Control of 3D Printed Ambidextrous Robot Hand Actuated by Pneumatic Artificial Muscles

SAI Intelligent Systems Conference 2015
November 10-11, 2015 | London, UK
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Control of 3D Printed Ambidextrous Robot Hand
Actuated by Pneumatic Artificial Muscles
Mashood Mukhtar
Department of Electronic and Computer Engineering
Brunel University, Kingston Lane, Uxbridge
London, UK
Mashood.Mukhtar@brunel.ac.uk
Emre Akyürek
London, UK
Tatiana Kalganova
London, UK
Nicolas Lesne
Department of System Engineering
ESIEE Paris
Noisy-le-Grand Cedex, France
Abstract—Production of robotic hands have significantly
increased in recent years due to their high demand in industry
and wide scope in number of applications such as tele-operation,
mobile robotics, industrial robots, biomedical robotics etc.
Following this trend, there have been many researches done on
the control of such robotic hands. Since human like clever
manipulating, grasping, lifting and sense of different objects are
desirable for researchers and crucial in determining the overall
performance of any robotic hand, researchers have proposed
different methods of controlling such devices. In this paper, we
discussed the control methods applied on systems actuated by
pneumatic muscles. We tested three different controllers and
verified the results on our uniquely designed ambidextrous
robotic hand structure. Performances of all three control
methods namely proportional–integral-derivative control (PID),
Bang-bang control and Back stepping control has been compared
and best controller is proposed. For the very first time, we have
validated the possibility of controlling multi finger ambidextrous
robot hand by using Back stepping Control. The five finger
ambidextrous robot hand offers total of 13 degrees of freedom
(DOFs) and it can bend its fingers in both ways left side and right
side offering full ambidextrous functionality by using only 18
pneumatic artificial muscles (PAMs). Pneumatic systems are
being widely used in many domestic, industrial and robotic
applications due to its advantages such as structural flexibility,
simplicity, reliability, safety and elasticity.
Keywords—Robot Hand; Ambidextrous Design; Pneumatic
Muscles; Grasping Algorithms; Backstepping control; PID
Control; Bang-bang Control; Control Methods; Pneumatic Systems
I. INTRODUCTION
The world is overwhelmed with incredible advances in
engineering. This advancement has resulted in production of
many robotics that are currently being used across various
industries (Miller, 1989) (Edwards, March 1984). The use of
robotics not only allows more productivity and safety at
workplace but also save time and money. The history of robot
development goes back to the ancient world (History of
robots, 2014). It all started from a basic idea and reached
today at a point where most complicated and risky tasks are
being handled by robots (Koren, 1985). This rapid growth
resulted is production of complicated robots (Kopacek, 2005)
and intelligent control algorithms (Saridis, 1983). In the past
considerable research has been done and as a result many
control algorithms were proposed (Marchal-Crespo &
Reinkensmeyer, 2009), (Hsia, 1986), (Hashimoto, 2003),
(Abdallah, Dawson, Dorato, & Jamshidi, 1991), (Lorenzo &
Siciliano, 2000), (Ali, Noor, Bashi, & Marhaban, 2009) and
(Aníbal Ollero, 2004). The first theoretical basis of the
pneumatic system control was made by Prof. J. L. Shearer in
1956 (Shearer, 1956). The pneumatic systems are widely used
in robotics (Deshpande A. , Ko, Fox, & Matsuoka., 2009)
(Shadow Dexterous Hand E1M3R, E1M3L, 2013), food
packaging (Wang J. , 1999), construction (Choi H.-S. , 2005),
biomechanics industry (Verrelst, Vanderborght, Ham, Beyl, &
Lefeber, 2006) and manufacturing applications (Shaojuan,
2008). In this paper we will first present the detail
classification of control systems and then review the related
work that has been done in the past. In particular, our focus
would be on control algorithms implemented on pneumatic
systems using PID controller, Bang-bang controller and
Backstepping controller. We will further test these controllers
on an ambidextrous robot hand and compare the results to find
the best option available to drive such devices.
Although number of control schemes are found in the
literature (Control theory,Main control strategies, 2014),
(Andrikopoulos G. , Nikolakopoulos, Arvanitakis, & Manesis,
2014) such as adaptive control (Åström & Wittenmark,
Adaptive Control Second Edition, 2008), (Ortega & Spong,
1989), direct continuous-time adaptive control (Lilly, 2003),
neurofuzzy PID control (Chan, Lilly, Repperger, & Berlin,
2003) hierarchical control (Albus, Barbera, & N.Nagel, 1980),
(Pattee, 2012), slave-side control (Li, Kawashima, Tadano,
Ganguly, & Nakano, 2013), intelligent controls (Gupta, 1996),
neural networks (Omidvar & Elliott, 1997) (Hesselroth,
Sarkar, Smagt, & Schulten, 1994), just-in-time control
(Kosaki & Sano, 2012) ,Bayesian probability (Gelman, Carlin,
Stern, Dunson, Vehtari, & Rubin, 2013), equilibrium-point
control (Ariga, Pham, Uemura, Hirai, & Miyazaki, 2012),

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fuzzy logic control (Ross, 2009), (Zadeh, 1994), (Klir &
Yuan, 1995), (Chang & Lilly, 2003), (Balasubramanian &
Rattan., 2003), machine learning (Domingos, 2012), (Zhou,
Wu, & Ying., 2014), evolutionary computation (De Jong,
2014) (Kendall, 2014) and genetic algorithms (Grefenstette,
2014) (Lin, Anderson Cook, Hamada, Moore, & Sitter.,
2014), nonlinear optimal predictive control (Reynolds,
Repperger, Phillips, & Bandry, 2003),optimal control (Lewis,
Vrabie, & Syrmos., 2012), (Kirk, 2012) (Vinter, 2010),
stochastic control (Åström, Introduction to stochastic control
theory, 2012), variable structure control (Repperger, Johnson,
& Phillips, A VSC position tracking system involving a large
scale pneumatic muscle actuator, 1998), chattering-free robust
variable structure control (Choi & Lee., 2010) and energy
shaping control (Navarro-Alarcon, David, & Yip., 2011), gain
scheduling model-based controller (Repperger, Phillips, &
Krier, Controller design involvng gain scheduling for a large
scale pneumatic muscle actuator, 1999), sliding mode control
(Harald & Schindele, 2008), proxy sliding mode control (Van
Damme, Vanderborght, Verrelst, Ham, Daerden, & Lefeber,
2009), neuro-fuzzy/genetic control (Chang & Lilly, 2003)
(Chan, Lilly, Repperger, & Berlin, 2003) but there are five
types of control systems (Fig.1) mainly used on pneumatic
muscles. These are feedback control system, feed-forward
control System, non-Linear control system, artificial
Intelligence based control system and hybrid Systems.
Fig. 1. Classification of control algorithm implemented on pneumatic
systems
In this research, we investigated the feedback control
system and non-linear control systems. Concept of feedback
system was first introduced by Greeks around 2000 years ago
(Visioli, 2006). Feedback is a control system in which an
output is used as a feedback to adjust the performance of a
system to meet expected output. Control systems with at least
one non-linearity present in the system are called nonlinear
control systems. The purpose of designing such system is to
stabilise the system at certain target. In order to reach a
desired output value, output of a processing unit (system to be
controlled) is compared with the desired target and then
feedback is provided to the processing unit to make necessary
changes to reach closer to desire output.
Grasping abilities of the ambidextrous hand has been
investigated using tactile sensors. Uses of tactical sensors are
quiet common and it has been implemented on robotic hands
driven by motors several time as it can be seen in (Shadow
Dexterous Hand E1M3R, E1M3L, 2013), (Srl, 2010),
(Laboratory, 2009), (Gunji, et al., 2008) and (Zollo, Roccella,
Guglielmelli, Carrozza, & Dario, 2007) or robot hands driven
by PAMs ((2013b), 2013), (Chua, Bezdicek, Davis, Caldwell,
& Gray) and (Tsujiuchi N. , Koizumi, Nishino, Komatsubara,
Kudawara, & Hirano, 2008). The automation of the
ambidextrous robot hand and its interaction with objects are
also augmented by implementing vision sensors on each side
of the palm. Similar systems have already been developed in
the past. For instance, the two-fingered robot hand discussed
in (Yoshikawa, Koeda, & Fujimoto, 2009) receives vision
feedback from an omnidirectional camera that provides a
visual hull of the object and allows the fingers to
automatically adapt to its shape. The three-fingered robot hand
developed by Ishikawa Watanabe Laboratory (Laboratory,
2009) is connected to a visual feedback at a rate of 1 KHz.
Combined with its high-speed motorized system that allows a
joint to rotate by 180 degrees in 0.1 seconds, it allows the
hand to interact dynamically with its environment, such as
catching falling objects. A laser displacement sensor is also
used for the two-fingered robot hand introduced in (Gunji, et
al., 2008). It measures the vertical slip displacement of the
grasped object and allows the hand to adjust its grasp. In our
research, the aim of the vision sensor is to detect objects close
to the palms and to automatically trigger grasping algorithms.
Once objects are detected by one of the vision sensors,
grasping features of the ambidextrous robot hand are
investigated using three different algorithms, which are
proportional-integrative-derivative (PID), bang-bang and
Backstepping controllers. Despite the nonlinear behavior of
PAMs actuators (Chou & Hannaford, 1996), (Kelasidi,
Andrikopoulos, Nikolakopoulos, & Manesis, 2012) previous
researches indicates that these three algorithms are suitable to
control pneumatic systems.
This research aims to validate the possibility of controlling
a uniquely designed ambidextrous robot hand using PID
controller, Bang-bang controller and Backstepping controller.
The ambidextrous robot hand is a robotic device for which the
specificity is to imitate either the movements of a right hand
or a left hand.

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(a) (b)
Fig. 2. Ambidextrous Robot Hand, where (a) is the ambidextrous mode and
(b) is the left mode
As it can be seen in Fig.2 (a), its fingers can bend in one
way or another to include the mechanical behavior of two
opposite hands in a single device. The Ambidextrous Robot
Hand has a total of 13 degrees of freedom (DOFs) and is
actuated by 18 pneumatic artificial muscles (PAMs).
II. RELATED WORK
A. PID Controller
PID stands for Proportional, integral and derivative. It is
by far the most commonly used controller in industry due to
its simplicity and robust performance under various operating
conditions. PID controllers are indeed widely used in the
robotics area. They can drive either motorized systems, such
as the ACT hand (Deshpande A. D., Ko, Fox, & Matsuoka,
2009) and the Shadow hand (Shadow Dexterous Hand
E1M3R, E1M3L, 2013). In (Tsujiuchi N. , Koizumi, Kan,
Takeda, Kudawara, & Hirano, 2009)] and (Jiang, Xiong, Sun,
& Xiong, 2010), PID controllers were used to regulate both
the position of the system and the pressure of its muscles.
Similar concept of loops was applied to robot hands in
(Nishino, Tsujiuchi, Koizumi, Komatsubara, Kudawara, &
Shimizu, 2007), (Tsujiuchi N. , Koizumi, Nishino,
Komatsubara, Kudawara, & Hirano, 2008). In (Wang, Pu, &
Moore., 1999) a control strategy using modified PID
controller and pusher mechanism is proposed to achieve
position and time accuracy required for the task. PID is also
sometime combined with artificial intelligent controller such
as neural networks to get the best results as can be seen in
(Ahn & Anh., 2006) or (J. Wu, Wang, & Xing., 2010) or
fuzzy logic in (Anh & Ahn, Hybrid control of a pneumatic
artificial muscle (PAM) robot arm using an inverse NARX
fuzzy model, 2011). An adaptive fuzzy PD controller and
adaptability of such controller with pneumatic servo system
was presented in (Xiang & Zheng, 2005). In (Tu & Kyoung,
2006), a non-linear PID controller and neural network is used
to improve the control of PAM suitable for plants with
nonlinearity uncertainties and disturbances. Particle swarm
optimization (PSO) algorithm is used in (Yanbing &
W.Xiaoxin, 2010) to self-tune PID controller of a joint
introduced. In (Ham, Verrelst, Daerden, & Lefeber, 2003),
(Vanderborght B. , Verrelst, Ham, Vermeulen, & Lefeber,
Dynamic Control of a Bipedal Walking Robot actuated with
Pneumatic Artificial Muscles, 2005), (Vanderborght B. ,
Verrelst, Ham, Damme, & Lefeber, A pneumatic biped:
experimental walking results and compliance adaptation
experiments, 2005) and (Vanderborght B. , Verrelst, Ham,
Damme, Beyl, & Lefeber, Torque and compliance control of
the pneumatic artificial muscles in the biped "Lucy", 2006)
PID controls implemented on a bipedal walking robot called
“Lucy. Another approach is performed in (Andrikopoulos,
Nikolakopoulos, & Manesis), where the positioning of PAMs
is driven by PID loops combined to nonlinear coefficients. In
(Anh & Ahn, Hybrid control of a pneumatic artificial muscle
(PAM) robot arm using an inverse NARX fuzzy model)
authors investigated the possibility of applying a hybrid feed-
forward inverse nonlinear autoregressive with exogenous
input (NARX) fuzzy model-PID controller to a nonlinear
pneumatic artificial muscle (PAM) robot arm to improve its
joint angle position output performance.
B. Bang-bang Controller
Bang-bang controllers are a nonlinear style of feedback
controller also known as on-off controller or hysteresis
controller. It is used to switch between two states abruptly.
Bang-bang controllers are widely used in systems that accept
binary inputs. System makes decision to turn controller on or
off based on threshold and target values (Bang–bang control,
2014). Application to regular and Bang-bang control is
discussed in great detail in (Osmolovskii & Maurer, 2012).
Bang-bang controller is not popular in robotics because its
shooting functions are not smooth (Silva & Trélat., 2010) and
need regularisation (Bonnard, Caillau, & Trélat, 2007). Fuzzy
logic (Nagi, Perumal, & Nagi, 2009), (Nagi, Zulkarnain, &
Nagi., 2013) and PID are usually combined with bang-bang
controller to add flexibility and determine switching time of
Bang-bang inputs. Bram Vanderborght et al. in (Ham,
Verrelst, Daerden, & Lefeber, 2003), (Verrelst, Vanderborght,
Vermeulen, Ham, Naudet, & Lefeber, 2005), (Vanderborght
B. , Verrelst, Ham, & Lefeber, Controlling a bipedal walking
robot actuated by pleated pneumatic artificial muscles, 2006),
(Vanderborght B. , Verrelst, Ham, Damme, & Lefeber, A
pneumatic biped: experimental walking results and
compliance adaptation experiments, 2005), (Vanderborght,
Bram, Ham, Verrelst, Damme, & Lefeber, 2008) and
(Vanderborght B. , Verrelst, Ham, Vermeulen, & Lefeber,
Dynamic Control of a Bipedal Walking Robot actuated with
Pneumatic Artificial Muscles, 2005) controlled a bipedal robot
actuated by pleated pneumatic artificial muscles using bang-
bang pressure controller. Stephen M Cain et al. in (Cain,
Gordon, & Ferris., 2007), studied locomotor adaptation to
powered ankle-foot orthoses using two different orthosis

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t
dtte
0
te
dt
d
control methods. The pressure in the pneumatic muscles was
controlled by footswitch control and proportional myo-electric
control. In footswitch control, bang-bang controller is used to
regulate air pressure in pneumatic muscle. Dongjun Shin et al.
in (Shin, Sardellitti, & Khatib, 2008), proposed the concept of
hybrid actuation for human friendly robot systems by using
distributed macro-Mini control approach (Zinn, Khatib, Roth,
& Salisbury., 2002). The hybrid actuation controller employ
modified bang-bang controller to adjust the flow direction of
pressure regulator. Zhang, Jia-Fan et al. in (Zhang, Yang,
Chen, Zhang, & Dong., 2008), presented a novel pneumatic
muscle based actuator for wearable elbow exoskeleton. Hybrid
fuzzy controller composed of bang-bang controller and fuzzy
controller is used for torque control.
H. X. Zhang et al. in (Zhang, Wei Wang, & Zhang., 2009),
presented the improved full pneumatic climbing robot.
Effectiveness of two approaches was tested to check the
system stiffness and control quality. Bang-bang controller is
used to control the cylinder movement and eliminate
oscillation. Juan Gerardo Castillo Alva et al. in (Alva,
Sanchez, Meggiolaro, & Castro., 2013), discussed the
development of fatigue testing machine using a pneumatic
artificial muscle. Using learning control techniques, a special
control system is developed for the machine. The proposed
methodology consists on implementing a bang-bang controller
to control the solenoid valves.
C. Backstepping Controller
Backstepping is a control technique originally intruded by
Peter V. Kokotovic in 1990 to offer stabilise control with a
recursive structure based on derivative control.and it was
limited to nonlinear dynamical systems. Mohamed et al.
presented a synthesis of a nonlinear controller to an electro
pneumatic system in (Mohamed, Xavier, & Daniel, 2006).
Nonlinear Backstepping control and nonlinear sliding mode
control laws were applied to the system under consideration.
First, the nonlinear model of the electro pneumatic system was
presented. It was transformed to be a nonlinear affine model
and a coordinate transformation was then made possible by
the implementation of the nonlinear controller. Two kinds of
nonlinear control laws were developed to track the desired
position and desired pressure. Experimental results were also
presented and discussed. P. Carbonell et al. compared two
techniques namely sliding mode control (SMC) and
Backstepping control (BSC) in (Carbonell, Jiang, &
Repperger., Nonlinear control of a pneumatic muscle actuator:
backstepping vs. sliding-mode, 2001) and found out BSC is
somewhere better than SMC in controlling a device. He
further applied BSC coupled with fuzzy logic in (Carbonell,
Jiang, & Repperger., A fuzzy backstepping controller for a
pneumatic muscle actuator system, 2001). In (Soltanpour &
Fateh., 2009), a paralleled robot project is discussed which is
controlled by BSC.
Since literature review revealed no multifinger robot hand
(actuated by PAMs) is ever driven using BSC, research
presented in this paper validates the possibility of driving
multifinger robot hand using BSC. We used an ambidextrous
robot hand to test the Backstepping controller that goes even a
step further to prove the originality of research.
III. IMPLEMENTATION OF A PID CONTROLLER
As the name suggests, PID controller is a combination of
three different controller’s (Fig. 3) proportional, integral,
derivative. Proportional controller serves as a heart of a
control system; it provides corrective force proportional to
error present. Although proportional control is useful for
improving the response of stable systems and considered a
building block of many applications but it comes with a
steady-state error problem which is eliminated by adding
integral control. Integral control restores the force that is
proportional to the sum of all past errors, multiplied by time.
On one hand integral controller solves a steady-state error
problem created by proportional controller but on the other
hand integral feedback makes system overshoot.
Equation of proportional control:
teKP pout
outP = System output
pK = Proportional gain constant
te = Error E at specific time
)()( outputmeasurablePVoutputidealSPE
Equation of integral control:
t
ioutI dtteKI
0
outI = System output
IK = Integral gain constant
= Sum of the instantaneous error over time
To overcome overshooting problem, derivative controller
is used. It slows the controller variable just before it reaches
its destination. Derivatives controller is always used in
combination with other controller and has no influence on the
accuracy of a system. All these three control have their
strengths and weakness and when combine together it offers
the maximum strength whilst minimizing weakness.
Equation of derivative control:
te
dt
d
KdDout
outD = System output
Kd = Derivative gain constant
= Rate of change (error)
When combine all three controller, the
equation becomes:
te
dt
d
KdtteKteKOutput d
t
iPPID
0

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]
1
[
dt
tde
Dtdte
I
teKcOutput
dt
tde
Dtdte
I
teKpOutput
1
][
]1][
1
[
dt
d
Dtdte
I
teKcOutput
t
dtte
0
te
dt
d
PIDOutput = output from PID controller
outP = Proportional control gain
outI = Integral control gain
outD = Derivative control gain
te = Error E at specific time
)()( outputmeasurablePVoutputidealSPE
= Sum of the instantaneous error over time
= Rate of change (error)
Fig. 3. Block diagram of PID Controller
PID algorithms can be divided into three main categories:
Serial, ideal and parallel.
Ideal PID Algorithm:
Parallel PID Algorithm:
Serial PID Algorithm:
PID Control loops were implemented on an ambidextrous
robot hand using the parallel form of a PID controller, for
which the equation is as follows:
(1)
Snapshots of experiments can be seen in Fig.4. The force
targets are fixed at 13N in Fig.4 (a) and at 15N in Fig.4 (b). It
is observed that medial and distal phalanges flex when force
applied remain below 13N and extends above 15N. Therefore,
the system reaches a stable state when the force feedback
stands between these two limit values and provide enough
force to hold light objects. In the snapshots Fig. 4 (c) and
Fig.4 (d), a single force target is fixed at 0.05 N and the
finger’s prototype goes backward when it touches a piece of
paper.
(a) (b)
(c) (d)
Fig. 4. Interactions of light weight objects and an early design of an
ambidextrous finger is shown in the figure. According to the force put as
target, the prototype provides enough force to maintain pieces of metal in (a)
and (b) whereas the medial and distal phalanges go backward when they touch
a piece of paper in (c) and (d)
Output (t) should be calculated exactly in the same way
as described in equation (1) but this is not the case due to
asymmetrical tendon routing of ambidextrous robot hand
Error! Reference source not found.[107]. Mechanical
specifications are taken into consideration before calculating
the (t). It is divided into three different outputs for the three
PAMs driving each finger. These three outputs are ,
and , respectively attributed to the proximal
left, medial right and medial left PAMs. The same notations
are used for the gain constants. The adapted PID equation is
defined as:
(2)
To imitate the behaviour of human finger correctly, some
of the pneumatic artificial muscles must contract slower than
others. This prevents having medial and distal phalanges
totally close when the proximal phalange is bending. The
proportional constant gains are consequently defined as:
(3)
When object interact on the left side of the hand, equation
can be written as follows:
(4)
Same ratios are applied to the integrative gain constants
when object interact on right side of the hand.

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Using equation (2), PID control loops with identical gain
constants are sent to the four fingers with a target of 1 N and
an error margin of 0.05 N, whereas the thumb is assigned to a
target of 12 N with an error margin of 0.5 N. A can of soft
drink is brought close to the hand and data is collected every
0.05 sec. The experiment result is illustrated in Fig.5 and data
collected from the left hand mode during experiment is shown
in Fig.6. If we notice Fig.6, we will realise that data is only
collected from four of the five figured ambidextrous robot
hand and graph started plotting from 0.1 sec. This is due to the
fact that the thumb stabilises at 12.23N far higher than other
fingers and no interaction was reported before 0.1 sec.
Fig. 5. The Ambidextrous Robot Hand holding a can (both right and left)
with a grasping movement implemented with PID controllers
Fig. 6. Graph shows force against time of the four fingers while grasping a
drink can with PID controllers
From Fig.6, it can be seen that grasping of a can of soft
drink began at 0.15 approximately and it became more stable
after 0.2 sec. An overshoot has occurred on all fingers but
stayed in limit of 0.05N where system has automatically
adjusted at the next collection. These small overshoots
occurred because different parts of the fingers get into contact
with the object before the object actually gets into contact with
the force sensor. This results bending of fingers slower when
phalanges touches the object. Since the can of soft drink does
not deform itself, it can be deduced that the grasping control is
both fast and accurate when the Ambidextrous Hand is driven
by PID loops.
IV. IMPLEMENTATION OF A BANG-BANG CONTROLLER
The bang-bang controller allows all fingers to grasp the
object without taking any temporal parameters into account.
Execution of algorithm automatically stops when the target set
against force is achieved. The controller also looks after any
overshooting issue if it may arise. To compensate the absence
of backward control, a further condition is implemented in
addition to initial requirements. Since the force applied by the
four fingers is controlled with less accuracy than with PID
loops, the thumb must offset the possible excess of force to
balance the grasping of the object. Therefore, a balancing
equation is defined as:
(5)
Where is the minimum force applied by the thumb,
is the force applied by each of the four other fingers. is
an approximate weight of the object to grabbed. In the case of
light weight objects, since weight is not very much of
importance but should be defined anything more than 25N.
Equation (5) is only suitable for light weight objects. In order
to be more accurate, a mathematical model that
counts the weight of all four fingers is preferable. Moreover,
as the summation of is close to 7 N, it does not interfere
either with heavier objects, which is why is not included in
(5).
Fig. 7. Bang-bang loops driven by proportional controllers
Fig. 8. The Ambidextrous Robot Hand holding a can with a grasping
movement implemented with bang-bang controllers. It is seen the can has
deformed itself
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
0.1 0.15 0.2 0.25 0.3
Force(N)
Time (sec)
Forefinger
Middle
finger
Ring finger
Little finger

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As discussed in section III, the phalanges must close with
appropriate speed’s ratios to tighten around objects when
interacting with object. By repeating the experiments realized
in section III, the pictures obtained with the bang-bang
controller are provided in Fig.8. This time, it is noticeable
from (a) that the can of soft drink deforms itself when it is
grasped on the left hand side. The graph obtained from the
data collection of the left mode are provided in Fig. 9.
drink can with bang-bang controllers
It is noted during experiment that speed of fingers does not
vary when it touches the objects. That explains why we got
higher curves in Fig.9 than the previously obtained in Fig.6.
This makes bang-bang controller faster than PID loops. The
bang-bang controllers also stop when the value of 1 N is
overreached but, without predicting the approach to the
setpoint, the process variables have huge overshoots. The
overshoot is mainly visible for the middle finger, which
overreaches the setpoint by more than 50%. Even though
backward control is not implemented in the bang-bang
controller, it is seen the force applied by some fingers
decreases after 0.2 sec. This is due to the deformation of the
can, which reduces the force applied on the fingers. It is also
noticed that the force applied by some fingers increase after
0.25 sec, whereas the force was decreasing between 0.2 and
0.25 sec. This is due to thumb’s adduction that varies from
7.45 to 15.30 N from 0.1 to 0.25 sec. Even though the fingers
do not tighten anymore around the object at this point, the
adduction of the thumb applies an opposite force that
increases the forces collected by the sensors. The increase is
mainly visible for the forefinger and the middle finger, which
are the closest ones from the thumb.
Contrary to PID loops, it is seen in Fig.9 that the force
applied by some fingers may not change between 0.15 and 0.2
sec, which indicates the grasping stability is reached faster
with bang-bang controllers. The bang-bang controllers can
consequently be applied for heavy objects, changing the set
point of defined in (5).
V. IMPLEMENTATION OF A BACKSTEPPING CONTROLLER
BSC consists in comparing the system’s evolution to
stabilizing functions. Derivative control is recursively applied
until the fingers reach the conditions implemented in the
control loops. First, the tracking error of the BS
approach is defined as:
(6)
Where is the force put as target and is the force
received for each finger. The stability of this close loop
system is then evaluated using a first Lyapunov function
defined as:
(7)
(8)
The force provided by the hand is assumed not being
strong enough as long as exceeds a minimum grasping
force defined as . In (8), it is noted that as
long as keeps varying. Therefore, cannot be
stabilized until the system stops moving. Thus, a stabilizing
function is introduced. This stabilizing function is noted as a
second error :
(9)
Fig. 10. Basic Backstepping controller is shown in above figure..
with a constant > 1. indirectly depends on the speed,
as the system cannot stabilized itself as long as the speed is
varying. Consequently, both the speed of the system
and are equal to zero when one finger reaches a stable
position, even if . aims at increasing to
anticipate the kinematic moment when becomes too low.
In that case, the BSC must stop running as is close to .
Both of the errors are considered in a second Lyapunov
function:
(10)
(11)
where refers to a stable force applied on the object. This
second step allows stabilizing the system using derivative
control. Using (9), (11) can be simplified as:
(12)
0.9
1
1.1
1.2
1.3
1.4
1.5
0.1 0.15 0.2 0.25 0.3
Force(N)
Time (sec)
Forefinger
Middle finger
Ring finger
Little finger

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Fig. 11. Ambidextrous hand grasping a can of soft drink using backstepping
controllers (Right hand mode and left hand mode)
The block diagram of backstepping process is illustrated in
Fig.10. According to the force feedback , the fingers’
positions adapt themselves until the conditions of the
Lyapunov functions and are reached.
drink can with Backstepping controllers
The grasping features obtained with the BSC are illustrated
in Fig.11. The force against time graph is obtained from the
data collection is shown in Fig.12.
During the experiment, it was noticed that speed of finger
tightening using backstepping control was much slower
compared to PID controller and bang-bang controller. Since
the backstepping controller’s target is based on force feedback
and speed stability, it offers greater flexibility than PID and
bang-bang but takes longer to stablise. Finger provided
enough force to grab the can of soft drink at 0.30 sec, but it is
seen the system carries on moving until 0.40 sec. Therefore it
was dedcused that BSC takes longer to stablise. The force
collected for the thumb at the end of the experiment is 13.10
N, which is a value close to the one obtained with the PID
control. It can also be noted that the fingers’ speed is slower
using BSC, as none of the sensors collect more than 0.80 N
after 0.15 sec. The higher speeds of the PID and bang-bang
controllers are respectively explained because of the
integrative term and the lack of derivative control.
Fig. 13. Ambidextrous Robot hand holding water bottle and ball
VI. EXPERIMENTAL ANALYSIS
A table has been constructed outlining the key difference
found from the results of all three controllers.It can be seen
from Table 1 that the best performances are reached with PID
and BS controls, as both of them are accurate and permit the
fingers to adapt to the shape of objects with backward
movements. However, PID loops proved faster than any other
controller, which could be one of the main reason of finding
high number of resources in literature review.
Despite its accurate implementation, the BSC did not
reveal as robust results. The fingers stabilize themselves after
0.35 sec with BSC, against 0.20 sec for PID and bang-bang
controls. Indeed, as for sliding mode control (SMC), the main
advantage of BSC is its ability to regulate nonlinear actuators.
This is the reason why these two algorithms receive feedbacks
from pressure or position sensors in (Carbonell, Jiang, &
Repperger, Nonlinear control of a pneumatic muscle actuator:
backstepping vs. sliding-mode, 2001) and (Aschemann &
Schindele, 2008). Nevertheless, in the case considered in this
paper, the feedback is received from force sensors directly
implemented on the mechanical structure instead of the
actuators themselves.
TABLE I. COMPARISON BETWEEN PID, BANG-BANG AND BACKSTEPPING
CONTROLS AND AN IDEAL CONDITION
Speed Accuracy Adaptability Implementation
PID Fast High High Fast
Bang-
bang
Fast Low Low Fast
BSC Average High High Long
Ideal
Option
Fast High High Fast
Even though bang-bang control is the fastest of the three
compared algorithms, it is not smooth enough to adapt itself to
the shape of the objects and can crush them. The shooting
function of the bang-bang controller is too sudden without
additional controllers, which is why it is cascaded in (Bram
Vanderborght, Ham, Vermeulen, & Lefebe, 2005) and
(Vanderborght B. , Verrelst, Ham, Damme, Beyl, & Lefeber,
Torque and compliance control of the pneumatic artificial
muscles in the biped "Lucy"", 2006). However, bang-bang
0.6
0.7
0.8
0.9
1
1.1
0.1 0.15 0.2 0.25 0.3 0.35 0.4
Force(N)
Time (s)
Forefinger
Middlefinger
Ring finger
Little finger

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control can be used to grab heavy object. The higher is the
PAMs’ pressure, the slower the PAMs contract, which is why
their elasticity automatically opposes itself to the shooting
function effect in that case.
Fig. 14. Ambidextrous Robot hand grabbing a can in ambidextrous fashion
By implementing force sensors both on right and left sides
of the fingers, the Ambidextrous Hand can also grab objects in
atypical positions, as shown in Fig 14.
VII. CONCLUSION
Three different controllers namely PID, Bang-bang and
BSC are tested and their performance in controlling an
ambidextrous robotic hand is analyzed in great detail. PID
controller was found the best when applied as compare to
Bang-bang and Backstepping control. Backstepping control
technique was validated for the first time on an ambidextrous
robot hand. By combining PID controllers and force sensors,
this research proposes one of the cheapest solutions possible.
In future, PID controller could be used with artificial
intelligent controllers to further improve the controls.
ACKNOWLEDGMENT
The authors would like to cordially thank Anthony Huynh,
Luke Steele, Michal Simko, Luke Kavanagh and Alisdair
Nimmo for their contributions in design and development of
the mechanical structure of a hand, and without whom the
research introduced in this paper would not have been
possible.
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