position control of an Industrial Robot Manipulator

Third International Conference on Advances in Control and Optimization of Dynamical Systems March 13-15, 2014. Kanpur, India

Fuzzy PD+I based Hybrid force/ position control of an Industrial Robot Manipulator Himanshu Chaudhary*. Vikas Panwar** N. Sukavanum***. Rajendra Prasad**** * Department of Electrical Engineering, IITR, INDIA, (e-mail: himan.74@ gmail.com). ** School of Vocational Studies & Applied Sciences, GBU, INDIA, (e-mail:[email protected]) *** Department of Mathematics, IITR, INDIA, (e-mail: [email protected]) **** Department of Electrical Engineering, IITR, INDIA, (e-mail: [email protected])

Abstract: A hybrid fuzzy PD+I (FPD+I) based force plus position controller with unspecified robot dynamics has been proposed for a robot manipulator under constrained environment. The FPD+I controller has been utilized as a principal controller to tune up orthodox PID gains throughout the complete trajectory tracking process. The validity of the proposed controller has been studied using a 6Degree of Freedom (DOF) PUMA robot manipulator. Simulation results show that the projected hybrid FPD+I force / position controller adheres to the desired path closer and smoother. Keywords: Degrees Of Freedom, fuzzy control, force/position control, PUMA robot manipulator. 1. INTRODUCTION In many industrial applications it is desirable for the robot manipulator to exert a prescribed force normal to a given surface while following a prescribed motion trajectory tangential to the surface. A Modified Hybrid Control scheme was presented in (Zhang and Paul, 1985) which accomplished an accurate position and force control for a robot manipulator in joint space by specifying the desired compliance in Cartesian space. A neuro-fuzzy (NF) hybrid position/force control with vibration suppression is presented in (Sun et al., 2004). In which an impedance force control algorithm is derived using force decomposition, and then singular perturbation method is used to construct the composite control, where an adaptive NF inference system is employed to approximate the inverse dynamics of the space robot. The quadratic optimization and sliding-mode based hybrid position and force control approach for a robot manipulator is presented in (Panwar and Sukavanam, 2007) where the optimal feedback control law is derived solving matrix differential Riccati equation, which is obtained using Hamilton Jacobi Bellman optimization which is shown to be globally exponentially stable using Lyapunov function approach. The dynamic model uncertainties are compensated with a feed forward neural network. A neural network based adaptive control scheme for hybrid force/position control for rigid robot manipulators is presented in (Kumar et al., 2011). Based on decomposed robot dynamics into force, position and redundant joint subspaces, a neural network based controller is proposed to learn the parametric uncertainties, existing in the dynamical model of the robot manipulator. A novel neuro-adaptive force/position tracking controller for a robotic manipulator in compliant contact with a surface under non-parametric uncertainties is proposed in (Karayiannidis et al., 2007) which assumes structural 978-3-902823-60-1 © 2014 IFAC

429

uncertainties to characterize the compliance and surface friction models, as well as the robot dynamic model. The problem of the configuration dependent dynamics of the manipulator in constrained motion was dealt in (Jatta et al., 2006) with the implementation of a hybrid force/velocity control for contour tracking tasks of unknown objects performed by industrial robot manipulators. An adaptive robust hybrid position/force control technique based on Lyapunov stability and bound estimation for a robot manipulator was proposed in (Ha and Han, 2004). The controller does not need the information of uncertainty bound. A position/ force controller based on the principles of invariancy which decomposition of the task space into force and position subspaces as well as consistency which relates the free motion and constrained force to the characteristics of the environment, was introduced in (Goldenberg and Song, 1997), which guarantees the overall stability and the reduction of interactions between the position and force controllers. An augmented hybrid impedance force / position control scheme is developed and presented in (Patel et al., 2009) for a redundant robot manipulator. The outer-loop controller improves transient performance, while the inner loop consists of a Cartesian-level potential difference controller, a redundancy resolution scheme at the acceleration level, and a joint-space inverse dynamics controller. An adaptive fuzzy neural position/force controller is proposed for a robot manipulator in (Kiguchi and Fukuda, 1997). The proposed controller deals with the human expert knowledge and skills for planning and control. A stable as well as generalized architecture for hybrid position/force control is presented in (Fisher and Mujtaba, 1992), which can influence both joint positions and torques. It was shown that kinematic instability is due to inverse of the manipulator Jacobian matrix. A robust learning control algorithm for precise path tracking of constrained robotic manipulators in 10.3182/20140313-3-IN-3024.00062

2014 ACODS March 13-15, 2014. Kanpur, India

the presence of state disturbances, output measurement noises and errors in initial conditions was presented in (Wang et al., 1995). The (Qingjiu and Enomoto, 2009) proposed a hybrid position, posture, force, and moment control for a six-degree-of-freedom (6-DOF) robot manipulator for the surface contact work by expansion of the conventional hybrid position and force control. The issue of hybrid adaptive network-based fuzzy inference system (ANFIS) tuning methodology based force/position control of the robot manipulators mounted on oscillatory was successfully applied in (Lin et al., 2010). When the system is in sliding mode, force, position, and redundant joint velocity errors will approach zero irrespective of parametric uncertainties so a novel sliding-adaptive controller Based on a decomposition of the rigid robot system with motor dynamics was developed in (Kwan, 1995), which can achieve robustness to parameter variations in both manipulator and motor. A hybrid adaptive fuzzy control approach based position/force control of robot manipulators is proposed in (Feng-Yi and Li-Chen, 2000) to solve the overwhelming complexity of the deburring process and imprecise knowledge about robot manipulators. A fuzzy neural networks based Position/force control, which enables the controller to deal efficiently with force sensor signals was presented in (Kiguchi and Fukuda, 2000), which include noise and/or unknown vibrations caused by the working tool, to search the direction of the constraint surface of an unknown object. There are many theoretical as well as practical hurdles which are still unachievable because of unspecified robot manipulator dynamics as well as environmental complexities. Standard approaches are appropriate when one has the precise mathematical modeling of all the fundamental parameters vital, are available. On the other hand, most of the time one has to work in real environment where the dynamic model as well as external environmental variables are unidentified(Castillo and Melin, 2003). Conventional controllers like PD and PI alone do not perform well in case of removing steady state error as well as to enhance the transient response. Recently, some of the hybrid intelligent type fuzzy proportional integral derivative (FPID) controller techniques have been combined with conventional techniques and presented in (Khoury et al., 2004), which illustrates the improved steady state as well as transient response. A two input fuzzy system (TIFS) based digital type proportional integral derivative (PID) controller was presented in (Li et al., 2001b). In (Misir et al., 1996), the author proposed a modified conventional proportional integral plus derivative (CPI+D) controller based on discrete-time fuzzy system (DTFS). This was able to improve the self-tuning control capability while containing the simplicity of its conventional counterpart. A hybrid fuzzy logic proportional plus conventional integral derivative (HFP+CID) controller was presented in(Li, 1998) by using an incremental fuzzy logic (IFL) controller after replacing the proportional term in a conventional PID controller. A fuzzy proportional integral derivative (FPID) controller based real-time solution was offered in (Carvajal et al., 2000). It was computationally useful analytical scheme suitable for implementation in closed-loop digital 430

control for some known nonlinear systems, like robotic manipulators. (Kazemian, 2001) did a comparative analysis of self-organising fuzzy PID (SOF-PID) controller with selftuning controller with extra learning capability to control a robot manipulator for a predefined path. (Li et al., 2001a) presented a different hybrid fuzzy proportional plus integral derivative (FP+ID) controller for better functioning under uncertainty for the control of robot manipulator. An automatic strategy based on specifically reduction in rule size of fuzzy logic controllers for robot manipulators was presented in (Bezine et al., 2002). For achieving high robustness opposed to noise, (Su et al., 2004) accumulated twin nonlinear differentiators with a conventional fuzzy proportional and derivative (CFPD) controller to develop a different hybrid fuzzy proportional and derivative (HFPD) controller. To unravel the nonlinear control snag, (Ya Lei and Meng Joo, 2004) integrated the fuzzy gain scheduling method with a fuzzy proportional, integral and derivative (FPID) control for industrial robot manipulator. To eliminates the requirement of precise dynamical models in Computed Torque Control (CTC) in the presence of structured/unstructured uncertainty, (Song et al., 2005) combined the Fuzzy Control (FC) concept with CTC to solve the trajectory control problems of robot manipulators. A fuzzy PD+I controller based method was presented in (Alavandar and Nigam, 2008), which in turns improves the trajectory tracking problem of a six-DOF(Degree of Freedom) over usual PID as well as fuzzy PID controllers. In (Piltan et al., 2011), an on-line tuneable gain model free PID-like fuzzy controller (GTFLC) was designed for three degrees of freedom (3DOF) robot manipulator with satisfactory functioning. (Salas et al., 2013) presented a SelfOrganizing Fuzzy Proportional Derivative (SOF-PD) control scheme, which exploits the simplicity and toughness of the plain PD control and enhances its gain, was offered for robot manipulators. In the present research paper, a hybrid force/position control approach is proposed for trajectory control of robot manipulator, which works well in the absence of anonymous dynamics of a robot manipulator in a constraint environment. The constraint has been taken in joint space by restricting the manipulator to move in Z direction. The proposed FPD+I force/position controller follows the trajectory exceptionally smoothly with bare minimum error. Section 2 establishes the actuator dynamic model for the n degrees of freedom (DOF) robot manipulator. The hybrid FPD+I force/position controller is discussed in Section 3. Section 4 presents simulation outcome to reveal the efficiency of the proposed controller, followed by conclusions in Section 5. 2. DYNAMICS OF ROBOT MANIPULATOR The traditional dynamic model of an n DOF robot manipulator is presumed to be in the subsequent form(Lewis et al., 1999)

M (q)q  Vm (q, q)  G(q)  F (q)  

(1)

2014 ACODS March 13-15, 2014. Kanpur, India

Where

M (q)  R nxn represents

the

inertia

matrix,

Vm (q, q)  R nxn represents the centripetal-coriolis matrix,

G (q)  R n represents the gravity effects, F (q)  R n denotes

the friction effects,  (t )  R

n

After including nonlinear unmodelled disturbances, the (6) can be rewritten as ..

signifies the torque input

J M qM  BqM  FM  R  KM v Where

v  Rn

(2)

is the control input motor voltage, n

qM  vec{qMi }  R with qMi is the i rotor angle, J M is motor inertia, BM is the rotor damping constant, FM is the actuator friction. The actuator coefficient matrices are constants, specified as th

0  J J M   Mi   0 J Mi  0 ( B  K bi K Mi / Rai )  B   Mi 0 ( BMi  K bi K Mi / Rai )   r Ri 0 KM

0 ri  K / R   Mi ai 0 

..

.

+

-

Fuzzy PD+I Controller

+

-

Robot manipulator with uncertainty and actuator dynamics

a

-

Kf

(3)

+

d



Fig. 1. Fuzzy PD + I hybrid force/position controller

 / Rai 

0

3.1 Force/Position Controller

qi  ri qM i

(4)

q  RqM

Where ri is a constant less then1 if qi is revolute else units of

m/rad if qi is prismatic. By putting qM from (4) and  from (1), the actuator dynamics for a robot manipulator may be written as (Lewis et al., 2003) .

( J M  R 2 M ) q  ( BM  R 2Vm ) q  ( RFM  R 2 F )  R 2G  RK M v

(5)

.

.

M (q) q Vm (q, q)  G(q)  F (q)  K v

The dynamic model of an n DOF robot manipulator with environmental contact on a prescribed surface is presumed to be in the subsequent form(Lewis et al., 1999)

M (q)q  Vm (q, q)  G (q)  F (q)   d     J T (q)

(10)

Where q(t )  R n , J (q) a Jacobian matrix is associated with the contact surface geometry, and  is a vector of contact forces exerted normal to the surface described to the surface. The constraint surface for robot manipulator is considered in Z direction in joint space. The Jacobian matrix is

J (q) 

Z q

(11)

The constraint equation reduces the number of degree of freedom to

or ..



J T (q)



..

(9)

velocity error ( em ). The integral error ( em ) has been used simply to perform orthodox integral action.

Q1a  q1a ,q1a

K Mi

(8)

3. HYBRID FUZZY PD+I FORCE/POSITION CONTROLLER DESIGN A hybrid FPD+I force/position controller applied to six DOF PUMA robot arm has been shown in Fig. 1. The fuzzy controller applied, is having two inputs and single output (TISO) structure. The inputs used are position error ( em ),

Q1d   q1d , q1d 

Here Rai is armature resistance, K Mi is torque constant, Kbi is back emf constant and J Mi is the motor inertia of the ith motor. ri is the gear ratio of the coupling or

.

M (q) q N (q, q)   d  K v   

n

control vector and q(t ), q(t ), q(t )  R signify link position, velocity and acceleration correspondingly. If armature inductance is insignificant in the case of electric motors then the dynamics of n decoupled armaturecontrolled DC motors are [34]

.

M (q) q Vm (q, q)  G(q)  F (q)   d  K v

(6)

n1  n  m

(12)

To find the constraint motion along the Z direction the reduced order dynamics for robot manipulator is

Where .

M (q)  ( J M  R 2 M );Vm (q, q)  ( BM  R 2Vm ) 2

.

(7)

2

G (q)  R G; F (q)  ( RFM  R F ); K   RK M 431

M (q1 ) L(q1 )q1  Vm (q1 , q1 )q1  F (q1 )  G (q1 )   d     J T (q1 )

(13)

2014 ACODS March 13-15, 2014. Kanpur, India

Where q1 (t )  R n1 , L(q1 ) is an extended Jacobian matrix given by  I n1    L ( q1 )   Z   q1 

(14)

The reduced order dynamics describing the motion in the plane of constraint surface is Mq1  V1q1  F  G   d  

(15)

Where:

In proposed controller, only the proportional and estimated derivative signals are applied to the fuzzy controller, while the integral control is being given directly to take care of steady state error. The above mentioned components have been utilised in a following way: 1. Two input crisp variables fed to the FPD controller are joint position error em and velocity error em . Both inputs are fuzzified through fuzzification component. The linguistic terms of input and output variables are evenly distributed between a range of [-1 1], with the help of a triangular membership function defined in(MathWorks and Wang, 1998) as

  xa cx  f ( x, a, b, c)  max  min  ,1,  , 0  (17)  ba c b   

M  LT M (q1 ) L;V1  V1 (q1 , q1 ) LT  LT (Vm L  M (q1 ) L), F  LT F ; G  LT G ; d  LT  d ;  LT  

J (q1 ) L(q1 )  0

As

(16)

The suppositions and the necessary properties of the model given in (6) have been utilized in the proposed controller development are given as Property 1: The inertia matrix M (q1 ) is positive definite symmetric and bounded above and below. Property 2: symmetric.

The

matrix

( M (q1 ) - 2V1 ( q1 , q1 )) is

F (q1 )  a  b q1 Property 3: positive constants a, b. Property 4: c.

skew

for some unknown

 d  c for some unknown positive constants

The parameters a, c trace the base of the triangle and the parameter b pinpoints the top peak. 2. The inference engine supervised by fuzzy rules later on infers the output fuzzy variable. Each input crisp variable as well as output crisp variable are fuzzified into seven linguistic fuzzy sets, namely NEL (Negative extra-large), NL (Negative Large), N (Negative), ZO (Zero), P (Positive ), PL (Positive Large) and PEL (Positive Extra Large) respectively. The index values calculated for all the linguistic variables are NEL (-0.9046), NL (-0.3342), N (0.6658), ZO (-2.0715e-18), P (0.3342), PL (0.6658) and PEL (0.9046). A total 49 rules are applied to train the Mamdani type FPD controller as given in Table 1. 3. At last the Centroid Defuzzification (Takagi and Sugeno, 1985), which is given by the expression:

3.2 FPD+I Controller

uf 

Controls of robot manipulator using Fuzzy logic are widely reported in literature. According to zadeh in (Zadeh, 1996), our two input single output (TISO) configuration based normalized fuzzy PD (FPD) controller is developed on four main components i.e. fuzzification, inference engine, fuzzy rule base and Defuzzification only, which is shown in Fig. 2.

em

(18)

This converts the output fuzzy variable into a crisp output u f of the FPD controller. The primary relationship functions of the fuzzy sets, for the position errors, velocity errors, and control inputs and their fuzzy control surfaces are shown in Fig. 3.

Fuzzy PD Controller

Kd

uf

0.5

+

Kp

Ku

u

output

em

 i (u)ui  i (u)

0

-0.5

+

Ki

1

1 S

0.5

1

em

0.5

0

0

-0.5

-0.5 -1

Fig. 2. Fuzzy PD + I controller

-1

em

Fig. 3. Output surface of fuzzy PD controller 432

2014 ACODS March 13-15, 2014. Kanpur, India

The output of the fuzzy PD controller is a two input function, as a result u f (t )  [ f ( K p * em (t ), K d * em (t ))]

(20)

Then the output of the hybrid FPD+I force/position controller is, therefore t

u (t )  [u f (t )  K i  em (t ) dt ]* K u

(21)

0

Here u f is the output FPD controller. Thus a hybrid force

4.

Without External Disturbances (WED): controllers are developed on a modified dynamic model based on (8) for this case. The only difference from first case is the absence of external disturbances.

The performance of the controller can be checked through their output response which is shown in the Fig. 4, which clearly depicts that the proposed controller is efficient enough to track the desired trajectory with minimum steady state error.

   u (t )  J T (q ) d  K f  

(22)

4. SIMULATIONS AND RESULTS The simulation has been performed for a six DOF PUMA robot manipulator using MATLAB 2012b by considering the PUMA-560 robot manipulator dynamics from (Armstrong et al., 1986). The following four cases have been considered to study the simulation results: Complete(C): In this, we developed all the controllers based on (8), which represents the complete dynamical system including actuator dynamics. Without Friction (WF): In this, we developed all the controllers based on (8), which represents the complete dynamical system including actuator dynamics. The only difference with the first case is that friction term is absent.

Desired Trajectory Vs. Actual Trajectory

position controller has the structure

2.

Without Gravity (WG): For this case we have designed the controllers based on a modified version of (8), which lacks of gravity term in it only.

(19)

f ( K p * em (t ), K d * em (t ))  K p em (t )  K d em (t )

1.

3.

8 Desired Joint1 Desired Joint3 Desired Joint4 Desired Joint5 Desired Joint6 Actual Joint1 Actual Joint3 Actual Joint4 Actual Joint5 Actual Joint6

6 4 2 0 -2 -4 -6 0

5

10

Fig. 4. Output response of hybrid FPD+I force/position controller The simulation experiments were conducted for 24 observations with the identical gain value statistically, to study the performance of the proposed controller with other controllers(Alavandar and Nigam, 2008).

Table 1. RMS Error for Trajectory sin (2t) 5 seconds

Joint Angle

10 seconds

15 seconds

q1

C 0.03

WF 0.02

WG 0.03

WED 0.03

C 0.03

WF 0.02

WG 0.03

WED 0.03

C 0.03

WF 0.02

WG 0.03

WED 0.03

q3

0.11

0.10

0.10

0.10

0.11

0.10

0.10

0.10

0.11

0.10

0.10

0.10

q4

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.03

0.03

q5

0.06

0.06

0.06

0.06

0.06

0.06

0.06

0.06

0.06

0.06

0.06

0.06

q6

0.09

0.09

0.09

0.09

0.09

0.09

0.09

0.09

0.09

0.09

0.09

0.09

Table 2. RMS Error for trajectory 0.15cos ((pi/2) t) 5 seconds

Joint Angle

10 seconds

15 seconds

q1

C 0.02

WF 0.02

WG 0.02

WED 0.02

C 0.02

WF 0.02

WG 0.02

WED 0.02

C 0.02

WF 0.02

WG 0.02

WED 0.02

q3

0.07

0.06

0.07

0.07

0.07

0.06

0.07

0.07

0.07

0.06

0.07

0.07

q4

0.06

0.06

0.06

0.06

0.06

0.06

0.06

0.06

0.06

0.06

0.06

0.06

q5

0.08

0.08

0.08

0.08

0.08

0.08

0.08

0.08

0.08

0.08

0.08

0.08

q6

0.10

0.10

0.10

0.10

0.10

0.10

0.10

0.10

0.10

0.10

0.10

0.10

433

15

Time(sec)

2014 ACODS March 13-15, 2014. Kanpur, India

Dissimilar trajectories, dissimilar robot parameters and dissimilar simulation time (5s, 10s, and 15s) have been employed for all 24 observations. The RMS values of path errors for joint angles q1 to q6 except q2 are calculated for each experiment. The RMS values average for all four cases has been calculated over 24 sets are given in Table 1 and Table 2 respectively. The working efficiency of the controller has been analyzed by the data recorded through simulation for all the cases, which is shown in the following figures. The proposed controller is able to deal with the continuous as well as discontinuous friction, gravity and other external disturbances while successfully following the desired trajectory by looking at the Fig. 5 to Fig. 8.

3.00 2.50

2.00

q1

1.50

q3

1.00

q4

0.50

q5 q6

0.00 PID

FPID

FPD+I

case1 when trajectory is sin2t

PID

FPID

FPD+I

case2 when trajectory is 0.15(cos((pi/2)t))

Fig. 7. RMS error for case: WG The two desired trajectories are taken for which the whole data has been recorded. The trajectories are: (1) sin(2t) (2) 0.15cos((pi/2)t).

3.00 2.50

2.00

q1

3.00

1.50

q3

1.00

q4

0.50

q5

2.00

q6

1.50

q3

1.00

q4

0.50

q5

0.00 PID

FPID

FPD+I

case1 when trajectory is sin2t

PID

FPID

2.50

FPD+I

case2 when trajectory is 0.15(cos((pi/2)t))

q1

q6

0.00 PID

Fig. 5. RMS error for case: C

FPID

FPD+I

case1 when trajectory is sin2t

PID

FPID

FPD+I

case2 when trajectory is 0.15(cos((pi/2)t))

3.00 2.50

Fig. 8. RMS error for case: WED

2.00

The friction term as well as the gravity term and external disturbances taken are as follows:

q1

1.50

q3

1.00

q4

0.50

q5

0    2 2 3 2   37.196*cos(t )  8.445*sin(t  t )  1.023*sin(t )    0.248*cos(t 2  t 3 ) *cos(t 4 ) *sin(t 5 )  sin(t 2  t 3 )  G   0.028*sin(t 2  t 3 ) *sin(t 4 ) *sin(t 5 )   0.028*[cos(t 2  t 3 ) *sin(t 5 )]  [sin(t 2  t 3 ) *cos(t 4  t 5 )]   0   q *sin 3 t  q ' 0.2*sin t * q '        2 2 2  q *0.5*sin(2t )  q '*1.2* t  0.1*sin(t ) * q '    3 3  3  dc   q *1.2*sin(t )  q '*0.8* t  , dd   0.1*sin(t ) * q '      0 0     0 0         0 0

q6

0.00 PID

FPID

FPD+I

case1 when trajectory is sin2t

PID

FPID

FPD+I

case2 when trajectory is 0.15(cos((pi/2)t))

Fig. 6. RMS error for case: WF

434

2014 ACODS March 13-15, 2014. Kanpur, India

Where

CARVAJAL, J., CHEN, G. & OGMEN, H. 2000. Fuzzy PID controller: Design, performance evaluation, and stability analysis. Information Sciences, Elsevier, 123, 249-270.

10  2* randomwaveform( pi * t )  5  2* randomwaveform( pi * t )      2  2* randomwaveform( pi * t )  Fc    , Fd    0  2* randomwaveform( pi * t )  0  2* randomwaveform( pi * t )       0   2* randomwaveform( pi * t )   d   dc   dd ; F  Fc  Fd .

CASTILLO, O. & MELIN, P. 2003. Intelligent adaptive model-based control of robotic dynamic systems with a hybrid fuzzy-neural approach. Applied Soft Computing, Elsevier, 3, 363-378.

The actuator parameters are:

K bi  K Mi  [0.189 0.219 0.202 0.075 0.066 0.066]

FENG-YI, H. & LI-CHEN, F. 2000. Intelligent robot deburring using adaptive fuzzy hybrid position/force control. IEEE Transactions on Robotics and Automation, 16, 325-335. FISHER, W. D. & MUJTABA, M. S. 1992. Hybrid position/force control: a correct formulation. The International journal of robotics research, 11, 299311.

La 1  1000 Rai  [2.1 2.1 2.1 6.7 6.7 6.7] Gear Ratio =

[62.61 107.36 53.69 76.01 71.91 76.73] All other parameters are taken from (Armstrong et al., 1986). The PID gain parameters are taken as:

GOLDENBERG, A. A. & SONG, P. 1997. Principles for design of position and force controllers for robot manipulators. Robotics and Autonomous Systems, 21, 263-277. HA,

K P  [20 10 10 10 8 6] K D  [20 8 3 2.0 2.2 2.0] K I  [0 2.5 1 0 0 0] The mean RMS error of the proposed FPD+I force/position controller is lower than other controllers(Alavandar and Nigam, 2008). 5. CONCLUSIONS A hybrid FPD+I force/position controller is suggested for the trajectory control of a robot manipulator arm with unspecified robot dynamics in real constraint environment. The system performance has been investigated extensively through simulation outcomes. The 6 DOF PUMA robot manipulator’s simulation results are used to show that the proposed controller is efficient enough to handle odd situations while following the desired trajectory. The practicability of the projected controller with an appropriately defined automatic tuning of the fuzzy system using evolutionary techniques may be explored further. REFERENCES ALAVANDAR, S. & NIGAM, M. 2008. Fuzzy PD+ I control of a six DOF robot manipulator. Industrial Robot, Emerald, 35, 125-132. ARMSTRONG, B., KHATIB, O. & BURDICK, J. The explicit dynamic model and inertial parameters of the PUMA 560 arm. IEEE Int. Conf. on Robotics and Automation, 1986. IEEE, 510-518. BEZINE, H., DERBEL, N. & ALIMI, A. M. 2002. Fuzzy control of robot manipulators:: some issues on design and rule base size reduction. Engineering Applications of Artificial Intelligence, Elsevier, 15, 401-416. 435

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2014 ACODS March 13-15, 2014. Kanpur, India

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