Simulating Side Slopes on Locomotion Interfaces using Torso Forces
John M. Hollerbach
Univ. of Utah, School of Computing
50 S. Central Campus Dr., Salt Lake CityUT 84112 USA
jmh@cs.utah.edu

Damaso Checcacci
PERCRO Lab, Scuola Superiore S. Anna
P.zza Martiri della Libertà 33, 56127 Pisa, Italy
checcacci@sssup.it

Haruo Noma, Yasuyuki Yanagida, Nobuji Tetsutani
ATR Media Information Sciences Laboratories
2-2-2 Hikaridai, Keihanna Science City
Kyoto, 619-0288, Japanfnoma,yanagida,tetsutanig@atr.co.jp
Abstract
This paper describes the biomechanical experimental
validation of simulating side slope during walking on atreadmill style locomotion interface. The side slope effectis achieved by means of a lateral force applied to the waistof the walking subject. Results are provided and discussed
for both simulated and real side slopes, showing a substantial biomechanical equivalence in the walking pattern for
the real side slope and lateral torso force.

1 Introduction
A key issue for locomotion interfaces is the presentationof sloping terrain. One approach is programmable foot platforms, which can simulate adjustable stair-like terrain, as in
the Sarcos Biport [6] or Iwata’s Gaitmaster [7]. A common approach for treadmill style locomotion interfaces isan up-down tilting platform. In addition, sideways tilt canbe added to present sideslope walking as in the ATR ATLAS[11].
Instead of tilting a treadmill, which increases mechanical complexity and complicates the use of CAVE-like visualdisplays, another approach is to apply forces to the torso ofa user. It was shown in [4] that horizontal forces in the forward direction applied by the active mechanical tether in the
Sarcos Treadport locomotion interface yield realistic simulation of uphill slope walking, both from psychological andbiomechanical standpoints. Other demonstrated advantagesof torso force feedback are collision simulation and inertial
force simulation [1].

A natural follow-on question is whether applying sideforces to a subject walking on a level treadmill could produce an effect similar to walking on a real side slope. If
so, then there may not be any need to move the treadmill
platform at all. The required actuator forces for application
to the torso are much less than for tilting a platform, especially a large platform such as in the Sarcos Treadport. The
bandwidth would also be higher, allowing faster slope transients to be displayed. The vision of future treadmill-style
locomotion interfaces would therefore consist of a stationary platform, perhaps with some form of two-dimensionalsurface [2, 8], with terrain and other effects provided bytorso force feedback.
This paper performs a biomechanical comparison ofwalking on a treadmill tilted sideways versus walking on ahorizontal treadmill with passive torso forces. The ATLAS
system was employed throughout.

2 Methods
The ATLAS locomotion interface [11] has a treadmill
platform mounted on an active spherical joint. It can rotate
around a vertical axis and tilt both sideways and longitudinally, in order to reproduce a general ground orientation.
In the present study, its sideways tilting capability was essential. Side forces were applied by a simple pulley/weightsystem. An active tether for side forces is not available yet;the decision to build one hinges upon the successful outcome of these feasibility studies.
Eleven subjects (8 males, 3 females, aging 20  3 years)
were asked to walk on the ATR treadmill both in a real sideslope condition and under the application of a lateral force.

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Figure 1. Layout of the experiment with indication of the reference planes.
Figure 2. The experimental setup on the ATLAS system.
The real slope was varied in the range [ 16o, +16o ] withincrements of 2o . The force was applied using weights thatwere connected to the subject’s waist belt by a cable/pulleyapparatus. Several weights were successively added to provide a force in the range [-120, +120] N, with increments of
15N.
Two walking speeds were employed under each condition, 3 km/h and 5 km/h. The treadmill speed was ramped
up and down at a rate of 1 km/h/sec. Once the desired treadmill speed had been attained, enough data was collected forroughly 5 step cycles, then the speed was ramped down.
Considering a coordinate system with the z and x axes
directed upward and in the forward direction of walking respectively (Figure 1), then a positive side slope angle meansa positive rotation around the x axis. A positive force, instead, is intended in the negative direction of the y axis. In
Figure 1 both force and slope are reported in their positive
direction. With this convention we expect a positive force
to be required to simulate a positive slope and vice versa.
To track the walking motion of the subjects, the QuickMAG IV by OKK Inc., Japan, was used. The system employs two cameras and colored markers, which are sampled
at 60 Hz with an accuracy of 1.5 mm in the side and uphill
directions, and 2.5 mm in depth. Five markers were used to
track points located on the torso, hip, knee, ankle and foottip, on the left side of the body. In Figure 2, the marker positions are shown as well as the side force apparatus. Two
additional markers were used to deﬁne a plumbline in order to determine the vertical reference for data postprocessing. Calibration data were collected for the axes orientation(plumbline and treadmill direction) and the zero positionsof the markers during static standing, for every subject.

3 Experimental Results
The aims of this study were (1) an investigation of thepossibility to realistically simulate a side slope by means ofan externally applied force, and (2), in the case of a positive
result, the establishment of a force-slope analytical relationthat could be used in order to actually implement such asimulation in a locomotion interface.
To compare the gait data for the real and simulated walking, the following angles have been computed starting fromthe markers’ 3D positions:

 the upper body angle in both sagittal and frontal
planes; the hip, knee and ankle angles, that are typically used
to parameterize 2D gait in the sagittal plane [3];

 the thigh and ankle abduction angles (formed with thesagittal plane). The last is projected onto the frontal
plane.

In Figure 1 a layout of the experimental procedure andthe above mentioned reference planes are sketched, while
Figure 3 shows the angles in both the sagittal and frontal
planes. The abduction angles and the upper body orientation in the frontal plane seemed particularly useful for analyzing the effects of side slope and force. Indeed no particular effect is expected in the sagittal plane since all the perturbations (both geometric and static) occur in the frontal
plane.
Figures 8 and 9 show the results (mean angles values)
over all subjectss and all applied slopes and forces, at a 3

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15

15

Ankle abduction mean angle [deg]Exp. data
Fitting

Figure 3. Reference angles sketch.

10

10

5

5

0

0

−5

−5

−10

−10

−15

−15

−20
−20

−10

0

10

20

Real side slope

km/h walking speed. The corresponding ranges are reported
in Figures 10 and 11.
The plots refer to the tracking of the subject’s left side
only, but the data have been collected over symmetric intervals. Opposite points (i.e. slope 16o and +16o ) can be
regarded as data collected from the two opposite legs in thesame walking conditions.
From previous experiments on uphill slopes [5], it wasdetermined that one of the most linear features with slope isthe hip range, but from Figure 10 it is clear that this relation
no longer holds for side slope walking. Instead, from Figure 9 it can be seen that the only feature that varies consistently with the side slope is the ankle abduction mean angle.
Thus, on side slope walking, the subjects basically maintainthe same walking posture and simply change the ankle abduction angle in order to adapt the foot to the current ﬂoor
inclination. Indeed the thigh abduction mean angle is unchanged, thus showing that the legs continue to lie on thesame plane as in level walking.
By similar considerations for the case of side force walking, it can be seen that, again, the ankle abduction mean angle varies consistently with slope, thus providing a reliableequivalence mean between the real and the simulated sideslope.
Nevertheless, by applying a side force this is not the only
effect that is achieved. The thigh mean angle changes as
the subject widens the legs in order to provide a more stable support to contrast the lateral force, see Figure 9. Thismeans that the relative position of the legs with respect tothe treadmill platform is the same, but, since the platform is
now horizontal, the absolute orientation of the subject’s legswith respect to the vertical reference must have changed.
The other features being basically equivalent, both in realslope and in the simulated one, leads to the conclusion thatthe gait of the subjects, in the two different conditions, werepractically the same, thus providing a biomechanical proof

−20
−0.2

−0.1

0

0.1

0.2

Applied fractional force

Figure 4. Equivalence of applied fractional
force to real slope, for one subject, on thebasis of ankle abduction mean angle.

of the simulation method validity.
Moreover a good linear relation seems to hold between
the ankle abduction mean angle and both the side slope andthe applied force, thus providing a good basis to ﬁnd a linear
relation between the simulated slope and the applied weight.
This is carried on in the following section.

4 Relation between Simulated Side Slope andLateral ForceTo compare results across subjects, it is necessary to normalize the lateral forces W according to each subject’s massm, which ranged from 46.5 to 75.5 kg. The ratio of lateralforce to body weight mg is termed the applied fractional
force F = W=mg . By comparing the plots of ankle abduction angle versus side slope  and versus applied fractional
force, a relation could be determined between side slope andapplied lateral force.

 For every subject, the data of side force versus ankle
abduction angle was replotted in terms of applied fractional force (right side of Figure 4).

 A straight line was ﬁt between the ankle abduction angle and the real slope (left side of Figure 4).

 An applied fractional force was correlated to a sideslope by matching the ankle abduction angles using thestraight-line ﬁt above.

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Table 1. Summary of interpolation resultsover individual subjects. Speed = 3 km/h
k1

k0

0.922
0.985
1.242
0.798
0.853
0.900
0.900
0.811
0.768
1.001
0.839

0.002
0.038
0.000
-0.014-0.0010.001-0.027-0.0320.018-0.051-0.023

Stnd.D.
0.011
0.030
0.039
0.009
0.007
0.013
0.011
0.012
0.022
0.020
0.011

Corr. C.
0.997
0.977
0.938
0.996
0.999
0.993
0.996
0.994
0.986
0.989
0.997

W =0

-0.123-2.187-0.012
0.978
0.091-0.0791.724
2.237-1.3192.902
1.562

Applied Fractional Force [ N / Body Weight ]Subject
1
2
3
4
5
6
7
8
9
10
11

Theor. value
mH = 75.5
fit.H
mL = 46.5
fit.L

0.25

0.2

sin(S)

0.15

0.1

0.05

0

−0.05

−0.1

−0.15

−0.2

−0.25

Table 2. Summary of interpolation resultsover individual subjects. Speed = 5 km/h
Subject
1
2
3
4
5
6
7
8
9
10
11

k1

k0

0.899
0.937
1.156
0.705
0.805
0.766
0.904
0.854
0.785
0.871
0.768

0.000
0.037
-0.003-0.013-0.003-0.002-0.031-0.0300.017-0.027-0.007

Std. Dev.
0.013
0.037
0.030
0.007
0.013
0.013
0.011
0.008
0.014
0.014
0.015

Corr. C.
0.995
0.965
0.964
0.998
0.997
0.992
0.996
0.997
0.994
0.994
0.995

−20

W =0

-0.013-2.284
0.129
1.089
0.238
0.113
1.970
2.037
-1.251
1.800
0.551

=

= k1 tan  + k0  k1  + k0
(1)
where the approximation tan    has a maximum error of
only 2:6% at the slope of 16o . The individual interpolationWmg

results are summarized in Tables 1-2.
For the 3 km/h walking speed, the means of the results
for all subjects is:
k13km=h= 0:911k03km=h= 0:008

−10

−5

0

5

10

15

20

Side slope [deg]A simple theoretical model predicts a relation W=mg
, but because the data do not exactly ﬁt this theoreticalmodel a more general straight-line equation was ﬁt:

tan

−15

(2)

with mean standard deviation of error of 0.016 and correlation coefﬁcient of 0.987. The fact that the intercept k0
is not zero is due to experimental errors. For a subject of
70 kg, this means an error of about 5.5 N at zero slope (orFigure 5. Interpolation of fractional force versus real perceived slope. Raw experimental
points and ﬁttings are shown for the lightest
and heaviest subject. Speed = 3 km/h.
0
k0 =k1 rad: o in terms of slope at zero force
for the inverse relation). In Figure 5 the line of the theoreti is also given.
cal relation W=mg
For the 5 km/h walking speed, there are no substantialchanges but a slight general increase of the ranges over all
measured angles. In this case the ﬁtting over all subjects
provides the following mean results:=[ ] = 05
= tan( )k15km=h= 0:859

k05km=h= 0:0057(3)

with mean standard deviation of error of 0.015, correlation
coefﬁcient of 0.989, and a slope error at zero force of : o .
In Figure 5 the raw data and the interpolation for thelightest and heaviest subject are compared for the 3 km/h
walking speed. Since the lateral forces were the same overall subjects, the fractional force varies over a wider range
for a light subject than for a heavy one. As a consequence
there are more data points for small values of slopes andfractional forces than for large ones.
The similarity shows that normalization based upon a
subject’s weight has identiﬁed a general trend across subjects. While the relation between side slope and applied
fractional force is strongly linear for all subjects, there isa signiﬁcant variation in slope for different subjects,  : .
Since the mean coefﬁcients k13km=h and k15km=h are also
very similar to each other, the general trend seems to hold
across walking speeds.

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0 37

02

Lateral ForceSide Slope [deg]
60

60

−10

−120N

+10

50

40

40

Knee angle

50

Knee

30

20

30

20

10

10

0

0

−10
−35

+120N

−30

−25

−20

−15

−10

−5

0

5

10

Ankle abduction angle

−10
−35

−30

−25

−20

−15

−10

−5

0

5

10

Ankle abduction angle

Figure 6. Ankle abduction/knee cyclograms
for a single subject walking on a real slope of10o. Speed = 5 km/h

Figure 7. Ankle abduction/knee cyclograms
for a single subject walking with an appliedlateral force of 120 N. Speed = 5 km/h

That the k1 coefﬁcients are less than 1 means that asmaller lateral force than predicted by the simple model
W = mg tan  is required, roughly 90%. This is consistent
with previous tether force studies: 80% of predicted force
for inertial force display [1] and 65% of predicted force for
uphill force display [5].

be reliably established yet. Nevertheless, a value of roughly
90% of the theoretical lateral force is probably good enoughfor locomotion display purposes without the need for tuningfor each individual.
That this proportionality coefﬁcient is less than 1 is not
surprising, since in previous studies a correction factor of
about 0.65 had already been established for uphill slopes [4]and 0.8 for inertial forces [1]. A thorough investigation for
the reason for these discrepancies awaits further analysis.
Nevertheless, a ﬁrst explanation on the difference between
the fractional force that is required in the sagittal and frontal
planes (simulation of uphill and side slope respectively) canbe intuitively found by energetic considerations.

5 Discussion
In this paper a ﬁrst result for the understanding and implementation of side slope simulation on treadmill style locomotion interfaces has been presented. The existence ofa linear relation, between the mean abduction ankle angle
and both the real side slope and the lateral applied fractional force, has been proven by experimental results. Examples of cyclograms for ankle abduction versus knee angle
are reported in Figures 6 and 7 for both the real and simulated slope. The cyclograms show a close similarity bothfor shape and position.
The ankle abduction angle has been used as a biomechanical basis of equivalence between side slope and lateral force. The results demonstrate that a side slope 
can be simulated by application of a lateral force W =k1 mg. The proportionality coefﬁcient k1 is around 0.9(0.88 with standard deviation of 0.12), and shows somevariation across subjects and walking speed. A more precise
and reliable proportional value could be deﬁned by further
experiments over a larger number of subjects. Since only
two walking speeds, 3 km/h and 5 km/h, were employed,a more exact relation with respect to walking speed cannot

 In uphill walking, the slope acts in the walking direction, requiring a net work for subjects to advance andincrease their potential energy (even if this does nothold in tilted treadmill walking). So the main goal of
the simulation force is matching the energy cost of thereal uphill walking.
 In the side slope experiments, instead, the slope acts ina direction that is orthogonal to that of walking. So,
theoretically, no different power is required to the user
to advance. The lateral static balance is the main factor
affecting the choice of the simulation force.
An interesting test would be that of performing the complimentary experiments of side walking on a side slope (energy involved) and side walking on a uphill slope (balance
involved).

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However the biomechanics of the human body itself
must be taken into account. The human body, indeed, is particularly suited to control the balance in the sagittal plane(that is the main plane of swing during normal walking).
Consistent lateral perturbations, instead, are much more uncommon to us, and balancing against side forces is more
difﬁcult [9]. Indeed, in the performed experiments, thesubjects showed a particular difﬁculty in balancing themselves while walking with an applied lateral force. This resulted also in a slight increase of the frontal angles ranges
in the case of lateral force with respect to side slope (lastthree graphs of Figures 10 and 11), as well as a generalhigher standard deviation across subjects. This difﬁculty
was higher at the lower speed, when the natural step-bystep balance correction process occurs at a lower rate.
The results of this paper further support the notion thatgeneral slopes can be displayed without tilting the treadmill platform. This can simplify the locomotion interface
design while providing additional beneﬁts from torso force
feedback, such as inertial force display and collision forces.
The results therefore support the next step of building anactive force display in the side direction, adding to the existing force display of the Treadport in the frontal direction. Such planar torso force feedback would be usefulfor any treadmill-style locomotion interface, including twodimensional belt surfaces [2, 8]. The active side force could
also assist users to balance by a combination of position andforce control. More complete body tracking would probably be required to infer a subject’s lean.

[4] Hollerbach, J.M., Mills, R., Tristano, D., Christensen,
R.R., Thompson, W.B. and Xu, Y. 2001. “Torso force
feedback realistically simulates slope on treadmillstyle locomotion interfaces.” Intl. J. Robotics Research. 20:939-952.
[5] Hollerbach, J.M., Xu, Y., Christensen, R., and Jacobsen, S.C. “Design speciﬁcations for the second generation Sarcos Treadport locomotion interface” Haptic Symposium, Proceedings of ASME Dynamic Systems and Control Division, DSC-Vol.69-2, Orlando,
FL, November 2000, pp. 1293–1298.
[6] Hollerbach, J.M., “Locomotion interfaces,” in: Handbook of Virtual Environments Technology, K.M. Stanney, ed., Lawrence Erlbaum Associates, Inc., 2002,
pp. 239-254.
[7] Iwata, H. 2000. Locomotion interface for virtual environments. Robotics Research: The Ninth International Symposium. pp. 275-282.
[8] Iwata, H., and Yoshida, Y. 1999. Path reproduction
tests using a Torus Treadmill Presence: Teleoperators
and Virtual Environments. 8:587-597.
[9] Leroux, A., Fung, J., Barbeau, H. 2002. Postural
adaptation to walking on inclined surfaces: I. Normal
strategies. Gait & Posture, Vol. 15, pp.:64-74.

6 Acknowledgments[10] Noma, H., Sugihara,T., and Miyasato, T. “Development of ground surface simulator for tel-E-merge system”. Preceedings of IEEE Virtual Reality 2000,New
Brunswich, NJ, March 2000, pp.217-224.

This research was supported by NSF Grants
ITR/SY(IIS)-0113996 and ITR/SY-0121084, and by
the Telecommunications Advancement Organization ofJapan. We acknowledge the technical assistance of Mamoru
Saijyo.

[11] Noma, H., and Miyasato, T. “Design for locomotion interface in a large scale virtual environment. ATLAS:ATR Locomotion Interface for Active Self Motion”. Preceedings of ASME Dynamic Systems andControl Division, DSC-Vol. 64, 1998, pp.111-118.

References[1] Christensen, R.R., Hollerbach J.M., Xu, Y., and Meek,
S.G. 2000. Inertial-force feedback for the Treadport
locomotion interface. Presence: Teleoperators andVirtual Environments. 9: 1-14.
[2] Darken, R.P., and Cockayne, W.R. 1997. The OmniDirectional Treadmill: a locomotion device for virtualworlds. Proc. UIST. pp. 213-221.
[3] Goswami, A. 1998. A new gait parameterization technique by means of cyclogram moments: application tohuman slope walking. Gait & Posture. 8:15-36

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MEAN angles [deg]MEAN angles [deg]

40
40

0
10

20

−20
−150
40

−10

0

10

20

Ankle

100
80
−10

0

10

20
Upper sagittal

60
−20
10

0

−10
−20
20

−10

0

10

20

0

−20
−20

−10

0

10

Upper frontal

Ankle abd.

0
−20
−20
10

−10

0

10

20

0
−10
−20

0

50

100

150

−100

−50

0

50

100

150

−100

−50

0

50

100

150

−100

−50

0

50

100

150

−100

−50

0

50

100

150

−100

−50

0

50

100

150

−100

−50

0

50

100

150

80
60
−150
10

0

−10
−150
20

0

20

−10

0

10

20

Side Slope [deg]Figure 8. Mean angles over all subjects walking on a real side slope. Standard deviation
across subjects is aslo shown.

0
−20
−150
10

Upper frontal

Ankle abd.

20

−50

100

−20
−150

20

−100

20

0
−150
120

Thigh abd.

Ankle
Upper sagittal

0

20

0
−20
120

Thigh abd.

−10

0

Knee

Knee

−20
−20
40

20

Hip

Hip

20

0
−10
−150

Side force [N]Figure 9. Mean angles over all subjects walking with an applied side force.

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Angles RANGE [deg]
50

40

40

30

Hip

Hip

Angles RANGE [deg]
50

20
10
−20

20

−10

0

10

10
−150

20

Ankle

Knee

60

−10

0

10

20
Upper sagittal

10

−10

0

10

20
Thigh abd.

20
10
−10

0

10

20

−10

0

10

15
10
−10

0

10

20

Side Slope [deg]Figure 10. Measured ranges over all subjects
walking on a real side slope. Standard deviation across subjects is aslo shown.

−150
20

100

150

−100

−50

0

50

100

150

−100

−50

0

50

100

150

−100

−50

0

50

100

150

−100

−50

0

50

100

150

−100

−50

0

50

100

150

−100

−50

0

50

100

150

10

0
−150
30
20
10

20

0
−150
25

20

20

5
−20

50

40

0
−150
40

20
Ankle abd.

Ankle abd.

0

30

0
−20
25
Upper frontal

−10

10

0
−20
40

0

20

Upper frontal

Thigh abd.

Upper sagittal

20

0
−20

−50

60
40
−150
60

20

40

−20
20

−100

80

Ankle

Knee

80

40
−20
60

30

20
15
10
5
−150

Side force [N]Figure 11. Measured ranges over all subjects
walking with an applied side force.

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