Implementation of PID, Bang-bang and Back-stepping 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 KalganovaDepartment of Electronic and Computer Engineering, Brunel University, Kingston Lane, Uxbridge, London, UK, e-mail: Mashood.Mukhtar@brunel.ac.uk

Nicolas LesneDepartment of System Engineering, ESIEE Paris, Noisy-le-Grand Cedex, France1 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 re-duction in task completion. Number of control schemes are found in the literature1 to control such robot such as adaptive control2, direct continuous-time adaptive control 3, neurofuzzy PID control 4 hierarchical control 5, slave-side control 6, intelligent controls 7, neural net-works 8, just-in-time control 9 ,Bayesian probability 10, equilibrium-point 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 control20 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 perform-ance 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 tar -get.

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 au-tomatically 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 dis-placement 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 automati-cally trigger grasping algorithms. Once objects are detected by one of the vision sensors, grasp-ing 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 actuators33, 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 Backstep-ping 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 fin-gers 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 ControllerPID controller is a combination of proportional, integral and derivative controller34.Propor-tional 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 propor-tional 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 over-shooting 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 con-troller 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 mini-mizing weakness.

Output PID=KP×e<t >+ K i×∫0

t

e<t>¿dt+K d׿¿

2.1.1 PID controller adapted to the Ambidextrous HandPID control loops were implemented on an ambidextrous robot hand using the parallel form of a PID controller, for which the equation is as follows:

u ( t )=K p e ( t )+K i∫0

t

e (τ ) dτ+Kdddt

e (t) (2)

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 areupl ( t ), umr (t ) anduml ( 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:

[upl ( t )umr ( t )uml ( t )]=[ K p pl

K i plK d

K pmrK imr

K d

K pmlK iml

K d] [

e (t )

∫0

t

e (τ ) dτ

ddt

e( t) ] (2)

No. of position Proximal left PAM (bars)

Medial left PAM (bars)

Medial right PAM (bars)

1 2.497 1.173 0.0172 4.028 0.250 0.7823 3.129 0.175 1.4814 1.972 1.406 0.0175 2.954 1.115 2.3636 1.643 0.357 2.6177 0.038 2.725 1.2278 0.022 1.411 2.0399 0.008 0.491 2.990

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 ex-treme 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 me-dial/distal phalanges are straight. Position 3 refers to the proximal phalange being on its maxi-mum range on its left side, whereas the medial/distal 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.

1 2 3 4 5 6 7 8 90

1

2

3

4

Proximal left PAM

Medial left PAM

Medial right PAM

Fingers' position number

Pres

sure

var

iatio

n (b

ars)

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 ra-tios but in opposite ways. Therefore, the proportional constant gains are consequently defined as:

[K pml

K iml]=[ K ppl

/3K i pl

/3 ]=[−K pmr

−K imr] (2)

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:

[K pmr

K imr]=[0.4 X K pml

0.4 X K iml]=[−K p pl

−K ipl] (2)

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 controllerUsing 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 res-ult is illustrated in Fig.4

0.1 0.15 0.2 0.25 0.30.75

0.8

0.85

0.9

0.95

1

1.05

1.1

ForefingerMiddle fingerRing fingerLittle finger

Time (sec)

Forc

e (N

)

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 ap-proximately 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 de-duced 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 PIDMechanical 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. in38 is the most accurate and the slowest engineered after 2010. As for fuzzy logic, it is ob-served 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

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 ro-botic model that can grab objects with an ambidextrous behavior, either as a left or a right hand, equally performing well.

Rob

ot h

and

# fin

gers

Type

of a

ctua

tors

# D

OFs

Gra

spin

g al

gorit

hms

Ant

hrop

omor

phic

po-

sitio

ning

of f

inge

rsTh

umb

oppo

site

to

othe

r fin

gers

dur

ing

Gra

spin

g tim

e (s

ec)

Max

. ove

rsho

ot o

r er-

ror (

%)

Am

bide

xter

ity

Gifu Hand II 39 5 Motors 16 PID 0.55ab 16%ab

High-speed hand 40 3 Motors 8 PD 0.05a N/AITU Hand 41 2 SMAs 1a N/A 3.76 N/A

I. Yamano and T. Maeno 42 5 SMAs 20 N/A N/A 6%a

L. Zollo et al. 43 3 Motors 10a PD N/A N/AS. Nishino et al. 29 5 PAMs 13a PID, Cascade 1.0a 6%a

D. Gunji et al.32 2 Motors 1 PD 0.6a N/AT. Yoshikawa 44 2 Motors 4a PID 0.55a 22%a

J.Y. Nagase et al. 45 4 PAMs N/A Fuzzy logic 0.9a 9%ad

DLR Hand II 46 4 Motors 16a N/A 28.7 N/ADLR Hand 47 5 Motors 19 Cascade 0.1a N/A

Shadow Hand 26 5 Motors 20 PID 0.15a N/A

ACT Hand 48 5 Motors 23 N/A N/A N/AT. Nuchkrua et al. 49 3 PAMs 3 N/A N/A N/A

TU Bionic Hand 50 5 Motors 15 PID 0.208 N/ADEXMART Hand 51 5 Motors 20 NN 0.25a 25%ad

Ambidextrous Hand52 5 PAMs 13 PID 0.20 8%

a Estimations made from curves, pictures or videos of the robot handsb Experiments do not concern grasping but contact tasks

c Only for graspingd For a target of 1 N ± 10%, whereas the error can exceed 30% for lower

force targetsTable 2. Comparison of various robot hands with our ambidextrous robot hand.

3.1 Bang-bang ControllerBang-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 bang-bang controller and fuzzy controller is used for torque control.

3.1.1 Bang-bang control adapted to the Ambidextrous HandThe 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 bal-ancing equation is defined as:

F tmin=W o+∑f =1

4

F f (2)

Fig.5. Bang-bang loops driven by proportional controllers.

3.1.2 Results obtained with bang-bang controlThe phalanges must close with appropriate speed’s ratios to tighten around objects when interacting with object. Results obtained from experiment using the bang-bang 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.

0.1 0.15 0.2 0.25 0.30.9

1

1.1

1.2

1.3

1.4

1.5

Forefinger

Middle finger

Ring finger

Little finger

Time (sec)

Forc

e (N

)

Fig.6. Graph shows force against time of the four fingers while grasping a drink can with bang-bang controllers. The ambidextrous robot hand holding a can with a grasping movement imple-mented 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 over-shoots. 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 ap-plied on the fingers. It is also noticed that the force applied by some fingers in-crease 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 be -

tween 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 F f defined in (2).

3.1.3 Comparison with other bang-bang controlsThe 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 Am-bidextrous 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 to-tally different from one project to other; it is nevertheless observed that the execu-tion 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 effi-ciency 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.

Ban

g-ba

ng c

on-

trol

Rob

otic

stru

ctur

e

Type

of a

ctua

tors

Aim

of t

he b

ang-

bang

con

trol

Con

trolle

r use

d as

an

oute

r loo

p

# D

OFs

# ac

tuat

ors

Exec

utio

n tim

e (s

ec)

Erro

r max

. (%

)

Am

bide

xter

ityR. Van Ham et

al. 57

Modular part of a

legPAMs Pressure control PID N/

A 2 0.2a N/A

B. Vander-borght et al.

64Two legs PAMs Generate a joint tra-

jectory PI 3 6 0.4a 4% for pressurea

0.27% for anglea

B. Vander-borght et al.

65Two legs PAMs Generate a joint tra-

jectory PID 3 6 0.2a 3% for pressure4.5% for anglea

B. Vander-borght et al.

63Two legs PAMs Generate a joint tra-

jectory Delta-p 6 12 0.15a17% for pressurea

17.5% for posi-tiona

Z. Xu et al. 62 Index of a hand

Air cylin-ders

Evaluation of speed capabilities None 2b 4b 0.33 N/A

Ambidextrous Hand 37 Hand PAMs Force control Proportional 9b 14b 0.15 53% for

the force

a Estimations are made from curvesb These numbers do not correspond with the actuators of the robotic structure but with the ones used for the bang-bang control

Table 3. Comparison of bang-bang controls’ characteristics between the Ambidextrous Hand and other robotic models.

4.1 Backstepping ControllerBackstepping 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 elec-tro pneumatic system in66. First, the nonlinear model of the electro pneumatic sys-tem was presented. It was transformed to be a nonlinear affine model and a co-ordinate transformation was then made possible by the implementation of the non-linear 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 some-where better than SMC in controlling a device. He further applied BSC coupled with fuzzy logic in 68. In69, a paralleled robot project is discussed which is con-trolled by BSC. Since literature review revealed no multifinger robot hand (actu-ated by PAMs) is ever driven using BSC, research presented in this chapter vali -dates the possibility of driving multifinger robot hand using BSC.

4.1.1 BSC adapted to the Ambidextrous HandBSC consists in comparing the system’s evolution to stabilizing functions. Deriva-tive control is recursively applied until the fingers reach the conditions imple-mented in the control loops. First, the tracking error e1 (t )of the BS approach is de-fined as:

[e1( t)e1 ( t ) ]=[F t−F f (t )

−F f (t) ] (2)

then evaluated using a first Lyapunov function defined as:

V 1 (e1)=12

e12( t)<Fgmin (2)

V 1 (e1)=e1 (t )∗e1 ( t )=−F f (t )∗e1 (t ) (2)

The force provided by the hand is assumed not being strong enough as long as e1

2/2 exceeds a minimum grasping force defined asFgmin. In (2), it is noted thate1 ( t ) ≠0 as long asF f (t )keeps varying. Therefore, V 1 (e1) cannot be stabilized until the system stops moving. Thus, a stabilizing function is introduced. This sta-bilizing function is noted as a second errore2 ( t ):

e2 (t )=k∗e1 ( t ) (2)

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 ande2 (t )are equal to zero when one finger reaches a stable position, even ifF f (t )≠ Ft . kaims at increasing e1 ( t ) to anticipate the kinematic moment when e1 ( t ) becomes too low. In that case, the BSC must stop running asF f (t )is close toF t. Both of the errors are considered in a second Lyapunov function:

V 2 (e1, e2 )=12(e1

2 ( t )+e22 ( t ))<F s (2)

V 2 (e1 , e2 )=e1 (t )∗e1 (t )+e2 (t )∗e2 ( t ) (2)

where F srefers to a stable force applied on the object. This second step allows sta-bilizing the system using derivative control. Using (2), (2) can be simplified as:

V 2 (e1 , e2 )=e1 ( t )∗(e1 ( t )+k e1 (t )) (2)

The block diagram of backstepping process is illustrated in Fig.7. According to the force feedbackF f (t ), the fingers’ positions adapt themselves until the condi-tions of the Lyapunov functions (V ¿¿1 , V 1)¿ and (V ¿¿2 , V 2)¿ are reached.

4.1.2 Results obtained with the BSCThe 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.

0.1 0.15 0.2 0.25 0.3 0.35 0.40.6

0.7

0.8

0.9

1

1.1

Fore-finger

Mid-dlefinger

Ring finger

Little finger

Time (s)

Forc

e (N

)

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 BSCsBackstepping control implemented on various hands is compared with the am-bidextrous 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 ambidex-trous 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 im-plemented 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 70and 71 that have execution times estimated to 0.3 sec, as well as 72 with an ex-ecution time of 0.45 sec. However, the maximum error of 4% for the ambidex-trous hand’s BSC is much higher than the ones obtained with the practical results introduced in 68, 72 and73. 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 on the ambidex-trous 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.

BSC

Rob

otic

stru

ctur

e

Type

of

actu

ator

s

Aim

of

the

BSC

Alg

orith

ms

to w

hich

it is

com

bine

d

# D

OFs

# ac

tuat

ors

Exec

utio

ntim

e (s

ec)

Erro

r max

.(in

%)

Am

bide

xte

rity

C.-Y Su and Y. Stepanenko 74 Manipulator Motors Trajectory

control None N/A N/A 0.3a 10%a

P. Carbonell et al. 67 N/A, single PAM PAM

PAM’s length control

None N/A 1 2.4a 8%a

P. Carbonell et al. 68 N/A, single PAM PAM

PAM’s length control

Fuzzy logic N/A 1 7a 1%a

D. Nganya-Kouya et al. 75 Manipulator N/A

Force and position control

None 4 N/A 9a N/A

Lotfazar et al. A. 76 Manipulator Motors Trajectory control None 5 5 2a N/A

S.-H. Wen S.-H. Wen and B. Mao.77

Manipulators N/A

Force and position control

NN N/A N/A 1.9ab 9%ab

H. Aschemann and D. Schindele 71

Parallel robot PAMs Position

control None 2 4 0.3a 4%a

M.R. Soltanpour and M.M. Fateh 78 Manipulator Motors Trajectory

control SMC 2 N/A 7.6ab <10-3%b

X. Liu and A. Liadis 79 Parallel robot Motors Position

control Fuzzy logic 2 2 N/A N/A

L. Qin et al. 72 Arm N/A Trajectory control SMC 6 N/A 0.45a 2%a

H. Aschemann and D. Axis PAMs Position None 1 2 4a 1.4%a

Schindele 73 control

Ambidextrous Hand, 2014 80 Hand PAMs Force

control None 9c 14c 0.37 4%

a Estimations are made from curve b Results are obtained through a simulationc Four DOFs and four actuators are unused for the BSC

Table 4. Comparison of BSCs’ characteristics between the Ambidextrous Hand and other ro-botic mode

CONCLUSIONPID, Bang-bang and BSC are tested and their performance in controlling an am-bidextrous robotic hand is analyzed. PID controller was found the best when ap-plied as compare to Bang-bang and Backstepping control. Backstepping control technique was validated for the first time on an ambidextrous robot hand. By com-bining 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.

ACKNOWLEDGMENTThe 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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