Parallel Robotic Manipulation via Pneumatic Artificial Muscles

Dimitris Gryparis, George Andrikopoulos and Stamatis Manesis

Department of Electrical and Computer Engineering, University of patras, Eratosthenous str., Rio, Greece

Keywords: Pneumatic Artificial Muscles, Parallel Manipulator, PID Control.

Abstract: In this article, a 6 Degree-of-Freedom (DOF) parallel manipulator, actuated by Pneumatic Artificial Muscles

(PAMs), is being presented. Incorporated in a two Stewart Platform-based design, the novel manipulator’s

motion capabilities are being examined through kinematic analysis, while the open-loop operation

characteristics and performance of the manipulator’s control via a multiple PID-based scheme are being

experimentally evaluated.

1 INTRODUCTION

Over the last decade, there has been an increasing

scientific interest in robotic manipulators that are

lightweight, safe and compliant (Calabria et al.,

2012; Radojicic & Surdilovic, 2009; Denkena et al.,

2008). In such cases, the selection of the type of

actuation that will power the manipulator is of

utmost importance. The Pneumatic Artificial Muscle

(PAM) has drawn the attention of the scientific

community regarding its merits for utilization in

biorobotic, medical and industrial applications

(Andrikopoulos, Nikolakopoulos & Manesis, 2011).

By mimicking the operation and properties of the

organic muscle, the PAM provides a suitable

solution for safer user interaction, as well as more

strong and natural motion through inherent

compliance, absence of mechanical parts, as well as

an impressive power-to-mass ratio. The most

utilized PAM-type is the McKibben Artificial

Muscle which was invented by the physician Joseph

L. Mckibben in the 1950s and was incorporated in

artificial limps (Stewart, 1965).

So far, similar PAM-actuated manipulator

approaches have included one Degree-of-Freedom

(DOF) per platform concepts (Calabria et al., 2012),

Stewart-based platforms via the utilization of 3

PAMs conically incorporated (Radojicic &

Surdilovic, 2009) and via more complex pneumatic

actuation mechanics (Denkena et al., 2008).

Parallel manipulator aproaches with the

utilization of other actuation means have included 3-

DOF parallel manipulators actuated by servomotors

(Cazalilla et al., 2014), (Khosravi et al., 2014),

(Ning et al., 2006) and 6-DOF Stewart-based

platforms actuated via hydraulic actuators placed at

the base of the robots (Guo, et al., 2007), (Pi et al.,

2010).

This article presents the development and control

of a parallel manipulator with 6 DOFs, which was

implemented in a two Stewart Platform-based

design. In this novel approach, each platform

consists of four PAM actuators in parallel

configuration, which are being operated as

antagonistic pairs, while a pneumatic cylinder is

being incorporated in the center of each platform,

thus, achieving 3 DOFs per moving platform.

The presented manipulator possesses the

advantage of incorporating more DOFs than the

manipulators found in related literature, thus

possessing enhanced motion capabilities, improved

motion range and increased relative workspace. In

addition, the cascaded configuration of the two

platforms is enhanced by the placement of all the

PAMs on the lower segment of the manipulator in

order to provide a novel mechanical approach on the

actuated motion of this parallel robotic structure.

The PAM-actuated manipulator is being depicted in

Figure 1.

In the following sections, the experimental setup

components and the kinematic analysis of the

manipulator’s structure are being presented, followed

by a presentation of the open-loop operation

characteristics of the manipulator. Finally, the

performance of the setup’s control via a multiple

PID-based scheme is being experimentally evaluated.

Gryparis D., Andrikopoulos G. and Manesis S..

Parallel Robotic Manipulation via Pneumatic Artiﬁcial Muscles.

DOI: 10.5220/0005008700290036

In Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2014), pages 29-36

ISBN: 978-989-758-040-6

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

2 EXPERIMENTAL SETUP

COMPONENTS AND

KINEMATIC ANALYSIS

2.1 Setup Components

Figure 1: The parallel robotic manipulator.

The structure utilizes eight PAMs that have been

incorporated on the lower segment of the

manipulator. Four PAMs are utilized for the

actuation of the lower platform, which are placed

closer to the center of the ground plate and are

characterized by 170 mm nominal length and 20mm

inner diameter. Additional four PAMs are being

utilized for the actuation of the upper platform,

which are placed in the outer formation of the

ground plate and are characterized by 220 mm

nominal length and 20mm inner diameter. These

PAMs are being connected to the upper platform via

Teflon flexible shafts. All utilized PAMs are

manufactured by Festo AG & Co. KG and feature a

maximum pulling force of approximately 2000 N

and a weight of less than 300 g.

In order to augment the rigidity of the

construction and increase the DOF motion

capabilities, two non-revolute pneumatic cylinders

were placed in the center of each platform. The

operational range of each cylinder is 0-6 bar and

their nominal length is 300 mm. The non-rotating

pistons are connected to the platforms via universal

(cardan) joints. These joints allow rotations only

around x or y axis.

Twelve Festo proportional pressure regulators

are being utilized in order to provide compressed air

to each muscle and to each pneumatic cylinder

independently. In addition, two dual axis

inclinometers manufactured by Level Developments

Ltd were utilized featuring an effective angle

measurement range of in both x and y axis, in order

to provide the necessary angle feedback for the

control loop that is being described in the sequel.

Furthermore, two input/output cards manufactured

by Measurement & Computing are being utilized

for the interconnection of the pressure regulator and

sensor equipment with the personal computer. The

interface between the setup and the computer system

components is being composed via LabVIEW

software.

2.2 Forward Kinematic Analysis

A simplified axial representation of the manipulator

is being presented in Figure 2. It must be noted that

due to the design concept of placing all PAMs at the

ground plate, the upper platform is being rotated by

with respect to the z axis of the lower platform in

order to achieve ameliorated performance and more

compact design implementation.

Figure 2: Simplified axial representation of the

manipulator.

metallic

plate

Flexible

shafts

PAMs

metallic

plate

Immobile

ground plate

Proportional

Regulators

Pneumatic

Cylinder

ICINCO2014-11thInternationalConferenceonInformaticsinControl,AutomationandRobotics

The symmetrical design concept of the manipulator

and the utilization of universal joints, which allow

independent movements in relation to the x-y axes,

provide the advantage of considering the PAM-

induced motion in each plane for the both platforms

as decoupled, thus simplifying the kinematic

analysis of each platform. In this way, it is possible

to study the forward kinematics of each plane

independently without introducing complexities due

to motion coupling. The following kinematics

analysis is based on a geometric analysis, as is

commonly practiced in parallel robotic theory. The

symbolic representation A(i,j)

indicates the point

where the i-th PAM (i ∈{1,…4}) is attached to the j-

th link (j ∈{1,2}) in the first. The immobile ground

plate denoted as 0, the middle plate as 1 and the

upper plate as 2, yields the kinematic analysis of a

single antagonistic segment presented in Figures 3

and 4. The symbolic representations O

, q ∈ {0,1,2}

and

, w ∈ {1,2} indicate the geometric center of

the q-th metallic platform and the w-th universal

joint’s geometric center respectively.

Figure 3: Geometrical analysis of a single antagonistic pair

of PAMs in the y-z plane of the lower platform.

Figure 4: Geometrical analysis of a single antagonistic pair

of PAMs in the x-z plane of the lower platform.

To simplify the analysis of the manipulator, the

lengths of the pneumatic cylinders are being

considered as constants and are noted as l

and l

respectively.

Furthermore, the angle in x and y axis

are being denoted as



and ,



respectively, where i

indicates the lower (i=1) or the upper (i=2) platform.

To further simplify the mathematical analysis,

the following notations are being utilized:

01 1

OO l



12 2

||OO l

(1)

111 1

OA c



11 2

|O |Oc

(2)

212 3

||OA c



(3)

In addition, constraints posed by the structural

properties of the design ensure that:

||OO

(4)

2.2.1 Kinematic Analysis of the Lower

Platform

The methodology used to obtain the coordinates of

the endpoints of the manipulator’s platforms’ is

being presented below in the following equations.

The coordinates of the middle point of the straight-

line segment, which is being formulated from the

aforementioned endpoints, are the coordinates of the

platforms’ centers. The coordinates of the points

and O

are geometrically derived from Figure 3.

(0,0, )lO 

(5a)

121121

(0, sin(), cos())clcO



 

(5b)

There is only one unique straight line that passes

from both

and

O in the y-z plain in the form of

zkyb





where k

is the slope of the line and b

is a static constant. The straight line that intersects

is being described by:

tan( )zy l







(6)

The straight line that intersects the

points

and

O , and by design is vertical to (6) is

being presented below:

12 11

ztan()cos()yc l





 

(7)

The following y-plane coordinate equations are

being geometrically deduced via Figure 3 as:

(1,1) 2 1 1 1

sin( ) c cos( )







(8a)

(2,1) 2 1 1 1

sin( ) c cos( )







(8b)

ParallelRoboticManipulationviaPneumaticArtificialMuscles

and substitution of (8a) and (8b) in (7) give the z-

plane geometrical equations:

(1,1) 2 1 1 1 1

cos( ) sin( )

zc c l





(9a)

(2,1) 2 1 1 1 1

cos( ) sin( )

zc c l





(9b)

From Figure 4, the coordinates of O

can be derived

as:

12 1 2 11

(c sin( ),0,c cos( ) )





(10)

There is only a unique defined straight line that

passes from both

and

in the x-z plane, the

form of which is

zkxb where k

stands for

the line’s slope and b

for the constant coefficient:

tan( )zx l





(11)

The straight line that intersects both

O and

perpendicular to (11) based on the manipulator’s

design properties, thus giving:

112 1

z tan( ) cos( )xlc





(12)

The following x-plane coordinate equations are

being geometrically deduced via Figure 4 as:

(3,1) 2 1 1 1

sin( ) cos( )

xc c





(13a)

(4,1) 2 1 1 1

cos( ) c cos( )





(13b)

Substitution of (13a) and (13b) in (12) gives:

211(3,1) 1 1

cos( ) sin( ) l

zc c





(14a)

211(4,1) 1 1

cos( ) sin( ) l

zc c





(14b)

Thus, Equations (8), (9), (13) and (14) can be

utilized in order to compute the first platform’s

center Ο

coordinates (x,y,z) via the following

geometrical representation:



1(3,1)(4,1)

xA A

Ox x

(15a)



1(1,1)(2,1)

yA A

Oy y

(15b)



1 (1,1) (2,1) (3,1) (4,1)

zA A A A

Oz z z z

(15c)

2.2.2 Kinematic Analysis of the Upper

Platform

Utilization of the exact same methodology and by

introducing the coordinates of the point

O as the

new starter point, the coordinates of

are being

deduced in order to compute later the coordinates of

2122

sin( )( ) 2

Olc





(16a)

2122

sin( )( ) 2

Olc



 

(16b)





2 (1,2) (2,2) (3,2) (4,2)

zB B B B

Oz z z z

(16c)

where

(, )

are auxiliary points in the three

dimensional space utilized in order to simplify the

geometrical analysis and their coordinates are being

derived as:

(1,2) 1 2 2 1 1 1

cos( )( ) c sin( )

zlc l





 

(17a)

(2,2) 1 2 2 1 1 1

cos( )(c ) sin( )

zlcl





 

(17b)

(3,2) 1 2 2 1 1 1

cos( )( ) sin( )

zclcl





 

(17c)

(4,2) 1 2 2 1 1 1

cos( )( ) c sin( )

zlc l





 

(17d)

Following the previous methodology and by rotating

the computed coordinates by 45

with respect to the

z axis, posed by the manipulator’s upper platform

design, the coordinate equations of the upper

platform’s respective geometrical points are being

computed as:



(1,2) 2 2 2 3 2

sin( ) c cos( )

xOc

yOc

zOc



  

  

 

(18a)



 

(2,2) 2 2 2 3 2

(2,2) 2 2 3 2 2

sin( ) c cos( )

cos sin

xOc

yOc

zc c O



  

  



(18b)

 



 



 

(3,2) 2 2 2 3 2

sin cos

cos sin

xOcc

yOcc

zOc c



 

 

(18c)

 



 



 

(4,2) 2 2 2 3 2

sin cos

cos sin

xOcc

yOcc

zOc c



 

 

(18d)

Thus, the coordinates of the endpoint O

of the

manipulator are being computed as presented below:

ICINCO2014-11thInternationalConferenceonInformaticsinControl,AutomationandRobotics



2 (1,2) (2,2) (3,2) (4,2)

xA A A A

yA A A A

zA A A A

Ox x x x

Oy y y y

Oz z z z



(19)

3 ANTAGONISTIC OPERATION

PROPERTIES AND CONTROL

ALGORITHM FORMULATION

3.1 Antagonistic Open-Loop Operation

of PAM Pairs

The law that governs the antagonistic motion of the

PAM pairs i=1,2 and i=3,4 of the j-th platform link

in the presented manipulator applies an initial state

of pressure P

0,j

in the PAMs of the j-th link, which

is increased by a quantity ΔP in those specified by

i=1,3 and is decreased by the same quantity in the

their antagonistic ones specified by i=2,4. The

aforementioned antagonistic law is being presented

below:

,0,

(1)

ij j k

PP

(20)

where k indicates the pair of PAMs and is being

defined as:

1, for 1, 2 and 1

2, for 3, 4 and 1

3, for 1, 2 and 2

4, for 3, 4 and 2























and w=i+1.

In this way, all spectrum of the operating

pressure range is being exploited and this law is

expected to give the maximum motion range, but,

due to the nonlinearities and intense hysteresis

phenomena during the inflation and deflation states

of the PAMs, it fails provide a smooth antagonistic

operation. The symmetric around P

0,j

nature of the

pressure spectrum, which is posed by (20), does not

lead to symmetrical length alterations due to the

highly nonlinear relationship describing PAM’s

length with relation to the operating pressure.

In order to achieve a smoother antagonistic

behavior and to avoid the various phenomena that

are caused by the nonlinearities and hysteretic

behavior of the PAMs a modified antagonistic law is

being utilized with the appropriate insertion of

corrective coefficients as shown below:

,0,

(1)

ij j





(21)

With the experimentally derived corrective terms C

i,j

regarding the i-th

PAM attached to the j-th platform

link, it is made possible to compensate for the

PAM’s nonlinearities and improve the overall

antagonistic cooperation between PAMs. The

utilized PAMs operate in a range of 0-6 bar of

pressure and the experimental values of the

coefficients are being derived for initial pressure

state P

0,j

=3 bar in all the PAMs. The coefficient

values are being displayed in Table 1.

Table 1: Corrective coefficients.

i j

ΔP[bar]

1 1.5 2 2.5 3

i,j

1 1.2 1.92 2 2.1

2 1.04 1.12 1.39 1.69 1.8

3 1.28 1.48 1.92 2.13 2.31

4 1 1.23 1.49 1.68 1.91

1 1.05 1.15 1.64 2.05

2 1.09 1.22 1.7 2.09 2.25

3 1.2 1.43 1.21 2.12 2.41

4 1.12 1.21 1.48 1.69 2

3.2 Control Algorithm Formulation

The symmetric nature of the manipulator’s design

and the setup’s components (non-revolute cylinders,

universal joints) leading to the analysis

simplification of decoupled movements in the x, y

axis of both platforms, led to the utilization of four

independent PID controllers for controlling each

manipulated value ΔP

of the k-th pair of PAMs. The

formulated multiple PID control structure is

presented in Figure 5.

Figure 5. Multiple PID-based Control Scheme.

The following PID law is being utilized for every

independent controller:

ParallelRoboticManipulationviaPneumaticArtificialMuscles

,, D,

() () ( ) ()

kPkkIkk kk

Pt K e t K e d K e t



  



(22)

where e

(t) stands for the error signal imposed by the

k-th pair of PAMs and is being formulated by

subtracting the angle values θ

, φ

that are being

measured by the inclinometers from the reference

values θ

j,ref

, φ

j,ref

that are being provided by the user,

respectively.

As presented in Figure 5 the closed loop control

is being performed via four independent PID

controllers, each for every PAM antagonistic pair.

Every PID receives as input the respective error

signal and the control effort produced is utilized as

the pressure quantity ΔP

regarding the k-th PAM

pair. Finally, the antagonistic law (20) is being

computed and the antagonistic pressure signals are

being supplied into the PAM-actuated manipulator

system. The control structure’s goal is to bring the

manipulator to the reference pose governed by the

set-point platform angles.

4 SIMULATED PROPERTIES

AND EXPERIMENTAL

RESULTS

4.1 Open-Loop Performance

Characteristics

In the open-loop operation of the manipulator, the

user can choose moving each platform

independently or both platforms combined as it is

being depicted in Figure 6. The initial height of the

manipulator can be adjusted by the proper selection

of the initial pressure feeds of the cylinders P

j,cyl

and

the respective initial pressure states P

0,j

of the

utilized PAMs.

Forward kinematic analysis of the platform’s

movement has been simulated in order to produce

the theoretically derived workspace of the

manipulator for initial PAM lengths l

PAM

(j=1)

=15 cm

and l

PAM

(j=2)

=18.5 cm initial cylinder lengths

CYL,j

=27 cm, which correspond to P

0,j

=3 bar initial

PAM pressures and P

CYL,j

=1.5 bar initial cylinder

pressures, respectively, It has to be noted that

throughout the simulation trials the length of the

cylinders remained unaltered, blocking any

movements in the z

axes, an approach that has been

also followed in the following experimental trials.

The simulated workspace of the central point of

the lower platform, as computed from (15a)-(15c),

whereas the simulated workspace of the upper

platform’s central point is being derived by utilizing

the same methodology presented in (19). The total

workspace, featuring the upper and lower platforms’

workspace in green and blue color respectively, is

being displayed in Figure 7.

(a) (b) (c)

Figure 6: The robotic manipulator during (a) movement of

the lower platform, (b) movement of the upper platform

and (c) movement of both platforms.

The simulated workspace of the central point of

the lower platform, as computed from (15a)-(15c),

whereas the simulated workspace of the upper

platform’s central point is being derived by utilizing

the same methodology presented in (19). The total

workspace, featuring the upper and lower platforms’

workspace in green and blue color respectively, is

being displayed in Figure 7.

4.2 Closed-Loop Performance Results

In this Subsection the performance of the multiple

PID-based scheme in controlling the manipulator

setup is being evaluated. All experimental results

presented have been performed with initial PAM

lengths l

PAM

(j=1)

=15 cm and l

PAM,(j=2)

=18.5 cm and

initial cylinder lengths l

CYL,j

=27 cm, which

correspond to P

0,j

=3 bar initial PAM pressures and

CYL,j

=1.5 bar initial cylinder pressures, respectively.

Throughout the experimental trials the length of the

cylinders remained unaltered, blocking any

movements in the z

axes. With the aforementioned

initial values, the platform achieves a range of

motion from -15.5

to +15.5

in both x and y axes of

the lower platform and from -9 to +9 degrees for the

upper platform.

The responses of (θ

, φ

) of the lower platform

and (θ

, φ

) of the upper platform during a set-point

experiment, as well as the disturbance rejection

capabilities of the control scheme are being

displayed in Figures 8 and 9, respectively. The PID

ICINCO2014-11thInternationalConferenceonInformaticsinControl,AutomationandRobotics

gains K

P,k

, K

I,k

and K

D,k

have been experimentally

tuned via an extensive trial-and-error search and the

values utilized for the presented experimental trials

are being displayed in Table 2.

Figure 7: Simulated workspace of the lower (blue) and

upper (green) platform.

Table 2: PID Parameter Values.

P,k

I,k

D,k

Lower Platform 0.019 0.0102 0.0007

Upper Platform 0.019 0.0055 0.001

As shown in Figure 8, the platform reaches its

steady state in both x and y axis in less than one

second from the time that the step inputs are applied.

The control structure’s robustness is being tested and

the system manages to cancel two large-amplitude

and short-duration disturbances, which are being

properly added on the system’s output signals in the

form of manually-induced shocks, and return to

previous tracking performance. The absolute mean

steady-state errors from the reference angles θ

1,ref

and φ

1,ref

are being kept in low percentages,

specifically 0.51% for the y axis and 0.68% for the x

axis in its steady state, respectively, which further

proves the efficacy of the PID-based control scheme.

As presented in Figure 9, the upper platform

reaches its steady state in about 1.5 seconds and the

absolute mean steady-state error from the reference

angles θ

2,ref

and φ

2,ref

are being kept in low

percentages, specifically 0.64% for the y axis and

0.50% for the x axis, respectively. The small

increase in the response time and the steady-state

error are mainly caused by the elastic behavior of the

material selected for the flexible shafts, which are

being made of Teflon – a choice made as a trade-off

between rigidity during motion and overall

performance. In addition, Figure 9 shows the control

structure’s capabilities cancelling high amplitude

disturbances that are being properly added on the

system’s output signals in the form of manually-

induced shocks.

Figure 8: Set-point tracking performance and disturbance

cancellation capabilities of the control scheme during

lower platform movements.

Figure 9: Set-point tracking performance and disturbance

cancellation capabilities of the control scheme during

upper platform movements.

In addition, the responses of the θ

, θ

, φ

and φ

angles during simultaneous operation of both

Outpu

Disturbances

Outpu

Disturbances

ParallelRoboticManipulationviaPneumaticArtificialMuscles

platforms during a set-point experiment, as well as

the disturbance rejection capabilities of the control

scheme are being displayed in Figure 10. It can be

easily seen that all the controllers successfully lead

the manipulator to the desired angles, which justifies

the choice of utilizing independently structured PID

controllers instead of a more complex MIMO based

scheme to counteract for coupled system variables.

The absolute mean steady-state errors of the first

platform, which are also being kept in low

percentages, 0.9% and 0.62% for the y and x axes of

the lower platform and 0.59% and 0.56% for the y

and x axes of the upper platform, respectively. The

control structure again manages to cancel the high-

amplitude and short-duration disturbances added in

the four measured angle signals and return the

manipulator to its former state.

Figure 10: Set-point tracking performance and disturbance

cancellation capabilities of the control scheme during both

platform movements.

5 CONCLUSIONS

In this article, a PAM-actuated robotic manipulator

has been presented. The research attention has been

focused on the structural novelties of the

experimental set-up, the forward kinematic analysis

of the set-up platform components, as well as its

simulated workspace characteristics. The open-loop

operation of the structure’s movement has been

tested in various motion paterns. Finally, the closed

loop control of the manipulator via a multiple PID-

based control scheme based on a decoupled

movement theorysis has been evaluated, giving

smooth and fast responses along with high

disturbance cancellation capabilites. In the future,

different control schemes will be evaluated along

with flexible shafts of different rigidities.

REFERENCES

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180(15).

Outpu

Disturbances

ICINCO2014-11thInternationalConferenceonInformaticsinControl,AutomationandRobotics