Design of a Rehabilitation Exoskeleton with Impedance Control:

First Experiments

Gaëtan Courtois

, Jason Chevrie

, Antoine Dequidt

1,2

, Xavier Bonnet

and Philippe Pudlo

Univ. Polytechnique Hauts-de-France, LAMIH, CNRS, UMR 8201, F-59313 Valenciennes, France

INSA Hauts-de-France, F-59313 Valenciennes, France

Institut de Biomécanique Humaine Georges Charpak, Arts et Métiers Paristech,

151 Boulevard de l'Hôpital, F-75013 Paris, France

Keywords: Lower-Limb Exoskeleton, Impedance Control, Gait Rehabilitation.

Abstract: In this paper, we disclose the design strategy, control design and preliminary works leading to the

development of a post stroke gait rehabilitation exoskeleton. The strategy is established based on the

conventional gait rehabilitation currently used in rehabilitation centers and defines the exoskeleton as an

interface between the therapist and the patient. The final purpose of this interface is to complete the

conventional rehabilitation by intensifying the work of the patient while relieving the physical burden on the

therapist. As the conventional rehabilitation is based on successive exercises the control is designed to have

several operating modes triggered depending on the currently processing exercise. A test bench was realised

to evaluate quantitatively as well as qualitatively these operating modes. Preliminary results of quantitative

experiments on the transparent operation mode are then presented. These results validate the control design

and comfort us on our development method.

1 INTRODUCTION

Today the most important cause of hemiplegia is

cerebrovascular accident or stroke. Each year around

13.7 million cases are counted in the world (Feigin

et al., 2019). Only 85% of the survivors of a stroke

can walk after 6 months. Among them 5% are said

to be severe hemiplegics and don't regain their full

autonomy (Olney et al., 1996). Then around 20% of

the survivors of a stroke never recover even if some

of them followed a rehabilitation therapy.

In this context of ever-increasing number of

people suffering from hemiplegia, due to a lack of

manpower rehabilitation centers are forced to select

the accepted patients. Hence a lot of people cannot

follow a gait rehabilitation therapy and eventually

lose their autonomy.

One of the solutions to help the therapists to

accept more patients is to propose tools like

exoskeletons to increase the chances of

rehabilitation of post stroke patients, even for the

most severe cases.

Nowadays there are numerous lower-limb

exoskeletons which are used or studied for the

rehabilitation. And even among only the

anthropomorphic ones it is still possible to find a lot

of exoskeletons used for rehabilitation (Denis et al.,

2016 and Esquenazi et al.,2017). However, this kind

of exoskeletons is not proven to improve the gait

rehabilitation compared to conventional

rehabilitation (Pennycott et al., 2012). Furthermore,

to the best of our knowledge none of them was

designed specifically for post stroke gait

rehabilitation. This way the final aim of this work is

to design an exoskeleton specifically thought for the

gait rehabilitation of hemiplegic patients.

During conventional rehabilitation post stroke

patients pass through different stages, namely

passive, semi-active and active patient. Each can be

seen as a functioning mode of the developed

exoskeleton.

Impedance control is very well-suited for the

interaction between patient and exoskeleton and is

really adaptable to these 3 phases of the

rehabilitation. Hence, in this context, impedance

control is the most appropriate for gait rehabilitation

(Akdoğan et al., 2018). Moreover, one of the most

important operating modes of rehabilitation

exoskeletons is the transparent mode (Andrade et al.,

2019) and impedance control is one of the most

suitable to achieve transparency (Tucker et al. 2015).

Courtois, G., Chevrie, J., Dequidt, A., Bonnet, X. and Pudlo, P.

Design of a Rehabilitation Exoskeleton with Impedance Control: First Experiments.

DOI: 10.5220/0010580004690476

In Proceedings of the 18th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2021), pages 469-476

ISBN: 978-989-758-522-7

469

Figure 1: Schematic representation of the rehabilitation strategy.

In this context this paper focuses on the

preliminary works on transparency made to develop

the first prototype of this exoskeleton designed for

post stroke gait rehabilitation. Section 2 displays the

elements leading to the design of a hip only actuated

exoskeleton. Section 3 details the formulation of an

hybrid impedance control law and how it applies to

transparent operation mode. Section 4 describes the

preliminary experiments on transparency made on a

test bench and shows the results. Finally, Section 5

concludes this paper and opens the way for further

developments.

2 DESIGN OF A HIP ACTUATED

EXOSKELETON

The first prototype we developed is a hip only

actuated exoskeleton. According to the therapists the

hip is indeed the most important joint to start the

rehabilitation. However, to understand the design of

this first prototype the first thing to explain is the

rehabilitation strategy.

2.1 Rehabilitation Strategy

Rehabilitation is a domain which requires

knowledge and know-how that only specialists can

show. So, we choose to work with therapists to

design the exoskeleton as a tool for the therapists

made by the therapists.

In other words, for further developments the

exoskeleton is described as an interface between the

therapist and the patient as shown in Figure 1. Its

purpose is to intensify the conventional

rehabilitation and to allow sub-acute patients to

access to the rehabilitation platforms.

2.1.1 Therapist-exoskeleton Interface

The interaction between the therapist and the

exoskeleton is made by a human-machine interface

(HMI). This interface is designed with the therapists

to make full use of their know-how thanks to the

several functionnalities available.

This HMI is designed to allow the therapist to

plan a rehabilitation session following the pattern of

the conventionnal rehabilitation. It means that the

therapist will choose exercises for the patient to

realise while assisted by the exoskeleton.

These exercises are designed by the therapists

and then translated to write the control laws. Thus

each exercise corresponds to a control with

personalized parameters. Moreover, all these

parameters can be adjusted in real time by the

therapists via the HMI.

2.1.2 Exoskeleton-patient Interface

Some choices were needed about the exoskeleton-

patient interaction to design our gait rehabilitation

exoskeleton. First, to lessen the power consumption

needed to stabilise the patients and to sustain their

weight our first choice was to use a body weight

support.

Moreover, the gait pattern has been known for

decades by the therapists and they also know that the

hip can be actuated only in the sagittal plane for the

gait rehabilitation. Then as shown in Figure 2, the

design can be simplified to put only one actuator in

this plane, which simplifies the control as well.

Figure 2: First prototype - Hip only actuated exoskeleton.

ICINCO 2021 - 18th International Conference on Informatics in Control, Automation and Robotics

470

To sum up the exoskeleton's final version's

purpose is to replace the hands of the therapist to

improve the rehabilitation of the patient while

maintaining the comfort of both of them.

2.2 Actuation Design

The actuation design regroups 3 important devices:

the servodrive, the motor and the gear. First, the

most important requirements are set as the weight

and the bulkiness of the system that need to be as

low as possible. Since the controller is used to

compensate the mechanical impedance, it is not

included in the design requirements. Thus, the

servodrive should allow implementing custom

control laws for this compensation. The controller

(Embedded PC) and the servo drive must therefore

be able to implement customized control laws for

this compensation. The servodrive must then be

configured in cyclic synchronous torque (CST)

mode and the EtherCAT fieldbus, which is widely

used in industry, is therefore particularly suitable for

ensuring controller-servodrive communication with

cycle times of less than 1 ms.

Moreover, to be freed from the problem of

homologation, all the components were picked from

supplier's catalogs to meet reliability and safety

standards (ISO 13849-1, IEC 62061).

The last important requirement that drives the

design is the torque needed for the gait

rehabilitation. The average torque needed at the hip

joint is around 1Nm normalized per patient weight

(Giovacchini et al., 2014 and Seo et al., 2016). This

way some of the already available exoskeletons can

develop more than 100 Nm at the hip to fit a large

population (Chen et al., 2019). However, due to the

bodyweight support, it was fixed with the therapists

that the max repeated torque needed can be reduced

to around 40 Nm at the hip.

Eventually at the scale of a wearable

exoskeleton, the most suitable device for the

actuation is a brushless DC motor because of its

power density (Manna et al. 2018). Then the three

devices we have chosen are a servodrive EL7411

from Beckhoff company, a BLDC motor EC 90 Flat

(+ Encoder MILE 2) from Maxon company and a

CPU-17A from HarmonicDrive company with

reduction ratio of 80:1. This actuation allows a max

repeated torque of 43Nm for a weight of 1.55kg,

which fulfills the requirement.

3 IMPEDANCE CONTROL FOR

LOWER LIMB EXOSKELETON

The hybrid impedance control law used is based on

the work of Akdogan et al. (2018). This control

appears to be well suited for the purpose of

exoskeleton assisted rehabilitation as it can be

adapted to nearly every kind of environment

(Anderson et al., 1987 and Akdogan et al., 2018).

However, as this study is about the preliminary work

of a hip only actuated exoskeleton, it is necessary to

adapt the controller used by Akdogan et al. for 3

joints upper-limb actuation to a 1 joint lower-limb

actuation.

3.1 System Dynamic Model

First, let us define the model used to describe the

system dynamics as:

τ=Iq



(

q,q

)

+ G

(

)

−τ



(1)

where τ is the gear output actuation torque, q, q and

q are, respectively, the position, velocity and

acceleration of the revolute joint, I is the inertia

term, F(q,q) is the friction term, G(q) is the gravity

term and τ



is the torque resulting from the force

applied by the human limb.

3.2 Position-based Impedance Control

Applied to Lower-limb Exoskeleton

One of the components of the hybrid impedance

control law is the position-based impedance control.

This controller is mostly used to help as needed

when the patients are passive or when they don't

have too much difficulties following the desired

trajectory.

Then based on Akdogan et al. (2018) the desired

dynamic behavior written in the exoskeleton joint

space after applying the position-based impedance

control can be given as:



(



−q





)



(

q −q



)



(

q−q



)

=−τ



,(2)

where I



, B



and K



are, respectively, the desired

inertia, damping and stiffness at the joint and

,q

and q

are, respectively, the desired position,

velocity and acceleration of the joint.

Still based on Akdoganet al. (2018) it is possible

to rewrite the position-based impedance control as:

Design of a Rehabilitation Exoskeleton with Impedance Control: First Experiments

471

τ=







q



−B



(

q −q



)

−



(

q−q



)



− (1+



)τ



+τ



(q,q)

,(3)

where τ



(q,q) expresses the compensation terms

depending on the system.

3.3 Force-based Impedance Control

Applied to Lower-limb Exoskeleton

It can be said that the force-based control is more

appropriate for the cases where the environment

impedance is more important than the system

impedance. As the patient represents the greater part

of the exoskeleton environment the force-based

impedance control becomes more suitable when the

rehabilitation progresses (Tucker et al. 2015).

3.3.1 Force-based Impedance Control for

Semi-active Patient

When the patient becomes more active then the

exoskeleton should be proportionally less active to

favour the patient's progress.

Then the force-based impedance control gains in

pertinence starting from the semi-active patient. This

control allows managing the start of the exercises by

perceiving the patient's intention and reacting

accordingly (this issue is beyond the scope of this

paper). Moreover, it can be used to help the patient

when this one is not able to follow the trajectory by

providing a greater torque allowing to complete the

movement. In a rehabilitation context it is more

important for the patient to finish the exercise than

perfectly following the trajectory.

The desired dynamic behavior of the joint for the

force-based impedance control inspired by Akdogan

et al. (2018) can be written as follows:



q +B



q −τ



=−τ



, (4)

where τ



is the desired torque applied on the limb.

Then the force-based impedance control law can be

written as follows:

τ =





(



−B



q

)

−(1+





)τ



+τ



(q,q).

(5)

3.3.2 Transparent Operation Mode

Since impaired people are easier to hinder, it is then

necessary to lessen everything that can be perceived

as a burden for them (Andrade et al., 2019). The

transparency consists in minimizing the perception

of the resistance of the system. Hence, it is the first

operating mode that needs to be operational in case

of rehabilitation.

In the case of post stroke gait rehabilitation, the

transparency is mostly useful for two things. The

first one is to let the patients move their unimpaired

limb. Indeed, hemiplegia means that only one side of

the body needs rehabilitation. Then as the patients

are already weak from the stroke, the exoskeleton

should not hinder their movements.

The second one is for patients near the end of the

rehabilitation, who are more active. Then for the

rehabilitation to pursue effectively, the exoskeleton

should not assist nor hinder the patients during the

exercises.

As these two cases are mostly for active or semi-

active limbs the most appropriate control for the

transparency is the force-based impedance control

and the desired torque τ



is set to 0 for the patients

to perceive no resistance. Hence (5) becomes:

τ=−







q −(1+





)τ



+τ



(q,q).

(6)

Finally, this transparent operation mode is the

default mode. Otherwise, while not in transparent

operation mode nor in an exercise the exoskeleton

could be perceived as in a resistive mode. With

transparency as the default mode, the exoskeleton

can just assist as needed when it is needed.

3.4 Hybrid Impedance Control Applied

to Lower-limb Exoskeleton

In the end, the hybrid impedance control is a

combination of the previously presented control

laws. Following the same pattern as in Section3.2

and Section 3.3 the desired dynamic behavior

resulting from the combination of (2) and(4) is as

follows:



(

q −Sq



)



(

q −Sq



)



(

q−q



)

+(1 − S)τ



=−τ



, (7)

where S can take the value 0 and 1 to switch

between (4) and (2), respectively.

Hence the overall control law can be written as a

combination of (3) and (5) as follows:

τ=



(



q



−B



(

q −Sq



)

−S



(

q−q



)

(

1−S

)



)

−(1+



)τ



+τ



(

q,q

)

. (8)

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472

Roughly speaking, giving the value 0 or 1 to S

allows switching the control in real time and thus

adapting the comportment of the exoskeleton to assist

the patients as needed. Moreover, the three parameters



, B



and K



can also be modified according to the

therapist's needs to adapt to each patient.

This versatility will be useful for the chosen

rehabilitation strategy. Indeed, each exercise will

depend of the patient rehabilitation state and this

evolution of the patient also means an evolution of

the environment's impedance.

4 EXPERIMENTS AND RESULTS

This section's purpose is to display the results of

preliminary experiments. The first part is about the

test bench and the identification of its model. Then

the last two parts explain the first experiment about

transparency and the first experiment with a simple

position-based impedance control.

4.1 Test Bench

The test bench shown in Figure 3 is made using the

same actuation system described in Section 2.2. Its

purpose is to test this actuation system and the

control law.

4.1.1 Bench Description

This bench is designed to be used for qualitative

experiments with the therapists as well as for

quantitative experiments to validate the software and

the devices.

For the qualitative tests the bench is designed to

reproduce the kinematics of the hip exoskeleton

according to the features mentioned in Section 2.1.2

and to be driven with a manual handle. The human

hand being much more sensitive, it is expected that

future experiments on transparency and on the

Figure 3: Test bench for preliminary experiments.

exercises will be more conclusive. This bench

allows a wide range of tests to be carried out with

several different users, including therapists.

For the quantitative experiments the bench is

driven by a linear actuator controlled in position or

velocity to ensure the reproducibility of the protocol.

A cable wound up on a circular drum attached to the

joint is connected to the linear actuator carriage. The

tension force of the cable is measured by a

monodimensional Scaime ZFA force sensor with a

rated capacity of 25kg as shown in Figure 3. Knowing

the radius of the drum, the measured force allows

computing the torque τ



while the joint position and

velocity are derived from the servodrive's processing

of the motor's encoder signals.

4.1.2 Identification of a Compensation

Model

In order to implement the compensation term,



(

q,q

)

, in the control law given in (8) an adequate

representation of the system behavior should first be

chosen and estimated. In this work, the test bench is

assumed to follow the dynamic model given in (1).

The friction term F

(

q,q

)

is chosen as a Coulomb-

viscous model, the nonlinear term G(q) accounts for

the effect of the gravity and the external torque τ



set to zero, such that:

τ=Iq





q +F



sign

(

q

)

+ C



sin

(

)

(9)

where F



and F



are the viscous and dry friction

coefficients, respectively, C



is a gravity coefficient

and I was defined in (1).

The values of the parameters for the test bench

are identified from experimental measures using the

DIDIM algorithm (Gautier et al., 2013). A 10

seconds periodic trajectory represented as a finite

Fourier series is computed for optimal excitation of

the parameters (Swevers et al., 1997) and 25 periods

of this trajectory are applied to the system. Motor

torque measures are acquired at a sample rate of 2

kHz and the average period is computed to reduce

torque noise. The averaged samples are then filtered

by a 10.66 Hz Chebyshev filter and decimated by a

factor of 150 before being used as input for the

DIDIM algorithm. Identified values of the

parameters are given in Table 1.

The compensation term in (8) is then computed

according to:



(

q,q

)



q +F



tanh











+ C



sin

(

)

(10)

where the sign function in (9) is replaced by a

hyperbolic tangent function for stability purposes,

using a coefficient empirically tuned to r = 0.0375.

Design of a Rehabilitation Exoskeleton with Impedance Control: First Experiments

473

Table 1: Results of the DIDIM identification.

Parameter [unit]

Estimated value

(relative standar

deviation)



[N.m]

2.000 (6.06%)



[N.m.s/°]

5.584  10



(5.26%)



[N.m] 2.602 (2.21%)

I [kg.m²] 2.042 (3.31%)

4.2 Transparent Operation Mode:

Preliminary Experiment

Knowing a model of the test bench, this section

presents a first experiment to validate quantitatively

the effect of the transparent operation mode. For this

purpose, an experimental protocol was followed on

the test bench.

4.2.1 Protocol

For the transparency, the control law is force-based

as shown in (6). However, without a closed-loop in

force τ



=0 and I



is set to I and B



to 0. The

implemented control law thus becomes:

τ = τ



(

q,q

)

. (11)

The experiment consists of 20 successive

trajectories at constant velocities between 10°/s and

30°/s. This way a curve can be drawn to display the

evolution of the torque depending on the velocity.

Thus, the comparison between the curves with and

without compensation can show the effect of the

transparent operation mode.

4.2.2 Results

The results of this first experiment are displayed in

Figure 4. The blue points are the average torque

without compensation and the red ones represent the

average torque with the compensation for the same

velocity values.

Figure 4: Comparison of the average torque needed for

several velocities with and without compensation.

As anticipated the average torque measured with

the compensation is quasi constant and very close to

0. These results show that this model can achieve

transparency.

However, this diagram shows that the

transparency can be improved. Even if the torque

should not reach 0, for stability purposes, it seems

possible to adjust the parameters to move closer to 0.

Furthermore (6) is not fully exploited. Hence, these

results are quite encouraging for further

developments about the transparent operation mode.

4.3 Position-based Impedance Control:

Preliminary Experiment

This second experiment is presented to test the

identified compensation model while applying a

position-based impedance control. The purpose of

this experiment is to compare the behavior of the

system with and without the compensation.

4.3.1 Protocol

In this experiment the control law (3) is used with



=I, q



=0, B



=0 and without closed-loop in

force so τ



=0. This way it applies a constant

stiffness mimicking a spring and can be written as

follows:

τ=−



(q − q



)+τ



(q,q), (12)

where q



= −45° is the initial angular position of

the handle and K



= 0.3686Nm/° is the stiffness of

the virtual spring attached to q



The experiment consists of 20 successive round

trips of the linear actuator between -45° and 35° of

the handle. The velocity is maintained during all the

successive experiments at a constant value of

20.25°/s (seen at the handle). This way the measures

allow the comparison of the system's response with

and without the compensation.

4.3.2 Results

The results of this second experiment are shown in

Figure 5. In green is displayed the theoretical value

of the torque given by the virtual spring. The blue

curve displays the torque of the average cycle

without the compensation and the red one with the

compensation.

First of all, the compensation shows clearly its

effects during the going part. In this part of the cycle

the compensation corresponds to the expectations

based on the results in Section4.2.2.

ICINCO 2021 - 18th International Conference on Informatics in Control, Automation and Robotics

474

Figure 5: Comparison of the average torque with and

without compensation while applying a compliance τ



(q).

Two other details are also noticeable. The first

one is the presence of the oscillations seen during

the transient phases. (Knowing that B



= 0 this could

be expected.) In practice, these disturbances are not

desired for future applications. However, it should

not be forgotten that the control law used in this

preliminary experiment is not the full one as shown

in (3) so the other terms, especially B



, could be

used to attenuate these oscillations.

The second and the most important issue on this

diagram is the non symmetry of the red curve around

the green one. This non symmetry shows the limit of

our test bench which is quite usable for this

preliminary experiment but lacks some precision in

the metrology.

5 CONCLUSIONS

The developments to achieve the first prototype of

this gait rehabilitation-oriented exoskeleton are near

to the end and the results of the preliminary tests are

encouraging. Currently the expectations were met

even if the results showed some of the test bench

limits.

For the next developments the first thing to do

will be to optimise the test bench to be able to apply

the full control law.

In a second time it is planned to implement a

disturbance observer to estimate the interactive force

between the patient and the exoskeleton. Therefore,

it will be possible to analyze some robust control

schemes with force closed loop.

These two points will allow us to implement the

overall control law and test it quantitatively on the

test bench. Furthermore, it will also be possible to

qualitatively test it with the manual handle to

improve the perception according to the therapists'

feedback.

ACKNOWLEGEMENTS

This work was supported by the Carnot ARTS

Institute in the framework of RehaByEXO project

and the Région Hauts-de-France.

The authors gratefully acknowledge the support

of these institutions.

REFERENCES

Anderson R., Spong M., 1987, "Hybrid impedance control

of robotic manipulators", Proceedings. IEEE

International Conference on Robotics and Automation.

Andrade R. et al., 2019, "Development of a “transparent

operation mode” for a lower-limb exoskeleton

designed for children with cerebral palsy", 16th

International Conference on Rehabilitation Robotics.

Akdoğan E. et al., 2018, " Hybrid impedance control of a

robot manipulator for wrist and forearm rehabilitation:

Performance analysis and clinical results",

Mechatronics, Vol.49, P. 77-91.

Chen B. et al., 2019,"Knee exoskeletons for gait

rehabilitation and human performance augmentation:

A state-of-the-art», Mecanism and machine theory.

Denis L. et al., 2016,"Powered robotic exoskeletons in

poststroke rehabilitation of gait: a scoping review",

Journal of NeuroEngineering and Rehabilitation

13:53.

Esquenazi A. et al., 2017, "Powered Exoskeletons for

Walking Assistance in Persons with Central Nervous

System Injuries: A Narrative Review", American

academy of physical medicine & rehabilitation,

PM&R 9, P. 46-62.

Feigin V. et al., 2019, " Global, regional, and national

burden of stroke, 1990–2016: a systematic analysis for

the Global Burden of Disease Study 2016», The

Lancet Neurology, Vol. 18, No. 5,P. 439-458.

Gautier M & al., 2013, "A New Closed-Loop Output Error

Method for Parameter Identification of Robot

Dynamics », IEEE Transactions on Control Systems

Technology, Vol. 21, No. 2, P. 428-444.

Giovacchini F. et al., 2014, "A light-weight active orthosis

for hip movement assistance", Robotics and

autonomous system.

Manna S. et al., 2018, "Comparative study of actuation

systems for portable upper limb exoskeletons",

Medical Engineering & Physics.

Olney S. et al., 1996, "Hemiparetic gait following stroke.

Part I: Characteristics", Gait and posture, Vol. 4, P.

136-148.

Pennycott A. et al., 2012, "Towards more effective robotic

gait training for stroke rehabilitation: a review",

Journal of Neuro Engineering and Rehabilitation.

Seo K. et al., 2016, "Fully Autonomous Hip Exoskeleton

Saves Metabolic Cost of Walking», IEEE International

Conference on Robotics and Automation (ICRA).

Design of a Rehabilitation Exoskeleton with Impedance Control: First Experiments

475

Swevers J. & al., 1997, "Optimal robot excitation and

identification", IEEE Transactions on Robotics and

Automation, Vol. 13, No. 5, P. 730‑740.

Tucker M. et al., 2015, "Control strategies for active lower

extremity prosthetics and orthotics: a review», Journal

of Neuro Engineering and Rehabilitation, 12:1.

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