Accepted for publication at the IEEE International Conference on
Rehabilitation Robotics (ICORR), 2023

# Virtual Physical Coupling of Two Lower-Limb Exoskeletons

Emek Barış Küçüktabak1,2, Yue Wen1, Matthew Short1,3, Efe Demirbaş2, Kevin
Lynch2, and Jose Pons1,2,3 1 Legs and Walking Lab of Shirley Ryan AbilityLab,
Chicago, IL, USA2 Center for Robotics and Biosystems of Northwestern
University, Evanston, IL, USA3 Department of Biomedical Engineering,
Northwestern University, Evanston, IL, USA

###### Abstract

Physical interaction between individuals plays an important role in human
motor learning and performance during shared tasks. Using robotic devices,
researchers have studied the effects of dyadic haptic interaction mostly
focusing on the upper-limb. Developing infrastructure that enables physical
interactions between multiple individuals’ lower limbs can extend the previous
work and facilitate investigation of new dyadic lower-limb rehabilitation
schemes.

We designed a system to render haptic interactions between two users while
they walk in multi-joint lower-limb exoskeletons. Specifically, we developed
an infrastructure where desired interaction torques are commanded to the
individual lower-limb exoskeletons based on the users’ kinematics and the
properties of the virtual coupling. In this pilot study, we demonstrated the
capacity of the platform to render different haptic properties (e.g., soft and
hard), different haptic connection types (e.g., bidirectional and
unidirectional), and connections expressed in joint space and in task space.
With haptic connection, dyads generated synchronized movement, and the
difference between joint angles decreased as the virtual stiffness increased.
This is the first study where multi-joint dyadic haptic interactions are
created between lower-limb exoskeletons. This platform will be used to
investigate effects of haptic interaction on motor learning and task
performance during walking, a complex and meaningful task for gait
rehabilitation.

##  I Introduction

During shared motor tasks, humans physically interact with one another by
exchanging forces to coordinate their movements. A common example of this
occurs during physical therapy, where clinicians provide physical support to
patients with sensorimotor impairments in order to assist them in regaining
lost motor functions (e.g., guiding paretic limb foot-placement during post-
stroke gait therapy). With recent advancements in human-robot interfaces,
various aspects of complex physical behaviors have been explored by using
robotic devices to render virtual physical environments (e.g., spring-damper)
between two or more individuals [1]. With this approach, individuals can
interface with separate robotic end effectors and move independently with one
or more degrees of freedom (DoF) while experiencing forces based on their
position and/or velocity relative to a partner’s.

Considering the positive outcomes observed in assistive and resistive training
methods [2], collaborative and competitive physical dyadic interaction has
great potential for improved task performance and individual motor learning
[1]. Upper-limb studies in this field have shown that individuals are able to
track sinusoidal trajectories more accurately while haptically coupled with a
partner, and that these improvements are dependent on the skill level [3, 4,
5] and the properties of the virtual connection [6]. Moreover, some findings
indicate that training while haptically coupled to a partner through a
compliant connection improves the rate of individual learning after the
coupling is removed, in the context of 1-DoF position tracking [7] as well as
multi-DoF adaptations to visuomotor rotations [3] and force fields [8]. Though
further investigation is warranted to generalize findings across motor tasks,
studying human-human physical interaction has great promise in the development
of more naturalistic controllers and interventions for individuals with
neurological impairments.

Most work involving haptic coupling between individuals has focused on upper-
limb tasks, and there is limited evidence of similar behaviors in the lower
limbs, despite the clear need for improved control methods in lower-limb
robotic therapy [9]. Our group was the first to explore haptic interactions
between pairs of individuals (dyads) performing 1-DoF ankle movements,
developing infrastructure for different interactive scenarios (e.g.,
collaboration, competition) and coupling properties (e.g., soft, hard), as
described in Kim et al. [10]. In an initial study involving a sinusoidal
tracking task, we found that healthy individuals improved their tracking
accuracy during compliant haptic coupling with a partner, and that these
improvements were linearly related to the abilities of each partner (i.e.,
tracking with a better partner resulted in greater improvements) [11].
Additionally, we observed no difference in short-term, individual learning
rates when comparing training alone or with a partner, consistent with the
aforementioned upper-limb studies [7, 12, 5], indicating some similarity
between upper- and lower-limb responses to human-human interaction.

One limitation of the lower-limb infrastructure mentioned above is that the
system can only support evaluation of seated, single joint movements which may
lack translation to ambulatory activities critical for a healthy lifestyle
[13]. In physical rehabilitation for lower-limb motor impairments associated
with stroke, for instance, there is a focus on multi-joint coordination,
usually through repetitive gait training supported by a therapist and/or
robotic device in order to gradually achieve kinematics and muscle activation
patterns which resemble unimpaired gait [14]. With this in mind, we have
developed a control scheme for floating-base lower-limb exoskeletons with
feet, capable of interaction torque control during walking [15]. This approach
also allows us to render virtual physical coupling between two or more
individuals wearing these devices. In this paper, we demonstrate the
feasibility of rendering virtual spring and damper elements between two
individuals during treadmill walking. To the best of our knowledge, this is
the first study where virtual physical coupling is created between two multi-
DoF lower-limb exoskeletons during walking.

##  II Methods

###  II-A System Description

Two lower-limb exoskeletons (ExoMotus-X2, Fourier Intelligence, Singapore),
shown in Figure 1, were adapted and used as a platform to test the proposed
dyadic physical interaction scheme. The X2 exoskeleton is designed for
overground walking, has four total active DoF at the hip and knee joints,
allows passive motion at the ankle joints, and has feet that help transfer its
weight to the ground.

Figure 1: ExoMotus-X2 lower-limb exoskeleton (left) and its modified version
with a user (right).

The exoskeletons were modified to include an IMU on the backpack to measure
the angular orientation and four strain gauges at each of the hip and knee
joints to measure torques. Furthermore, one exoskeleton was equipped with a
custom sensorized sole with 16 force sensitive resistors at the bottom of the
foot. The other exoskeleton was used on a sensorized treadmill with eight
3-DoF force plates (9047B, Kistler). Measurements from these sensors were used
to estimate the continuous gait states.

Communication with motors and onboard sensors was established over CAN bus
using the CANOpen communication protocol. To minimize communication delay and
allow real-time visualization, an external PC was connected to both
exoskeletons by tethers. The controllers were implemented on a ROS and C++
based open-source software stack called CANOpen Robot Controller (CORC) [16]
and were run at 333 Hz on the external PC.

A Unity application was created to provide visual feedback of a reference
trajectory for the ankle position and to visualize the state of the user. The
communication between the CORC and the Unity application was obtained through
ROS serialized messages. This visual feedback through Unity application was
available only to user A.

Two separate instances of the whole-exoskeleton closed-loop compensation
(WECC) controllers [15] receive the desired interaction torque values, which
are commanded by the _virtual coupling_ node. This node subscribes to the
instantaneous states of both exoskeletons and sends the desired interaction
torques based on the properties of the virtual physical coupling. The overall
communication scheme is shown in Figure 2.

WECC control compensates for the whole-body dynamics of the exoskeleton and
can render zero or nonzero interaction torques. In this control loop,
interaction torques between the human and exoskeleton are calculated using the
joint torque measurements during the whole gait cycle. Then, with a virtual
model controller, interaction torque errors are converted to desired
acceleration commands. Desired acceleration commands are fed into a
constrained optimization scheme to track the reference values under physical
and safety limitations. Interested readers may refer to [15] for the details
of this interaction torque controller and the whole-body model of the used
exoskeleton.

Figure 2: Overall schematic of the dyadic interaction.

###  II-B Physical Dyadic Interaction

The main characteristics of the virtual coupling can be divided into three
groups: (1) properties of the virtual coupling (e.g., stiffness, damping), (2)
interaction space (i.e., joint space, task space), and (3) directionality
(i.e., unidirectional, bidirectional). In this validation study, we focus on
rendering virtual spring and damper elements with different characteristics.

####  II-B1 Interaction in joint space

Interaction in the joint space is created by commanding interaction torques
based on differences in the instantaneous positions and velocities of the
users’ joints. Desired interaction torques for the bidirectional case are

$\begin{split}\bm{\tau}_{\text{int}}^{\text{A}}&=\bm{K}(\bm{q_{\text{A}}}-\bm{q_{\text{B}}}-\bm{q^{0}})+\bm{C}(\dot{\bm{q}}_{\text{A}}-\dot{\bm{q}}_{\text{B}})\\\
\bm{\tau}_{\text{int}}^{\text{B}}&=-\bm{\tau}_{\text{int}}^{\text{A}},\end{split}$
(1)

where $\bm{K}\in\mathbb{R}^{4\times 4}$ and $\bm{C}\in\mathbb{R}^{4\times 4}$
are the diagonal torsional stiffness and damping matrices, respectively. The
variables $\bm{q_{\text{A, B}}}\in\mathbb{R}^{4}$ represent the hip and knee
joint angles from both legs of user A and B. The neutral angles of the spring
are shown by the vector $\bm{q^{0}}\in\mathbb{R}^{4}$.

####  II-B2 Interaction in task space

In addition to rendering torsional elements between the joints, it is also
possible to render linear physical elements between any two points of the
users on their lower limbs. To demonstrate this, we rendered virtual linear
spring and dampers between the swing ankle positions of the users in the
sagittal plane.

The force due to the virtual elements for the bidirectional case is

$\begin{split}\bm{F}_{\text{int}}^{\text{A}}&=\bm{K}(\bm{r_{\text{A}}}-\bm{r_{\text{B}}}-\bm{r^{0}})+\bm{C}(\dot{\bm{r}}_{\text{A}}-\dot{\bm{r}}_{\text{B}})\\\
\bm{F}_{\text{int}}^{\text{B}}&=-\bm{F}_{\text{int}}^{\text{A}},\end{split}$
(2)

where $\bm{r_{\text{A,B}}}\in\mathbb{R}^{2}$ is the swing ankle’s horizontal
and vertical position expressed in a coordinate frame attached to the stance
ankle which is assumed to be fixed on the ground. $\bm{r_{\text{A,B}}}$ are
functions of hip and knee joint positions and angle of backpack with respect
to the gravity vector. Horizontal and vertical stiffness and damping are
expressed with diagonal $\bm{K}\in\mathbb{R}^{2\times 2}$ and
$\bm{C}\in\mathbb{R}^{2\times 2}$ matrices, respectively. The neutral
horizontal and vertical length of the spring are represented by
$\bm{r^{0}}\in\mathbb{R}^{2}$.

The resultant torques determined by the virtual linear forces on the ankle are
calculated and sent to the interaction torque controllers as shown in Equation
3.

$\bm{\tau}_{\text{int}}^{\text{i}}=\bm{J_{\text{i}}^{T}}\bm{F}_{\text{int}}^{\text{i}},\;\>i\in\\{\text{A},\text{B}\\},$
(3)

where $\bm{J_{\text{i}}^{T}}\in\mathbb{R}^{5\times 2}$ is the Jacobian of the
swing ankle expressed in the coordinate frame of the stance ankle. Note that
this results in five-dimensional desired interaction torques, which include
the backpack as well as the hip and knee joints. Moreover, even though the
virtual connection is created between the swing ankles, the effect of the
connection is felt on all joints including the stance leg.

####  II-B3 Unidirectional interaction

In clinical scenarios where a therapist needs to assess the capabilities of a
patient or demonstrate a desired motion, it might be beneficial to implement
this virtual physical coupling as unidirectional (i.e., only one user feels
forces due to the virtual coupling). In such cases,
$\bm{\tau}_{\text{int}}^{\text{A}}$ and $\bm{F}_{\text{int}}^{\text{A}}$ in
Equations (1) and (2), respectively, can be set to zero to provide haptic
transparency to one of the users.

###  II-C Validation Setup

A preliminary validation experiment was conducted on an able-bodied dyad to
evaluate the performance and technical feasibility of the proposed framework.
The demonstration of the infrastructure is also shown in this
video111https://tinyurl.com/ExoDyad.

Two users walked on treadmills simultaneously under different virtual physical
connections. In addition, user A received visual feedback displayed on a
monitor in some trials. The experimental setup is shown in Figure 3.

Figure 3: Validation setup with a dyad.

One minute treadmill walking was done under the the following conditions with
interactions in joint space:

  * •

No connection (NC). Both users walked in _haptic transparency_ mode with zero
desired interaction torques.

  * •

Bidirectional soft connection with zero neutral angle
($\bm{K}=30~{}\text{Nm/rad},\bm{C}=4~{}\text{Nms/rad}$).

  * •

Bidirectional hard connection with zero neutral angle
($\bm{K}=70~{}\text{Nm/rad},\bm{C}=10~{}\text{Nms/rad}$).

  * •

Bidirectional hard connection with $\bm{q}^{\text{hip}}_{0}=30^{\circ}$.

  * •

Bidirectional hard connection with $\bm{q}^{\text{knee}}_{0}=20^{\circ}$.

  * •

Unidirectional harder connection with zero neutral angle while only user A
receives the visual feedback of the desired and actual position of his left
ankle, and only user B feels the coupling force
($\bm{K}~{}=~{}100~{}\text{Nm/rad},\bm{C}~{}=~{}10~{}\text{Nms/rad}$).

Treadmill speeds were set to 0.8 km/h. A relatively slow speed was chosen as a
safety precaution during the connected trials. The treadmills of both users
were manually started around the same time. For each of the conditions, the
initial two gait cycles were not used in the analysis.

In the unidirectional condition, the desired ankle trajectory for user A was
obtained by scaling up the displacement magnitude of the recorded ankle motion
of a previous experienced user by 20% along the vertical direction and 35%
along the horizontal direction in a hip-centered coordinate frame similar to
the study of Marchal-Crespo et al. [17]. The desired trajectory was only for
the left ankle, and no feedback was provided for the right leg. This resulted
in an asymmetric desired gait pattern. The visual feedback is presented in
Figure 2.

For the task space interaction, a preliminary test was conducted with both
subjects stationary in single stance (no walking). Unidirectional spring and
damper elements were rendered between the vertical positions
($\bm{K_{y}}~{}=~{}250~{}\text{N/m},\bm{C_{y}}~{}=~{}50~{}\text{Ns/m}$) of the
user’s ankles. The leader (user A)’s robot rendered zero interaction torques
while the follower (user B)’s robot rendered interaction torques determined by
the unidirectional spring and damper elements. User A was asked to move his
ankle vertically several times, and user B was asked to follow the forces he
experienced. The users were not able to see each other during the task space
interaction experiments.

##  III Results

###  III-A Rendering Different Stiffness

Figure 4: Joint angles of users A and B with respect to normalized gait
duration during different interaction properties. The data includes all steps
of both legs during the one-minute trials. The shaded area represents $\pm$
one standard deviation.

Figure 4 shows the joint angles of the users during no connection (NC), soft
interaction and hard interaction with zero neutral angles. Note that the NC
plots are normalized with respect to the individual heel strikes of each user;
the horizontal axes of the plot does not include any temporal correlation
between the users in this non-connected trial.

During the NC condition, we observed that user B had a smaller range of motion
for his hip and knee joints compared to user A. The peak angle difference
between the subjects during the NC condition was around 20∘ for both the hip
(at 80% of gait duration) and knee (at 0% of gait duration) joints. For the
soft and hard interaction conditions, these differences decreased to 12∘ and
8∘, respectively, at the hip joints. For the knee joint, the connection
resulted in 6∘ and 4∘ difference during the soft and hard interactions,
respectively, at the heel strike instances. It is worth noting that the
$x$-axes of the connected trials are normalized with respect to user A’s heel
strikes for both users. This shows that the connected trials also resulted in
synchronization in the time domain.

Figure 6 presents the mean absolute joint angle differences between user A and
user B. It was seen that the average differences were 10∘, 6∘, and 3∘ at the
hip joint for NC, soft and hard conditions, respectively. At the knee joint,
average differences were observed as 11∘, 5∘ and 3∘.

###  III-B Changing the Neutral Angle

Figure 5 shows the joint angles of each user with respect to the normalized
gait duration for the non-zero neutral angle conditions. For the non-zero
neutral angle at the hip, the hip joints of the users are offset from one
another while their knee joints are aligned and synchronized. Similar behavior
was also observed for the non-zero neutral angle at the knee as shown in
Figure 5 and 6. The right column of Figure 6 shows the mean absolute
difference in joint angles during these trials. The average difference in hip
and knee joints was 24∘ and 17∘ for the trials with non-zero
$q_{0}^{\text{hip}}$ and $q_{0}^{\text{knee}}$, respectively.

Figure 5: Joint angles of users A and B with respect to normalized gait
duration for virtual springs with different neutral angles. The data includes
all steps of both legs during the one-minute trials. The shaded area
represents $\pm$ one standard deviation. Figure 6: Mean absolute joint angle
difference between the users for trials with different stiffnesses (left) and
neutral angles (right). Mean absolute values of the whole gait cycle for each
leg are used as a single data point.

###  III-C Unidirectional Interaction

Joint angles during the trials with joint space unidirectional interaction are
presented in Figure 7. Following the visually-displayed, scaled ankle
trajectory resulted in an asymmetric gait for user A (leader, feels no
interaction force). The difference between his left and right legs during peak
flexion was around 15∘ and 36∘ for the hip and knee joints, respectively. The
unidirectional interaction also resulted in an asymmetric gait for user B,
even though he was not provided visual feedback. The difference between his
left and right legs during peak flexion was around 15∘ and 30∘ for the hip and
knee joints, respectively.

Figure 8 shows the vertical ankle positions of the users in the sagittal plane
during the task space unidirectional interaction trial. The leader voluntarily
moved his ankle vertically to a position of 40 cm, approximately. It was seen
that the unidirectional force applied to user B moved his ankle to around 30
cm in the vertical direction.

Figure 7: Hip and knee joint angles during joint space unidirectional
interaction trial. The data includes all steps of the one-minute trials. The
shaded area represents $\pm$ one standard deviation. Figure 8: Ankle vertical
position with respect to time during the task space unidirectional interaction
trial.

##  IV Discussion

###  IV-A Rendering Spring and Damper Elements with Different Characteristics

During the walking trial without interaction, user B used a smaller range of
motion for his knee and hip joints. This resulted in shorter, faster and
unsynchronized steps with respect to user A. As the stiffness of the virtual
connection increased during connected trials, the difference between each
users’ joint angles decreased, and their steps became more synchronized. In
connected trials, knee joint angles of the users were closer to each other
compared to their hip angles. This is because the same stiffness parameters
were used for the hip and knee joints, and the hip joints must carry a larger
weight than the knee joints. In future studies, larger stiffness parameters
can be used for the hip joint to overcome this difference.

Rendering virtual springs with non-zero neutral angles resulted in the users’
joints being pushed away from each other by an offset. This caused subjects to
“agree” on new gait patterns due to the forces they experienced. There was 6∘
and 3∘ difference on average between the neutral angles of the virtual springs
and observed mean absolute difference for the hip and knee joints,
respectively. This is due to the compliant nature of the rendered spring and
damper elements. Increasing the stiffness would enforce the neutral angle more
strictly while decreasing it would allow more deviation.

Figure 9: Desired interaction torques commanded to WECC and actual interaction
torques.

Desired and realized interaction torques are presented in Figure 9. It can be
seen that the difference between the desired and actual interaction torques
increases near the end of the gait cycle (during swing). This is due to the
fact that smaller control gains were used compared to [15] as a safety
precaution in these preliminary trials.

In the unidirectional trial, the leader (user A) demonstrated an asymmetric
gait while following the visually-displayed, scaled ankle trajectory. User B
was not provided the scaled desired trajectory. However, the proposed
framework allowed the information of this modified gait pattern to be
transmitted through the virtual physical coupling between the subjects.

###  IV-B Implementation of Interaction Modes

Physical interaction between two individuals can be divided mainly into three
modes [1]: (1) collaboration: partners work together to achieve a common goal,
(2) cooperation: partners have a common goal but different roles (e.g.,
teacher-student), (3) competition: partners can negatively affect one another
in pursuit of their goals.

In a clinical scenario, two impaired users can be provided with a visual
display of a desired gait trajectory depending on their needs. Different
interaction modes can be implemented by modifying the characteristics of the
virtual coupling. For example, a bidirectional interaction can be used for a
collaborative task where individuals help each other to better track the given
trajectory. This interaction mode can be useful for the initial stages of
rehabilitation, where users have limited ability due to their sensorimotor
impairments. Unidirectional interaction can be used for a teacher-student
scenario to demonstrate a desired trajectory through virtual physical
interaction. Moreover, virtual springs with large neutral angles or negative
stiffnesses can be used to generate conflicting goals between users for a
competitive task. This interaction mode can be useful in the later stages of
rehabilitation to promote motivation and higher exerted effort [2]. In future
studies, we will use this framework to implement these interaction modes,
investigating the effect of lower-limb haptic interaction on task performance
and individual motor learning.

###  IV-C Different Interaction Paradigms

In the case of significant differences between the users’ physical properties
(i.e., weight, strength), symmetric bidirectional spring and damper elements
might result in an unbalanced interaction in favor of the stronger user. In
these situations, two sets of unidirectional spring and damper elements with
different properties can be used to have a more balanced interaction (e.g., a
stiffer spring attached to the stronger user and a softer spring attached to
the weaker user).

In teleoperation, it is also common to create a two-port communication where
the force on user A is transmitted to user B while the velocity of user B is
transmitted to user A [18]. Such a virtual connection might be helpful in a
scenario where a therapist can apply corrective forces to the patient while
feeling how they move and their limitations. In future studies, these
different interaction paradigms can also be implemented into this framework.

###  IV-D Safety Considerations

The forces due to the virtual coupling might cause unexpected disturbances,
resulting in loss of balance, trembling or falls. Moreover, an unsafe movement
on one side would be transferred to the other user through the virtual
physical coupling. The WECC control running for both of the exoskeletons
limits the maximum joint velocity, torque and power as constraints in the
optimization scheme. However, it does not consider the balance of the user or
the effects of the virtual coupling between two exoskeletons. Therefore, in
future studies, it is necessary to implement higher-level safety precautions
that would consider the balance of each user and the stability of the physical
interaction.

##  V Conclusion

In this study, we developed an infrastructure to create virtual physical
coupling between the lower-limbs of two individuals. The desired interaction
torques are calculated and given to WECC control based on the properties of
the virtual environment and instantaneous kinematics of the users. In this
feasibility study, we tested the capability of this system to render virtual
environments with different properties (e.g., soft, hard, non-zero neutral
angle), directionality (e.g., unidirectional, bidirectional), and interaction
space (e.g., joint, task). In the future, we will validate the capabilities of
this infrastructure extensively with more users and implement additional
safety features. Moreover, this framework will be used for the investigation
how haptic interaction affects task performance and motor learning to improve
motor outcomes of robot-mediated stroke rehabilitation.

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