GaitEnable: An Omnidirectional Robotic System for Gait

Rehabilitation

Aliasgar Morbi and Mojtaba AhmadiDepartment of Mechanical and Aerospace Engineering

Carleton UniversityOttawa, Ontario, K1S 5B6, Canada

amorbi@connect.carleton.ca, mahmadi@mae.carleton.ca

Avi NativNeuroGym Technologies Inc.

Ottawa, Ontario, K1V 7Y6, Canadaavi@neurogymtech.com

Abstract— This paper introduces GaitEnable, a robotic gaittrainer composed of an actuated omnidirectional mobile base,a passive body weight support (BWS) system, and a reactivecontrol system that can initiate, sustain, stabilize or perturba user’s gait. The device is designed to provide minimalconstraints to the user’s natural motion, and its actuated mobilebase can move cooperatively with the user in any direction.Data from preliminary experiments performed by a healthymale subject confirm that the reactive control system cancompensate for the device’s inertial effects and that the device’somnidirectional mobile base reduces pelvis and torso motionconstraints. The results also demonstrate that GaitEnable caneasily be programmed to simulate different types of behavioursor motion constraints.

I. INTRODUCTION

Focused and repetitive gait rehabilitation therapy encour-

ages functional recovery, minimizes a patient’s need for long-

term physical assistance, and improves a patient’s quality of

life [1]. However, therapist-assisted overground gait training

is physically demanding and poses an injury risk for both

the patient and the therapist. These challenges have prompted

many researchers to design robotic gait rehabilitation devices

that reduce therapist workload and enhance patient and

therapist safety.

Generally speaking, robotic gait rehabilitation devices may

be separated into three different categories depending on

their function and design: i) end-effector-type robots like the

Haptic Walker [2] that attach to the user’s feet and guide the

motion of the user’s feet [2], [3]; ii) exoskeleton-type robots

like the LOPES [4] that attach parallel to a patient’s lower

extremities and assist the patient during treadmill walking [4],

[5]; and iii), mobile gait trainers with actuated mobile bases

like the KineAssist [6] that enable overground gait practice

[7]–[9]. The actuated body-weight support (BWS) and fall

prevention mechanisms incorporated into these mobile gait

trainers differentiate them from the intelligent mobility aids

described in [10].

This work was supported by the Natural Sciences and EngineeringResearch Council of Canada

End-effector-type and exoskeleton-type robots are effective

at reducing therapist workload but tend to be large, compli-

cated, and expensive. Additionally, they are less effective for

balance training because they limit training to the sagittal

plane. This is also true of the more complex robots [4], [11]

that are designed to impose minimal motion constraints - even

these devices cannot easily be used for activities like side-

stepping or turning while walking since they are designed to

be used with a treadmill.

As task specificity is crucial to optimizing functional

outcomes [12], mobile gait trainers that provide realistic

overground gait practice may be more effective than end-

effector and exoskeleton-type rehabilitation robots. However,

the mobile gait trainers described in [7]–[9] employ non-

holonomic differential steering systems that can constrain

a patient’s lateral pelvis motions. Furthermore, their mobile

bases cannot be used for important balance training activities

such as side-stepping or one-leg balance. As such, these

mobile gait trainers may not provide realistic practice of

overground walking either. In contrast, the KineAssist [6] was

deliberately designed with an omnidirectional mobile base,

and separate powered trunk and pelvis support mechanisms.

KineAssist enables realistic practice of overground walking

precisely because it imposes minimal constraints on the

patient’s torso and pelvis motions.

The development of the mobile gait trainer presented

in this paper, GaitEnable, was motivated by our goal of

creating a simple robotic mobile rehabilitation device that

facilitates safe overground gait therapy. GaitEnable enables

realistic practice of overground walking and balance training

because it imposes minimal pelvis and torso motion con-

straints. Additionally, its actuated mobile base can generate

force and motion cues for initiating, sustaining, perturbing,

or stabilizing a user’s gait. Though designed primarily for

therapeutic purposes, this device could also be used to carry

out biomechanics experiments with healthy individuals or

for performing quantitative gait and balance assessments.

Furthermore, its design enables a therapist to manually ma-

nipulate the patient’s leg if necessary, and its simple attach-

ment system results in a rapid setup time. Additional details

936978-1-4673-1278-3/12/$31.00 ©2012 IEEE

Proceedings of 2012 IEEEInternational Conference on Mechatronics and Automation

August 5 - 8, Chengdu, China

Fig. 1: The Bungee Mobility Trainer

about GaitEnable are discussed in Section II, and results

from preliminary experiments performed with a healthy male

subject follow in Section III.

II. THE GAITENABLE SYSTEM

The GaitEnable system is composed of a passive BWS

system, an actuated omnidirectional mobile base, and a

reactive control system that commands the device to shadow

the user’s pelvis motion. The patented BWS system used

on the device is currently used on a commercially available

gait trainer called the Bungee Mobility Trainer (BMT) [13].

A description of the BMT’s BWS system, the actuated

omnidirectional mobile base, and the control system follow.

A. The Bungee Mobility Trainer

The (BMT) [13] is a patented mobile BWS system. As

shown in Figure 1, the device consists of a passive mobile

base and a passive 3-DOF linkage that supports the patient’s

pelvis from below. Clinical applications of the BMT include

rehabilitation of brain or spinal cord injury, stroke, multiple

sclerosis, cerebral palsy, and Parkinson’s disease [13].

The design of the passive linkage ensures that the bungee

cords are engaged and provide BWS whenever the patient

loses their balance. If the patient is unable to recover and

both feet lose contact with the ground, the patient eventually

approaches a safe, seated position within the device. Patients

can similarly remain suspended within the device - in a safe

and comfortable seated position - if they become tired.

The BMT is effective for balance training, and allows pa-

tients to practice and learn protective trunk postural reactions

precisely because it provides support from below. In contrast,

the harness-based BWS systems used in other systems may

limit natural postural responses because they artificially sta-

bilize trunk motion [14]. When necessary though, optional

forearm supports and a torso harness can be attached to the

BMT to allow patients with a weak trunk to safely use the

device.

Fig. 2: The passive linkage connecting the user’s pelvis to

the body weight support mechanism

B. Overview of the GaitEnable System

The BMT enhances patient and therapist safety and im-

poses minimal constraints on the patient’s pelvis and torso

motion. However, it lacks many of the features that robotic

gait rehabilitation systems offer. Accordingly, GaitEnable was

realized by combining the BMT’s passive BWS system with

an actuated omnidirectional mobile base. The mobile base

can: compensate for the device’s inertial effects; stabilize,

assist, or resist the user; and, generate gentle gait perturba-

tions to facilitate balance training and gait assessments. In

addition to reducing the constraints imposed on the patient’s

pelvis and torso motion, the holonomic mobile base also

allows practice of important balance training activities such

as side-stepping, and one-leg balance. While the padded groin

support on user’s seat imposes a larger than normal thigh

separation distance, healthy subjects can still run, hop, or

play soccer when attached to GaitEnable.

The current prototype does not include an actuated BWS

system for regulating bodyweight unloading. The choice to

exclude this feature was motivated by our conjecture that the

combination of an actuated mobile base and a passive BWS

system are sufficient for addressing the needs of many patient

populations. This conjecture stems, in part, from recent re-

search that suggests that applying a constant pushing force on

the pelvis can reduce the metabolic cost of walking by nearly

42% [15]. Thus, using a mobile base to propel the patient’s

center of mass forward may be an effective alternative to

using an actuated BWS system to assist a patient. However,

we acknowledge that assisting center of mass propulsion

alone may not be adequate for all patient populations, and that

experiments with different patient populations are necessary

for verifying this conjecture.

C. The Actuated Mobile Base

The differential-steering drive systems used on most mo-

bile gait trainers [7]–[9] are simple to implement and allow

users to walk in a straight line or along a curved path. How-

ever, differentially-steered mobile bases are non-holonomic

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(i.e., incapable of achieving any arbitrary linear and angular

velocity combination in a plane). Thus, if a user is attached to

the motion base, then the base’s intrinsic motion constraints

will be transferred to the portion of the body in direct contact

with the base. Gait trainers with sophisticated BWS systems

that accommodate natural pelvis motions [8], [9] are less

problematic, but will similarly constrain the user’s motion

when the mechanical limits of the BWS system are exceeded.

These effects would be most prevalent during any rapid body

motions (e.g., during balance training activities that involve

rapid change-in-support reactions).As shown in Figure 1, GaitEnable attaches below the

user’s body via a passive-elastic BWS system installed on

the mobile base. The passive linkage allows the user to freely

translate and rotate with respect to the mobile base in the

sagittal plane. However, the user’s lateral pelvis translation

is constrained to follow the lateral motion of the mobile base.

As a result, the user’s lateral pelvis motion will be effected by

the motion constraints of the mobile base. Given the evidence

that indicates the importance of minimizing pelvis motion

constraints - particularly those on the lateral translation of

the pelvis [16] - an actuated holonomic mobile base was

deemed to be essential for this device.While a variety of different omnidirectional drive sys-

tems exist (see [17] for examples), drive systems based

on omnidirectional wheels require the minimum number of

actuators. Since omniwheels are relatively inexpensive and

readily available from several different manufacturers, and

since the use of omniwheels over other wheel types simplifies

the mechanical design of the mobile base, an omniwheel-

based actuated mobile base was developed for GaitEnable.

While using omnidirectional wheels has several advantages,

drive systems based on these wheels tend to exhibit higher

vibrations, reduced traction, and less robustness to varia-

tions and obstructions in the terrain. These drawbacks were

deemed to be acceptable in this application since the device

is meant to be used in controlled environments (e.g., a clinic

or hospital with commercial flooring) where ground surface

irregularities are less prominent.The omidirectional drive system employed on GaitEnable

is composed of three motor assemblies placed in a triangle-

like configuration on the frame of the device. Each assembly

consists of three 125 mm Rotacaster single omniwheels

[18] powered by a Maxon servomotor. The batteries and

electronics required to power and control the motors are

mounted at various locations on the device. In the current pro-

totype, National Instruments data acquisition cards are used

to interface the sensors and actuators to a control computer,

and Matlab’s xPC Target toolbox is used to implement a real-

time motion control system that operates at 2 kHz.

D. Control SystemGaitEnable’s control system should automatically synchro-

nize the mobile base’s motion with the user’s motion, com-

pensate for the inertial effects of the device, and provide force

and motion cues that correspond to the rehabilitation therapy

goals. The admittance controller described in this section

satisfies all theses requirements and has been implemented

and tested on the prototype shown in Figure 5.

The primary contact area between GaitEnable and the user

occurs between the seat cushion and the user’s pelvis. The

interaction forces and torques developed at the contact inter-

face are measured by an ATI Delta 6-axis force/torque sensor

mounted between the seat and the frame. After filtering the

raw data and implementing a deadband approximately equal

to the sensor’s precision, the interaction forces and torque

measured from the sensor are expressed with respect to a

device-fixed coordinate frame. Three of the six components

associated with the device’s motion in the ground plane, fx,i,

fy,i, and τz,i, are used as inputs to the following reference

model:

mxxr−bxxr = fx,i + fx,v (1)

myyr−byyr = fy,i + fy,v (2)

jθr−bθ θr = τz,i + τv (3)

where: xr, and yr define the reference position of some

point of interest on the mobile base (that may or may not

be coincident with device’s center of mass); θr is the desired

orientation of the device centred about the point of interest;

m, b, bθ and j are selectable parameters that determine the

device impedance sensed by the user; and, fx,v, fy,v, and

τz,v are the virtual forces and torque. The virtual forces and

torque may be designed to reflect specific therapy goals or

requirements (e.g., a sinusoidal force along the yr axis may

be used for training lateral weight shift).

The approximate midpoint of the support polygon formed

by the subject’s feet is taken as the point of interest. This

point corresponds to the projection of the user’s centre-of-

mass in the ground plane. Defining the reference point in this

way allows the moment input τz,i to generate device rotation

commands that are (approximately) centered about the user’s

centre of mass instead of the device’s center of mass.

Equations (1)-(3) are numerically integrated in time to

generate the mobile base’s reference velocities xr, yr, and

θr. These reference velocities are then decomposed into

corresponding desired omniwheel speeds via a kinematic

relationship - the Jacobian in Figure 3 - that relates task-space

velocities (reference velocities) to the desired joint space

velocities (omniwheel velocities). This kinematic relationship

is unique to the wheel configuration and is derived using

the procedure outlined in [19]. Next, the desired omniwheel

velocities are integrated, and position controllers at each

motor assembly track the desired omniwheel orientations.

The entire process is summarized in the block diagram shown

in Figure 3.

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Reference Model Position Controllers User and Device

Reference Velocities

Omniwheel Velocities and Orientations

Motor Torques

Encoder Feedback

Desired Mass and Damping

Virtual Forces and Torque

Measured Interaction Forces and Torque

Jacobian

Fig. 3: A block diagram of the controller

The mobile base exhibits the desired impedance specified

in (1)-(3), (i.e., users will feel the application of the virtual

forces and torques and the mass and damping properties

specified in (1)-(3)), if omniwheel slip is minimal and if the

position controllers accurately track the desired omniwheel

orientations. In practice though, the reference accelerations

xr, yr, and θr must saturated prior to integration to limit

the device’s acceleration and omniwheel slip during dynamic

maneuvers. Accordingly, the fidelity of the impedance dis-

play cannot be guaranteed when the acceleration limits are

exceeded.

III. EXPERIMENTAL RESULTS

A. Overview

A single healthy subject was recruited to participate in

an experiment that investigated how GaitEnable’s omnidi-

rectional mobile base can reduce pelvis motion constraints.

In addition to highlighting how the device can be used for

biomechanics studies, this experiment also demonstrates how

the device can be programmed to emulate different types of

behaviour. Only a single subject performed the experiment

as the experiment was only meant to illustrate the operation

of the device and the control system.

Measurements of the mobile base kinematics collected

with an Optotrack Certus Motion capture system were used to

estimate the user’s pelvis motion. This was necessary since

markers could not be placed directly on the user’s pelvis

during the experiment. During data analysis, the mobile base

was assumed to behave as a planar rigid body and the position

and velocity trajectories of several markers attached to mobile

base were used to estimate the velocity of the reference point.

As noted previously, the reference point corresponds to the

projection of the user’s centre-of-mass. Thus, the measured

reference point trajectory was assumed to approximate the

user’s pelvis motion during the experiment.

In addition to mobile base kinematics, interaction force

and torque data were also collected during the experiment.

B. Procedure

The experiment required the subject to slowly walk in a

straight line at a self-regulated speed for a short distance

corresponding to the range of the motion capture system.

The subject was instructed to walk slowly so that his walking

speed and gait would more closely emulate a patient’s gait.

Additionally, studies suggest that lateral pelvis excursions

are largest at slower walking speeds [20]. Thus, the effects

of lateral pelvis motions constraints, the key feature to

be investigated in this experiment, should have been more

pronounced at the slow walking speeds considered in this

experiment.

The parameters of the reference models (1)-(3) were

specified as m = 40 Kg, b = 20 Nm/s, j = 3 Kg·m2, and

bθ = 5 Nm·rad/s2. These desired mass and inertia parameters

correspond to approximately one third of the device’s actual

mass and inertia. Studies suggest that a desired mass greater

than 10 kg can noticeably affect a subject’s gait [21]. Thus,

using a desired mass of 40 kg may not be appropriate during

rehabilitation therapy. However, using a larger desired mass

was not a limiting factor as the experiment was designed to

investigate how mobile base motion constraints effect pelvis

kinematics and kinetics at a given desired mass setting.

The subject was asked to repeat the experiment at two

different test conditions: i) the omnidirectional motion test

condition which corresponded to the mobile base being

commanded to display the impedance specified by (1)-(3);

and ii), the constrained motion test condition which corre-

sponded to having the impedance control active only in the

forward/backward direction. The mobile base’s lateral motion

and rotation during the constrained motion test condition was

constrained by setting xr = θr = 0. This test condition was

meant to emulate the user-device interaction that would arise

with a gait trainer that limited motion to the sagittal plane.

The experiment was repeated 5 times at each test condition,

and the corresponding data sets from both test conditions

indicating the greatest similarity in forward walking speed

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(a) Lateral Velocity (b) Forward Velocity (c) Measured Interaction Torque

Fig. 4: Comparing Walking with Omnidirectional Motion and Lateral Motion Constraints

were selected for the comparison presented in Figure 4.

C. Results

Figure 4(a) compares the measured and commanded for-

ward speed (i.e., yr) for the two test conditions. In the figure

legends, O corresponds to the omnidirectional motion test

condition, and C corresponds to the constrained motion test

condition.

The results presented in Figure 4(a) confirm that the

subject performed the experiment at both test conditions with

approximately the same average walking speed. These results

also confirm that the open loop reference velocity controller

is capable of tracking the commanded velocity. However, the

mobile base consistently moved slower than the commanded

velocity during the steady state walking portion of the test

(i.e., between 5 and 13 seconds in Figure 4(a)), suggesting

that the effects of omniwheel slip were not negligible.

The velocity tracking errors did not interfere with the sub-

ject’s ability to walk. However, they did reduce the accuracy

with which the gait trainer displayed the desired impedance.

The actual impedance displayed by the device was estimated

using the least squares method and was calculated to be 45.3

kg and 23.2 Nms/rad2 in the forward/backward direction.

This result is reasonable considering that there is no platform

velocity feedback to correct for omniwheel slip. Though the

accuracy of the impedance display could be improved, we

note that the results do confirm the key features of the control

system - the device moves cooperatively with the user, and

the admittance controller can compensate for the inertial

effects of the device. For the experiments shown in Figure

4, the admittance controller allowed the device to display a

mass and inertia that is nearly one-third of its actual mass

and inertia.

Figure 4(b) compares the measured and commanded lat-

eral reference velocity xr for the two test conditions. It is

important to note that the results in Figured 4(a) and 4(b) for

the omnidirectional motion test condition are consistent with

the pelvis motion data presented in [20]. The key similarities

Fig. 5: The GaitEnable system prototype

include: i) forward/backward and lateral pelvis excursions are

approximately sinusoidal; ii) lateral pelvis excursions have

approximately half the frequency of the foreward/backward

pelvis excursions; and iii) foreward/backward pelvis ex-

cursions have a smaller amplitude than the corresponding

lateral pelvis excursions. These similarities are worth noting

since they suggest GaitEnable’s omnidirectional mobile base

preserves many of the key features of pelvis motion observed

in the gait of healthy individuals [16].

The primary motivation of this experiment was to compare

how pelvis kinematics and kinetics vary between the con-strained motion and omnidirectional motion test conditions.

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This difference was found to be most noticeable in the

interaction torque τz,i data plotted in Figure 4(c). These

results confirm that constraining the mobile base’s lateral

translation and rotation has a noticeable impact on pelvis

kinetics. As expected, the interaction torque is significantly

larger when the user’s pelvis motion is constrained to the

sagittal plane. More interestingly, however, the sinusoidal

nature and approximate frequency of the interaction torque

data at the constrained motion test condition in Figure 4(c) is

strongly correlated to the lateral velocity of the mobile base

at the omnidirectional motion test condition in Figure 4(b).

This results suggest that limiting pelvis motion to the sagittal

plane causes a compensatory torso reaction that results in an

increased reaction torque at the user-device interface.

IV. CONCLUSIONS AND FUTURE WORK

This paper introduced GaitEnable, a holonomic robotic

gait trainer composed of an actuated omnidirectional mobile

base and a passive body weight support (BWS) system.

This device is designed to provide minimal constraints to

the user’s natural motion, and its actuated mobile base can

provide the actuation forces necessary to initiate, sustain and

stabilize a user’s gait. Data from experiments performed by

a healthy male subject indicated that GaitEnable’s control

system compensated for the device’s inertial effects, and

automatically synchronized the device’s motion with the

user’s motion. The results also demonstrated that GaitEn-

able’s omnidirectional motion capability noticeably reduced

pelvis motion constraints. In the future, the control system

will be augmented with specific gait and balance training

operating modes, and experiments with healthy subjects and

patients with mobility disorders will be performed to asses

the clinical applications of this device.

REFERENCES

[1] K. J. Sullivan, D. A. Brown, T. Klassen, S. Mulroy, T. Ge, S. P. Azen,C. J. Winstein, and P. T. C. R. N. (PTClinResNet), “Effects of task-specific locomotor and strength training in adults who were ambulatoryafter stroke: results of the steps randomized clinical trial.” Phys Ther,vol. 87, no. 12, pp. 1580–1602, Dec 2007.

[2] H. Schmidt, S. Hesse, R. Bernhardt, and J. Kruger, “Hapticwalker—anovel haptic foot device,” ACM Trans. Appl. Percept., vol. 2, no. 2,pp. 166–180, 2005.

[3] J. Yoon, B. Novandy, C.-H. Yoon, and K.-J. Park, “A 6-dof gaitrehabilitation robot with upper and lower limb connections that al-lows walking velocity updates on various terrains,” Mechatronics,IEEE/ASME Transactions on, vol. 15, no. 2, pp. 201 –215, Apr. 2010.

[4] J. F. Veneman, R. Kruidhof, E. E. G. Hekman, R. Ekkelenkamp, E. H.F. V. Asseldonk, and H. van der Kooij, “Design and evaluation of thelopes exoskeleton robot for interactive gait rehabilitation.” IEEE TransNeural Syst Rehabil Eng, vol. 15, no. 3, pp. 379–386, Sep 2007.

[5] G. Colombo, M. Wirz, and V. Dietz, “Driven gait orthosis for im-provement of locomotor training in paraplegic patients.” Spinal Cord,vol. 39, no. 5, pp. 252–255, May 2001.

[6] J. Patton, D. A. Brown, M. Peshkin, J. J. Santos-Munn, A. Makhlin,E. Lewis, E. J. Colgate, and D. Schwandt, “Kineassist: design anddevelopment of a robotic overground gait and balance therapy device.”Top Stroke Rehabil, vol. 15, no. 2, pp. 131–139, 2008.

[7] K.-H. Seo and J.-J. Lee, “The development of two mobile gaitrehabilitation systems.” IEEE Trans Neural Syst Rehabil Eng, vol. 17,no. 2, pp. 156–166, Apr 2009.

[8] Y. Stauffer, Y. Allemand, M. Bouri, J. Fournier, R. Clavel, P. Me-trailler, R. Brodard, and F. Reynard, “The walktrainer; a new gener-ation of walking reeducation device combining orthoses and musclestimulation,” Neural Systems and Rehabilitation Engineering, IEEETransactions on, vol. 17, no. 1, pp. 38 –45, feb. 2009.

[9] H. Lim, K. Hoon, K. Low, Y. Soh, and A. Tow, “Pelvic controland over-ground walking methodology for impaired gait recovery,”in Robotics and Biomimetics, 2008. ROBIO 2008. IEEE InternationalConference on, feb. 2009, pp. 282 –287.

[10] L. Saint-Bauzel, V. Pasqui, and I. Monteil, “A reactive robotizedinterface for lower limb rehabilitation: Clinical results,” Robotics, IEEETransactions on, vol. 25, no. 3, pp. 583 –592, jun. 2009.

[11] D. Aoyagi, W. E. Ichinose, S. J. Harkema, D. J. Reinkensmeyer, andJ. E. Bobrow, “A robot and control algorithm that can synchronouslyassist in naturalistic motion during body-weight-supported gait trainingfollowing neurologic injury.” IEEE Trans Neural Syst Rehabil Eng,vol. 15, no. 3, pp. 387–400, Sep 2007.

[12] J. A. Kleim and T. A. Jones, “Principles of experience-dependentneural plasticity: implications for rehabilitation after brain damage.”J Speech Lang Hear Res, vol. 51, no. 1, pp. S225–S239, Feb 2008.

[13] A. Nativ, “The bungee mobility trainer,” http://www.neurogymtech.com/pdf/neurogym bungee walker.pdf.

[14] M. K. Aaslund and R. Moe-Nilssen, “Treadmill walking with bodyweight support effect of treadmill, harness and body weight supportsystems.” Gait Posture, vol. 28, no. 2, pp. 303–308, Aug 2008.

[15] J. S. Gottschall and R. Kram, “Energy cost and muscularactivity required for leg swing during walking.” J Appl Physiol,vol. 99, no. 1, pp. 23–30, Jul 2005. [Online]. Available: http://dx.doi.org/10.1152/japplphysiol.01190.2004

[16] J. M. Hidler and A. E. Wall, “Alterations in muscle activation patternsduring robotic-assisted walking.” Clin Biomech (Bristol, Avon), vol. 20,no. 2, pp. 184–193, Feb 2005.

[17] H. Yu, M. Spenko, and S. Dubowsky, “Omni-directional mobility usingactive split offset castors,” Journal of Mechanical Design, vol. 126,no. 5, pp. 822–829, 2004.

[18] Rotacaster, http://www.rotacaster.com.au/omnidirectional-wheels—mounts.html.

[19] T. Kalmar-Nagy, P. Ganguly, and R. D’Andrea, “Real-time trajectorygeneration for omnidirectional vehicles,” in American Control Con-ference, 2002. Proceedings of the 2002, vol. 1, 2002, pp. 286 – 291vol.1.

[20] L. Zhao, L. Zhang, L. Wang, and J. Wang, “Three-dimensional motionof the pelvis during human walking,” vol. 1, jul. 2005, pp. 335 – 339Vol. 1.

[21] J. Meuleman, W. Terpstra, E. van Asseldonk, and H. van der Kooij,“Effect of added inertia on the pelvis on gait,” in RehabilitationRobotics (ICORR), 2011 IEEE International Conference on, 29 2011-july 1 2011, pp. 1 –6.

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