Towards Restoring Locomotion for Paraplegics: Realizing Dynamically Stable Walking on Exoskeletons

Towards Restoring Locomotion for Paraplegics:
Realizing Dynamically Stable Walking on Exoskeletons
Thomas Gurriet1, Sylvain Finet2, Guilhem Boeris2, Alexis Duburcq2, Ayonga Hereid3, Omar Harib3,
Matthieu Masselin2, Jessy Grizzle3 and Aaron D. Ames1
Abstract—This paper presents the first experimental results
of crutch-less dynamic walking with paraplegics on a lower-
body exoskeleton: ATALANTE, designed by the French start-up
company Wandercraft. The methodology used to achieve these
results is based on the partial hybrid zero dynamics (PHZD)
framework for formally generating stable walking gaits. A direct
collocation optimization formulation is used to provide fast and
efficient generation of gaits tailored to each patient. These gaits
are then implemented on the exoskeleton for three paraplegics.
The end result is dynamically stable walking in an exoskeleton
without the need for crutches. After a short period of tuning
by the engineers and practice by the subjects, each subject was
able to dynamically walk across a room of about 10 m up to a
speed of 0.15 m/s (0.5 km/h) without the need for crutches or
any other kind of assistance.
I. INTRODUCTION
Regaining autonomy in their daily lives through the ability
to walk again is a central aspiration for many people with
lower limb paralysis, i.e. paraplegics. Among the promising
solutions to restore locomotion are robotic devices that fit
around the legs of a user, called lower-limb exoskeletons for
rehabilitation. A comprehensive review of the state-of-the-
art lower-limb exoskeletons can be found in [10]. Research
in this field began in the early 1960s independently at the
Mihailo Pupin Institute in Belgrade [18], [26] and at the Uni-
versity of Wisconsin [15], [24]. The resulting exoskeletons
were able to physically advance the legs of a user, but the
user had to use crutches to maintain balance. Additionally,
there has been a broad body of work on different aspect of
exoskeletons [10], [25], [29] from assistive knee devices [11]
to soft exoskeletons [27]. Throughout the years, in addition to
regaining autonomy, clinical tests showed the health benefits
of walking for paraplegics: improvement of blood circulation,
of respiratory, urinary, and intestinal functions, and positive
psychological effects [20].
Due to the physical and psychological advantages of
exoskeletons, multiple companies have emerged over the past
decade and have started to commercialize their products for
*This work has been conducted under IRB No. 16-0693.
1Thomas Gurriet and Aaron Ames are with the Department of Mechanical
and Civil Engineering, California Institute of Technology, Pasadena, CA
91125. Their work was supported by NSF NRI award 1526519.
2Matthieu Masselin, Sylvain Finet, Guilhem Boeris and Alexis Duburcq
are with Wandercraft, Paris, France.
3Ayonga Hereid, Omar Harib and Jessy Grizzle are with the Department
of Electrical Engineering and Computer Science, Univ. of Michigan, Ann
Arbor, MI 48109. The work of A. Hereid was supported by NSF under
Grant CPS-1239037. The work of J. W. Grizzle was partially supported by
a gift from Ford Motor Company.
Fig. 1: Image of two paraplegic patients walking in the
ATALANTE exoskeleton developed by Wandercraft.
use in rehabilitation centers. Nevertheless, these exoskeletons
still have very limited capabilities: either they require the use
of crutches for balance or direction control, which is tiring
for the user [1], [2], or they provide slow static gaits with
velocities on the order of 0.05 m/s [3]. The ultimate goal
is to have a device that provides fast, robust and dynamic
gaits for safe daily use anywhere. By ”dynamic”, as opposed
to ”static”, we mean that the high level control goal is to
stabilize periodic motions that do not necessarily keep the
center of mass (or even of center of pressure) within a
support polygon of the feet. From an outside perspective,
during a step the exoskeleton is falling forward only to
have the swing foot reach out and catch the user before
beginning the process again. This is the behavior naturally
achieved by humans when they walk, and the objective is
thus to endow exoskeletons with these behaviors. The French
start-up company Wandercraft has emerged with the goal of
designing such devices [5].

Hybrid System Model Gait Optimization Simulations
Stable Dynamic Walking
Gait Tunning
Domain graph
Hybrid System
Nominal trajectory
generation
Model data
+
Fig. 2: The methodology developed that yielded dynamically stable exoskeleton walking experimentally for paraplegics.
Recent progress in the field of robotic bipedal locomotion,
both in terms of hardware development and control algorithm
design, is making dynamic locomotion on exoskeletons a
possibility. Of particular note for this work is the the method
of virtual constraints and hybrid zero dynamics (HZD method
for short) which has resulted in dynamic walking on multiple
robots by facilitating the design of gaits that are provably sta-
ble and experimentally realizable; they enforce the unilateral
ground contact as well as friction and input torque bounds
[8], [12], [13], [17], [28]. Virtual constraints are relations
between the joints or links of a device that are induced by
feedback control instead of a physical connection. They thus
induce a reduced-order dynamic model of the hybrid system
that is called the hybrid zero dynamics. The method of HZD
was extended to allow for multi-contact walking for robots
with feet in the context of partial hybrid zero dynamics, or
PHZD for short [7]. PHZD has been successfully realized
to achieve dynamic and efficient locomotion on humanoid
robots with feet [17], [22], [23] and, as a result, is a natural
framework in which to control exoskeletons with the goal of
dynamic and human-like gaits. Quite recently, preliminary
simulation results showed the application of PHZD to the
control of an exoskeleton worn by a paraplegic; see [6] for
details as well as later in the paper.
Wandercraft has designed an exoskeleton, named ATA-
LANTE, which has realized for the first time, using con-
trollers based on the PHZD method, dynamic stable walking
for paraplegics without the use of crutches or any other kind
of assistance (as illustrated in Fig. 1). This paper describes
the formal foundations along with the methodology used
for achieving this performance and presents some promising
experimental results: after a short period of tuning by on-
site engineers and practice by the subjects, each subject was
able to dynamically walk across a room of about 10 m up to
a speed of 0.15 m/s (0.5 km/h). Although it reports results
obtained with patients in clinical settings, it is not a clinical
report of any sort. Therefore, the contributions of this paper
are:
• The application of the PHZD method to the experimental
control of a lower-limb exoskeleton.
• The realization of dynamically stable walking for para-
plegics without the use of crutches or any other kind of
assistance.
The remainder of the paper is organized as follows (fol-
lowing the methodology in Fig. 2). Section II presents a
hybrid model of the human exoskeleton system and the
PHZD framework. This leads to our framework for the design
of stable dynamic walking gaits represented as a nonlinear
optimization problem under constraints. The resolution of this
problem using direct collocation is described in Section III.
Finally, Section IV presents the implementation of the gaits
on the exoskeleton and the experimental results.
II. MATHEMATICAL FOUNDATION
In this section, we summarize our approach for gen-
erating stabilizing controllers for the powered lower-limb
exoskeleton ATALANTE by building upon the (PHZD)-
based theoretical foundation [7]. More precisely, we utilize
the hybrid nature of bipedal locomotion and implement
stable periodic behaviors by enforcing invariant reduced
dimensional manifolds via virtual-constraint-based feedback
controllers. Because in these experiments, the user is not yet
able to use his or her upper body to select the speed of
the gait, the presentation does not require the decentralized
implementation presented in [6].
A. Hybrid System Model
ATALANTE is a lower-limb exoskeleton designed by the
French startup company Wandercraft. It is intended to be used
by paraplegics in medical center settings for rehabilitation.
The exoskeleton has 12 degrees of freedom (6 per leg).
Except for the ankle, where a special mechanism is mounted,

(a) Human Exoskeleton Model (b) Kinematic Tree
Fig. 3: Kinematic diagram of the human exoskeleton system.
The green links in (b) are adjustable in length.
each degree of freedom is independently actuated by a brush-
less DC motor. A digital encoder is mounted on each motor
to estimate joint position and velocity. Sensors installed in
the feet allow for impact detection when the feet hit the
ground. The exoskeleton is controlled by a central computer
board running a real-time operating system and in charge of
all high-level computations. The dimensions of ATALANTE
can be easily adjusted to fit the patient through mechanical
adjustments. The patient is secured to the exoskeleton by
means of fasteners located at the ankle, the shin, the thigh,
and the abdomen. ATALANTE is self-powered with a battery
pack.
One key assumption in the current paper1 is that the user’s
legs are rigidly attached to the exoskeleton and there is no
actuation from the human body. The upper human body is
modeled as a single rigid link—ignoring the relative motion
of the waist, neck and arm joints of the human—rigidly
attached to the pelvis of the exoskeleton. The lumped human-
exoskeleton system then can be modeled as a kinematic tree
of rigid links, as shown in Fig. 3. Specifically, we use floating
base coordinates: assuming Rb is a body-fixed reference
frame of the pelvis link with Cartesian position p ∈ R3 and
orientation φ ∈ SO(3) with respect to the world frame R0,
the configuration coordinates, Q, of the system, given as
q = (p,φ,qb) ∈ Q = R3
×SO(3)×Qb, (1)
represents the generalized coordinates of the system. The
body coordinates, qb ∈ Qb, represent the 12 actuated lower-
limb exoskeleton joints—each leg consists of 3 hip joints, 1
knee joint, and 2 ankle joints.
The dynamic behavior of bipedal locomotion is often
characterized as a hybrid system consisting of a series of
continuous phases (e.g., when the leg swings forward) and
discrete events (e.g. when the foot strikes the ground) [14].
In particular, we model the walking behavior of the human
1In [6] we allow the user to control the exoskeleton via upper body
posture; hence an articulated model of a human is used.
exoskeleton system as a hybrid control system (see [6] for
full definition):
H C = {D,U ,S,∆,FG}, (2)
where D ⊆ TQ is a smooth manifold representing the
admissible domain of the states, U is the admissible control
inputs, S ⊂ D is a switching surface, ∆ is the reset map of
the discontinuous dynamics, and FG is the control system
defined on the continuous domain. The definition of each
element of (2) is discussed briefly below.
Continuous Dynamics. For flat-footed walking, the contin-
uous domain D is determined by the planar contact of the
stance foot with the ground. Assuming the ground is rigid, we
will use holonomic constraints to model the contact, i.e., the
position and the orientation of the stance foot link remain
constant during the course of one step. Let µ(q) ∈ R6 be
the collection of stance foot position and orientation, the
kinematic constraint of the foot contact is J(q) ˙q = 0, where
J(q) = ∂µ(q)
∂q is the Jacobian of holonomic constraints.
Given the mass, inertia, and length properties of each link
of the human exoskeleton system, the equation of motion
(EOM) of the continuous dynamics is then determined by the
classical Euler-Lagrange equation and holonomic constraints
of the domain [14], [21]:
D(q) ¨q+H(q, ˙q) = Bu+JT
(q)F (3)
where D(q) is the inertia matrix, H(q, ˙q) = C(q, ˙q) ˙q + G(q)
is the vector containing the Coriolis and gravity term, B is
the actuator distribution matrix, u ∈ U ⊆ R12 is the actuator
inputs vector. The contact wrenches, F, can be calculated
by solving the second order derivative of the holonomic
constraints,
J(q) ¨q+ ˙J(q, ˙q) ˙q = 0, (4)
and (3) simultaneously. Substituting the closed form solution
of F yields the affine control system, FG, given as,
˙x = f(x)+g(x)u, (5)
with x = (q, ˙q) ∈ D being the state of the system.
Discrete Dynamics. When the swing foot hits the ground,
an instantaneous change in contact occurs. We denote the
triggering condition of the event as a guard S ⊂ D. Moreover,
we assume that the impact with the ground is perfectly
plastic. As a consequence, the joint configuration remains the
same during impact, but the joint velocities undergo a discrete
change. More precisely, using the derivation proposed by
Hurmuzlu et al. [19], we get:
˙q+
= I −D−1
(q+
)JT
(q+
)Ξ(q+
)J(q+
) ˙q−
:= ∆˙q(q) ˙q−
,
(6)
where, for simplicity, Ξ(q) = (J(q)D−1(q)JT (q))−1. This
discrete dynamics of the system can be captured as a reset
map, ∆, that maps the pre-impact states to post-impact states:
(q+
, ˙q+
) = ∆(q−
, ˙q−
) :=
q−
∆˙q(q) ˙q− . (7)

(a) Periodic Orbit (b) Hybrid Invariance
Fig. 4: Illustration of the hybrid invariant periodic orbit on
the partial hybrid zero dynamics (PHZD) surface. A PHZD
surface is constructed via choosing the proper parameters set
α through optimization.
Moreover, applying the feedback controllers to the hybrid
control system given in (2) yields a hybrid system model,
given as
H = (D,S,∆,F). (8)
with U = /0. In the next section, we introduce virtual con-
straints as a means to synthesize feedback controllers that
realize stable walking of the human exoskeleton system.
B. Partial Hybrid Zero Dynamics
At the core of our controller approach is designing a
set of virtual constraints that modulate the system behavior
in order to achieve certain desired trajectories [7], [28].
Enforcing virtual constraints results in a reduced dimensional
representation of the full order system that captures the
natural dynamics of the robot.
Virtual Constraints. For the particular case of the human
exoskeleton system with actuated ankle joints, we choose the
actual outputs to be a combination of velocity regulating term
ya
1 and position modulating terms ya
2. Specifically, the velocity
regulating term is chosen to be the forward hip velocity with a
constant desired velocity vd, and position modulating outputs
are chosen to represent the synchronized motion of the rest
of the mechanical system. The virtual constraints are defined
as the difference between the actual and desired outputs:
y1(q, ˙q,α) = ya
1(q, ˙q)−vd, (9)
y2(q,α) = ya
2(q)−yd
2(τ(q),α), (10)
where y1 and y2 are relative degree 1 and (vector) relative
degree 2 by definition, yd
2 is a vector of desired trajectories. In
this paper, we use Bézier polynomials to represent the desired
outputs with α being a set of Bézier coefficients, and τ(q)
the state-based timing variable for synchronization [6].
Feedback Linearization. With the goal of driving the virtual
constraints in (9) and (10) to zero exponentially, we use the
following feedback control law,
uα,ε
=−A −1 0
L2
f y2(q, ˙q,α)
+
Lf y1(q, ˙q)
2εLf y2(q, ˙q,α)
+
εy1(q, ˙q,α)
ε2y2(q,α)
, (11)
with a control gain ε > 0 and decoupling matrix
A =
Lgya
1(q, ˙q)
LgLf y2(q, ˙q,α)
, (12)
which is invertible due to the specific choice of virtual
constraints. Applying this control law to (5) yields linear
output dynamics of the form:
˙y1 = −εy1, (13)
ÿ2 = −2ε ˙y2 −ε2
y2. (14)
Under the control law, the system in (5) renders an invari-
ant reduced dimensional surface, termed as zero dynamics
[28]:
Zα = {(q, ˙q) ∈ D|y1(q, ˙q,α) = 0,
y2(q,α) = 0, ˙y2(q, ˙q,α) = 0}. (15)
Since the velocity ˙q undergoes a jump at impact (6), and vd
is a constant, then the output y1 necessarily undergoes a jump
(see (9)), and the zero dynamics surface cannot be invariant
through impact. Thus, we prefer to ignore this output and
consider the following partial zero dynamics surface, given
by:
PZ α = {(q, ˙q) ∈ D|y2(q,α) = 0, ˙y2(q, ˙q,α) = 0}. (16)
It is straightforward to show that the control law in (11)
renders the partial zero dynamics submanifold invariant, i.e.,
any solution that starts in PZ α remains in PZ α until
reaching a guard [7]. However, it is not necessarily invariant
through impacts. To this end, the set of parameters α is
constrained to be such that the partial zero dynamics is
invariant through impacts. There exists a set of parameters α
so that the submanifold PZ α is impact invariant if
∆(S∩PZ α ) ∈ PZ α (17)
A manifold PZ α is called hybrid invariant if it is invariant
through impacts, and thus the hybrid system in (8) has a
partial hybrid zero dynamics (PHZD), denoted as H |PZ α .
By enforcing partial hybrid zero dynamics, the full order
dynamics of the hybrid system can be captured in a reduced-
dimension dynamical system that is independent of control
inputs. Finding such parameters is typically formulated as a
nonlinear constrained optimization problem [7], [17].
Theorem 1. If the hybrid system H in (8) satisfies (17),
then there exists ε > 0 such that for all ε > ε the feedback
controller (11) yields a periodic orbit O = ι0(OPZ), for
OPZ ⊂ PZ α and ι0 : PZ α → D the canonical embedding,
that is a locally exponentially stable periodic orbit of H .
Importantly, this theorem implies that the robot represented
by the hybrid system H has an exponentially stable walking
gait. Space constraints do not allow for a proof of this result,
but it follows in a straightforward manner from the results of
[7].
Remark 1. Introducing partial zero dynamics not only allows
us to command a constant desired velocity, but also the
evolution of y1 is now solely determined via the linear output
dynamics given in (13) and is independent of τ. This allows
for a driving element that pushes the robot forward regardless
of the state of the phase variable.

III. GAIT GENERATION AND SIMULATIONS
Using the PHZD framework described above, we want to
design the desired profile of the virtual constraints that when
enforced leads to a stable walking gait. This is done through
a nonlinear constrained optimization process using direct
collocation. Others ways of solving the optimization can be
used like single shooting methods, but direct collocation was
found to be the fastest and most efficient way to solve this
problem [17]; stable walking gaits are obtained in minutes. In
this section we presents an overview of how we used direct
collocation to obtain stable dynamic walking gaits.
A. Direct Collocation Optimization
Direct collocation methods have been widely used for
trajectory optimization of dynamical systems governed by
ordinary differential equations [9], [16]. In this work, we in-
corporated the virtual constraints based feedback controller in
the direct collocation based trajectory optimization problem.
The PHZD constraint in (17) is enforced at impact, such that
the optimized trajectory is a hybrid invariant periodic orbit.
The end result is a set of parameters α for a stable walking
gait.
The mathematical foundation of the direct collocation
optimization is based on the finite step implicit Runge-Kutta
methods [9]. Specifically, we divide the continuous dynamics
solution into a fixed number of intervals. Let
0 = t0 < t1 < t2 < ··· < tN = TI, (18)
be the discrete time instances, a.k.a., nodes, defined at the
terminal of these intervals, where TI > 0 is the time at
which the swing foot hits the ground. Also, we introduce
xi, ˙xi, ui, and Fi as decision variables of the optimization
problem to approximate the state variables, control inputs,
ground reaction forces of the system at node i, and introduce
α∗ as decision variables for the virtual constraints param-
eters, respectively. Next, we modify the classical Hermite-
Simpson method over time intervals between two neighboring
even nodes. Specifically, the following equality constraints—
termed as defect constraints—are enforced:
˙xi
−3(xi+1
−xi−1
)/2∆ti
+(˙xi−1
+ ˙xi+1
)/4 = 0, (19)
xi
−(xi+1
+xi−1
)/2−∆ti
(˙xi−1
− ˙xi+1
)/8 = 0, (20)
for all i ∈ {1,3,··· ,N − 1}, where ∆ti = ti+1 − ti−1 is the
time interval. If the Lagrangian dynamics in (3) and holo-
nomic constraints in (4) are satisfied at each node, then the
piecewise cubic polynomials that connect all xi represent an
approximated solution of the differential equations in (5) [9],
[17].
Considering that our goal is to find virtual constraints
parameters instead of open-loop trajectories, we incorporate
the feedback controller into the optimization in a way that
is similar to holonomic constraints. Instead of enforcing the
control input ui directly as in (11), we impose equality
constraints on system states such that they satisfy the output
dynamics in (13) and (14). Further, the hybrid invariant
condition in (17) between states at the last and first nodes.
Fig. 5: Simulation of the gait for the exoskeleton with a
dummy inside.
For detailed setup of the optimization problem, we refer the
readers to [6].
In this work, we state the direct collocation based human
exoskeleton gait optimization to minimize the mechanical
cost of Transport (CoT), ΦCoT , of the gait, i.e.,
argmin
z∗
ΦCoT (z) (21)
s.t zmin ≤ z ≤ zmax, (22)
cmin ≤ c(z) ≤ cmax, (23)
where z is the set of all decision variables, and c(z) is a
collection of necessary constraints presented in [17]. Torque
limits and joint position and velocity limits of the ATA-
LANTE are directly enforced as boundary conditions of
decision variables in (22), whereas friction cone and zero
moment constraints of the foot contacts are enforced as
extra physical constraints. In addition, several constraints are
considered in the optimization in order to narrow down the
search space and address certain aspects specific to human-
friendly walking. Impact velocities, ZMP position, CoM
position and torso orientation are an example of the many
constraints that need to be considered.
A challenge arises here, as each patient has a specific mass
distribution and dimensions which lead to unique dynamics
for each individual. In order to accelerate this process, Wan-
dercraft has derived a fast way to recompute the dynamics for
each case, making it possible to rapidly adapt to new patients.
For now, the details of this process must be kept private to
protect the intellectual property of the company. The result
of this process (cf. Fig. 2) is a provably stable walking gait
that minimizes a cost function (eg. energy consumption) and
satisfies all of the desired constraints.
B. Simulation results
Even though the generated gaits are consistent with the
dynamics by design, with collocation optimization, this only
holds at the few specific node points selected for the virtual
constraints. Therefore, in order to verify the validity of these

Nominal
trajectory
Filtering
Impact detection
High level control
Tracking
Trajectory tracking
Low Level Hardware
Joints
targets
Current
targets
Actual joints
positions
Feet contact
sensors
Fig. 6: Structure of the control loop.
gaits, a feedback-linearizing controller tracking the nominal
outputs is implemented in a simulation. This way, the full
trajectory of the robot is recovered and the periodicity and
stability of the gait are assessed. The joint positions generated
by these simulations are then used as the nominal joint
trajectories to be tracked on the hardware. Gait tiles simulated
walking gait obtained via this procedure is shown in Fig. 5
with the corresponding phase portrait plotted in Fig. 7 as the
nominal gait (red), prior to modification of the trajectories on
the hardware (shown in blue). The fact that the phase portraits
are periodic orbits imply that a valid periodic walking gait is
generated.
IV. IMPLEMENTATION ON THE EXOSKELETON
The final step of this work is the implementation of the
generated gaits on hardware. This section details some of
the implementation on ATALANTE, and presents the results
obtained with multiple users (1 dummy and 3 paraplegic pa-
tients). Importantly, dynamically stable locomotion is realized
in all cases, and the walking is compared across patients.
A. Implementation of gaits on hardware
In order to translate the gaits obtained in simulation
into actual dynamical walking on hardware, the following
methodology has been followed (as illustrated in Fig. 2).
Adjusting the Exoskeleton dimensions. Since all patients
have different sizes and body shapes, the hardware has been
designed so that certain dimensions can be adjusted (cf.
green links in Fig. 3). Using the measurements made to
generate the patient model, the dimensions of the exoskeleton
are adjusted to align the robot’s joints with the patient’s
joints. This allows to minimize the internal stresses at the
attachment points between the patient and the exoskeleton
arising from the highly hyper-static nature of the human-
exoskeleton mechanism.
Embedded systems structure. The exoskeleton is controlled
by a central computer board running a real-time operating
system and in charge of all high level computations. This
central computer then sends commands to motor controllers
that handle the low-level operation of brushless motors.
Digital encoders are present on all the joints of the exoskele-
ton. IMU’s are located in different parts of the exoskeleton
allowing for a better estimation of the pose of the robot.
Furthermore, sensors are present in the feet and provide a
measurement of the center-of-pressure during walking.
In order to get the exoskeleton to realize the desired
gait, trajectory tracking is implemented (cf. Fig. 6). Given
Fig. 7: Phase portraits for the dummy during 20s of unas-
sisted walking.
one chosen cyclic gait, articular targets for each joints are
generated. These targets are the nominal trajectories of the
joints but modified online based on foot impact detection to
allow for a better transition between steps. These targets are
then sent to a control loop which generates current commands
at the joint level. The current command is then sent to the
motor controller that handles the high-frequency low-level
control of the motor.
Tuning of the trajectory. Finally, the nominal trajectory is
tuned in order to accommodate for the mechanical imper-
fections and asymmetries of the robot. This tuning happens
during a series of walking experiments with a mannequin
until the desired behavior is achieved. Tuning generally
improves the stability and robustness of the gait after a few
trials.
B. Experimental results with a dummy
To evaluate the controllers, experiments are first carried
out using a mannequin or dummy (cf. Fig. 5). As we can
see in Fig. 7, the nominal and target trajectories (in red and
blue respectively) are marginally different after the tuning
and high-level filtering of the nominal trajectories (cf. Fig.
6). The target gait is followed with relatively good accuracy
resulting in stable dynamic walking of the hardware.
C. Experimental results with human subjects
As a result of the successful results obtained with the
dummy, experiments are carried out with paraplegic patients.
Some characteristics of these patients are summarized in
Table I.
Clinical Set-Up. Experiments were conducted in a certi-
fied medical center and approved by the ANSM (French
regulatory administration for health products). To prevent

TABLE I: Patients data
Patient Height(m) Weight(kg)
Distance
traveled(m)
speed(m/s)
A 1.80 68 8.9 0.11
B 1.69 80 10.56 0.15
C 1.80 75 9.5 0.13
Fig. 8: Phase portraits for patient A during 60s of unassisted
walking.
injury from a fall, one person is placed at each side of a
patient. In case of loss of balance, the two assistants catch
the exoskeleton by handles on its sides. Furthermore, a safety
cable is attached to the exoskeleton and an overhead rail (or
gantry). This is a secondary means to secure a patient and
prevent a fall. Hence, assistance is provided only in case of
loss of balance. During walking, the exoskeleton and its user
are self stabilized and no outside assistance was given.
Results. As can be seen in the video at [4] and Fig.
9c, crutch-less dynamically stable exoskeleton walking of
paraplegic patients is achieved as a result of the method-
ology developed in this paper. All patients managed to walk
unassisted for the entire length of the room after a few trials
during which a best gait was chosen and then tuned; Table I
includes the speed of walking and distance traveled.
The ability to successfully transfer the formal gaits gener-
ated to hardware is illustrated in Fig. 8 for Patient A, wherein
the nominal (blue) and measured (shaded) trajectories are
consistent throughout the experiment. The motors torques
resulting from tracking the nominal trajectories (cf. Fig. 9b)
are also consistent with simulation. Note that motor-torque
saturations are relatively uncommon as the gaits are designed
to account for all hardware limits. To compare the walking
between patients, a representative selection of phase portraits
for each patient are presented in Fig. 9a; even though the gaits
are not the same (as they have been generated to best suit each
patient), they all display a common fundamental structure.
(a) Selection of phase portraits. The solid lines are the target
trajectories. The shaded regions are the measured joints positions.
(b) Measured motor torques.
(c) Walking tiles of patients A, B and C (in this order from top to
bottom).
Fig. 9: Experimental results for all three patients.

This is further illustrated in gait tiles of the patients walking
in the exoskeleton (cf. Fig. 9c). While the dynamic walking
gaits obtained are preliminary, and in no way constitute any
kind of clinical evaluation, the ability to consistently realize
them on patients points toward the validity of the framework
developed.
V. CONCLUSIONS
This paper has demonstrated the first ever experimental
realization of hands-free dynamic walking by subjects with
a lower spine injury. The keys to realizing this were novel
hardware, stiff enough to physically support a subject, pow-
erful enough to move the device’s legs quickly, and novel
control mathematics developed over the past 15 years to allow
bipedal robots to walk stably in uncertain environments and
with imprecise dynamic models. Importantly, these results
concretely mark the first steps toward the vision of restoring
locomotion for paraplegics.
The preliminary results demonstrated very slow walking on
the order of 0.1 m/s. Stable gaits at 0.4 m/s were achieved in
simulation, and such speeds can be expected to be reached
on the current hardware and with patients. Future work will
also provide the ability to stand from a chair, initiate a gait,
stop, turn, and sit in a chair. However, before providing more
gait features, focus will be on improving the basic posture
of the gaits to be more upright and comfortable, with foot
roll and heel strike. Better robustness of the overall closed-
loop system is also a general goal. The hope is that these
future research directions will enable dynamic exoskeleton
locomotion in everyday life settings, from traversing up and
down stairs to walking outdoors in natural environments.
ACKNOWLEDGMENT
The authors would like to thank the entire Wandercraft
team which designed ATALANTE, implemented and tested
the control algorithms both in simulation and in real condi-
tions. Additionally, the authors are grateful to Laurent Praly
and Nicolas Petit, researchers at CAS (Mines ParisTech,
PSL Research University) for their precious scientific support
since the beginning of Wandercraft, and to Koushil Sreenath
at UC Berkeley for collaborative efforts on realizing dynamic
walking on exoskeletons.
REFERENCES
[1] Ekso bionics. http://eksobionics.com/eksohealth/patients/. Accessed:
2017-09-15.
[2] Rewalk. http://rewalk.com/. Accessed: 2017-09-15.
[3] Rex bionics. http://www.rexbionics.com/. Accessed: 2017-09-15.
[4] Video of the experimental results. https://youtu.be/V30HsyUD4fs.
[5] Wandercraft. http://www.wandercraft.eu/. Accessed: 2017-09-15.
[6] Ayush Agrawal, Omar Harib, Ayonga Hereid, Sylvain Finet, Matthieu
Masselin, Laurent Praly, Aaron D. Ames, Koushil Sreenath, and
Jessy W. Grizzle. First steps towards translating HZD control of bipedal
robots to decentralized control of exoskeletons. IEEE Access, 5:9919–
9934, 2017.
[7] Aaron D Ames. Human-inspired control of bipedal walking robots.
IEEE Transactions on Automatic Control, 59(5):1115–1130, 2014.
[8] Aaron D Ames, Kevin Galloway, Koushil Sreenath, and Jessy W
Grizzle. Rapidly exponentially stabilizing control lyapunov functions
and hybrid zero dynamics. IEEE Trans. on Automatic Control,
59(4):876–891, 2014.
[9] John T Betts. Survey of numerical methods for trajectory optimization.
Journal of guidance, control, and dynamics, 21(2):193–207, 1998.
[10] Aaron M. Dollar and Hugh Herr. Lower extremity exoskeletons and
active orthoses: Challenges and state-of-the-art. IEEE Trans. Robot.,
24(1):144–158, 2008.
[11] Kevin Fite, Jason Mitchell, Frank Sup, and Michael Goldfarb. Design
and control of an electrically powered knee prosthesis. In Rehabilita-
tion robotics, 2007. ICORR 2007. IEEE 10th international conference
on, pages 902–905. IEEE, 2007.
[12] Kevin Galloway, Koushil Sreenath, Aaron D. Ames, and Jessy W.
Grizzle. Torque saturation in bipedal robotic walking through control
lyapunov function based quadratic programs. IEEE Access, 3:323–332,
April 2015.
[13] Brent Griffin and Jessy Grizzle. Walking gait optimization for ac-
commodation of unknown terrain height variations. In 2015 American
Control Conference, pages 4810–4817, 2015.
[14] J. W. Grizzle, C. Chevallereau, R. W. Sinnet, and A. D. Ames. Models,
feedback control, and open problems of 3D bipedal robotic walking.
Automatica, 50(8):1955 – 1988, 2014.
[15] J Grundmann and A Seireg. Computer control of multi-task exoskele-
ton for paraplegics. In Proceedings of the Second CISM/IFTOMM
International Symposium on the Theory and Practice of Robots and
Manipulators, pages 233–240, 1977.
[16] Charles R Hargraves and Stephen W Paris. Direct trajectory opti-
mization using nonlinear programming and collocation. Journal of
Guidance, Control, and Dynamics, 10(4):338–342, 1987.
[17] Ayonga Hereid, Eric A Cousineau, Christian M Hubicki, and Aaron D
Ames. 3D dynamic walking with underactuated humanoid robots: A
direct collocation framework for optimizing hybrid zero dynamics. In
Robotics and Automation (ICRA), 2016 IEEE International Conference
on, pages 1447–1454. IEEE, 2016.
[18] D Hristic, M Vukobratovic, and M Timotijevic. New model of
autonomous’ active suit’for distrophic patients. In Proceedings of the
International Symposium on External Control of Human Extremities,
pages 33–42, 1981.
[19] Y. Hurmuzlu, F. Génot, and B. Brogliato. Modeling, stability and con-
trol of biped robots–a general framework. Automatica, 40(10):1647–
1664, 2004.
[20] H Igo Krebs, Neville Hogan, Mindy L Aisen, and Bruce T Volpe.
Robot-aided neurorehabilitation. IEEE transactions on rehabilitation
engineering, 6(1):75–87, 1998.
[21] R. M. Murray, Z. Li, S. S. Sastry, and S. S. Sastry. A mathematical
introduction to robotic manipulation. CRC press, 1994.
[22] Jacob Reher, Eric A Cousineau, Ayonga Hereid, Christian M Hubicki,
and Aaron D Ames. Realizing dynamic and efficient bipedal loco-
motion on the humanoid robot durus. In Robotics and Automation
(ICRA), 2016 IEEE International Conference on, pages 1794–1801.
IEEE, 2016.
[23] Jacob P Reher, Ayonga Hereid, Shishir Kolathaya, Christian M Hu-
bicki, and Aaron D Ames. Algorithmic foundations of realizing
multi-contact locomotion on the humanoid robot durus. In Twelfth
International Workshop on Algorithmic Foundations on Robotics, 2016.
[24] A Seireg and JG Grundmann. Design of a multitask exoskeletal
walking device for paraplegics. Biomechanics of Medical Devices,
pages 569–644, 1981.
[25] Frank Sup, Amit Bohara, and Michael Goldfarb. Design and control
of a powered transfemoral prosthesis. The International journal of
robotics research, 27(2):263–273, 2008.
[26] M Vukobratovic, D Hristic, and Z Stojiljkovic. Development of active
anthropomorphic exoskeletons. Medical and Biological Engineering,
12(1):66–80, 1974.
[27] Michael Wehner, Brendan Quinlivan, Patrick M Aubin, Ernesto
Martinez-Villalpando, Michael Baumann, Leia Stirling, Kenneth Holt,
Robert Wood, and Conor Walsh. A lightweight soft exosuit for
gait assistance. In Robotics and Automation (ICRA), 2013 IEEE
International Conference on, pages 3362–3369. IEEE, 2013.
[28] E. R. Westervelt, J. W. Grizzle, C. Chevallereau, J. H. Choi, and
B. Morris. Feedback control of dynamic bipedal robot locomotion.
CRC press Boca Raton, 2007.
[29] Juanjuan Zhang, Chien Chern Cheah, and Steven H Collins. Experi-
mental comparison of torque control methods on an ankle exoskeleton
during human walking. In Robotics and Automation (ICRA), 2015
IEEE International Conference on, pages 5584–5589. IEEE, 2015.

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