ETH Library
Towards Dynamic Transparency:
Robust Interaction Force Tracking
Using Multi-Sensory Control on an
Arm Exoskeleton
Conference Paper
Author(s):
Zimmermann, Yves ; Kücüktabak, Emek Baris; Farshidian, Farbod; Riener, Robert; Hutter, Marco
Publication date:
2020
Permanent link:
https://doi.org/10.3929/ethz-b-000466461
Rights / license:
In Copyright - Non-Commercial Use Permitted
Originally published in:
https://doi.org/10.1109/IROS45743.2020.9341054
This page was generated automatically upon download from the ETH Zurich Research Collection.
For more information, please consult the Terms of use.
Towards Dynamic Transparency: Robust Interaction Force Tracking Using
Multi-Sensory Control on an Arm Exoskeleton
Yves Zimmermann
1,2
, Emek Barıs¸ K
¨
uc¸
¨
uktabak
1
, Farbod Farshidian
1
, Robert Riener
2,†
, and Marco Hutter
1,†
Abstract— A high-quality free-motion rendering is one of
the most vital traits to achieve an immersive human-robot
interaction. Rendering free-motion is notably challenging for
rehabilitation exoskeletons due to their relatively high weight
and powerful actuators required for strength training and sup-
port. In the presence of dynamic human movements, accurate
feedback linearization of the robot’s dynamics is necessary to
allow for a linear synthesis of interaction wrench controllers.
Hence, we introduce a virtual model controller that uses two 6-
DoF force sensors to control the interaction wrenches of a multi-
DoF torque-controlled exoskeleton over the joint accelerations
and inverse dynamics. Furthermore, we propose a disturbance
observer for controlling the joint acceleration to diminish the
influence of modeling errors on the inverse dynamics. To
provide a high-bandwidth, low-bias estimation of the system’s
acceleration, we introduce a bias-observer which fuses the
information from joint encoders and seven low priced IMUs.
We have validated the performance of our proposed control
structure on the shoulder and arm exoskeleton ANYexo. The
experimental comparison of the controllers shows a reduction
of the felt inertia and maximum reflected joint torque by a
factor of more than three compared to state of the art. The
controllers’ robustness w.r.t. a model mismatch is validated.
The experiments show that the closed-loop acceleration control
improves the tracking, particularly at joints with low inertia.
The proposed controllers’ performance sets a new benchmark
in haptic transparency for comparable devices and should be
transferable to other applications.
I. INTRODUCTION
Physical human-robot interaction gained significance dur-
ing the last years propelled by the increased fusion of robots
into the human’s workplace. Many of these devices render
haptic environments to the user. While robots dedicated to
this task perform reasonably well, more universal devices
often struggle to achieve the desired rendering fidelity. An
epitome of this challenge is rehabilitation robots.
On the one hand, these devices should provide high-quality
free motion (transparency) to avoid interfering with the
patients’ movements while supporting them [1]. On the other
hand, they need high torque actuation to allow for strength
training, dynamic assessments [2], and to assist severely
affected patients [3]. Limited transparency is acceptable for
the first steps in therapy of severely affected patients [4],
[5]. However, state-of-the-art devices strive to make robot-
assisted therapy useful also for patients able to perform more
1
Y. Zimmermann, E.B. K
¨
uc¸
¨
uktabak, F. Farshidian, and M. Hutter are
with Robotic Systems Lab, ETH Zurich, Switzerland yvesz@ethz.ch
2
Y. Zimmermann and R. Riener are with Sensory-Motor Systems
Lab, ETH Zurich, Switzerland. R. Riener is additionally with Spinal
Cord Injury Center, University Hospital Balgrist, Zurich, Switzerland
riener@ethz.ch.
†
R. Riener and M. Hutter contributed equally as lead of the project.
GH
GPR
GED
GHA
GHB
GHC
EFE
d
1
d
2
d
4
FA
UA
d
3
z
x
y
SG
Fig. 1. The kinematic structure of the robot with the shoulder girdle
joints (SG): protraction/retraction (GPR) and elevation/depression (GED);
the glenohumeral joints (GH): GHA, GHB, and GHC; elbow joint (EFE);
fixed passive link length adjustments d
i
; contact points upper arm (UA) and
forearm (FA) with attached coordinate systems [6].
agile movements [6].
With these powerful and thus, bulky devices it is challeng-
ing to render haptic transparency for dynamic movements.
First, often high transmission ratio gears are installed to
achieve the required joint torques at reasonable weight and
footprint. This design choice leads to increased joint friction
and high reflected motor inertia at the joint [7]. Many
state-of-the-art robots address this concern by series elastic
actuation [2], [6], [8], [9]. Second, the mechanical impedance
at the interaction point is comparatively large. Therefore, the
non-linear dynamics should be compensated to control the
device accurately. For trailing of fast human motions, vig-
orous control actions are required. Noise on the interaction
force measurement, the actuator bandwidth, and controller
sampling frequency limit the controller bandwidth. Hence
advanced control designs have been proposed to improve the
performance [10], [11]. Some devices have been developed
with remote actuation to reduce the moving mass [12], [13].
However, due to the transmission, the bandwidth is further
restricted, and additional non-linear friction is caused.
In this paper, we present a method to tackle the challenge
mentioned above through a virtual model controller (VMC)
using inverse dynamics (ID) for feedback linearization. We
elaborate on the advantage of using the measured interaction
wrench state for the linearization instead of the desired
wrench when interacting with a soft, unknown impedance.
To compensate errors in the ID model, we propose a closed-
loop acceleration controller. This control method uses a
multi-sensor signal with direct acceleration measurement as
feedback. Further, we investigate the method’s performance
on the series elastic actuated exoskeleton ANYexo shown in
Fig. 1.
II. SYSTEM DESCRIPTION
The hardware we use in this paper is a 6-DoF torque-
controlled shoulder and arm exoskeleton designed as a
research platform for methods concerning neural rehabili-
tation [6]. The device was developed with a focus on an
extensive range of motion (ROM) and particularly activities
that involve interaction with other parts of the user’s body.
Additional emphasis was put on swift motions to prevent
limitation of speed recovery, as described in [6]. However,
methods proposed in this paper should be transferable to any
other torque controlled haptic device.
The device has two actuated DoF at the shoulder girdle
(SG), three at the glenohumeral joint (GH), and one at the
elbow, as shown in Fig. 1. There are two physical interaction
points between user and robot: one at the upper arm (UA)
and one at the forearm close to the wrist (FA).
Six series elastic actuators drive the robot. A forerunner
version of these drives was presented in [14]. The version
used for the experiments provides 40 N m peak torque at
a bandwidth of 60 Hz at 3 N m amplitude and a resolution
smaller than 0.1 N m. The maximum joint speed is 12 rad/s.
At both interaction points (UA/FA), there are 6-DoF force-
torque sensors (Rokubi Mini 1.1 by Bota Systems) mounted.
They provide force and torque measurements in a range of
±1000 N and ±8 N m in the x-direction and ±500 N and
±5 N m in the yz-plane with less than 0.02 % noise. The
integrated IMUs attached to the shell of the drives and the
force-torque sensors provide inertial acceleration and angular
velocities. Their properties are identified in section VI-A.
The controllers, state estimation, and the model description
are updated at 800 Hz by a ROS and C++ based software
stack. Control PC, actuators, and sensors communicate over
an EtherCAT bus. The low-level torque controller for the
SEA runs at 2.5 kHz on the integrated electronics of the
drive.
A. Dynamics
The system of the human interacting with the robot is
described in generalized coordinates by
M
i
(q
i
)
¨
q
i
+ h
i
(q
i
,
˙
q
i
) + g
i
(q
i
) = J
>
C,i
(q
i
)λ
C
+ τ
i
, (1)
where i ∈ {R, H}. Indices R and H denote the robot and hu-
man system respectively, q are the generalized coordinates,
M is the mass matrix, h the centrifugal and Coriolis terms,
g the gravitation terms, J
C
the stacked spatial Jacobian of the
interaction points, τ the joint torques, and λ
C
the interaction
wrench. For the high level control design, the actuators can
be considered as perfect torque or position source within the
bandwidths typical for humans that is around 7 Hz [6], [15].
Therefore, we assume
τ [k + 1] = Π
ctrl
(q
R
[k],
˙
q
R
[k],
¨
q
R
[k], λ
C,meas
[k]), (2)
where Π
ctrl
is the control policy defining the target joint
torque for the actuators and λ
C,meas
is the measured inter-
action wrench.
The human H part of equation (1) is unknown regarding
the parameters of the system dynamics as well as its exact
state. The equations of motion (EoM) for R and H are
only coupled over λ
C
. Therefore, we can model the human
dynamics as unknown disturbance d
H
on the interaction
wrench λ
C
. Therefore
λ
C
=
ˆ
f
C
(q
R
,
˙
q
R
,
¨
q
R
, d
H
), (3)
where
ˆ
f
C
is the unknown function describing the interaction
depending on the relative motion of the interaction points.
B. Optimization Framework
We use a hierarchical null-space projection based opti-
mization (HOC) as a standard on our hardware to manage
safety relevant constraints and other tasks on different pri-
orities [6], [16]. This method typically uses the following
optimization vector ξ = (
¨
q, τ , λ
C
).
The tasks T are then defined as linear equality T
p
: A
p
ξ =
b
p
or inequality T
p
: D
p
ξ ≤ c
p
constraints at priority p,
where small p means high priority. The equations of motion
(1) and physical constraints should be defined on the first
priority as a solution deviating from physics is never valid.
The second priority can be used to define safety constraints
and the lower priorities to set therapy relevant tasks, and
regularization [6]. The next sections will discuss how to set
the tasks for the HOC to track interaction wrenches.
III. ENVIRONMENT ANALYSIS
The optimal choice for an interaction force control method
is highly dependent on the hardware and expected environ-
ment. Admittance controllers are generally used for systems
that are primarily position-controlled (e.g., hydraulic actu-
ated devices), Impedance controllers are used for systems
with low impedance (e.g., pneumatics, SEA), and torque-
controlled systems often use only feedforward control [17],
[18], [19]. In this section, we explain why an admittance con-
troller can be a better fit for a torque-controlled system in the
presence of an environment with unknown low impedance,
e.g., a human arm.
A. Environments with Known Impedance
Torque controlled robots offer a fairly easy method to
control interaction wrenches towards a fixed environment
(e.g., hard floor). In this case, all active contact DoF C
can be assumed motionless
˙
x
C
,
¨
x
C
= O. This constraint
allows projecting the EoM into the support consistent space.
This assumption for fixed contact points is eligible for, e.g.,
legged robots, as they mostly assume a fixed and rigid floor
[16], [11]. Also, for systems where the impedance of the
environment at the interaction points is well known, the same
method can be used. There the expected acceleration of the
interaction point
¨
x
C,exp
under the desired load λ
C,des
can be
estimated and compensated for by setting the equality task
J
C
¨
q =
¨
x
C,exp
−
˙
J
C
˙
q. (4)
This task assures that all solutions of the HOC are chosen
within the null-space of the support consistency constraint
(4). As next priority, the HOC receives the desired interaction
wrench λ
C
= λ
C,des
as an equality task and as last priority
the regularization
¨
q = 0. If no other tasks are defined, the
optimal joint torque τ
∗
to achieve the desired interaction
wrench λ
C
derives from equation (1)
τ
∗
= M
¨
q
∗
+ h + g − J
>
C
λ
C,des
, (5)
where
¨
q
∗
is the generalized acceleration resulting from the
HOC. As we assumed perfect torque sources for our model,
the desired interaction wrench would instantaneously be
established. This means that on the non-perfect hardware the
interaction wrench controlling task is converted to a joint
torque control task without any loss in accuracy. Whereas
the joint torque control performance is only dependent on
the actuation system.
B. Environments with Unknown Impedance
For systems that interact with a mostly unknown environ-
ment like a human arm, it is not possible to estimate
¨
x
C,exp
.
Without or with an inaccurate constraint (4) the torques from
equation (5) do not establish the desired interaction wrench
as the environment reacts unexpectedly to the robot’s action.
Consequently a deviation of the robot’s acceleration from
¨
q
∗
occurs. Employing linear control synthesis for the interaction
wrench tracking is sub-optimal due to the cross-coupling in
the robot’s wrench-acceleration dynamics.
IV. CONTROL APPROACH
As the model of the robot dynamics is significantly more
accurate than the model of the environment, we suggest
using all available information to define the robot’s EoM
as accurately as possible. Thereby at least the robot behaves
as expected, even when coupled to a completely unknown
environment. Furthermore, linear controller design is eligible
as the feedback linearization is valid. Hence, we set the
equality task λ
C
= λ
C,mes
at the same priority as the EoM.
This results in the best possible estimate of the real system
dynamics at the time of the measurement. For rather low
impedance environments as a human arm, this guess is also
more accurate during the whole control cycle (i.e. after
1.25 ms) than assuming λ
C
= λ
C,des
. Thus the feedback
linearization is as accurate as possible and only limited
by the accuracy of the robot model and interaction force
measurement. Hence, the system should track a desired
accelerations task
¨
q =
¨
q
des
precisely as long as none of
the safety constraints are active. In this case, the optimum
joint torque is expressed by
τ
∗
= M
¨
q
des
+ h + g − J
>
C
λ
C,mes
. (6)
Hence, we are looking for an admittance controller with
desired accelerations as output.
A. Wrench Controller
In this paper, we demonstrate this strategy with a straight
forward and easy to tune virtual mass controller (VMC).
A good guess for the unknown environment’s admittance is
that it behaves as decoupled one-dimensional systems with
a mass that is attached to the robot via a spring-damper
force element. Hence, accelerating the interaction points in
the direction of the interaction wrench error λ
C,err
= λ
C,mes
−
λ
C,des
will diminish the same. Large acceleration gains im-
prove the tracking performance. However, a stable controller
design is limited by the robots dynamics, actuation, and
communication delay. The idea of the VMC is to schedule
the acceleration gains so that the desired accelerations
¨
q
des
mimic a desired virtual admittance under the influence of the
residual interaction wrench error λ
C,err
. We want to control
a 12-DoF interaction wrench with six or less DoF of the
exoskeleton. Therefore, we do not have full controllability
over λ
C,err
. Hence, we define the VMC in the generalized
coordinates where the controllable part of the interaction
wrench is mapped to the joint space. We propose to chose
the virtual admittance so that it behaves like a down-scaled
reflected inertia of the real robot system M
virt
= αM
sys
.
Where α is a tuning parameter. The robot’s gravitational,
centrifugal, and Coriolis terms can be compensated entirely
without stability issues, as shown in [6]. Therefore, these
terms are not included in the virtual admittance. The HOC
obtains the desired joint accelerations
¨
q
des
as an equality task
¨
q
des
= M
−1
virt
J
>
C
λ
C,err
=
1
α
M
−1
sys
J
>
C
λ
C,err
. (7)
Due to the memoryless structure of the controller, this
method is not prone to windup if a higher priority task is
active on a subset of the controlled DoF. Hence, this free-
motion controller can always be defined as a task of priority
p
VMC
. If other haptic interactions i should be modelled they
can be added with a higher priority p
i
< p
VMC
. In this case,
the haptic interaction i is rendered on its DoF while the VMC
still controls the rest of the device’s DoF.
To give an intuition about the feeling of this controller,
we can investigate the admittance at joint level
¨
q
sys
= M
−1
sys
J
>
C
1
α
λ
C,err
+ ∆λ
C
, (8)
where ∆λ
C
= (λ
C,R
− λ
C,mes
) is the difference between
the delay afflicted, measured interaction wrench λ
C,mes
and
the continuous interaction force of the real system λ
C,R
.
Assuming a small delay and accurate measurement, this term
gets negligible. Then the system behaves as a down-scaled
impedance in the presence of λ
C,err
.
B. Acceleration Tracking Controller
The inverse dynamics (ID) for joint torque control are
known to be sensitive to modeling errors. Hence, pure joint
torque control finds its application in robots with closed
kinematic chains, e.g., legged robots [16] or open kinematic
chains with large inertia compared to the torque inaccuracy.
The distal parts of open kinematic chains usually have a
small inertia. Therefore, they are often position and velocity
controlled in addition to the feedforward torque. In our case,
we have a hybrid system. The robot itself is an open kine-
matic chain. While during therapy, there is always a human
arm attached that closes the kinematic chain. We control the
Software
Sensing
Dynamics
System
VMC HOC Q
r
ID P
RR
ENCAcE
IMU
LPF
Q
d
f
C
F/T-S
CBD
d
M
¨
q
sys
¨
q
∗
¨
q
des
λ
C,err
λ
C,des
λ
C,mes,fil
λ
C,mes
λ
C
d
H
-
+
-
+
+
+
-
τ
∗
τ
corr
τ
cmd
¨
x
IMU
¨
x
IMU,mes
¨
q
est
¨
q
dist
N (0, σ
2
FT
)
N (0, σ
2
ENC
)
N (µ
IMU
, σ
2
IMU
)
q
sys
q
mes
¨
x
C
ˆ
P
¨
q
exp
¨
q
corr
Fig. 2. Control diagram of the virtual mass controller (VMC) with closed loop acceleration control and sensor fusion based acceleration estimation (AcE).
The assumed sensor noise for the force-torque sensors (F/T-S), encoder (ENC), and inertial measurement units (IMU) is indicated as gaussian noise. The
lowpass filter (LPF) for λ
mes
is a butter worth filter. The filters for the other sensor signals contained in the AcE. The real system is built from links
with finite stiffness. Hence, the IMUs measure the accelerations of the compliant body dynamics (CBD)
¨
x
IMU,i
and not the accelerations equivalent to the
mapped joint acceleration
ˆ
¨
x
IMU,i
= J
C
¨
q
sys
+
˙
J
C
˙
q
sys
.
interaction forces over the robot accelerations and assume
the human arm to be of rather low impedance. Therefore
we expect that the open kinematic chain characteristics of
the arm could have a negative influence on the acceleration
control. We want to avoid to control all or a subset of the
joints in position-control, as we intend to keep the benefits of
torque control. Therefore we suggest using an acceleration
tracking controller to lower the error.
1) Controller Synthesis: We use a 2-DoF Internal Model
Controller structure for the controller [20]. This controller
design includes the plant’s model
ˆ
P and allows separate
tuning of reference tracking Q
r
and disturbance rejection
Q
d
, as shown in Fig. 2. The HOC computes the optimum
generalized acceleration
¨
q
∗
as well as optimum actuation
torques τ
∗
. Without the acceleration tracking controller we
use the torques from HOC directly as torque commands for
the actuators τ
cmd
= τ
∗
. If we want to correct for errors
d
m
of the modeled plant, τ
∗
has to be augmented by the
term that compensates for the disturbance resulting in τ
corr
.
As mentioned before, we can assume perfect torque sources
in the bandwidth of humans. We assume that τ
corr
does
not contain higher frequency content. Therefore the plant P
including the ID can be modelled as pure delay
ˆ
P = e
−T
s
s
,
were T
s
is the sampling time.
To assume perfect torque sources without loss of accuracy,
Q
r
and Q
d
need a cutoff frequency lower than the actuator
bandwidth. This requirement is feasible, as the human band-
width is much lower. Reference and disturbance tracking
controllers are synthesized as H
2
Optimal Controller for
ramp references and disturbances as the model errors are
mostly continuous (see [20]). Hence, we assume the model
disturbance to be of type
ˆ
d
M
= 1/s
2
. Applying the methods
in [20] to our assumptions results in following control
synthesis
ˆ
P = e
−T
s
s
≈
−s + 2/T
s
s + 2/T
s
˜
Q
i
= (
ˆ
d
M
)
−1
{
ˆ
P
−1
ˆ
d
M
}
∗
= T
s
s + 1
(9)
The operator {·}
∗
omits all terms of the operand’s par-
tial fraction expansion that contain the poles of
ˆ
P
−1
. For
causality, the controller needs a filter F
i
that yields a proper
controller Q
i
=
˜
Q
i
F
i
for i ∈ {d, r}. Further, (1 −
ˆ
P Q
i
)d
M
must be stable to reject disturbances asymptotically. The
filters F
i
are synthesized according to [20]
F
i
=
a
k−1
s
k−1
+ . . . + a
1
+ a
0
(Λ
i
s + 1)
m+k−1
=
2Λ
i
s + 1
(Λ
i
s + 1)
2
, i ∈ {d, r},
(10)
where m = 1 and k = 2 as the controller has a zero-pole
excess of 1 and d
M
has double poles at the origin. The time
constants Λ
d
and Λ
r
for disturbance rejection and reference
tracking respectively can be tuned independently.
2) Acceleration Estimation: The quality of the accel-
eration estimation restricts the maximum performance of
the acceleration tracking. Typically a system acceleration
estimate
¨
q
diff
is derived by double differentiation of the joint
position measurements. A low pass filter with a low cutoff
frequency and a large delay has to be used to attenuate the
dominant noise of the signal resulting in
ˆ
¨
q
diff
. We strive for
prompt correction of acceleration errors, hence this delay is
not acceptable. Therefore, we use the integrated IMUs to
measure the system acceleration directly. First, the measured
gravitational acceleration of the IMU signals is compensated.
Then, the linear accelerations are fused to an estimate of the
generalized accelerations using least squares.
¨
x
IMU
i
,noG
=
¨
x
IMU
i
− R
IMU
i
I
g
ˆ
¨
q
IMU
= J
+
IMU
(
¨
x
IMU,noG
−
˙
J
˙
q),
(11)
where R
IMU
i
I
is the rotation from inertial coordinates to IMU
frame, g is the gravity vector, and J
IMU
and
¨
x
IMU
are the
stacked Jacobian respectively acceleration measurements of
all IMUs.
Inaccuracies of IMU pose and calibration can lead to
severe artifacts of the gravity in the acceleration measure-
ment. Therefore,
ˆ
¨
q
IMU
is not qualified as control feedback.
However, if we merge the information of the delayed (t
delay
),
bias-free
ˆ
¨
q
diff
and the high bandwidth, bias polluted
ˆ
¨
q
IMU
we
![Fig. 1. The kinematic structure of the robot with the shoulder girdle joints (SG): protraction/retraction (GPR) and elevation/depression (GED); the glenohumeral joints (GH): GHA, GHB, and GHC; elbow joint (EFE); fixed passive link length adjustments di; contact points upper arm (UA) and forearm (FA) with attached coordinate systems [6].](/figures/fig-1-the-kinematic-structure-of-the-robot-with-the-shoulder-8b50vkyf.webp)