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Adapting Intelligence in Robot using Fuzzy Logic Vaishali Sood

Department of Electronics & Communication Engineering B.C.E.T, Gurdaspur, India

+91-9465204534 san1198@gmail.com

ABSTRACT Research in robot motion control offers research opportunities that will emulate human decision making capabilities to perfection in years to come. Autonomous robots roles are increasing in different aspects of engineering and everyday life. This paper describes an autonomous robot motion control system based on fuzzy logic Proportional Integral Derivative (PID) controller. Fuzzy rules are embedded in the controller to tune the gain parameters of PID and to make them helpful in real time applications. This paper discusses the design aspects of fuzzy PID controller for mobile robot that decrease rise time, remove steady sate error quickly and avoids overshoot. The performance of robot design has been verified with rule based evaluation using Matlab and results obtained have been found to be robust. Overall, the performances criteria in terms of its response towards rise time, steady sate error and overshoot have been found to be good.

Categories and Subject Descriptors I.2 [Artificial Intelligence]: I.2.0 [General]: Cognitive Simulation; I.5 [Pattern Recognition]: I.5.1 [Models]: Fuzzy Set

General Terms Design, Performance, Algorithms

Keywords Artificial Intelligence, Robotics, Robot design, PID controller, Fuzzy logic, Rise time, Steady state error, Overshoot.

1. INTRODUCTION Fuzzy Logic is a very important area of concentration in the study of artificial intelligence and is based on the value of information, which is neither true nor false. This kind of information is being used by human in their everyday lives to take intuitive decision depending on the situation on demand. The knowledge acquiredin this way can be helpful to handle the system response even in undesired conditions. The benefits of fuzzy logic in a control system are to quantify the input signal in a noisy environment. The noise that tends to corrupt the integrity of signal is dealt with common sense of the component operator.

Most of the real time applications that require automatic control are nonlinear in nature. With change in operating point over time, their parameter values alter. The conventional control schemes such as PID are linear in nature. A controller can be tuned to give good performance without changing the operating point. It needs to be returned if the operating point changes or if the process alter with time. This necessity to retune has driven the need to combine the fuzzy logic nonlinear controls with the PID controls as evident in recent development of the artificial intelligence. There are a lot of methods to design PID controller. The fuzzy logic has a good control effect for the processes with nonlinear characteristics. Fuzzy control is a real time expert scheme and it offers an improved user interface to the process to be controlled by translating all the responses of the system into controller nonlinearities. Nonlinear characteristics are grasped in fuzzy control by nonlinear membership functions. Current research in robotics aims to build autonomous intelligent robot systems to meet the increasing industrial demand for automatic manufacturing systems. One of the most important features needed for autonomous robot is its capability of motion planning. Motion planning enables a robot to move in its surroundings steadily for executing a given task. The main design constraints for robot are cost, reliability and adaptability. The different performance objectives in robot design are insensitivity to parameter variations, distribution rejection properties and stability of the system. This paper is organized as follows. In Section 2, the literature on fuzzy controller has been presented. Section 3 describes the design of robot with PID control loop and fuzzy inference mechanism. Section 4 discusses the design aspects based on different parameters and the results are presented. Section 5 concludes the paper.

2. LITERATURE REVIEW A lot of research work has been carried out to develop techniques for obstacle-free motion planning for robots. Still, it requires a lot of attention of researchers because it is the primary requirement for robotics in real time motion. Latonlbe [1] provides survey on graphical and analytical approaches for planning of motion. Various researchers have proved that exact motion planning methods are computationally intractable unless the situation is very simple and heuristic approaches have considerably lower computational time complexity. Determining fast and efficient solutions for motion planning problems is currently an important research area. The problem of mobile robot navigation using fuzzy logic approach in a totally unknown situation is an important area of research because it aims to find optimal collision-free path. PID controller has been broadly used to control various engineering objects because of its simple configuration, better robustness and high consistency. However, the performance of a PID controller totally depends on the tuning of its gain parameters. Researchers have suggested many methods based on artificial intelligence to design PID controllers such as the differential evolution (DE) algorithm [2], genetic algorithm (GA) [3], simulated annealing (SA) algorithm [4] and fuzzy logic control [5]. In these methods, the fuzzy logic control has a high quality control effect particularly for the processes with nonlinear

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or uncertain properties or the processes whose modeling are very difficult to build with higher accurately. In fuzzy PID controllers, the control rules are being designed from the knowledge of the experts in the correlated domains and hence are affected by the knowledge and experience of the experts. Therefore, in control systems with nonlinear property, the larger error may occur between the rules from the experts and ideal rules. In 2010, Zacharie [6] proposed a method consisted of two components: the process monitor that detects changes in the process characteristics and the adaptation mechanism that used information passed to it by the process monitor to update the controller parameters. They used Adaptive Fuzzy Knowledge Based Controller (AFKBC). The first part is the performance monitor that detects changes in the process characteristics by assessment of the controlled response of the process. The second part is the adaptation mechanism. It uses information passed to it by the performance monitor to update the controller parameters and so adapts the controller to the changing process characteristics. The selection of the appropriate membership functions is very important for the design of controller. The important problem for fuzzy PID controller is lack of a very efficient and universal design method that is widely suitable to various kinds of processes. Till now, several methods have been developed for robot motion planning but each of these methods has its own limitations for time complexity and suitability. Thus, a more versatile and efficient algorithm is desired. In the present work, an algorithm has been developed by combining the fuzzy logic approach with PID controller to solve the robot motion problem and tested on a number of scenarios. The proposed method can solve the motion planning problem in the presence of parameter variations. This paper discusses the efficient design method for the optimal fuzzy PID controller.

3. DESIGN OF ROBOT PID controller has been widely used to control various engineering and industrial objects because it can adjust process output based on the requirements and rate of change of error signal. The PID controller’s performance totally depends upon the tuning of its gain parameters. Their gain parameters have been controlled using fuzzy control logic because this logic has a good control effect for the objects with the non-linear characteristics. The basic idea behind our fuzzy control PID is to design a controller using fuzzy logic scheme on the PID controller to adjust its various parameters so that the robot motion can be controlled under various non-linear conditions. Based on the fuzzy logic control, a technique for fuzzy PID controller for adaptive robot motion is proposed. In this method, fuzzy control is used to optimize the input and output factors of controller so as to optimize the rise time (RT), to calculate the steady sate error (SSE) and control the overshoot (OS). If there is any variation in the dynamics of the robot motion then it will adapt the change automatically. The robot has an on board computer (Pentium IV Quad Core Processor), with which a fuzzy logic PID controller is interfaced. The robot acquires the information from sensors and based on this, fuzzy control rules are activated. The outputs of the activated rules are combined by the fuzzy logic operations to increase the

pk (proportional gain), ik (integral gain) and dk (derivative

gain) of the PID controller so as to reduce the rise time, eliminate the steady state error (SSE) quickly and to decrease the overshoot (OS) respectively.

3.1 PID Control Loop A PID control loop is useful in order to calculate whether it will actually reach a stable value. If the outputs are chosen incorrectly, the controlled process input oscillates and the output never stays

at the set-point. The generic transfer function for PID controller is as shown ahead in Equation 1.

2( )( ) *( )

DS S IH S PS C

)(*( )

…………………… Eq. 1

C is a constant which depends upon the bandwidth of the controlled system and S is the variable parameter. The output of the controller i.e. the input to the robot is given as Output (t) = P contribution + I contribution + D contribution

Output (t) = pk [e (t) + ipk0

t

0

te (t) dt + dpk (de/dt)]……Eq. 2

Where e (t) = set point – measurement (t) = error signal pk =

proportional gain, ipk = ik / pk , where ik is integral gain and

dpk = dk / pk , where dk is derivative gain.

The controller is implemented with pk gain applied to the I

contribution, D contribution according to Equation 2. We tune the gain parameters using the standard Zeigler-Nicholas tuning method. To tune the above mentioned gain parameters, following equations are used.

pk = pk (initial) + ∆ pk ………… Eq. 3

Equation 3 is used to reduce the rise time because larger the error, larger the feedback to compensate.

ik = ik (initial) + ∆ ik …………… Eq. 4

Equation 4 is used to eliminate the steady state error quickly.

dk = dk (initial) + ∆ dk ………… Eq. 5

Where pk (initial), ik (initial) and dk (initial) are initial PID

controller parameters and can be determined using the classical Zeigler-Nicolas formula and ∆ pk , ∆ ik , ∆ dk are the increments.

3.2 Fuzzy PID Controller With input variation for each step, the fuzzy controller examines the variation of e, fuzzfy it, makes online adjustment by using IF-THEN rule for gain parameters, get the crisp value by centre of sums defuzzification method.

Figure 1. Fuzzy PID Controller

Figure 1 gives the structure of a fuzzy PID controller where set-point is the input of the system and e (t) is error of the system.

pk , ik and dk are the output of fuzzy controller and u is the

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control action generated by PID controller and y is the output of system. The four main components shown in Figure 1 of the fuzzy controller are fuzzification interfaces so as to transform input crisp values into the fuzzy rules. If the data is vague or perturbed, it should be converted into a fuzzy number.

Fuzzification function X = fuzzifier (xo)………………………………….. Eq. 5 Where xo is observed crisp value, X is fuzzy set and Fuzzifier ( )

represents a Fuzzification operator.

3.3 Fuzzy Inference Mechanism The gain parameters pk , ik and dk of the PID controller must

be real time, so as to cope with the real time practical applications of robot. If there is a change in the input of the robot from the desired set-points, the robot must be able to handle it. Therefore, input of the robot must be real time so as to adjust with the changes. For this, a set of fuzzy IF-THEN rules is applied to the PID controller.

Figure 2. Fuzzy Controller for the Robot Motion

3.3.1 Design of Knowledge Base The knowledge base consist of two parts i.e. rule base and database. Rule based consist of fuzzy control IF- THEN rules and design of database consists of partition of variable space. Linguistic term such as fast, medium and slow are defined for robot motion (RM). Terms such as high, medium and low for gain parameters [rise time (RT), steady state error (SSE) and overshoot (OS)]. The membership functions are triangular or trapezoidal and inference mechanism used is Mamdani. Rules

1. If pk is pik and RT is (RT)j then RM is

RMij. 2. If ik is iik and SSE is SSEj then RM is

RMij. 3. If dk is dik and OS is OSj then RM is RMij.

Where i, j are having values 1, 2, 3 because each pk , ik , dk ,

RT, SSE, OS as well as RM has three membership functions. According to the usual fuzzy control mechanism, a factor Wij is defined for rules.

wij = kpikp ( disi ) ( )RT jdis j(RT

wij = ( )ki idisi(ki ( )SSE j

dis j(SSE

wij = ( )kd idisi(kd ( )os j

dis j(os

Where idis , jdis are the values of pk , ik , dk , RT, SSE and

OS. By applying the composition rules of inference, the membership function value of the robot motion (RM) is

( ) 'RMij

( ) ' = wij ( )RM ij( ) ij

motion RM domain The overall conclusion by combining the outputs of all fuzzy rules can be written as follow:

( )RM( ) = ( )'11RM( )' ( )'RM ij( )'ij)' ( )'33RM( )'

Figure. 3: Fuzzy Membership Functions

Using the center of sums defuzzification method, the crisp value of the pk , ik and dk has been obtained as follow:

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1 1

1 1

( )

*( )

N n

i ii k

N n

ii K

Ak

Ak

x x

xx

1k1 k

1 1K1 k

i

N

1k1

N n

i iAi iAk

Ak

N n

iA iAAk

N n

We used this method of defuzzification because it leads to rather fast inference cycles and can be implemented easily. Fuzzy rules used for the adaptive robot motion are listed in Table 1, 2 and 3.

4. DISCUSSION AND RESULTS The adaptive robot motion controller presented in this paper is a fuzzy logic controller that combines non-linear fuzzy rules to control the gain pararmeters of the linear PID controller to control the robot motion in its domain. The rules embedded in the fuzzy logic controller have to be designed by the designer of the controller. When the robot is facing a change in speed, the PID controller must change its pk , ik and dk parameters. The fuzzy

rules for this are listed in Table 1, 2 and 3. e.g. according to rule 3, if the value of pk is high and rise time (RT) is low then the

robot will move fast. An autonomous controller means a controller with adjustable parameter and a mechanism for adjusting parameter. Due to parameter adjustment, the controller becomes non-linear. In our purpose autonomous fuzzy PID controller, the adaptation is done by modifying the membership function in proportion to the undesired effect. The values of

pk , ik and dk are incremented so as to control the rise time,

eliminates the SSE quickly and to decrease the overshoot during robot motion. The system is more robust, faster and has a higher probability in obtaining the globally optimal solution. The results have been drawn from MatLab are represented ahead.

For Rule Number 3

For Rule Number 1

For Rule Number 3

5. CONCLUSION This paper presents a novel autonomous robot motion controller system by taking the conceptual advantages of fuzzy control rules to control the gain parameter of PID controller. This type of autonomous robot has a lot of real time applications. The proposed method is effective in terms of smooth response while considering overshoot, removal of steady state error quickly and its response towards rise time so that there is a faster and effective response. As compared with other methods based on fuzzy control rules, it has been found that the proposed PID controller has better performance in faster response, error removal and decrease in rise time. It has been tested in the MatLab and found that with change in operating point there is no need to retune it and results are found to be robust. The proposed method is used to deal with the rise time, steady sate error and overshoot problems efficiently.

6. REFERENCES [1] A. Soukkou, A. Khellaf and S. Leulmi, “Genetic Training of a

Fuzzy PID,” International Conference on Modelling and Simulation (ICMS’04), Spain, pp. 185−186, 2004.

[2] D. P. Kwok and F. Sheng, “Genetic Algorithm and Simulated Annealing for Optimal Robot Arm PID Control,” 1st IEEE Conference on Evolutionary Computation, Orlando, pp. 707−713, 1994.

[3] J.C. Latombe, “Robot Motion Planning,” Kluwer Academic Publishing, Norwell, MA, 1991.

[4] M. Zacharie, “Adaptive Fuzzy Knowledge based Controller for Autonomous Robot Motion Control,” Journal of Computer Science, vol. 6, no. 10, pp. 1019-1026, 2010.

[5] R.A. Krohling and J. P. Rey, “Design of Optimal Disturbance Rejection PID Controllers using Genetic Algorithms,” IEEE Transactions on Evolutionary Computation, vol 5, no. 1, pp. 78-82, 2001.

[6] S.L. Cheng and C. Hwang, “Designing PID Controllers with a Minimum IAE Criterion by a Differential Evolution Algorithm,” Chemical Engineering Communications, 1998, vol. 170, no. 1, pp. 83-115, 1998.