Optimized Fuzzy Logic Controller and Neural Network Controller- a comparative study

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1 Optimized Fuzzy Logic Controller and Neural Network Controller- a comparative study JOSÉ B. MENEZES FILHO, J. BOAVENTURA-CUNHA 2, NUNO MIGUEL FERREIRA 3 () Instituto Federal de Educação, Ciência e Tecnologia da Paraíba Av. Primeiro de Maio, 72, Jaguaribe - João Pessoa-PB BRAZIL jbmenezesf@hotmail.com (2) University of Trás-os-Montes and Alto Douro; INESC TEC - INESC Technology and Science Engenharias I, 5-8 Vila Real PORTUGAL jboavent@utad.pt; jose.boaventura@inesctec.pt (3) Instituto Superior de Engenharia de Coimbra Rua Pedro Nunes, Quinta da Nora, Coimbra PORTUGAL nunomig@isec.pt Abstract: - This work presents the use of a Mamdani Fuzzy controller and a Neural Network controller to detect and catch an object on a 2 axes (X,Y) workspace with a robot arm. The controllers use two inputs and one output for each of two controlled axes of the robot. The inputs are defined as the position errors and the derivative of the position errors regarding the setpoint position (X REF, Y REF ) of the object to catch. The outputs of the controllers drive the X and Y axes motors. The two axes motors are actuated with the objective of capturing an object on a workspace, being the object position, i.e. the setpoint position, computed by processing an image acquired with a video camera placed over the workspace. A genetic algorithm, developed in a previous work, was used to compute the characteristics of the membership functions of the Mamdani Fuzzy Controller. The robot positioning system, using the two axes transfer functions, the Fuzzy controller and the Neural Network controller were simulated in MATLAB environment being the results presented. Also, the performances of the controllers are compared regarding the setpoint tracking accuracy, the evolution of the (x,y) trajectories over time and the control effort. Key-Words: - Fuzzy control, Neural Network, Modeling, Optimization, Position control, Robot claw Introduction Positioning systems such as robotic manipulators are widely used in a wide variety of industrial processes. Particularly, systems that have motion control provides a continuous improvement of product quality associated with the minimization of manufacturing costs, which are possible through the use of high-precision equipment that combine flexibility with security and high-speed time response, such as robotic systems. Therefore, the modeling and control studies for robotic systems play an important role in the industrial development. This paper presents and compares two strategies to control a robot of two degrees of freedom with the goal of locate and catch an object over a workspace. A video camera is used to acquire an image of the object, the claw and the workspace. Afterwards, the image is processed to compute the object position, i.e. the setpoint position to be reached by the robot claw (X REF, Y REF ), and the actual claw position (x, y). A Mamdani fuzzy logic controller and a Neural Network controller were designed and tested to drive the X and Y robot motors with the goal of positioning the robotic claw on the object. Systems based on fuzzy logic and neural networks have great potential to solve several problems in the control engineering fields. Also, there are growing interests in the development of fuzzy logic and neural networks controllers, among other intelligent control techniques, since they are generally well ISBN:

2 suited to solve nonlinear control problems [, 2, 3, 4, 2, 3]. The fuzzy and neural controllers can efficiently regulate several variables of nonlinear processes, but the first one works in a way that mimics the reasoning of human operators while the neural network control exhibits a black-box nature. If both controllers are properly designed, they can cope with complex nonlinear input-output relationships, being robust for real time operation under noise environments. However, a neural network controller is more difficult to design since it must be determined the optimal number of nodes, hidden layers, activation functions, etc., being the computation load high. The pioneering work in application of fuzzy logic in process control is due to [], whose theoretical supports are described in the works of [3, 5, 6]. Although different methods are available in the literature, they can be classified into two major groups: The Mamdani and the Sugeno Fuzzy systems [2, 3]. In this work is shown the results obtained using an optimized Mamdani Controller and a neural network controller to drive a two axes robot. The methods are validated with the presentation of simulation results. Each axis is represented with a transfer function obtained by solving a previous identification problem using experimental data. The simulations use the same setpoints to evaluate and compare the performances of both controllers. This work is organized in the following way: In this first section is presented the overall view of the subject treated. In section two is presented the problem formulation, where is shown the complete system to be controlled. Section three describes the design and the implementation of the Fuzzy Controller. Section four presents the design and implementation of the Neural Network Controller. These two previous sections also present the simulation results obtained with both control strategies. Section five presents a comparative evaluation of the performances of the two controllers. Finally, in the sixth section, are drawn the conclusions and perspectives for future work. (G) and the ultimate array correspond to the blue color (B). Figure shows a detail of the original image acquired of the object in the workspace (a), and the images obtained by decomposition in the Red color (.b), Green color (.c) and Blue color (.d). a b c d Fig. - Image acquired with the video camera (.a) and its decompositions in the Red color (.b) Green color (.c) and Blue color (.d). To Process the camera video signal, the Green color array is used since it provides a better contrast. In this array, each element with values ranging from to 255 corresponds to one pixel. The value corresponds to white color and the value 255 to the black color. A binarization of the image is afterwards performed using a threshold value of. The values of the pixels with values greater than are transformed to 255, while the values of pixels with values less or equal than are transformed to. In this way, the values of all elements of the matrix have only two possibilities: to a white color and 255 to a black color. After transforming the values of all elements to the binary format, the computational program checks all elements of the array starting the first row and column up to the last. As in the beginning of process all elements are, corresponding to a background of the workspace, search continues until to the first time that the process find an element equal to 255. It is considered that the object on the workspace is detected when the first transition between and 255 is found. The following sequence is performed by the computational program: 2 Problem Formulation The image of the object in the workspace, which is the target to reach by the robot claw is acquired with a video camera in the format of array with dimensions (567,24,3). Afterwards the image is decomposed in three arrays, the first corresponding to the red color (R), the second is the Green color. Read the array of color that is sent by the web camera. 2. Extract the three arrays that contain the basic colors: Red, Green and Blue. 3. Reduce the values of each element of the array Green to two values: or 255, dependent upon of its original value compared to the previous defined threshold. 4. Identification of the object position ISBN:

3 The complete Robot system controller architecture is shown in Fig. 2. In the blocks called Controller and Controller is located either the Optimized Fuzzy Logic Controller or the Neural Network controller. The overall objective for both controllers, is that the claw must follow a computed trajectory to catch the object in the workspace according to defined project specifications regarding time responses and control effort. Image of target object obtained by web camera Image signal processing Calculating of speed Calculating of speed Computer Locating of object error(k) error(k-) error(k) error(k-) Controller Controller Locating of robot hand z - ex z - ^ R ey Robot + - V^ e^ Determining ex and ey Ux Uy Driving of Driving of Fig. 2. Complete Robot Hand Controller In Fig. 2 the signals Rˆ, Vˆ and ê represent the reference position of the target object, the position of the robotic hand, and the error, respectively, in the Cartesian coordinates (x,y). The signals e x and e y are the position errors and U x and U y the control signals driving the motors regarding the X and Y axes. In order to perform the simulations it were used two identical third order Transfer Functions for both X and in terms of Z transform. These functions have one sample time delay and their parameters were previously obtained with the use of identification techniques. Eq. () shows the Transfer functions used for the X and Y axes. The sample time in which the Transfer Functions were computed was ms. ( Z Z 2 ) KZ G, y ( z) = 69374Z Z Z 3 x () With the gain K= Fuzzy Controller The Mamdani Fuzzy Controller uses two input variables: The distance between the object and the robotic hand for both axes called Error and the variation of this error, which is called derror. The memberships functions used for the Error variable were formed by four membership functions with triangular shapes called Ze (Zero), Sp (Small positive), Mp (Medium positive) and Gp (Great positive). The Figures 3 and 4 show the Memberships Functions regarding the x and y axes of the controller for the Error and derror variables. Note that it is only necessary the use of the positive side of the universe of discourse owing to the fact that it is assumed the symmetry of the control. If the error is negative, the control signal is multiplied by - and applied to the Transfer Function. Fig. 3. Membership Functions of error variable Fig. 4. Membership Functions of derror variable In the preceding Figures are shown the points xsp and xmp. The determination of these points plays an important role in the construction of the membership functions. By means of shifting these points it is possible to modify the shape of the triangle of the membership functions Sp and Mp. It was performed an optimization of the membership functions using a genetic algorithm using a population of 8 chromosomes, wich of them with 8 genes, according to [7, 8]. The optimization procedure was performed to minimize a cost function given by the quadratic of the actuating signals multiplied by time. In this way it was founded the optimal values xsp=9 and xmp=8. ISBN:

4 3. Mamdani Fuzzy Controller Inference In the inference step of Mamdani Fuzzy Controller, the composition of each rule and the relationship between them is accomplished in accordance to Table (). In this step whenever the rule if then is activated the consequences are obtained with the minimum value between the Error and Derror. It was utilized the inference technique MAX-MIN. In this step the control variables, which drive the axes motors of the robot, are determined. The variables have four membership functions and are applied in the universe of discourse that range from to. In the defuzzification process it was utilized de Centerof-Area method. This method was successfully applied in [9]. Table. Fuzzy Rules Table of Fuzzy Mamdani controller Error Derror DZe DSp DMp DGp Ze Ze Sp Sp Mp Sp Sp Mp Mp Gp Mp Mp Gp Gp Gp Gp Gp Gp Gp Gp 3.2 Mamdani Fuzzy Controller Results The manipulator was driven from an initial point in the planar space given by the coordinates (.,) to a final position (.,.), being these values normalized. Both axis are driven by an individual Mamdani Fuzzy Controller. The trajectory performed by the and the are shown in Figures 5 and 6 and the planar trajectory, composed by two axis is shown in Fig. 7. trajectory Fig. 5. trajectory- Fuzzy Controller Y Axis Y Axis Y Axis trajectory Fig. 6. trajectory- Fuzzy Controller Initial position Final position ) Fig. 7. Planar trajectory- Fuzzy Controller Note that all the simulation results are presented as per unit value. In practical experimentation, the true measures may be in any units. In per unit values the results are not affected by the measurement units. So, the universe of discourse ranges between zero to one in accordance with the use of per unit value. 4. Neural Network Controller A Neural Network controller implemented in Matlab environment is used to perform the simulations using the same response specifications specified for the Fuzzy controller. The Neural Network has two layers. The input layer contains two neurons which receives the error and the derivative of the error of the position signals. The second layer, called the hiden layer, has 5 neurons. The Neural Network is trainned by the well known backpropagation scheme. The complete structure is shown by Fig. 8. The output layer of the Neural Network Controller have a single neuron. The output layers of each network provide the control signals to the axes motors. ISBN:

5 coordinates (.,) to the point (.,.). Both axis are driven by an individual Neural Network Control. The trajectory performed by the and the Y axis are shown in the Figures 9 and and the planar trajectory, composed by two axis is shown in Fig.. Fig. 8. Neural Network Controller Architecture The number of the neurons used in the hidden layer was specified after performing several tests. The Neural Network was tested with 4, 8, 2 and 5 neurons in this layer. The tests with 5 neurons showed better results. In this structure, the input layer serves only to connect the input signals to the hidden neural network. The connections between each input terminal and the hidden layer neurons occur through 3 synaptic weights called "win", forming an array of 2 rows and 5 columns. The connections between the neurons of the hidden layer and the output layer of neurons occur through synaptic weights called "whid". These synaptic weights form a matrix with 5 columns and row. All the activation functions of the hidden layer are hyperbolic tangents. The type of these functions was the same used in a previous work [9]. The neural controller is adaptive, since for each sampling time the synaptic weights and win whid are adjusted to provide a better control. For each sampling period, the processes occurring in the forward direction, or straight through processing (Feedforward) and backpropagation (Backpropagation) which starts at the output layer and propagates toward the input layer aims to update the synaptic weights [, ]. The synaptic weights were chosen initially randomly. The algorithm was executed several times until the signal output of the plant reach the reference signal without overshoot and whit a smaller time settling. 4.. Neural Network Controller Results In the same way as the simulation performed with the Fuzzy Controller, the manipulator was driven from an initial point in the planar space given by the X Axis Trajetory reference Fig. 9. trajectory- NN Controller Y trajectory Fig.. trajectory- NN Controller Initial position Final position.2 Fig.. Planar trajectory- NN Controller 5. Comparative study In order to compare the results of the two strategies the trajectories of both obtained outputs are shown in Fig. 2 for the and Fig. 3 for the. The planar trajectory obtained by the two strategies is shown in Fig. 4. Also, it were computed, for both controllers, the performance indexes expressed by Eq. 2 to 5. ISBN:

6 X Axis Fuzzy Logic result neural network result E ey = e y (t) 2.t (5) The values for each of these indexes are show in the Table 2. Table 2. Performance indexes of the Fuzzy Mamdani and the Neural Network controllers.2 Fig. 2. trajectories Performance indexes Controller E ux E uy E ex E ey Fuzzy Logic Neural Network X Axis Y Axis.2 Fuzzy logic result Neural Network result Initial point Fig. 3. trajectories Final point Fuzzy Controller trajectory Neural Network trajectory ) 6 Conclusions According to the results presented, we can conclude that the Fuzzy Logic Control, with the membership functions optimized using a genetic algorithm, showed better performances when compared to the Neural Network Controller. Also, it must be pointed that despite the settling times achieved are very similar for both controllers, the trajectories obtained with the Fuzzy Logic Controller were more close to the reference signals at each sample time. Acknowledgments The author José B. Menezes Filho thanks CAPES Foundation, Ministry of Education of Brazil, the financial supporting to this research trough the Project number Fig. 4. Planar trajectory- Comparative trajectory The E ux and E uy indexes express the energy consumption plus time used to drive the axes motors. The E ex and E ey indexes are the sum of the quadratic errors plus time. Moreover, it was performed the determination of the settling times, T sx and T sy, respectively for the and trajectories obtained with the 2 controllers. The settling time was specified as the time instant where the error follows below 2% of the defined setpoint. E ux = u x (t) 2.t (2) E uy = u y (t) 2.t (3) E ex = e x (t) 2.t (4) s [] Zadeh, L.A., Fuzzy Sets, Information and Control, Vol. 8, 965, pp [2] Mamdani, E.H., Assilan, S., An experiment in linguistic synthesis with a fuzzy logic controller, International Journal of Man- Machine Studies, Vol. 7(), 975, pp. 3. [3] Driankov, D., Rainer, P., Advances in Fuzzy Control, Physica-Verlag, 23. [4] Reel, S., Goel, A.K., Artificial Neural Networks and Fuzzy Logic in Process Modeling and Control, Springer, 2. ISBN:

7 [5] Passino, K. M., Yurkovich, S., Fuzzy Control, Addison Wesley Longman, Menlo Park, CA, 998. [6] Kazuo Tanaka, K., Wang, H., (2). Fuzzy control systems design and analysis: a linear matrix inequality approach, John Wiley and Sons, 2. [7] Menezes Filho, J.B., Ferreira, N.M.F., Boaventura-Cunha, J., Use of a Genetic Algorithm to Tune a Mamdani Fuzzy Controller Applied to a Robot Manipulator, Lecture Notes in Electrical Engineering, Vol. 32, 24, pp [8] Koza, J.R., Genetic Programming, MIT Press, 992. [9] Menezes Filho, J., Silva, S., Araujo, C., Filho, A., Controlador Vetorial Neural para Mesa de Coordenadas XY. Revista Controle & Automação, Vol. 2(4), 2, pp [] Douratsos I., Gomm J.B., Neural Network Based Model Adaptive Control for process with time delay. International Journal of Information and Systems Sciences, vol. 3 (), 27, pp [] Yang, C., Li, Z., Jing Li, Smith, A., Adaptive Neural Network Control of Robot with Passive Last Joint, Lecture Notes in Computer Science, Vol. 758, 22, pp 3-22, pp [2] J. Lin, F.L. Lewis, Two-time scale fuzzy logic controller of flexible link robot arm, Fuzzy sets and systems, vol. 39(), 23, pp [3] M.A. Ahmad, M.Z.M. Tumari, A.N.K. Nasir, Composite Fuzzy Logic Control Approach to a Flexible Joint Manipulator, International Journal Advanced Robotic Systems, vol.(58), 23, pp.-9. ISBN: