International Conference on Control, Automation and Systems 2008Oct. 14-17, 2008 in COEX, Seoul, Korea

Design and Control of Omni-Directional Mobile Robot

for Mobile Haptic Interface

Kyung-Lyong Han1, Oh Kyu Choi1, In Lee2, Inwook Hwang2, Jin S. Lee1 and Seungmoon Choi2

1Robotics and Automation Laboratory, POSTECH, Pohang, Korea(Tel : +82-54-279-5574; E-mail: {sidabari, hyh1004, jsoo}@postech.ac.kr)

2Haptics and Virtual Reality Laboratory, POSTECH, Pohang, Korea(Tel : +82-54-279-5661; E-mail: {inism, inux, choism}@postech.ac.kr)

Abstract: A Mobile Haptic Interface (MHI) refers to a system where a grounded force-feedback haptic interface ismounted onto a mobile robot to provide the user with unlimited workspace, especially for large virtual environments. InMHI, the mobile base needs to quickly change the movement direction, thus a omni-directional robot is preferred. In thispaper, we present a novel omni-directional mobile robot designed for a Mobile Haptic Interface (MHI), which uses fourcustom-made Mecanum wheels to provide higher operation stability. We also implemented two PI control methods (theconventional independent motor control and one combined with the Cartesian velocity control) and empirically evaluatedtheir performance through an experiment. The experimental results indicated that the developed holonomic mobile robotallows accurate velocity control required for the MHI.

Keywords: mobile robot, Mecanum wheel, omni-directional mobile robot, mobile haptic interface.

1 INTRODUCTION

A grounded force-feedback haptic interface has an in-herent limit on its workspace, which prevents the in-terface from rendering virtual objects larger than itsworkspace. This issue was challenged by building largehaptic interfaces, either of the manipulator type [1] or ofthe string type [2] [3]. However, their workspaces, al-though larger, are still limited, and their dynamic perfor-mance falls short of that of the desktop force-feedbackdevices.

A promising alternative that has received increasingattention is the Mobile Haptic Interface (MHI) whichrefers to a force-feedback haptic interface mounted on amobile base. The MHI can provide an unlimited hapticworkspace by autonomously moving the mobile base toa location where a user wants to interact with virtual ob-jects using the force-feedback haptic interface. The MHIis also easier to be installed or removed due to its mobil-ity, considerably smaller, and much safer than the large-scale force-feedback interface. Such advantages have re-cently brought about active research on the MHI.

The concept of MHI was originally introduced byNitzsche et al. using an omni-directional mobile robot,a simple motion-planning algorithm, and a simple hapticrendering method [4]. The possible effect of mobile-baseacceleration on the final force perceived by the user wasalso analyzed for a 1 Degree-Of-Freedom (DOF) case.Inspired by this work, Barbagli et al. presented two pro-totype MHIs [5] where commercial general-purpose mo-bile robots (a Nomad XR4000 and a Pioneer2 DX) wereused as the mobile base, respectively. In 2006, Pascaleet al. proposed a MHI that has two desktop haptic in-terfaces on a commercial mobile robot (Nomad XR4000)[6]. More recently, Peer et al. developed a MHI that fea-tured with two 7-DOF robot arms and two guide actuatorsto expand its workspace in the vertical direction [7].

In large virtual environments created using a largeimmersive visual display such as the CAVETM, a usercan freely walk around to interact with virtual objects.To cope with the user’s arbitrary locomotion, the mo-bile base of the MHI should be capable of changing itsmovement as quickly as possible. Therefore, between thetwo common types of mobile robot platform, the omni-directional type is more suitable to the MHI than the bidi-rectional type. Although the bidirectional type has highdriving speed and a simple structure using the differen-tial steering, its nonholonomic constraint makes it inap-propriate to the MHI. Since the omni-directional mobilerobot, despite its relatively slow driving speed and com-plex structure, can translate and rotate simultaneouslyand independently in any direction, it has an advantagewhen the robot needs to follow the user’s locomotion.

The first prototype of MHI of our research group waspresented in 2007 [8]. Unlike other MHIs, our sys-tem included all hardware components (a MHI and a 3Dtracker) and all software components (mobile robot con-trol, motion planning, and haptic rendering for generalvirtual object models), targeting for a MHI system thatcan be used with a large immersive visual display. Sincesuch integration requires an open platform for the mo-bile robot, we designed and constructed our own holo-nomic mobile robot based on a three-wheel design usingomni-directional wheels. In this paper, we introduce animproved mobile base with four custom-made Mecanumwheels. The base also has a lift that provides the hapticinterface with expanded workspace in the vertical direc-tion as well. Two motor control algorithms were testedusing the four-wheel robot, and their performances arereported. The results confirm that the mobile base andmotor control algorithms are adequately designed to cor-rectly and stably follow the velocity command, which isrequired for undesired force generated from the mobile

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Fig. 1 Mecanum wheel used for our MHI (left: CADdesign, right: prototype).

base to be imperceivable by the user.The remainder of this paper is organized as follows.

Section 2 introduces the mobile robot including the wheeldesign, robot structure, and kinematics. Section 3 de-scribes the two control algorithms, followed by perfor-mance evaluation in Section 4. Finally, we conclude thispaper in Section 5.

2 ROBOT DESIGN

In this section, we describe the design of Mecanumwheel used in our mobile robot, and then the structureand kinematics of the robot.

2.1 Wheel Design

A Mecanum wheel uses passive rollers positioned atan angle offset from the wheel rotation around it’s cir-cumference. As well as moving forward and back-ward like conventional wheels, the wheels allow side-ways movement by spinning wheels on the front and rearaxles in opposite directions [9]. We designed a Mecanumwheel for our four-wheel mobile robot shown in Fig. 1.The sub-wheels of the Mecanum wheel are made of MCnylon, and the other parts are of aluminum and stainlesssteel.

Figs. 2, 3, and 4 shows parameters used to design theMecanum wheel. We first selected the following param-eter values:• The number of sub-wheels: n = 6.• The angle between the axis of the sub-wheel and thedriving axis: η = 45◦.• The radius of the whole Mecanum wheel: RWheel =60 mm.• The radius of the sub-wheel: rRol = 15 mm.• The overlap angle between two neighbor sub-wheels:θt = 10◦.• The radius of the sub-wheel axis: α = 5 mm.

Other parameters needed to complete the Mecanumwheel design, the radius of sub-wheel from the axle sided and the length of sub-wheel L, must satisfy the follow-ing constraints:

(RWheel − rRol) tanπ

n> d. (1)

2

√R2

Wheel − (α + RWheel − rRol)2

sin2 η> L. (2)

Fig. 2 Bottom view of the Mecanum wheel at the contactpoint between the wheel and ground.

Fig. 3 View of the Mecanum wheel at the rotation-axisdirection.

Fig. 4 View of the Mecanum sub-wheel at the plane ofsub-wheel axis.

Eq. (1) represents the condition that the maximum radiusof each sub-wheel is limited to maintain space betweenthe sub-wheels. For the wheel to form a circle at the axleside, the length of the sub-wheel is restricted by (2). Thevalues of the left-hand terms in (1) and (2) are 25.9808and 93.8038 in our design, respectively. Then, L and dcan be derived as

L =2(RWheel − rRol) tan θ

2

sin η= 89.12, (3)

d =−B cos η +

√B2 cos2 η + ACrRol

A= 20.0236, (4)

where A = cos2 η + sin4 η = 0.75, B = RWheel −rRol = 45, and C = 2RWheel − rRol = 105. The pa-rameter values, L = 89.12 mm and d = 20.0236 mm,satisfy the two constraints in (3) and (4), . Further detailsfor designing a Mecanum wheel can be found in [9].

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Fig. 5 The four-wheel robot.

Fig. 6 Control architecture of the four-wheel robot.

2.2 Robot Structure

Our four-wheel mobile robot has a rectangular shapewith the four Mecanum wheels supporting the robot (seeFig. 5). It consists of five main parts: mobile base (in-cluding the four suspension sets, 4 Mecanum wheels, 4geared DC motors, and batteries), driving control box (in-cluding a DSP control board and 5 motor drivers), a lap-top, a desktop 3 DOF haptic interface (PHANToM Pre-mium 1.5A; SensAble inc., USA), and a linear unit thathas about 400 mm stroke. The width and length are bothabout 63 cm and the height is about 80 cm. The weight isabout 90 kg including the haptic device.

The four-wheel mobile robot has the control architec-ture shown in Fig. 6. The laptop runs a haptic render-ing program that also determines the next position of themobile robot based on the current and previous positionsof the user and the mobile robot measured using the 3Dtracker. A Cartesian velocity command is computed fromthe next robot position and sent to the DSP board. Thecommand is then converted to the corresponding angularvelocities of the four wheels for the control of each motor.

2.3 Robot Kinematics

The driving force of each wheel can be decomposedinto two force components (see Fig. 7). One componentis in the sub-wheel direction, and the other is the force

Fig. 7 Four-wheel structure on local coordinates.

that subtracts the sub-wheel direction force from the driv-ing force. The sub-wheel direction force is exhausted byrolling the sub-wheel. The addition of the net forces ofthe four wheels determines the moving direction of themobile robot. More details about this are described in[10].

The mobile robot is under velocity control. Giventhe Cartesian space velocity command, the velocity com-mand to each motor is computed using the inverse Jaco-bian in (5).⎡⎢⎢⎣

V1W

V2W

V3W

V4W

⎤⎥⎥⎦ =

⎡⎢⎢⎣

1 −1 −(LX + LY )1 1 (LX + LY )1 1 −(LX + LY )1 −1 (LX + LY )

⎤⎥⎥⎦

⎡⎣ VXL

VYL

ω

⎤⎦ , (5)

where i is the wheel index (i = 0, 1, 2, 3), ViW is the ro-tation velocity of wheel i, Vir is the tangential velocity ofthe free roller touching the floor, LX is the X−axis dis-tance from each wheel to the center of gravity, LY is theY −axis distance from each wheel to the center of gravity,and VXL

, VYL, ω are the linear and angular velocities of

the robot in the Cartesian space.

3 CONTROL ALGORITHMS

We tested two algorithms for motor control. The firstalgorithm (Algorithm 1) is the usual independent motorcontrol as shown in the block diagram in Fig. 8. First,the higher level haptic rendering program running in thelaptop determines the next position of the mobile baseusing its motion planning algorithm and sends the veloc-ity command to the motor control program. Then, thedesired reference angular velocity of each motor is com-puted using the kinematics described in Section 2. Theactual velocity of each motor is captured from the motorencoder. The difference between the desired and currentmotor velocities is treated as the error term, and subse-quently used in the PI controller that generates the controlinput of each motor.

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Fig. 8 Block diagram of Algorithm 1.

Fig. 9 Block diagram of Algorithm 2.

Algorithm 2 shown in Fig. 9 is improved from Algo-rithm 1 in that Algorithm 2 also compensates the Carte-sian velocity error. The Cartesian velocity commandis compared to the current Cartesian velocity calculatedfrom the measured motor angles, and the difference isfed back to the PI controller. This two-stage control lawis expected to control the mobile robot more accuratelyalong the maneuvering direction. Both algorithms wereset to run at the sampling rate of 500 Hz in our mobilerobot.

4 EXPERIMENT

In the MHI, the force delivered to a user mainly con-sists of two components. The first component is gener-ated by the desktop force-feedback haptic interface. Thiscomponent is usually very close to the response forceof virtual object interaction being simulated. The othercomponent is unintended additional force caused fromthe dynamics of the mobile base. This undesired com-ponent can be ignored when the mobile base is static,but can affect the final rendering force when the mobilebase is in motion. Thus, to reduce such effect as muchas possible, one need to move the mobile robot in a waythat minimizes its velocity change. In the experiment, wemeasured the step response along each Cartesian axis (X ,Y , and ω) to examine velocity control accuracy.

Figs. 10 – 12 shows the velocity step responses alongthe directions of X , Y , and ω for the three-wheel robotthat we developed earlier [8]. The blue-dashed line rep-

Fig. 10 Velocity profile of the three-wheel robot in X-direction.

Fig. 11 Velocity profile of the three-wheel robot in Y -direction.

Fig. 12 Velocity profile of the three-wheel robot in ω-direction.

resents the desired velocity profile, and the red-solid linethe real velocity profile calculated from the measured en-coder data. The percent RMS error for each directionis specified inside each figure. Note that the step refer-ence was applied only in X−, Y −, and ω−directions inFigs. 10, 11, and 12, respectively. The RMS errors of thevelocity-servoed directions ranged from 15.1% – 19.9%,which were relatively large.

Experimental results for the four-wheel robot usingAlgorithm 1 are provided in Figs. 13 – 16. Again, theblue-dashed lines and the red-solid lines represent the de-sired velocity profiles and the real velocity profiles, re-spectively. Figs. 13 – 15 were measured similarly withFigs. 10 – 12, respectively, for direct comparison. Thepercent RMS errors are also shown in the figures, andthey (4.77% – 6.43% for the main controlled directions)are clearly smaller than those of the three-wheel robot. Inaddition, example data for all Cartesian directions being

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Fig. 13 Velocity profile of the four-wheel robot in X-direction with Algorithm 1.

Fig. 14 Velocity profile of the four-wheel robot in Y -direction with Algorithm 1.

Fig. 15 Velocity profile of the four-wheel robot in ω-direction with Algorithm 1.

Fig. 16 Velocity profiles of the four-wheel robot withAlgorithm 1 in X , Y , and ω-directions.

velocity-controlled are given in Fig. 16.Figs. 17 – 20 shop the velocity profiles of Algorithm 2

measured under the same conditions with Algorithm 1 forthe four-wheel robot. We can confirm that Algorithm 2resulted in much better control performance, e.g., smaller

Fig. 17 Velocity profile of the four-wheel robot in X-direction with Algorithm 2.

Fig. 18 Velocity profile of the four-wheel robot in Y -direction with Algorithm 2.

Fig. 19 Velocity profile of the four-wheel robot in ω-direction with Algorithm 2.

Fig. 20 Velocity profiles of the four-wheel robot withAlgorithm 2 in X , Y , and ω-direction.

overshoot, smoother steady-state oscillations, and lowerRMS errors. Finally, the RMS errors of the mainly con-trolled directions are summarized in Fig. 21 for clearcomparison between the robots and control algorithms.As expected, Algorithm 2 exhibited much smaller RMS

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Fig. 21 Comparison of RMS errors.

errors than the other two cases. We extensively tested therobots and algorithms in a number of different conditions,and could obtain the same conclusion.

5 CONCLUSION

We presented the omni-directional mobile robot de-signed for MHI. The robot uses the custom-madeMecanum wheels and also has the vertical lift forworkspace enlargement. In addition, two velocity controlalgorithms were implemented, and their performanceswere evaluated comparatively. The results indicated thatour mobile robot provides accurate velocity control ade-quate for the MHI.

We are currently integrating the new mobile robot withthe software modules for the MHI, and also working ona new version of a four-wheel robot that has a more com-pact body and higher performance.

ACKNOWLEDGMENTS

This work was supported in part by grants No. R01-2006-000-10808-0 and No. R0A-2008-000-20087-0funded by the Korea Science and Engineering Foundationand in part by the Information Technology Research Cen-ter support program (C1090-0804-0002) supervised bythe Institute for Information Technology Advancement.

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