TA1-03
Proceedings of the 2005 IEEE/ASME International Conference on Advanced Intelligent Mechatronics Monterey, California, USA, 24-28 July, 2005
An Omnidirectional 4WD Mobile Platform for Wheelchair Applications Masayoshi Wada, Member, IEEE
Abstract—In this paper, a new type of omnidirectional mobile platform with four-wheel drive (4WD) mechanism is presented. The mobile platform includes a pair of normal wheels on the rear side of the platform and a pair of omni-wheels on the front side. The normal wheel in rear and the omni-wheel in front, mounted on the same side of the platform, are interconnected by a chain or a belt transmission to rotate in unison with a drive motor, i.e. a synchro-drive transmission. The omni-wheel allows the front end of the mobile platform to roll freely from side to side while it provides traction force in the heading direction. The third motor is installed to turn a chair about a vertical axis about the center of the platform. The two drive motors are coordinated by the omnidirectional control to translate the center of the chair in an arbitrary direction while chair orientation is controlled by the third motor individually. Thus a wheelchair with proposed 4WD mobile platform can move in any direction without changing the chair orientation and turn in a place, namely holonomic. The 4WD mechanism provides certain traction force even on the irregular surface and step climbing capability is enhanced since all wheels are actively driven and no passive caster is used. The non-redundant configuration with three motors contributes not only to a cost saving but also the high reliability of the mechanism. In the paper, kinematics and statics of the 4WD mechanism are analyzed and an omnidirectional control method is developed. The omnidirectional motions of the proposed 4WD drive system are tested by the computer simulations.
I
To enhancing these capabilities of the electric mobile system, omnidirectional 4WD mechanism is proposed in this paper. Kinematic model and omnidirectional control are developed for the proposed 4WD mechanism. II. CONVENTIONAL DRIVE MECHANISMS FOR WHEELCHAIRS A. 4WD Differential Drive The normal differential drive mechanism is applied to most of conventional wheelchairs including hand propelled and electric powered ones [1, 2]. For enhancing the traction and step climbing capability of such differential drive systems, a 4WD differential drive was invented [3]. The mechanism has a pair of omni-wheels on the front side and a pair of normal wheels on the rear side as shown in Fig.1. An omni-wheel and a normal wheel on the same side of the chair are interconnected by a transmission mean and driven by a drive motor for rotating in identical velocity in the rolling direction. The two motors allow the platform to present the differential drive motion with all four wheels providing traction forces. Thus 4WD system is controlled in the conventional differential drive manner, the center of rotation locates on the mid-point of the rear normal wheels. Therefore the motion of spin turn requires more space than the original differential drive systems as illustrated in Fig.1 by a dotted curve.
I. INTRODUCTION T is expected that the population of wheelchair users would
increase dramatically in the near future. For promoting barrier-free environments for all of the wheelchair users, re-construction of existing facilities could not be a feasible solution because of the limitations in economy and time. To overcome the problem, to improve the mobility of the personal mobile systems for surmounting the existing environments could be one solution. Maneuverability in crowded area and high mobility in rough terrain are among the most important requirements for the class of mobile systems. However, a current wheelchair design meets either of these requirements but no one meets both of them. Namely some wheelchair is well designed for maneuvering indoor environments but is not suitable for running outside. Other design provides enough mobility for driving outside with rough terrain while the maneuverability needs to be improved for moving in complicated environments.
Masayoshi Wada is with the Department of Mechanical Engineering, Saitama Institute of Technology, 1690 Fusaiji, Okabe, Saitama 369-0293 JAPAN (e-mail:
[email protected]).
0-7803-9046-6/05/$20.00 ©2005 IEEE.
Fig. 1. 4WD wheelchair [3, 4]
B. Omnidirectional Drive On the other hand, omnidirectional mechanisms are sometimes applied to wheelchairs for improving the maneuverability of the original differential drive systems[5, 6]. Mechanum wheel is a kind of omni-wheel which has plurality of free rollers on the rim which passive directions are inclined 45degrees from the main wheel shaft. A standard configuration with Mechanum wheels includes four wheels which form a car-like layout as shown in Fig.2[6]. The
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peripheral rollers form almost a complete circular envelope around the main wheel for suppressing unwanted vibrations. Because of the inclination of the free rollers on Mechanum wheel, the location of the contact point relative to the main wheel varies. Since exact locations of the contact points are difficult to detect, confliction among the motion of the four motors might occur which results in energy losses. It needs suspension mechanisms to get certain 3DOF motion since the four-point contact is always required.
vR
rZ R
vL
rZ L
(1)
The wheel motions allow the vehicle to rotate about a point on the ground indicated Or in the figure. The location of the rotation center Or varies on the floor however, it always stays on the line L which connects the wheel axes. Now we attach the coordinate frame 6O-XY on the platform to locate its origin on the midpoint of two wheels where Y-axis directing along wheel axes. Then the motion of 4WD mechanism is defined as rotation about the center Or at (0, R) in angular velocity Iv . Instantaneous translation and rotation of the platform at coordinate origin O are represented as, x v y v I v
RIv
0 I
(2)
The relationships between the wheel velocities and the vehicle motion are derived as, x v
Fig. 2. A Four-wheeled Omnidirectional Wheelchair [6]
y v
C. Summary Maneuverability in clouded area and high mobility in uneven terrain are among the most important requirements for promoting the barrier-free environments. To summarize above discussions, each wheelchair design meets one of these requirements but no one meets both of them. Namely the 4WD configuration provides enough mobility for driving around outside with rough terrain while the maneuverability needs to be improved for moving in complicated environments On the other hand, the omnidirectional wheelchairs are capable of maneuvering in indoor environments but are not suitable for running outside dynamically. For the purpose of satisfying these requirements by a single wheelchair design, a new omnidirectional 4WD system is proposed and discussed in the following sections.
Iv
1 v R v L 2 0
(3)
1 v R v L W
III. ANALYSIS OF 4WD DRIVE MECHANISM The original 4WD configuration described in the previous section is an old invention however, the kinematics and the statics of the mechanism have not been well discussed. We now analyze the 4WD systems in the kinematics of the front omni-wheel and the statics for climbing a step.
Fig. 3. Kinematics of a 4WD mechanism
From (2) and (3), wheel velocities are described by vehicle motion as,
A. Kinematics A schematic of the 4WD mechanism are illustrated in Fig.3. When rear two wheels are driven by independent motors to rotate in ZR and ZL with no slips on the ground, the wheel rotations provide translational velocities vR or vL on each wheel axes as, 577
vR vL
W Iv 2 W x v Iv 2 x v
(4)
where W is the tread of the mobile platform. Now consider the motion of the specific point p(x, y) on the platform. Velocity of the point p is represented as, x v "Iv sin T p
y p
"Iv cos T p
Note that " sin T p
(5)
y and " cos T p
Passive wheel
Motor
W
W
Active wheel
(a) Rear drive system Fig. 4. The rear drive system and 4WD system
Synchro-drive transmission
W
§1 y · §1 y · ¨ ¸ v R ¨ ¸v L W 2 © ¹ ©2 W ¹ x v R v L W
FcosT
x p ( y
W / 2 )
vORy
x p ( x
D)
WsinT
(6)
vOLx
x p ( y
W / 2)
vOLy
x p ( x
D)
vR D v R v L W
(7)
vL D v R v L W
(8)
W
W
F F cos T ! W sin T 2 2
F/2 r
(11)
The required motor torque is represented by,
W ! rW
2 sin T 1 cos T
(12)
Tan T, 2sinT/(1+cos T) and these ratio are plotted in Fig.6.
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㪍
㪈㪅㪉
㪌
㪈 㪩㪸㫋㫀㫆㩿㫋㪸㫅㱔㪆㩿㪉㫊㫀㫅㱔㪆㩿㪈㪂㪺㫆㫊㱔㪀㪀
㪋
㪇㪅㪏
㪊
㪇㪅㪍 㪫㪸㫅㱔
㪉
㪇㪅㪋
㪈
㪇㪅㪉 㪉㫊㫀㫅㱔㪆㩿㪈㪂㪺㫆㫊㱔㪀
㪇 㪇
W ! rW tan T
T
Note that F =W/ r. Fig.5(b) shows statics of the front wheel of 4WD system. In this case, a horizontal force F/2 is applied from the rear wheel. The front wheel is also active and applies a torqueW/2 on the front shaft. When the front wheel contacts an edge of a step, the front shaft torque provides a force F/2 in the direction T from the horizontal plane as shown in the figure. Therefore the front wheel can go over the step if following condition is satisfied.
B. Statics Consider the statics of the wheel contacting to an edge of a step. Fig.4 shows transmissions of the rear drive system and the 4WD system. Suppose a motor gives same torque W to each transmission. In the rear drive system, full torque is transmitted to the rear wheel and a front wheel is free to rotate. In the 4WD drive, motor torque is supposed to be distributed to the front and the rear wheels equally. Fig.5(a) shows statics of the front wheel of rear drive system. F is a horizontal force applied from the rear wheel. The front wheel can go over the step if following condition is satisfied. (9)
Therefore the required motor torque is given as,
T
(a) Rear drive system (b) 4WD system Fig. 5. Statics of a front wheel contacting a step edge
Thus, velocity of the omni-wheel in the X-direction becomes completely identical to the rear wheel velocity only when y equals to W/2 or -W/2. And the omni-wheels slide sideways in the identical velocity. From these analyses, it has been clarified that 4WD configuration allow the omni-wheel to follow the rear wheel motion with no slip.
F cos T ! W sin T
F/2
W F
The locations of the contact points of the omni-wheels are defined as pR(D, -W/2) and pL(D, W/2). From (6), the contact point velocities (voRx, voRy) and (voLx, voLy) are represented by, vORx
W
(b)4WD system
r
y p
Active wheel
x , following
relations are derived by substituting (3) into (5) as, x p
W
㪩㪸㫋㫀㫆
x p
Active wheel
㪇
㪉㪇 㪉㪇
㪊㪇
㪋㪇
㪋㪇 㪍㪇 㪏㪇 㪪㫋㪼㫇㩷㪟㪼㫀㪾㪿㫋㩷㫄㫄㩷㩿㪛㪔㪊㪇㪇㪀
㪈㪇㪇
㪌㪇 㪍㪇 㱔㩷㪻㪼㪾㪅㩷㩿㪛㪔㪊㪇㪇㪀
㪎㪇
㪇 㪈㪉㪇 㪏㪇
Fig.6. Comparison of step climbing capability between the rear drive system and the 4WD system
(10) 578
First two values are proportional to the minimum motor torques required to the rear drive system and the 4WD system respectively. The step height is also shown in horizontal axis when the wheel diameter D=300mm. As the height of the step increases, the tanT curve gets higher while 2sinT/(1+cosT) increases almost linearly. When it is required that a step of 100mm height must be overcame, 4WD system needs motor torque which is half of the rear drive system.
When the right and left wheels rotate in ZR and ZL respectively, the velocity in the heading direction and the rotation at the midpoint of two wheels are represented as follows. 1 v R v L 2 1 vR vL W
x 0
I0
IV. OMNIDIRECTIONAL CONTROL OF 4WD MECHANISM To achieve omnidirectional mobility of the 4WD platform, the powered-caster control is applied to the control of two drive motors. The powered-caster control is applicable to a wheeled mechanism with caster configuration 㨇7㨉. Two types of caster configurations are standard such as the single caster style (A normal wheel with a steering shaft supporting the wheel on an off-centered position) and the twin caster style (A pair of normal wheels supported by a steering shaft on an off-centered position). Now the 4WD configuration discussed in section III equips a pair of drive wheels on the off-centered position from the center of the chair. Therefore, the powered-caster control can be applied to the 4WD mechanism. Fig.7 shows an omnidirectional wheelchair with the 4WD drive mechanism. The distance between the midpoint of the two drive wheels and the center of a chair, called as caster offset S, and the distance of two wheels, called vehicle tread W, are respectively indicated in the figure. A chair is mounted on the top of a center shaft and is turned by the third motor. Thus the two wheels and the center shaft form a twin caster configuration. Coordination of these three motors allows the chair to move in an arbitrary direction with an arbitrary magnitude of velocity from any configuration of the 4WD platform.
In this instant, the rotation about the midpoint of two wheels, I0 , translates into sideways velocity on the center of the chair , y v ,as,
y v
Yv r
§ x v · ¨ ¸ ¨ y v ¸ ¨ T ¸ © v¹
c
Xo
Yo
Xc
Ov
Oo
vR
(15)
x v cos T v y v sin T v x v sin T v y v cos T v T Z v
(16)
s
Where the desired motion commands, xc , y c and Tc , are given along the chair coordinate system since a joystick is fixed and moves with the chair.
W
§ x c · ¨ ¸ ¨ y c ¸ ¨ T ¸ © c¹
ZR M idpoint between two wheels Fig. 7. Omnidirectional 4WD platform
1/ 2 · ¸§ v · s / W ¸¨¨ R ¸¸ v 1 / W ¸¹© L ¹
where Zs represents the rotation of the chair with relative to the platform, namely shaft rotation controlled by the third motor. Equations (1), (15) and (16) are resultantly united into vector style as shown bellow.
Tv
ZL
§ 1/ 2 ¨ ¨ s /W ¨ 1/W ©
Note here that the rotation of the 4WD platform Tv is not independent from the sideways velocity, the third motor is required to cancel the rotation of the platform and directing the chair to the desired direction. Therefore the motion of the chair is described as x c y c T
Xv
vL
(14)
From (14), heading velocity is identical to the average of the two wheel velocities and the sideways velocity is proportional to the velocity difference. Relationships between wheel velocities and the motion of the chair are derived as,
Platform s
1 v R vL 2 s v R v L W
x v
Yv
Chair
(13)
where,
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§ J 11 ¨ ¨ J 21 ¨ r /W ©
J 12 J 22 r /W
0 ·§ Z R · ¸¨ ¸ 0 ¸¨ Z L ¸ 1 ¸¹¨© Z S ¸¹
(17)
J 11 J 12 J 21 J 22
r cos T v rs sin T v W 2 r cos T v rs sin T v W 2 r sin T v rs cos T v W 2 r sin T v rs cos T v W 2
V. SIMULATION Omnidirectional motions of the 4WD wheelchair are presented by computer simulations for the verification of the proposed system. From a point view of mechanical design, all components including motors, motor drivers, a micro controller, batteries are supposed to be installed on the mobile platform. The specifications of a wheelchair in the simulation are shown below.
(18)
A 3x3 matrix in the right side of (17), called as Jacobian, is a function of orientation of the platform with relative to the chair, Tv. All elements in the Jacobian can always be calculated and determinant of the Jacobian could not be zero for any Tv. Therefore there is no singular point on the mechanism and an inverse Jacobian always exits. 3D motion commands given by the 3D-joystick are translated into three motor references by inverse of (17), so called the inverse kinematics. The three motors are controlled to provide the commanded rotations by independent speed controllers for omnidirectional movements. Thus 3DOF motion given by a joystick can be realized independently by the proposed 4WD platform. This class of omnidirectional mobility, so called “holonomic mobility”, is very effective to realize the high maneuverability of wheelchairs by an easy operation. Fig.8 illustrates a conceptional schematic of an omnidirectional wheelchair with the 4WD mechanism.
Fig. 8. Conceptional schematic of 4WD omnidirectional wheelchair
Chair dimension: Wheel diameter: Wheel base: Vehicle Tread: Caster offset:
950x600mm (top view) 300mm(normal and omni) 350mm 550mm 175mm
The simulation results are shown in Fig.9-12. In the simulations, typical three motions are tested, translational sideways and backward with chair orientation constant and spin turn. From these results, it can be seen that desired 3DOF motions are realized by the proposed omnidirectional 4WD mechanism. VI. CONCLUSION Conventional electric wheelchairs can not meet the requirements by a single design, maneuverability in clouded areas and high mobility in rough terrain environments. Enhancing the mobility of these mechanisms could be one solution for promoting barrier-free environments for wheelchair users without re-constructing existing facilities. In this paper, a new type of omnidirectional 4WD wheelchair has been proposed. The 4WD mechanism includes a pair of normal wheels on the rear end and a pair of omni-wheels on the front end. A normal wheel on rear and an omni-wheel in front are interconnected by a transmission and driven by a drive motor to make these two wheels rotate in unison. The third motor is additionally installed for rotating a chair on the 4WD platform individually from the omnidirectional translational motion. First the kinematics and statics of the original 4WD mechanism were analyzed. In the analysis, the non-slip condition for the front omni-wheels and improved step climbing capability of the 4WD system were clarified. A powered-caster control for omni-directional motion of the 4WD mechanism was discussed where the coordinated control, called powered-caster control, was applied to the rear two wheels. The control allows the center of wheelchair to translate in an arbitrary direction with an bitrary configuration of the 4WD mechanism. Orientation of a chair is controlled by the third motor additionally installed on the original 4WD platform. The powered-caster control for these three motors was verified by computer simulations in which 3DOF individual motions were successfully performed.
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REFERENCES [1] “Jazzy1113” Alcare Corporation, http://www.alcarecorp.co.jp/ [2] “M-Smart” Meiko Corporation, http://www.meikokk.co.jp/ [3] Jefferey Farnam, “Four-wheel Drive Wheel-chair with Compound Wheels,” US patent 4,823,900, 1989. [4] “Patrafour” Kanto Automobile Corporation, http://www.kanto-aw.co.jp/products/k-max/patrafour/patra_top. html [5] All-direction Power-driven Chair “FJ-UEC-600”, Fujian Fortune Jet Mechanical & Electrical Technology Co., Ltd, http://www.chinesewheelchair.com/
[6] All-direction Power-driven Chair “FJ-UEC-500”, Fujian Fortune Jet Mechanical & Electrical Technology Co., Ltd [7] M.Wada and S.Mori," Holonomic and Omnidirectional
Vehicle with Conventional Tires," Proceedings of the 1996 IEEE International Conference on Robotics and Automation, pp3671-3676, 1996. [8] M.Wada, A.Takagi and S.Mori, “Caster Drive Mechanisms for Holonomic and Omnidirectional Mobile Platforms with no Over Constraint,” Proceedings of the 2000 IEEE International Conference on Robotics and Automation, pp. 1531-1538, 2000.
Fig.9: Simulation of an omnidirectional 4WD wheelchair at initial
Fig.11: Backward motion with chair orientation constant (It’s during flip of the 4WD mechanism)
Fig.10: Sideways motion with chair orientation constant
Fig.12: Spin Turn (Just a chair rotates about the center while the 4WD mechanism provides no translational motion)
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