Control of 3D Printed Ambidextrous Robot Hand
Actuated by Pneumatic Artificial Muscles
Mashood Mukhtar
Tatiana Kalganova
Department of Electronic and Computer Engineering
Brunel University, Kingston Lane, Uxbridge
London, UK
Mashood.Mukhtar@brunel.ac.uk
Department of Electronic and Computer Engineering
Brunel University, Kingston Lane, Uxbridge
London, UK
Emre Akyürek
Department of System Engineering
ESIEE Paris
Noisy-le-Grand Cedex, France
Department of Electronic and Computer Engineering
Brunel University, Kingston Lane, Uxbridge
London, UK
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 Backstepping control has been compared
and best controller is proposed. For the very first time, we have
validated the possibility of controlling multifinger ambidextrous
robot hand by using Backstepping 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 [1] [2]. 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
Nicolas Lesne
ancient world [3]. It all started from a basic idea and reached
today at a point where most complicated and risky tasks are
being handled by robots [4]. This rapid growth resulted is
production of complicated robots [5] and intelligent control
algorithms [6]. In the past considerable research has been done
and as a result many control algorithms were proposed [7],
[8], [9], [10], [11], [12] and [13]. The first theoretical basis of
the pneumatic system control was made by Prof. J. L. Shearer
in 1956 [14]. The pneumatic systems are widely used in
robotics [15] [16], food packaging [17], construction [18],
biomechanics industry [19] and manufacturing applications
[20]. 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 [21], [22] such as adaptive control [23], [24], direct
continuous-time adaptive control [25], neurofuzzy PID control
[26] hierarchical control [27], [28], slave-side control [29],
intelligent controls [30], neural networks [31] [32], just-intime control [33] ,Bayesian probability [34], equilibrium-point
control [35], fuzzy logic control [36], [37], [38], [39], [40],
machine learning [41], [42], evolutionary computation [43]
[44] and genetic algorithms [45] [46], nonlinear optimal
predictive control [47],optimal control [48], [49] [50],
stochastic control [51], variable structure control [52],
chattering-free robust variable structure control [53] and
energy shaping control [54], gain scheduling model-based
controller [55], sliding mode control [56], proxy sliding mode
control [57], neuro-fuzzy/genetic control [39] [26] 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.
falling objects. A laser displacement sensor is also used for the
two-fingered robot hand introduced in [62]. 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 [68], [69] 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.
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
[59]. 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 nonlinearity 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 [16], [60],
[61], [62] and [63] or robot hands driven by PAMs [64], [65]
and [66]. 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 [67] 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 [61] 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
(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) [58].
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 [70] and the Shadow hand [16]. In [71]] and
[72], 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 [73], [74]. In [75] 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 [76] or [77] or fuzzy logic in
[78]. An adaptive fuzzy PD controller and adaptability of such
controller with pneumatic servo system was presented in [79].
In [80], 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 [81] to self-tune PID
controller of a joint introduced. In [82], [83], [84] and [85]
PID controls implemented on a bipedal walking robot called
“Lucy. Another approach is performed in [86], where the
positioning of PAMs is driven by PID loops combined to
nonlinear coefficients. In [87] 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 [88]. Application to
regular and Bang-bang control is discussed in great detail in
[89]. Bang-bang controller is not popular in robotics because
its shooting functions are not smooth [90] and need
regularisation [91]. Fuzzy logic [92], [93] and PID are usually
combined with bang-bang controller to add flexibility and
determine switching time of Bang-bang inputs [58].
Bram Vanderborght et al. in [82], [94], [95], [84], [96] and
[83] controlled a bipedal robot actuated by pleated pneumatic
artificial muscles using bang-bang pressure controller.
Stephen M Cain et al. in [97], studied locomotor adaptation to
powered ankle-foot orthoses using two different orthosis
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 [98], proposed the concept of hybrid actuation for human
friendly robot systems by using distributed macro-Mini
control approach [99]. The hybrid actuation controller employ
modified bang-bang controller to adjust the flow direction of
pressure regulator. Zhang, Jia-Fan et al. in [100], 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 [101], 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
[102], 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 [103]. 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 [104]
and found out BSC is somewhere better than SMC in
controlling a device. He further applied BSC coupled with
fuzzy logic in [105]. In [106], 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:
Pout  K p  e  t 
e  t  = Error E at specific time
E  SP(ideal  output )  PV (measurable  output )
t
 e  t  dt
= Sum of the instantaneous error over time
0
d

 e  t 
 dt

= Rate of change (error)
Pout = System output
K p = Proportional gain constant
e  t  = Error E at specific time
E  SP(ideal  output)  PV (measurable  output)
Equation of integral control:
t
I outI  K i   e  t  dt
0
I out = System output
K I = Integral gain constant
Fig.3. Block diagram of PID Controller
t
 e  t  dt
= Sum of the instantaneous error over time
0
PID algorithms can be divided into three main categories:
Serial, ideal and parallel.
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.
Ideal PID Algorithm:
Equation of derivative control:
Serial PID Algorithm:
Dout
d

 Kd   e  t  
 dt

Dout = System output
Kd = Derivative gain constant
d

 e  t   = Rate of change (error)
 dt
 When combine all three controller, the
equation becomes:
d

Output PID  K P  e  t   K i   e  t  dt  K d   e  t  
 dt

0
t
Output PID = output from PID controller
Pout = Proportional control gain
I out = Integral control gain
Dout = Derivative control gain
Output  Kc[e  t  
1
de  t 
e  t  d  t  D
]

I
dt
Parallel PID Algorithm:
Output  Kp[e  t ] 
Output  Kc[e  t  
1
de  t 
e  t  d  t  D

I
dt
1
d
e  t  d  t ][1  D ]

I
dt
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:
𝑡
𝑢(𝑡) = 𝐾𝑝 𝑒(𝑡) + 𝐾𝑖 ∫ 𝑒(𝜏)𝑑𝜏 + 𝐾𝑑
0
𝑑
𝑒(𝑡)
𝑑𝑡
(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)
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.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).
[
𝐾𝑝𝑝𝑙 /3
−𝐾𝑝𝑚𝑙
𝐾𝑝𝑚𝑙
]=[
]=[
]
−𝐾𝑖𝑟𝑙
𝐾𝑝𝑚𝑟
𝐾𝑖𝑝𝑙 /3
(3)
When object interact on the left side of the hand, equation can
be written as follows:
0.4 𝑋 𝐾𝑝𝑚𝑙
𝐾𝑝
−𝐾𝑝𝑚𝑟
[ 𝑚𝑟 ] = [
]=[
]
𝐾𝑖𝑚𝑟
−𝐾𝑖𝑚𝑟
0.4 𝑋 −𝐾𝑖𝑚𝑙
(4)
Same ratios are applied to the integrative gain constants when
object interact on right side of the hand.
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
Fig. 5. The Ambidextrous Robot Hand holding a can (both right and left) with
a grasping movement implemented with PID controllers.
Force (N)
Output 𝑢 (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
[107]. Mechanical specifications are taken into consideration
before calculating the 𝑢 (t). It is divided into three different
outputs for the three PAMs driving each finger. These three
outputs are 𝑢𝑝𝑙 (𝑡), 𝑢𝑚𝑟 (𝑡) and 𝑢𝑚𝑙 (𝑡), 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:
𝑒(𝑡)
𝑡
𝐾𝑝𝑝𝑙 𝐾𝑖𝑝𝑙 𝐾𝑑
𝑢𝑝𝑙 (𝑡)
∫ 𝑒(𝜏)𝑑𝜏
(2)
[𝑢𝑚𝑟 (𝑡)] = [𝐾𝑝𝑚𝑟 𝐾𝑖𝑚𝑟 𝐾𝑑 ] 0
𝐾𝑝𝑚𝑙 𝐾𝑖𝑚𝑙 𝐾𝑑
𝑢𝑚𝑙 (𝑡)
𝑑
[ 𝑑𝑡 𝑒(𝑡) ]
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:
1.1
1.05
1
0.95
0.9
0.85
0.8
0.75
Forefinger
Middle finger
Ring finger
Little finger
0.1
0.15
0.2
0.25
Time (sec)
0.3
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.
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:
4
𝐹𝑡𝑚𝑖𝑛 = 𝑊𝑜 + ∑ 𝐹𝑓
(5)
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.
1.5
Force (N)
IV.
𝑓=1
Where 𝐹𝑡𝑚𝑖𝑛 is the minimum force applied by the thumb, 𝐹𝑓 is
the force applied by each of the four other fingers. 𝑊𝑜 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 ∑4𝑓=1 𝑊𝑓 that
counts the weight of all four fingers is preferable. Moreover, as
the summation of 𝑊𝑓 is close to 7 N, it does not interfere either
with heavier objects, which is why 𝑊𝑓 is not included in (5).
Fig. 7. Bang-bang loops driven by proportional controllers.
1.4
Forefinger
1.3
Middle finger
1.2
1.1
Ring finger
1
Little finger
0.9
0.1
0.15
0.2
0.25
Time (sec)
0.3
Fig. 9. Graph shows force against time of the four fingers while grasping a
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
setpoint of 𝐹𝑓 defined in (5).
V.
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.
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 𝑒1 (𝑡) of the BS approach
is defined as:
[
𝐹𝑡 − 𝐹𝑓 (𝑡)
𝑒1 (𝑡)
]=[
]
𝑒̇1 (𝑡)
−𝐹𝑓̇ (𝑡)
𝑉2̇ (𝑒1 , 𝑒2 ) = 𝑒̇1 (𝑡) ∗ (𝑒1 (𝑡) + 𝑘𝑒̈1 (𝑡))
(12)
(6)
where 𝐹𝑡 is the force put as target and 𝐹𝑓 (𝑡) is the force
received for each finger. The stability of this close loop
system is then evaluated using a first Lyapunov function
defined as:
1 2
𝑒 (𝑡) < 𝐹𝑔𝑚𝑖𝑛
2 1
𝑉1̇ (𝑒1 ) = 𝑒1 (𝑡) ∗ 𝑒̇1 (𝑡) = −𝐹𝑓̇ (𝑡) ∗ 𝑒1 (𝑡)
𝑉1 (𝑒1 ) =
(7)
(8)
The force provided by the hand is assumed not being
strong enough as long as 𝑒12 /2 exceeds a minimum grasping
force defined as 𝐹𝑔𝑚𝑖𝑛 . In (8), it is noted that 𝑒̇1 (𝑡) ≠ 0 as
long as 𝐹𝑓 (𝑡) keeps varying. Therefore, 𝑉1̇ (𝑒1 ) cannot be
stabilized until the system stops moving. Thus, a stabilizing
function is introduced. This stabilizing function is noted as a
second error 𝑒2 (𝑡):
𝑒2 (𝑡) = 𝑘 ∗ 𝑒̇1 (𝑡)
(9)
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 𝐹𝑓 (𝑡), the fingers’
positions adapt themselves until the conditions of the
Lyapunov functions (𝑉1, 𝑉1̇ ) and (𝑉2, 𝑉2̇ ) are reached.
1.1
Forefinger
1
Middlefing
er
Force (N)
0.9
0.8
Ring finger
0.7
Little finger
0.6
Fig. 10. Basic Backstepping controller is shown in above figure..
with 𝑘 a constant > 1. 𝑒2 (𝑡) 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 𝑒2 (𝑡) are equal to zero when one finger reaches a stable
position, even if 𝐹𝑓 (𝑡) ≠ 𝐹𝑡 . 𝑘 aims at increasing 𝑒̇1 (𝑡) to
anticipate the kinematic moment when 𝑒̇1 (𝑡) becomes too low.
In that case, the BSC must stop running as 𝐹𝑓 (𝑡) is close to 𝐹𝑡 .
Both of the errors are considered in a second Lyapunov
function:
1
𝑉2 (𝑒1 , 𝑒2 ) = (𝑒12 (𝑡) + 𝑒22 (𝑡)) < 𝐹𝑠
2
(10)
𝑉2̇ (𝑒1 , 𝑒2 ) = 𝑒1 (𝑡) ∗ 𝑒̇1 (𝑡) + 𝑒2 (𝑡) ∗ 𝑒̇2 (𝑡)
(11)
where 𝐹𝑠 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:
0.1 0.15 0.2 0.25 0.3 0.35 0.4
Time (s)
Fig. 12. Graph shows force against time of the four fingers while grasping a
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.
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 [110] and
[111]. However, bang-bang 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. 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.
Fig. 14.
fashion.
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 [108] and [109]. 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.
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.
Speed
Accuracy
Adaptability
PID
Fast
High
High
Fast
Bangbang
BSC
Fast
Low
Low
Fast
Average
High
High
Long
Fast
High
High
Fast
Ambidextrous Robot hand grabbing a can in ambidextrous
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.
CONCLUSION
Implementation
ACKNOWLEDGMENT
Ideal
Option
Table 1 : Comparison between PID, bang-bang and
backstepping controls and an ideal condition.
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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