Implementation of PID, Bang-bang and Backstepping controllers on 3D Printed Ambidextrous Robot
Hand
Mashood Mukhtar, Emre Akyürek, Tatiana Kalganova, Nicolas Lesne
Abstract Robot hands have attracted increasing research interest in recent years
due to their high demand in industry and wide scope in number of applications.
Almost all researches done on the robot hands were aimed at improving
mechanical design, clever grasping at different angles, lifting and sensing of
different objects. In this chapter, we presented the detail classification of control
systems and reviewed the related work that has been done in the past. In
particular, our focus was on control algorithms implemented on pneumatic
systems using PID controller, Bang-bang controller and Backstepping controller.
These controllers were tested on our uniquely designed ambidextrous robotic
hand structure and results were compared to find the best controller to drive such
devices. The five finger ambidextrous robot hand offers total of 13 degrees of
freedom (DOFs) and it can bend its fingers in both ways left and right offering
full ambidextrous functionality by using only 18 pneumatic artificial muscles
(PAMs).
__________________________
Mashood Mukhtar, Emre Akyürek, Tatiana Kalganova
Department of Electronic and Computer Engineering, Brunel University, Kingston Lane,
Uxbridge, London, UK, e-mail: Mashood.Mukhtar@brunel.ac.uk
Nicolas Lesne
Department of System Engineering, ESIEE Paris, Noisy-le-Grand Cedex, France
1 Introduction
Robots play a key role in our world from providing daily services to industrial
use. Their role is in high demand due to the fact they offer more productivity,
safety at workplace and time reduction in task completion. Number of control
schemes are found in the literature [1] to control such robot such as adaptive control [2], direct continuous-time adaptive control [3], neurofuzzy PID control [4]
hierarchical control [5], slave-side control [6], intelligent controls [7], neural
networks [8], just-in-time control [9] ,Bayesian probability [10], equilibriumpoint control [11], fuzzy logic control [12], machine learning [13], evolutionary
computation [14] and genetic algorithms [15], nonlinear optimal predictive control [16],optimal control [17], stochastic control [18], variable structure control
[19], chattering-free robust variable structure control [20] and energy shaping
control [21], gain scheduling model-based controller [22], sliding mode control
[23], proxy sliding mode control [24], neuro-fuzzy/genetic control [25] but there
are five types of control systems (Fig.1) mainly used on pneumatic muscles.
Fig.1. Classification of control algorithm implemented on pneumatic systems.
Focus of our research was on the feedback control system and non-linear control systems. 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. 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. The purpose of designing such system is to stabilise the system
at certain target.
Tactical sensors are employed to investigate the grasping abilities of the ambidextrous hand. These sensors have been used several times in the past on the robot hands driven by motors [26], [27] and robot hands driven by pneumatic artificial muscles [28] and [29]. 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 [30] 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 [31] 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
[32]. 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 [33], previous researches indicates that these three algorithms are suitable to control pneumatic
systems.
The work presented in this chapter aim 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. As it can be seen in Fig.2, 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].
2 Implementation of Controllers
2.1 PID Controller
PID controller is a combination of proportional, integral and derivative controller
[34].Proportional controller provides corrective force proportional to error present. Although it is useful for improving the response of stable systems 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 [35]
Fig.2. Ambidextrous Robot Hand (Ambidextrous mode)
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. To overcome overshooting problem, derivative controller is used [36].
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 offers the maximum strength whilst minimizing weakness.
d

Output PID  K P  e  t   K i   e  t  dt  K d   e  t  
 dt

0
t
2.1.1 PID controller adapted to the Ambidextrous Hand
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)
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 [37].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:
𝐾𝑝𝑝𝑙
𝑢𝑝𝑙 (𝑡)
[𝑢𝑚𝑟 (𝑡)] = [𝐾𝑝𝑚𝑟
𝐾𝑝𝑚𝑙
𝑢𝑚𝑙 (𝑡)
𝐾𝑖𝑝𝑙
𝐾𝑖𝑚𝑟
𝐾𝑖𝑚𝑙
𝑒(𝑡)
𝑡
𝐾𝑑
∫ 𝑒(𝜏)𝑑𝜏
𝐾𝑑 ] 0
𝐾𝑑
𝑑
[ 𝑑𝑡 𝑒(𝑡) ]
left
(2)
No. of position
Proximal left PAM
(bars)
Medial
(bars)
PAM
Medial
(bars)
1
2.497
1.173
0.017
2
4.028
0.250
0.782
3
3.129
0.175
1.481
4
1.972
1.406
0.017
5
2.954
1.115
2.363
6
1.643
0.357
2.617
7
0.038
2.725
1.227
8
0.022
1.411
2.039
9
0.008
0.491
2.990
right
PAM
Table 1. Pressure at ambidextrous robot hand’s extreme positions.
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. Thus, experiments are done to collect PAMs’ pressure variation according to the fingers’
position. As the finger is made of one proximal phalange and two other phalanges
for which the movement is coupled, the finger has nine extreme positions. These
positions are numbered from 1 to 9. Position 1 refers to the proximal and medial/distal phalanges reaching both the maximum range on their left side. Position 2
refers to the proximal phalange reaching its maximum range on its left side,
whereas the medial/distal phalanges are straight. Position 3 refers to the proximal
phalange being on its maximum range on its left side, whereas the medial/distal
Pressure variation (bars)
phalanges are on their maximum range on the right side. Position 4 to 6 refers to
the finger when the proximal phalange is straight. Last position, position 9, is
when the proximal and medial/distal phalanges reach both the maximum range on
their right side. The experiment is summarized in Table 1 and Fig.3.
4
3
Proximal left
PAM
2
Medial left
PAM
1
Medial right
PAM
0
1
3
5
7
9
Fingers' position number
Fig.3. Pressure variations at extreme finger positions.
When the fingers’ close from vertical to left position (position 5 to the average
of positions 4 and 2), it is observed that the pressure of medial left PAM varies
thrice less than the pressure of the proximal left PAM, whereas the pressure of
the two medial PAMs vary from the same ratios but in opposite ways. Therefore,
the proportional constant gains are consequently defined as:
[
𝐾𝑝𝑝𝑙 /3
𝐾𝑝𝑚𝑙
−𝐾𝑝𝑚𝑟
]=[
]=[
]
𝐾𝑖𝑚𝑙
−𝐾𝑖𝑚𝑟
𝐾𝑖𝑝𝑙 /3
(3)
When the fingers’ close from vertical to right position (position 5 to the average
of positions 6 and 8), it is observed that the pressure of medial left PAM varies
0.4 times slower than the pressure of the medial right PAM. Moreover, the pressure of the medial right PAM varies in an opposite way as the one of the proximal
left PAM. Therefore, when the object interacts on the left side of the hand, equation can be written as follows:
[
−𝐾𝑝𝑝𝑙
0.4 𝑋 𝐾𝑝𝑚𝑙
𝐾𝑝𝑚𝑟
]=[
]=[
]
𝐾𝑖𝑚𝑟
−𝐾𝑖𝑝𝑙
0.4 𝑋 𝐾𝑖𝑚𝑙
(4)
Same ratios are applied to the derivative gain constants when object interact on
right side of the hand.
2.1.2 Results obtained with the PID controller
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.4
1.1
Force (N)
1.05
Forefinger
1
Middle
finger
Ring
finger
Little
finger
0.95
0.9
0.85
0.8
0.75
0.1
0.15
0.2
0.25
0.3
Time (sec)
Fig.4. The Ambidextrous Robot Hand holding a can (a grasping movement implemented with
PID controllers) and a graph representing data collected after every 0.05 seconds.
From Fig.4, 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.
2.1.3 Comparison with other grasping algorithms using PID
Mechanical and control features of the ambidextrous hand are compared with other
hands in table 2. The grasping algorithm designed by J.Y. Nagase et al. in [38] is
the most accurate and the slowest engineered after 2010. As for fuzzy logic, it is
observed that the movements are more precise but slower than the ones driven by
PID and PD controls. It is also noticed that PD control is implemented more often
Ambidexterity
Max. overshoot or error (%)
Grasping time (sec)
Anthropomorphic positioning of fingers
Thumb opposite to
other fingers during
grasping
Grasping algorithms
# DOFs
Type of actuators
# fingers
Robot hand
than PID control to grab objects. This is explained because the grasping time is
usually reached in a shorter delay than the full rotation of fingers from open to
close positions. The Ambidextrous Hand has a grasping time and a maximum
overshoot close to the best ones obtained with other robot hands. It can therefore
successively grab objects despite its limited number of DOFs, and it is the only robotic model that can grab objects with an ambidextrous behavior, either as a left or
a right hand, equally performing well.
Gifu Hand II [39]
High-speed hand [40]
ITU Hand [41]
I. Yamano and T. Maeno
[42]
L. Zollo et al. [43]
S. Nishino et al. [29]
D. Gunji et al. [32]
T. Yoshikawa [44]
5
3
2
Motors
Motors
SMAs
16
8
1a
PID
PD
N/A




5
SMAs
20
N/A


N/A
6%a
3
5
2
2
Motors
PAMs
Motors
Motors
PD
PID, Cascade
PD
PID






N/A
1.0a
0.6a
0.55a
N/A
6%a
N/A
22%a
J.Y. Nagase et al. [45]
4
PAMs
Fuzzy logic


0.9a
9%ad
DLR Hand II [46]
DLR Hand [47]
4
5
Motors
Motors
10a
13a
1
4a
N/
A
16a
19
N/A
Cascade




28.7
0.1a
N/A
N/A
Shadow Hand [26]
5
Motors
20
PID


0.15a
N/A
ACT Hand [48]
T. Nuchkrua et al. [49]
TU Bionic Hand [50]
DEXMART Hand [51]
Ambidextrous Hand [52]
5
3
5
5
5
Motors
PAMs
Motors
Motors
PAMs
23
3
15
20
13
N/A
N/A
PID
NN
PID



N/A N/A
N/A N/A
0.208 N/A
0.25a 25%ad
0.20
8% 




0.55ab 16%ab
0.05a N/A
3.76 N/A
a
Estimations made from curves, pictures or videos of the robot hands
b
Experiments do not concern grasping but contact tasks
c
Only for grasping
d
For a target of 1 N ± 10%, whereas the error can exceed 30% for lower force
targets
Table 2. Comparison of various robot hands with our ambidextrous robot hand.
3.1 Bang-bang Controller
Bang-bang controllers are used to switch between two states abruptly. They are
widely used in systems that accept binary inputs. Bang-bang controller is not
popular in robotics due to its shooting functions that are not smooth [53] and need
regularisation [54]. Fuzzy logic [55], [56] and PID are usually combined with
bang-bang controller to add flexibility and determine switching time of Bang-bang
inputs [37]. Bram Vanderborght et al. in [57] controlled a bipedal robot actuated
by pleated pneumatic artificial muscles using bang-bang pressure controller. Stephen M Cain et al. in [58], studied locomotor adaptation to powered ankle-foot orthoses using two different orthosis control methods. Dongjun Shin et al. in [59],
proposed the concept of hybrid actuation for human friendly robot systems by using distributed macro-Mini control approach [60]. The hybrid actuation controller
employ modified bang-bang controller to adjust the flow direction of pressure regulator. Zhang, Jia-Fan et al. in [61], presented a novel pneumatic muscle based actuator for wearable elbow exoskeleton. Hybrid fuzzy controller composed of bangbang controller and fuzzy controller is used for torque control.
3.1.1 Bang-bang control adapted to the Ambidextrous Hand
The bang-bang controller allows all fingers to grasp the object without taking any
temporal parameters into account. A block diagram of Bang-bang controller is
shown in Fig.5. 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
𝑓=1
Fig.5. Bang-bang loops driven by proportional controllers.
(5)
3.1.2 Results obtained with bang-bang control
The phalanges must close with appropriate speed’s ratios to tighten around objects
when interacting with object. Results obtained from experiment using the bangbang controller are provided in Fig.6. This time, it is noticeable 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 is provided in Fig. 6.
Force (N)
1.5
1.4
Forefinger
1.3
Middle finger
1.2
Ring finger
1.1
Little finger
1
0.9
0.1
0.15
0.2
0.25
0.3
Time (sec)
Fig.6. Graph shows force against time of the four fingers while grasping a drink can with bangbang controllers. The ambidextrous robot hand holding a can with a grasping movement implemented with bang-bang controllers. It is seen the can has deformed itself.
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.6 than the previously
obtained in Fig.4. 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.6 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).
3.1.3 Comparison with other bang-bang controls
B. Vanderborght et al. [63]
Z. Xu et al.
[62]
Ambidextrous
Hand [37]
Two legs
PAMs
Two legs
PAMs
Two legs
PAMs
Index of a
hand
Air cylinders
2
0.2a
PI
3
6
0.4a
PID
3
6
0.2a
Generate a joint trajectory
Delta-p
6
12
0.15a
Evaluation of speed
capabilities
None
2b
4b
0.33
Generate a joint trajectory
Generate a joint trajectory
Ambidexterity
N/
A
# DOFs
PID
Pressure control
Error max. (%)
Controller used
as an outer loop
Aim of the bangbang control
Type of actuators
PAMs
Execution time
(sec)
B. Vanderborght et al. [64]
B. Vanderborght et al. [65]
Modular
part of a
leg
# actuators
R. Van Ham et
al. [57]
Robotic structure
Bang-bang control
The features related to the bang-bang control implemented on the ambidextrous
hands are compared to others in Table 3. For example, the bipedal walking robot
discussed in [57] implemented bang-bang controller on robotic structure driven by
pneumatic artificial muscles. and hand designed by Z. Xu et al. [62] is actuated by
air cylinders instead of PAMs, its architecture is much closer to the one of the
Ambidextrous Hand. Table 3 shows that bang-bang control is not usually implemented on complex structures, as the ambidextrous hand and the two legs discussed in [63] are the only architectures that exceed ten actuators. The ambidextrous hand is also the only robotic structure in Table 3 that has more than ten
DOFs. The execution times are not very significant, given that the aims of the
bang-bang controls are totally different from one project to other; it is nevertheless
observed that the execution times never exceed 0.4 sec, as bang-bang controls aim
at making a system switch from one state to another as fast as possible. The system
proves its efficiency for the walking robot introduced in [57], but provides a huge
overshoot of 53% when it is implemented on the Ambidextrous Hand. Consequently, despite the originality of the bang-bang control to grab objects, its implementation on an ambidextrous device and its grasping time of 0.15 sec (25%
shorter than the one obtained with the PID control), the bang-bang control is not
accurate enough to control the fingertips’ force of the Ambidextrous Hand.
N/A
4% for pressurea
0.27% for anglea
3% for pressure
4.5% for anglea
17% for pressurea
17.5% for positiona
N/A
53% for

the force
a Estimations are made from curves
b These numbers do not correspond with the actuators of the robotic structure but with the ones used for the bang-bang control
Hand
PAMs
Force control
Proportional
9b
14b
0.15
Table 3. Comparison of bang-bang controls’ characteristics between the Ambidextrous Hand and
other robotic models.
4.1 Backstepping Controller
Backstepping was offered as a mean 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 [66]. 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 [67] and found out BSC is
somewhere better than SMC in controlling a device. He further applied BSC coupled with fuzzy logic in [68]. In [69], 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 chapter
validates the possibility of driving multifinger robot hand using BSC.
4.1.1 BSC adapted to the Ambidextrous Hand
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)
(6)
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.7. Basic Backstepping controller is shown.
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:
𝑉2 (𝑒1 , 𝑒2 ) =
1 2
(𝑒 (𝑡) + 𝑒22 (𝑡)) < 𝐹𝑠
2 1
𝑉2̇ (𝑒1 , 𝑒2 ) = 𝑒1 (𝑡) ∗ 𝑒̇1 (𝑡) + 𝑒2 (𝑡) ∗ 𝑒̇2 (𝑡)
(10)
(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:
𝑉2̇ (𝑒1 , 𝑒2 ) = 𝑒̇1 (𝑡) ∗ (𝑒1 (𝑡) + 𝑘𝑒̈1 (𝑡))
(12)
The block diagram of backstepping process is illustrated in Fig.7. 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.
4.1.2 Results obtained with the BSC
The grasping features and the force against time graph is shown in Fig.8. 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 deduced
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.
1.1
Forefin
ger
1
Middlef
inger
0.8
Ring
finger
0.7
Little
finger
Force (N)
0.9
0.6
Time (s)
0.1 0.15 0.2 0.25 0.3 0.35 0.4
Fig.8. Graph shows force against time of the four fingers while ambidextrous hand grasping a
can of soft drinks using backstepping controllers.
4.1.3 Comparison with other BSCs
Backstepping control implemented on various hands is compared with the ambidextrous hand in Table 4. Some robotic structures actuated by motors are also included in the table as their number of DOFs is closer to the one of the ambidextrous hand and some of their BSCs are related to force control. BSCs are usually
implemented on structures with less than five DOFs, such as manipulators, arms
or parallel robots. The ambidextrous hand is the only robotic structure in table 4
that has more than ten DOFs (BSC is only implemented on nine of them). It is
quite clear that the number of DOFs does not exceed two when the BSCs are implemented on structures driven by PAMs. The BSC of the ambidextrous hand has
an execution time of about 0.37 sec, which is one of the shortest of Table 4, with
[70]and [71] that have execution times estimated to 0.3 sec, as well as [72] with
an execution time of 0.45 sec. However, the maximum error of 4% for the ambidextrous hand’s BSC is much higher than the ones obtained with the practical results introduced in [68], [72] and [73]. The control algorithms introduced in [72]
appears to be ones of the most efficient, as the arm has 6 DOFs and the BSC is
both among the fastest and the most accurate. Nevertheless, the BSC of the ambidextrous hand is the only one that is implemented on an ambidextrous structure
and which is used to grab objects. In conclusion, the implementation of the BSC
Motors
P. Carbonell et al. [67]
N/A, single
PAM
PAM
P. Carbonell et al. [68]
N/A, single
PAM
PAM
D. Nganya-Kouya et al.
[75]
Manipulator
N/A
Lotfazar et al. A. [76]
Manipulator
Motors
S.-H. Wen S.-H. Wen
and B. Mao. [77]
Manipulators
N/A
Parallel
bot
PAMs
H. Aschemann and D.
Schindele [71]
M.R. Soltanpour and
M.M. Fateh [78]
ro-
Manipulator
Motors
X. Liu and A. Liadis [79]
Parallel
bot
Motors
L. Qin et al. [72]
Arm
N/A
H. Aschemann and D.
Schindele [73]
Axis
PAMs
Ambidextrous
2014 [80]
Hand
PAMs
Hand,
ro-
Trajectory
control
PAM’s
length
control
PAM’s
length
control
Force and
position
control
Trajectory
control
Force and
position
control
Position
control
Trajectory
control
Position
control
Trajectory
control
Position
control
Force
control
N/A
N/A
0.3a
10%a
None
N/A
1
2.4a
8%a
Fuzzy logic
N/A
1
7a
1%a
None
4
N/A
9a
N/A
None
5
5
2a
N/A
NN
N/A
N/A
1.9ab
9%ab
None
2
4
0.3a
4%a
SMC
2
N/A
7.6ab
<10-3%b
Fuzzy logic
2
2
N/A
N/A
SMC
6
N/A
0.45a
2%a
None
1
2
4a
1.4%a
None
9c
14c
0.37
4%
Execution
time (sec)
Error max.
(in %)
None
a
Estimations are made from curve
Results are obtained through a simulation
c
Four DOFs and four actuators are unused for the BSC
b
Table 4. Comparison of BSCs’ characteristics between the Ambidextrous Hand and other robotic mode
CONCLUSION
PID, Bang-bang and BSC are tested and their performance in controlling an ambidextrous robotic hand is analyzed. PID controller was found the best when applied
as compare to Bang-bang and Backstepping control. Backstepping control tech-
Ambidexterity
Algorithms
to which
it is
combined
# actuators
Manipulator
# DOFs
C.-Y Su and Y. Stepanenko [74]
Aim of
the BSC
BSC
Robotic
structure
Type of
actuators
on the ambidextrous hand is quite successful, as the obtained results are among
the best in Table 4. Nevertheless, its grasping time of 0.37 sec is 85% slower than
the grasping time obtained with PID control in, and also much slower than the
grasping times of most of robot hands summarized in Table 2. Consequently, the
BSC is not the best option to grab objects with the Ambidextrous Hand.


nique 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 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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