Knee Rehabilitation Device with Soft Actuation: An Approach to the

Motion Control

Leonardo Solaque, Marianne Romero and Alexandra Velasco

Universidad Militar Nueva Granada-Mechatronics Engineering Department, Bogota, Colombia

Keywords:

Feedback and Feedforward Control, Knee Rehabilitation Device, Soft Actuation.

Abstract:

Assistive devices in rehabilitation have gained much attention in robotics research. Recent actuation systems

include compliant elements to provide advantages as natural motions and safety in the interaction with humans.

These are the so-called soft actuators, among which there are series elastic actuators (SEA) and variable

stiffness actuators (VSA). On the other hand, control strategies are required in order to accomplish desired

tasks in a proper manner. In rehabilitation systems this is to reproduce a desired motion without affecting the

patient, so the control system is crucial. In this paper, we present a control strategy for a knee rehabilitation

device, with soft actuation. The goal is to control the system while maintaining the intrinsic softness of the

system when the patient is in the rehabilitation process. We propose a feedback control strategy, acting in

a deﬁned threshold to maintain the stiffness of the system, combined with a feedforward decision control to

reject disturbances.

1 INTRODUCTION

In recent years there has been an increasing need for

physical therapy for different reasons. E.g., accord-

ing to the World’ Health Organization

near 15% of

world’s population has some disability caused by ac-

cidents, chronic diseases, or other conditions. Be-

sides, people of all ages practice sports frequently to

maintain their quality of life, but in this way, they are

more exposed to joint injuries.

Any case of impairment or injury requires reha-

bilitation to reduce pain, to improve or to maintain

the remaining functional and structural characteris-

tics of the musculoskeletal system. Rehabilitation in-

cludes several practices that aim to recover functions

that have been lost or diminished by a disease or ac-

cident, though we will speciﬁcally refer to physical

rehabilitation of the knee (Andrade et al., 2014). Ac-

cording to (Jensen and Lorish, 1994), not all the pa-

tients comply with the physical treatments prescribed

due to costs, difﬁculty to reach the physiotherapy’s

place, and so on. On the other hand, performing the

exercises correctly might also be challenging due to

the pain, the lack of strength and the lack of range of

mobility, not to mention the risks for the physiothera-

pist when assisting some patients. For these reasons,

http://www.who.int/

Figure 1: Model representation for knee rehabilitation.

recent studies aim to contribute to improve the avail-

ability and effectiveness of physical therapy, as well

as to reduce risks to the physiotherapist, by design-

ing assistive rehabilitation devices. In the last years,

devices for upper limb (see e.g. (Balasubramanian

et al., 2008) or (Mghames et al., 2017)), and for lower

limb rehabilitation have notably increased. Other ex-

amples are presented in (Koller-Hodac et al., 2010),

(Rifa

ı et al., 2017) or (Vouga et al., 2017). The re-

quirements are speciﬁc, i.e. safety, natural motions.

In this sense, the actuation system is a key for robotic

devices. Regarding the requirements for rehabilita-

tion, the so-called soft actuators are used in recent de-

velopments due to the advantages that they provide

(Grioli et al., 2015).

A general concern in robotic devices, and partic-

156

Solaque, L., Romero, M. and Velasco, A.

Knee Rehabilitation Device with Soft Actuation: An Approach to the Motion Control.

DOI: 10.5220/0006861001560162

In Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2018) - Volume 2, pages 156-162

ISBN: 978-989-758-321-6

ularly when intended to use in applications that in-

volve interaction with humans, e.g. in rehabilitation,

is the control strategy to assure that the system is per-

forming the task with the required speciﬁcations, e.g.

zero tracking error. Classical control strategies, based

on feedback compensation are effective for this pur-

pose, however, they modify the system dynamics. Ac-

cording to (Della-Santina et al., 2017), these strate-

gies may cancel the compliant dynamics, eliminat-

ing the desired intrinsic characteristics of soft actua-

tion. In (Della-Santina et al., 2017) authors show that

an anticipative model of human motor control, using

a feedforward action, combined with low-gain feed-

back, can be used to achieve human-like behavior in

soft actuated devices. Following this idea, we intro-

duce a control strategy that does not cancel the com-

pliant dynamics, based on the combination of feed-

forward and feedback actions, oriented to control the

motion of a soft actuated knee rehabilitation device.

In the literature there are other works that tackle prob-

lems related to the control of rehabilitation devices.

For instance, (Witte et al., 2017), presents a closed

loop torque control using classical proportional feed-

back control with damping injection in conjunction

with iterative learning a knee exoskeleton. According

to (Grioli et al., 2015) and (Della-Santina et al., 2017)

many efforts have been done to control soft actuated

systems, as for example PD control strategies (De-

Luca and Flacco, 2011), feedback linearization (Pe-

tit and Albu-Schffer, 2011), backstepping (Petit et al.,

2015) immersion and invariance theories (Wimboeck

et al., 2010), optimal control (Ozparpucu and Albu-

Schaffer, 2014), and so on.

Regarding rehabilitation devices that use compli-

ant actuation and require a control strategy, some ap-

proaches are available. For instance, the control of

an assistive orthopedic system for rehabilitation based

on inherent compliant actuators has been presented in

(Wilkening et al., 2011). In (Mghames et al., 2017) a

one degree of freedom assistive platform to augment

the strength of upper limbs with VSA is presented.

Authors aim to control the system in feedforward by

mapping the Electromyographic signals (from mus-

cle activation), to exploit the muscle-like dynamics of

the mechanical device. However, a complete analysis

of the control problem for the system is left as future

work.

Furthermore, a compliant actuated parallel ankle

rehabilitation robot is presented in (Jamwal et al.,

2016). The robot allows the patients to modify the

robot motions according to their own level of dis-

ability by applying the strategy of interactive training

based on impedance control. This control scheme is

dependent on the therapists decision, therefore auto-

matic adaptation between impedance control modes

with low and high compliance is required.

In (Romero A. et al., 2017), a 5-bars-linkage un-

deractuated device for knee rehabilitation, using VSA

was presented, as shown in Fig.1. A control strategy

is required for the latter system, to perform desired

routines for knee rehabilitation. To gain an insight

of the control strategy and the requirements, we will

ﬁrst consider a one-Degree-of-Freedom (DoF) model.

In this way, here we deﬁne the control speciﬁcations

from the patient’s point of view, to perform a desired

motion during knee rehabilitation therapy. We pro-

pose a control strategy for the one DoF soft actuated

device, with the aim to maintain the intrinsic dynamic

properties of the system in order to exploit its advan-

tages. Results show that the global control strategy

proposed which combines feedback and feedforward

position control strategy, satisﬁes the conditions pre-

sented in (Della-Santina et al., 2017), allowing main-

tain the intrinsic softness of the system, while achiev-

ing the requirements of the one DoF system, i.e. com-

pensating with the feedforward strategy the distur-

bances due to the leg’s weight, keeping the stability

of the system. When approaching the 80% of the ref-

erence, we switch the control parameters in order to

have a lower velocity near to the reference. In future

works, we will study the validity of the control strat-

egy in the 5-bars-linkage-rehabilitation device.

2 DEVICE MODELING

APPROACH

This paper tackles an approach to controlling a soft-

actuated rehabilitation device - see Fig.1.

Figure 2: Model representation for knee rehabilitation.

To gain an insight of the control system behavior,

and taking into account that our scope is to control the

knee joint of the proposed assistive rehabilitation de-

vice, we will consider a one-DoF soft actuated model,

which represents the knee joint, as shown in Fig.2, de-

ﬁned by

˙q = ω

(−kq − Bω

+ kθ + τ

load

)

(1)

Knee Rehabilitation Device with Soft Actuation: An Approach to the Motion Control

157

where q and ω

are the link (calf) angular position

and angular velocity respectively; θ is the rotor (knee

join) angular position, which is considered as an input

to our system; τ

load

is the load torque, and M, k, B

are the mass, the stiffness and damping of the system,

respectively. Consider that the vector state is deﬁned

as X = [q, ω

]

In this paper we aim to control the link angular

position of the knee rehabilitation device, to comply

with deﬁned repetitive motions. It is worth to mention

that the soft actuators considered for the design have

a low level PD control that assures that the desired ro-

tor’s angular position is indeed the input angular po-

sition

θ.

3 COMBINED FEEDBACK AND

FEEDFORWARD CONTROL

STRATEGY

In this section we present the design of the combined

feedback and feedforward strategy, as shown in Fig.

3. We ﬁrst describe the control strategy requirements

based on the desired behavior of the patient’s knee

motion; then, we present the control law proposed.

3.1 Control Requirements

Let us describe Fig. 3. According to physical ther-

apy indications (Umivale, 2011), the control law must

keep the output position close to the desired reference

with a smooth approach, so the Reference Block pro-

vides a saturated reference. In this case, the reference

is the motor’s angular position θ. Then, the saturated

reference must be smooth in order to reach it with a

soft response, i.e. similar to an overdamped system.

Furthermore, the Feedback Block has an integral ac-

tion that ensures that the system follows the desired

reference and that disturbances are rejected.

The control strategy includes a feedforward ac-

tion such that loading disturbances are compensated.

Then, the Decision System Block acts as follows.

When the system, i.e. the knee approaches to the ﬁ-

nal value, over a threshold of 20%, the speed with

which it approaches to the reference is lower. This

is done because when performing rehabilitation train-

ing, the patient slowers in the critical angular posi-

tions, according to physiotherapists criterion. If the

force exerted by the patient is over the threshold, (e.g.

because the patient is in pain), the system will send a

zero reference to relax the patient’s leg.

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3.2 Control Design

Now, let us focus on the control design for the knee

rehabilitation assistive device. Based on pole place-

ment, we use low gains to approach the natural behav-

ior of the human motion, when performing exercises

to stretch and strengthen the knee muscles, guided by

a physiotherapist.

Consider the linear model of the system in (1).

Deﬁning k

, k

which are respectively the gain of the

angular position q; the gain of the angular velocity

. Furthermore, deﬁning k

as the gain of ξ, where

ξ = R − q; R is the desired knee angular position of

the rehabilitation system. Then, the feedback control

law is deﬁned by

θ = k[k

+ k

q + k

ξ]. (2)

Let us assume that the system is in equilibrium, this

is τ

load

= 0. Then, the closed-loop dynamics are

q(s)

R(s)

+ s

(B − kk

) + s(k − kk

) + k

. (3)

Here we assure that the feedback design, i.e. det(SI −

∗

)=0, is Hurwitz to tune the control coefﬁcients, so

the system is stable (pole placement). In a practical

way, these coefﬁcients modify the system dynamics.

So to maintain the intrinsic dynamics of the system,

i.e. the stiffness, the changes have to be such that the

system response is close to the natural response. Ac-

cording to (Della-Santina et al., 2017), a low-gain of

the feedback controller is required in order to have lit-

tle stiffness alteration in the model. The main differ-

ence, and the contribution of this proposal is that we

focus on the control design speciﬁcations for a soft

actuated knee rehabilitation device (i.e. actuated by

SEA or VSA), applying the sufﬁcient condition de-

rived in the previously mentioned work. The aim here

is to maintain the intrinsic characteristics of the actu-

ation system, this is to keep σ proportional to q − θ.

Regarding stiffness, it is deﬁned as

∂T (q−θ,σ)

∂q

where T (q − θ, σ) is the torque due to the compliant

element at the joint, and σ is a parameter used to set

joint stiffness in variable stiffness actuators. For the

design of the position controller presented in this pa-

per, we consider a constant stiffness.

In order to minimize the changes in the physical

compliance, the stiffness value in closed loop has to

remain in a δ-neighborhood of the value in the open

loop, along the system reference signal. Then, let us

consider that our controller is θ(q, ˙q,t, σ,r, ξ) as in

(2). Then, the partial derivative

∂θ(·)

∂q

results in the

controller coefﬁcients. Consider also that the natu-

ral stiffness along the system reference is deﬁned as

ICINCO 2018 - 15th International Conference on Informatics in Control, Automation and Robotics

158

Figure 3: Control structure used in the rehabilitation system.

∂T (0,σ)

∂q

, then, the sufﬁcient condition to maintain the

system stiffness is veriﬁed. In this case it is

∂θ(q, ˙q,t,σ, r,ξ)

∂q

k≤ δ k

∂T (0,σ)

∂q

−1

, (4)

where r is the reference trajectory, R is the desired

knee angular position, and ξ is the integral action on

the error. When

ξ = Π(q, ˙q,t, σ,r,ξ) exists (4) be-

comes

∂θ

∂q

∂θ

∂ξ

∂q

k≤ δ k

∂T (0,σ)

∂q

−1

(5)

The main idea of (5) is that the coefﬁcients of

feedback part of the controller have to be sufﬁciently

small, so we need to evaluate these coefﬁcients in the

case of the controller proposed here. If the right term

in (5) is zero, there will be no stiffness variation due

to the control action. This is k

∂θ

∂q

∂θ

∂ξ

∂q

k≤ 0. Re-

garding the controller designed in this case, it is true

that k

∂T (0,σ)

∂q

−1

= 0, which meets the sufﬁcient con-

dition.

3.3 Controller Implementation

We choose k

, k

y k

sufﬁciently small, applying the

poles placement method, according to the following

criteria. Using a Robust Control Toolbox, we test the

system to tune these values, such that with a varia-

tion up to 20% of k

, and k

, and up to 30% of k

the system is stable and the design speciﬁcations are

met, i.e. low speed when approaching to the desired

angular position, keeping the intrinsic stiffness of the

system. Observe Figs. 4 and 5, which show respec-

tively in time and frequency domain that the system

is stable when there is a change of the control param-

eters.

In this way, the condition (4) is accomplished, as

well as the control objective. Therefore, the natural

0 20 40 60 80 100 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Uncertainty response

Nominal response

Step Response

Time (seconds)

Amplitude

Figure 4: Variation of control parameters - Step response.

-100

-50

Magnitude (dB)

-3

-2

-1

-270

-225

-180

-135

-90

-45

Phase (deg)

Uncertainty response

Nominal response

Bode Diagram

Frequency (rad/s)

Figure 5: Variation of control parameters - Bode of the sys-

tem.

motion achieved using soft actuation allows to per-

form assisted knee rehabilitation exercises. For the

design and validation of the derived control law, we

use a stiffness preset constant value of σ = 6 Nm/rad.

4 RESULTS AND DISCUSSION

To analyze the results of the control strategy for the

rehabilitation device, we design a test in simulation.

We consider that the rehabilitation system can be con-

Knee Rehabilitation Device with Soft Actuation: An Approach to the Motion Control

159

Figure 6: Tracking system.

ﬁgured for patients heights h between 1.40 m and

1.90 m, and weight W between 40 kg and 90 kg ac-

cording to mean normal adult population. Accord-

ing to anthropomorphic proportions we can establish

mean length and weight of the leg according to h

and W . For the simulations, the parameters corre-

spond to a subject of h = 1.60 m and W = 60 kg.

Besides, damping and stiffness are obtained experi-

mentally as B = 1 First, let us consider the feedback

action. According to the proposed strategy, we de-

ﬁne the reference for the angular position that the

knee has to reach. When the angular position has

achieved 80% of the desired value, the structure of

the regulator changes by means of the integral action,

making the response slower, compared to the system

dynamics. It is worth to mention that the controller

was designed such that the stiffness is not affected, so

a change in the parameters will maintain this condi-

tion. Fig. 6 shows the system response to a reference

re f

rad. Notice that the output q follows the ref-

erence with zero tracking error. It is worth to mention

that the input to the control system is a saturated ref-

erence thus it is close to the real state of the system.

We observe that at time t = 190 s, when the output

reaches 80% of the ﬁnal value, indeed the dynamic

changes and the motion becomes slower, as desired

(see point labeled as 1 in Fig. 6 ). Let us deﬁne that

after t = 300 s, the patient needs to stop the system

(e.g. because of pain), then we simulate this require-

ment as an stop. In this case, the system has to go

back to an initial conﬁguration in order to relieve pain

(see point labeled as 2 in Fig. 6).

In ﬁg. 7 we show the control and error sig-

nals. Observe that there are no overshoots nor strong

changes, keeping the system stable, guaranteeing a

smooth motion for the knee joint.

Now, let us consider the feedforward action. The

idea of this action is to reject disturbances. Then, we

test the system with a step signal perturbation µ(t)

which may represent for instance the corresponding

component of the leg’s weight, that is an available

measurement of the system. The signal µ(t) acts from

Figure 7: Input to the system and Error.

Figure 8: Tracking system with perturbation.

t = 0 s to t = 100 s. In ﬁg.8, the results of the control

action are presented. Observe that the system perfor-

mance with the disturbance is close to that when there

is no disturbance, and that the response recovery starts

at t = 0 s (see point labeled as 1 in ﬁg.8). At the end of

the disturbance, at t = 100 s the system recovers and

continues to operate normally, as desired (see point

labeled as 2 in ﬁg.8).

Referring to the control signals, due to the com-

pliant behavior of the system it presents oscillations,

which are properly compensated. These oscillations

are due to the natural behavior of the system using

soft actuation.

Figure 9: Input to the system and Error with perturbation.

ICINCO 2018 - 15th International Conference on Informatics in Control, Automation and Robotics

160

5 CONCLUSION

In this paper, we have presented a global control strat-

egy that combines feedforward and feedback actions

for a soft actuated knee rehabilitation device. The de-

signed device is a 5-bars-linkage underactuated sys-

tem. However, to gain an insight of the control strat-

egy and the requirements, we have presented an ap-

proach to control a soft-actuated-one DoF system,

when performing the desired motion during physical

knee rehabilitation. The speciﬁc requirements of the

system, that we have proved to achieve with the pro-

posed combined control strategy are to keep intrinsic

stiffness of the system, stability, low velocity when

approaching to the reference, and disturbance rejec-

tion. The feedforward strategy compensates loading

disturbances while the feedback strategy acts in a de-

ﬁned threshold to maintain the stiffness of the sys-

tem. When approaching the 80% of the reference,

we switch the control parameters in order to have a

lower velocity near to the reference, meeting the de-

sired speciﬁcations. In future works, we will study the

validity of the control strategy in the 5-bars-linkage-

rehabilitation device.

ACKNOWLEDGMENT

This work is funded by Universidad Militar Nueva

Granada- Vicerrector

ıa de Investigaciones, under

research grant for project IMP-ING-2291, entitled

’Dise

no de un prototipo para rehabilitaci

on de rodilla

mediante el uso de actuadores ﬂexibles’.

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