Vrije Universiteit Brussel

Torque Control of a Push-Pull Cable Driven Powered Orthosis for the CORBYS PlatformRodriguez Guerrero, Carlos; Grosu, Victor; Grosu, Svetlana; Leu, Adrian; Ristic-Durrant,Danijela; Vanderborght, Bram; Lefeber, DirkPublished in:International Conference on Rehabilitation Robotics

Publication date:2015

Document Version:Final published version

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Citation for published version (APA):Rodriguez Guerrero, C., Grosu, V., Grosu, S., Leu, A., Ristic-Durrant, D., Vanderborght, B., & Lefeber, D.(2015). Torque Control of a Push-Pull Cable Driven Powered Orthosis for the CORBYS Platform. In InternationalConference on Rehabilitation Robotics (pp. 61-66). Singapore: IEEE.

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Torque Control of a Push-Pull Cable DrivenPowered Orthosis for the CORBYS Platform.

Carlos Rodriguez Guerrero∗, Victor Grosu∗, Svetlana Grosu∗, Adrian Leu†, Danijela Ristic-Durrant†, Bram Vanderborght∗ and Dirk Lefeber∗.

∗Robotics and Multibody Mechanics Group, Vrije Universiteit Brussel, Brussels Belgium†Institute of Automation, University of Bremen, Germany

Corresponding email: carodrig@vub.ac.be

Abstract—Rehabilitation robotics is a growing field whichis on the verge of exploring novel actuation technologies thatallows the designers to build assistive devices with large powerto weight ratios without compromising the transparency of thesystem. In this paper a novel push-pull cable driven technologyimplemented in the CORBYS rehabilitation system as a solutionfor a proximally actuated device is presented. A novel torquecontrol strategy enhanced with a machine learning compensa-tion method is proposed to deal with the inherent complexitiesof the system. Experiments will show results obtained on thepowered exoskeleton part of the platform.

I. INTRODUCTION

We have recently experienced in our times a boom in

the so called rehabilitation robotics domain, where robots

are designed to physically interact with patients and relief

therapists from the physical effort needed to carry the thera-

pies and giving them a more ’decision making’ supervisory

and scientific role. Several commercial and non-commercial

devices have appeared in the recent years such as the Au-

toAmbulator (ReoAmbulator) Healthsouth [1]), the Lokomat

[2], the WalkBot [3], [4] LOPES [5], ALEX [6], KNEXO

[7], WalkTrainer [8], ALTACRO [9].

In spite of this boom, a clear advancement over con-

ventional therapy stays out [10],[11],[12]. Pennycott [13]

made a review study on the outcome of robot-assisted gait

rehabilitation. They propose the inclusion of more degrees of

freedom (DOF) that allows more aspects of the gait such as

balance to be trained, and robots with greater transparency

for a more natural human robot interaction. They also pointed

out: ’These (robots) will provide an important opportunity in

the near future to intensively investigate the clinical impacts

of these various concepts.’ To tackle both, added DOF and

transparency at the same time, seems to have a fundamental

problem in the way that the addition of more active DOF,

faces the intrinsic problem of adding more actuators to the

structure and therefore adding more weight to it most likely

hindering the transparency and available output torque of the

system.

Decoupling the actuation system from the effector can

give freedom to design more powerful rehabilitation systems

without the inconvenience of the added weight due to the

inclusion of bigger motors that translates into added inertia

on the links. This type of actuation is so called proximal

Fig. 1. Subject walking on a treadmill with the CORBYS gait rehabilitationsystem while the system is being controlled in zero force mode.

actuation and aims to provide high power to weight ratios by

placing the actuators over a grounded structure rather than

directly on the joints and has been already implemented in

lower limb rehabilitation robots such as LOPES [5], LOPES

II and now the CORBYS platform [14]. In LOPES, the basic

idea was to detach the motor from the robot frame by the

use of flexible Bowden cables and series elastic elements

so that the exoskeleton legs could move unhindered, while

little weight is added to the robot construction, compared

to the relatively heavy electro motors [5]. Bowden cables

however, are not able to withstand compression forces, so all

the structure should ensure that all the cables remain tight

whatever the configuration of the structure [15]. CORBYS

uses instead push-pull cable (PPC) technology which can

stand both, tension and compression forces.

CORBYS - Cognitive Control Framework for Robotic

Systems is a colaborative project funded by the european

commission under the 7th framework program [16], [14].

CORBYS developed new principles for the way that human

and robot interact and share their cognitive capabilities.

Structurally, CORBYS includes a combination of a mobile

platform, a lower limb exoskeleton and a pelvis module that

acts like a weight support system and drives the exoskeleton

61978-1-4799-1808-9/15/$31.00 c©2015 IEEE

up, down, left and right, see Fig. 1.

This paper focuses on the compliant control of the ex-

oskeleton’s PPC novel actuation system that drives the active

degrees of freedom of the robotic orthosis in the sagittal

plane. The main contribution in this paper, is that of pre-

senting a novel control architecture that can be used to

deal with the major drawbacks of using PPCs for power

transmission. This architecture features a model compensa-

tion system based on machine learning. Section 2 includes

a brief description of the PPC actuated system and shows

data of the dynamics found at the hip and knee joints of

the powered orthosis. It also presents the joint space control

strategies used to make the PPC driven system act as a

torque source which is the base for any further haptic strategy

like impedance control. Section 3 describes experiments to

validate the proposed controller. In section 4 and 5 we present

and discuss the results achieved and finally conclusions are

presented in section 6.

II. MATERIALS AND METHODS

A. The CORBYS platform

The CORBYS powered orthosis assists the patients lower

limb joint motions. The configuration of the DOFs of the

CORBYS orthosis was implemented to follow natural human

limb kinematics. There are 6 DOFs at each leg: 3 DOFs

in the hip, 1 DOF in the knee, and 2 DOFs in the ankle

joints. The hip and knee joint motions on the sagittal plane

(flexion and extension), as well as ankle joint motions in the

sagittal plane (plantarflexion and dorsiflexion), are selected

as the active DOFs based on the biomechanics properties of

human walking, while the hip DOFs in the frontal and the

transverse plane (adduction/abduction and internal/external

rotation) as well as the ankle DOF in the frontal plane

(eversion and inversion) are passive. The orthosis of the

CORBYS system is attached to a mobile platform via a 4

DOFs pelvis interface mechanism (consisting of the pelvis

link and the linear unit), which enables pelvis rotation in the

frontal and transverse planes as well as the pelvis vertical

and side to side movement. Together with the 4 DOFs of the

pelvis interface mechanism, the CORBYS orthosis provides

a total of 16 DOFs for the body movement, which makes

it the first orthotic device with such a number of DOFs.

Additionally, the orthosis was designed in order to satisfy

the requirement of adaptability to the patients height and

weight, as well as the requirement of the range of motion

of the biomechanical joints.

The particular novelty of the CORBYS orthosis is that the

hip joint provides all 3 DOFs of the human hip joint where

only the rotation in sagittal plane is actuated which, however,

does not influence the rotations in the transverse and frontal

planes. This is achieved via a common center of rotation of

three hinge-joints. This common center of rotation is aligned

with the biomechanical hip joint of the human. As another

novelty, an angle independent weight compensation of the

orthosis in the frontal plane is implemented, as it is needed

Fig. 2. Representation of the CORBYS PPC actuation system. Actuatorsare placed on frame and power is transferred by push pull cables to the joint.

for the passive abduction/adduction joint. The movements of

the orthosis joints in the sagittal plane are controlled by a

push-pull control cable actuation system [14][17]. There are

three actuators (PRL+ modules, SCHUNK) per orthosis leg

that actuate the hip, knee and ankle joints in the sagittal plane.

B. PPC actuation system

The exoskeleton’s actuation system, see Fig. 2, The

actuators are placed on the mobile platform while the PPC

cables are flexible links to the joints used to transfer the

rotational movement of the motors to specifically designed

orthotic joints. This has the advantage of keeping the

powered orthosis weight low while the necessary torques are

applied through the PPC cables to the patients joints. In the

CORBYS system, PPCs of different diameters and lengths

are used, as different moments are required for actuation

of orthosis leg joints. Therefore, the rotary movement of

the actuator has to be transformed to a linear movement in

order to actuate PPC. This transmission is provided using

a mechanical lever construction where the actuation force

depends on the lever length and position. The transmitted

force changes with the lever angular position. This means

the wider the operation range of the actuator, the smaller

is the applicable force in PPC direction. The force applied

by the actuator is reduced by the system geometry and the

friction in the PPC. The efficiency of the PPC is essential

for the function of the powered orthosis.

The actuators for the active joints are placed in a proximal

way (related to the structure) back on the mobile platform

while the PPC is a flexible link to the joints. The static

(unmovable) part of the PPC is mounted to the demonstrator

base frame. The distance from the smart actuators center to

the static attachment of the PPC depends on the necessary

stroke of the PPC. This stroke is given by the kinematic

62 2015 IEEE International Conference on Rehabilitation Robotics (ICORR)

design of the orthotic joints. Because, each joint (hip, knee,

and ankle) has a different kinematic design various stroke

parameters will be attributed.

Fig. 3. Sketch of mechanism that transforms push-pull cable forces intotorques and vice versa

Figure 3 shows the skeleton diagram of the actuation

mechanisms. In order to get the torque to force relation that

the mechanism provides, we can start by assuming P1 and

P2 have always the same velocity. This will be the starting

and key point to get to our analytical solution. Figure 4

shows the mechanism decomposition where:

R = Distance between the joint and the slider.R1 = Length of the crank link.R2 = Length of the connector link.P = Slider velocity.τ1 = Joint Torque.F = Force component on the direction of R2.ω1 = Motor angular velocity.θ1 = Angle between R1 and the slider mechanism axis.θ2 = Angle between R2 and the slider mechanism.

Fig. 4. The skeleton diagram of the actuation mechanisms. This helps tovisualize the analytical solution that translates force-cell readings with thetorque at the crank link.

Assuming no important losses in the mechanism one can

safely state that the power transmitted from R2 to R1 is

constant and thus:

τ1ω1 = PF (1)

Solving the equations by using the principle of virtual

work, and solving for the angle θ2, we can get to the

following relation:

θ2 = arcsinR1(1− sinθ1)

R2(2)

Having the angle θ2, we can now find τ1, which is the

torque we are interested in with the following formula:

F cos(θ2) =τ1

R1(sin θ1 − cos θ1 sin θ2)(3)

Which leads to:

τ1 = F cos(θ2)(R1(sin θ1 − cos θ1 sin θ2)) (4)

Knowing F cos(θ2) is the load cell reading, R1 is a

constant value, θ1 is read from the joint encoder and θ2 is

computed from the motor position, we can easily obtain τ1from equation (4).

C. Torque Control of the CORBYS orthosis

Typically, electric motors have a linear relation between

the armature current and the torque output which makes

it straightforward to implement impedance control loops

whenever the power transmission between the motor and

the joint is direct, and there is nothing between the mo-

tors and the joints. The CORBYS system, however, uses

a proximal actuation system by means of push-pull cables

and the SCHUNK’s PRL+ units have large harmonic drives

which makes the system non backdrivable. The use of PPC’s

and non-backdrivable motors have different consequences for

the control. While there exists well known techniques such

as admittance control that can turn backdrivable systems

into force/position controlled systems by using force sensor

feedback and an inner position/velocity loop that tries to

render the virtual admittance output. This is not a suitable

solution in the CORBYS setup as we can’t just simply use

the internal position/velocity loop embedded in the PRL+ unit

since is the joint what we are aiming to control. What we

have instead is a non-collocated problem, as the sensor that

closes the loop is not sensing the actuators output directly.

That means that in order to control a virtual admittance at

the joint, we need to implement the inner position/velocity

loop at the joint side first. However, implementing a stable

position/velocity controller on a non collocated system with

considerable backlash and connected by a PPC system proved

not to be an easy task since most of the times it resulted in an

unstable system due to the big discrepancies on the motion

of the source reflected on the load and also in this case, the

resolution of the encoders on the motor side and the joint

side. Moreover the dynamics of the CORBYS PPC system

proved to be highly nonlinear.

In order to have an idea of how the system dynamics

at the joint level looked alike, we have performed some

experiments to gather data that maps the configuration of the

robot to the torques read at the joint levels. Figure 5(a) and

2015 IEEE International Conference on Rehabilitation Robotics (ICORR) 63

Fig. 5. Angle Vs Torque characteristics for hip and knee joints. Several nonlinear dynamics can be observed.

Figure 5(b) show the relationship between angles and torques

at the hip and knee level in response to a slow sinusoidal

trajectory commanded to the motor. In those figures we can

see complex nonlinear behavior such as mechanical backlash,

internal friction and flexibility mainly due to the influence of

the PPC internal bending.

D. Joint space torque control

In this paper, we propose to create a fast and robust torque

control that can later be used by an outer impedance or proxy

based sliding mode controller to render assistive/corrective

force fields. Figure 6 shows a block diagram of the imple-

mentation of the proposed joint space torque controller for

CORBYS.

In order to deal with the backlash and non-collocated

control problem, we have implemented a PI+D dual loop,

a variant of a PID for systems with backlash [18].

In this dual PID loop originally proposed for position

control systems, the proportional and integral terms operate

on the signal coming from the joint load, forming the main

feedback loop, while the derivative term acts on motor load

feedback, which is the best source of information for stabi-

lizing the system. The tuning of the PI+D torque controller

was made experimentally by using a square wave input

(alternating step signal) as a virtual desired torque, and tuning

the gains to improve bandwidth and disturbance rejection. It

is important to point out that the harmonic drives behavior

curves and therefore the output torque of the PRL+ unit is

Fig. 6. General proposed torque control block diagram. The system iscomprised by a dual loop torque controller, a velocity limiter controllerand a neural network robot model compensator.

dependent not only on the input current and the current/torque

relation, but also on the gearbox efficiency, which depends in

turn on the speed and on the gearbox temperature which will

require an extra sensor. Therefore the tuning was made while

the gearbox was warm after been exposed to some use (1

hour) as it increases its efficiency making it more responsive

and therefore changes the stability margins.

Another important implementation issue that is faced in the

CORBYS system, was the speed limit safety implementation

that the PRL+ units have by default. The maximum velocity

of the motors is 45 deg/s. For safety reasons, the motors

activate their brakes if this velocity is exceeded. Therefore,

a velocity limiter that observes the velocity, and counteracts

the commanded current to clamp the velocity to a desired

maximum level was designed. This was implemented by

means of a P controller that acts on the error signal between

the maximum and read velocities, with a counter-current

output that adds to the torque controller and prevents the

motor to get to an undesirable level.

E. Robot model compensation

One of the most important characteristics of any phys-

ically interactive robot is that of being able to properly

render reactive force fields. In order to achieve this, the

low level control system ideally should behave like a perfect

force/torque source independent of the system dynamics. This

means that in order to achieve transparency, we need to have

a good model compensation.

As the system dynamics resulted to be heavily non linear,

a parametric model to compensate for each joint would

most likely result in a very complex yet inaccurate solution.

Therefore a multi-layer perceptron (MLP) was trained to

learn a model to compensate for the hip and knee own

dynamics coming from both, position and velocity dependent

terms like gravity, Coriolis, centripetal and viscous friction.

Inertia was not compensated as there is no acceleration

feedback in CORBYS. The ankle was excluded since the

impact of the model compensation on the overall behavior

of the joint was not significant enough to justify for the two

64 2015 IEEE International Conference on Rehabilitation Robotics (ICORR)

extra inputs and one output on the MLP and since it is the

final link of the kinematic chain, there is no coupling dynamic

effects that propagates further to the structure.

The MLP was trained in MATLAB by using the neural

network toolbox algorithm and then exported to C++ using

the coder toolbox for optimized code generation. The training

data set was obtained by driving sinusoidal trajectories on

both hip and knee with amplitudes that covered all the

range of motion for both. Notice that the excitation function

frequency for the knee was 10 times bigger than that on the

hip to cover as much as possible the whole configurations of

the robot.

The results on the error from the real data and the MLP

estimation for the hip joint can be seen in Figure 7. The

resulting error (Fig 7b) from the difference between the

obtained data and the model estimation output for the hip

(Fig 7a) was in mean=-0.0067 and std=2.63 Nm while for

the knee was in mean=0.0012 and std=2.8501 N.m.

Fig. 7. On top, Hip torque data together with the perceptron prediction.At the bottom, the mean error between real hip data and estimated hip dataover 12000 samples at 100Hz (120 seconds). NN stands for neural network.

III. EXPERIMENTS

Two experiments were performed to test different aspects

of the proposed controller design. On the first one, we wanted

to see the tracking response of the torque controller and

specially the backlash rejection. For that, we commanded a

sinusoidal wave to the knee’s torque controller set point and

registered the commanded current to the motor, the motor’s

velocity, the joint’s position and joint’s torque feedback.

For the second experiment, the torque controller’s set point

was set to 0 and the maximum velocity was set to 41 deg/s,

while we applied alternating external forces to the joint by

hand to the knee joint back and forth, to accelerate the link

and see the effects of the velocity clamper over the current

output and the motor velocity signal.

IV. RESULTS

Figure 8 shows results on the first experiment, showing

a low tracking error between the commanded torque signal

and the read torque. Besides good torque tracking, we can

also see how the backlash rejection (black box in Figure

8) provides a smooth motion profile by looking at the

position signal. It is also visible the effect of the motor being

momentarily accelerated by an over current to deal with the

non contact zone (zero torque zone due to the backlash)

and provide a smooth output. In spite of that short burst of

current, the commanded current provided by the controller is

typically below the normal operation levels of the motor (10

A commanded current) which is important for durability of

the machine.

Fig. 8. Torque controller tracking and backlash rejection response (blackbox). We can see the controller’s fast reaction in response to the discontinuityin the torque signal.

Figure 9 show the action of the velocity clamper. We can

see the effectiveness of the limiter as we applied external

forces to the joint to accelerate it into a fast motion.

Fig. 9. Velocity clamper controller with a set point of 41 deg/s. Torque’scomputed, counter and output currents are displayed to show the effects ofthe limiter on the current sent to the motor.

2015 IEEE International Conference on Rehabilitation Robotics (ICORR) 65

V. DISCUSSION

The proximal actuation system proved to be an excellent

way of decoupling the motors from the structure allowing

the usage of bigger and more powerful motors. The use of

this technology however comes at its costs as the PPC’s

presented considerable losses due to the friction created by

the internal bending between the inner and outer cables.

Besides that, backlash was also induced by the PPC’s internal

bending which presented a challenge in the control design.

This however has been successfully solved by implementing

the control strategy proposed in section 2.D where the PI part

tends to drive the motor faster based on the joint’s torque

error signal, while the D part keeps the system stable in

response to the error signal on the motor’s side torque and the

outer loop command. The response of the proposed controller

was satisfactory in dealing with the mechanical design of the

system and we believe it can be extrapolated to any device

that uses PPC actuation with force control. It is also visible

that there is some ripple effect when the limit velocity is

reached. Although this phenomenon is not critical, it could

be compensated by using a PD controller instead of a pure P

action. However, since the feedback for the velocity limiter is

the motor’s velocity, and this is obtained by pure backwards

differentiation, a D controller could induce considerable noise

and may result unpractical.

VI. CONCLUSIONS

Using PPC’s as a form of transmission proved to be an

effective way of dealing with systems that requires high

power ratios with low added inertia at the end effector such

as the one present in the CORBYS powered orthosis. It

is important nevertheless to be aware of the lengths and

bending angles of the PPCs since we have noticed most of the

undesirable dynamic effects that we had in the platform came

from the excessive long cables as the longer they are the more

internal space for bending it will be and thus, more friction,

backlash and losses there will be. The use of PPC’s induces

several challenges from the control point of view such as

backlash and complex dynamics that may be difficult to

model using a classical robot parametric approach. However,

as shown in this paper, the use of machine learning to

compensate for the robot dynamics proved to be an excellent

and easy to use solution albeit the lack of flexibility that

an algebraic model gives. We are studying the possibility to

include an on-line learning algorithm in the near future using

an accelerated version of a Gaussian Process Ensemble [19]

designed under the CORBYS project. This could allow us to

re-train the system when needed as the system’s properties

may change due to machines wear or when considerably

changing the robot’s links to fit a new patient.

ACKNOWLEDGMENT

This research was supported by the European Commission

as part of the CORBYS (Cognitive Control Framework for

Robotic Systems) project under contract FP7 ICT-270219.

The views expressed in this paper are those of the authors,

and not necessarily those of the consortium.

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66 2015 IEEE International Conference on Rehabilitation Robotics (ICORR)