wall. The operator did not see the 4D mehanism during the task, howeer, the 4D mehanism hanged its orientation widely when the operator moed sideways to aoid olliding with the door (Fig. 9(d)-(g)). Figure 0 shows the 3D ommands (X, Y and Rotation)to the wheelhair during the task of Fig.9 whih means 3D simultaneous motion was exeuted for omplete the door opening task. Those are found in sub tasks inluding, ) approahing the door and 4-) turning after exiting the room. Indiidual lateral translation is often used in subtask 3) exiting the room. Position Y mm 800 600 400 00 000 800 600 heelhair Trajetory (Lateral motion) 400 300 400 500 600 700 800 900 Position X mm Fig. 5 Referene and atual trajetories of the 4D wheelhair 0.0 7.5 5.0.5 0.0 -.5-5.0-7.5-0.0 End Referene Path Traking Error (Lateral motion) 0 00 400 600 800 000 00 Path length mm Fig. 6 Traking error on the experiment using 4D wheelhair VII. CONCLUSION Atual Path Start Mehanism and omnidiretional ontrol of a 4D mehanism for wheelhairs are presented in this paper. The omnidiretional wheelhair system is proposed for improing maneuerability of standard wheelhairs The 4D mehanism has high mobility whih equips four wheels, two 4860
omni-wheels in the front and two normal tires in the rear, and all wheels proide tration een with two motors to drie these wheels. To realize holonomi and omnidiretional motion of a hair by utilizing the 4D mehanism, the proposed system inludes the third motor to rotate the hair at the enter of the 4D mehanism about the ertial axis. For omnidiretional ontrol of the 4D mehanism, powered-aster ontrol has been applied. To ahiee a oordinated ontrol of three motors, kinematis of the 4D wheelhair was analyzed and a kinemati model was deried whih represents the relationships between 3DOF wheelhair motion and the rotations of three motors. In the powered-aster ontrol, two wheel motors are oordinated to translate the enter of the hair in an arbitrary diretion while the hair orientation is ontrolled by the third motor separately. The omnidiretional motion was erified by a series of experiments using a wheelhair prototype. First, omnidiretional mobility was tested in whih the wheelhair made a lateral motion without hanging its orientation. Next, one of a appliations of the holonomi mobility was performed in whih the enter of rotation was aried by a ontrol program to ustomize per user request for simulating the wheelhair drie types, suh as front drie, rear drie, or enter drie. To present the high maneuerability of the proposed omnidiretional mobile system, a task example was performed in whih an operator maneuered the wheelhair by 3D joystik to exit a room with pulling the door open. The task was suessfully ahieed with no ollision with the door or walls. During the task, it was found that the simultaneous 3DOF motions, lateral translation are often ommanded as well as the forward translation for pursuing the task. From these experiments, the omnidiretional and holonomi mobile apability are shown to be ery effetie and useful for maneuering in rowded areas and ahieing ompliated tasks. ACKNOLEDGMENT This projet was supported by the Industrial Tehnology Researh Grant Program in 006 from the New Energy and Industrial Tehnology Deelopment Organization (NEDO), apan, researh ID 05A0675a. REFERENCES [] All-diretion Power-drien Chair F-UEC-600, Fujian Fortune et Mehanial & Eletrial Tehnology Co., Ltd. [] M.ada and H. H. Asada,"Design and Control of a Variable Footprint Mehanism for Holonomi and Omnidiretional Vehiles and its Appliation to heelhairs," IEEE Trans on Robotis and Automation, Vol.5, No.6, pp978-989, 999. [3] S.Hirose and S.Amano : The VUTON : High Payload High Effiieny Holonomi Omni-Diretional Vehile, 6th Int. Symp. on Robotis Researh, Otober, 993. [4] M.ada and S.Mori," Holonomi and Omnidiretional Vehile with Conentional Tires," Proeedings of the 996 IEEE International Conferene on Robotis and Automation (ICRA96), pp367-3676, 996. [5] efferey Farnam, Four-wheel Drie heel-hair with Compound heels, US patent 4,83,900, 989. [6] Patrafour Kanto Automobile Corp. http://www.kanto-aw.o.jp/jp/produts/wheelhair/ [7] M.ada, A.Takagi and S.Mori, "Caster Drie Mehanisms for Holonomi and Omnidiretional Mobile Platforms with no Oer Constraint," Proeedings of the 000 IEEE International Conferene on Robotis and Automation (ICRA000), pp53-538, 000. [8] Masayoshi ada, Omnidiretional and Holonomi Mobile Platform with Four-heel-Drie Mehanism for heelhairs, SME ournal of Robotis and Mehatronis, Vol.9, No.3, pp64-7, 007. [9] Masayoshi ada," Holonomi and Omnidiretional heelhairs with synhronized 4D Mehanism," Proeedings of the 007 IEEE/RS International Conferene on Intelligent Robots and Systems (IROS007) pp.96-0, De 007. (a) (b) () (d) (e) (f) Fig. 7. An example of omnidiretional motion : the lateral motion of the wheelhair prototype; it moes in sideways from the right side to the left of the piture frames while maintaining the hair orientation to be stable. 486
(a): Spin turn about the front position Fig. 8 Variable enter of rotation (b): Spin turn about the bak position (a) (b) () (d) (e) (f) (g) (h) (i) (j) Fig.9: An example of tasks using a eletri wheelhair: Getting out of a room with pulling a door open. Veloity ommandsx, y and θ m/s, rad/s.5.5 0.5 0-0.5 - -.5 heelhair task of getting out of a room with pulling a door open Motion in Y-diretion Rotation Motion in X-diretion - 4-) High ) Approahing to a door ) Pulling a door 3) Going to exit 4-) Turning speed drie -.5 0 5 0 5 0 5 30 35 40 45 Time s Fig. 0 3DMotion of wheelhair presenting a door opening task for exiting a room 486