W PO4 4:35 Proceedings of the 1996 IEEE International Symposium on Intelligent Control Dearborn, MI September 15-18, 1996

tive Study of Fuzzy Logic and Neural trol of the Truck Backer-Upper System

Abdulla Ismail and Emadeddin A. G. Abu-Khousa

Department of Electrical Engineering United Arab Emirates University

Al-An, United Arab Emirates abdulla 0eclsun.uaeu.ac. ae

Abstract

In this paper a simulated comparison of fuzzy logic and neural network control of the truck backer-upper system is presented. The aim of the controller is to back a truck to a loading dock which is a difficult task. It is a nonlinear control problem for which no traditional control system design method exists. We assumed that there were no linguistic rules available, and therefore the controllers were designed from the available numerical data only. We provided the same desired input-output pairs to both the neural and the fuzzy approaches, and compared the final control performance of both controllers. The results showed the superiority of the neural controller over the fuzzy one, when the later was influenced by the amount of overlapping between its sets and the missing rules from its rule base.

1. Introduction

Neural networks and fuzzy systems estimate sampled functions, and they are model-free estimators [l-21. In classical control theory a mathematical description of how the output behaves as a function of input variables is required; however both neural and fuzzy systems do not require an explicit formulation since they learn by example. Both neural network and fuzzy logic decision systems are excellent at developing human-made systems that can perform the same

type of information processing that our brains can perform. In this study fuzzy and neural controllers are applied to truck baker-upper system, i.e. backing a truck to a loading dock. It is a nonlinear control problem for which no traditional control system design method exists. Nguyen and Widrow [3] developed a neural network controller for the truck backer-upper problem, Kong and Kosko [2] proposed a fuzzy control strategy for the same problem, and Wang and Mendel [4] applied their numerical-fuzzy approach to this problem. The results of Kong and Kosko demonstrated the superior performance of the fuzzy controller over the neural controller; however, the proposed fuzzy and neural controllers used different information to construct the control strategies. It is possible that the used fuzzy rules are more complete and contain more information than the numerical data used to construct the neural controller; hence the comparison between the fuzzy and the neural controllers, from a final control performance point of view, is somewhat unfair. If the linguistic fuzzy rules were incomplete, where as the numerical information contained many very good data pairs, it is highly possible that the neural controller would outperform the fuzzy controller. The approach of Wang and Mendel, which was based on combining the fuzzy rules generated from numerical data points and the linguistic fuzzy rules into a common fuzzy rule base, provided a fair base for comparing fuzzy and

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neural controllers because both controllers used the same information to construct their control laws, and the final results of their work showed that the trajectories of the truck using the two controllers have no visible differences.

y(t+l) = y(t) + sin[@(t)+e(t)] - sin[0(t)]cos[@(t)]

sin[e(t)] Q(t+l) = Q(t> - sin-] [ ] In our work, we used a neural network to generate the fuzzy rules from numerical data pairs. The neural controller were trained using the same pure numerical data.

2. Statement of the truck backer-upper control problem

Figure 1 shows the simulated truck and loading zone. The three state variables $, x, and y exactly determine the truck position, where @ is the angle of the truck with the horizontal axis and the coordinate pair (x,y) specifies the position of the rear center of the truck in the plane[6].

3. Design 'of the controllers

In this study two intelligent controllers were used, namely, a Fuzzy Logic Controller (FLC), and a Neural Network Controller (NNC). The Wang-Mendel FLC's performance was utilized to train and verify both the FLC and the NNC. The Togai Infralogic TIL,Gen package [6] were used to generate the rules of the fuzzy controller based on neural network approach. In order to train the neural networks (the one used to generate the fuzzy rules and the one used in the NNC), we used the truck trajectories produced by the fuzzy controller as ideal trajectories. Eighteen initial states were used and the fuzzy controller generated the training samples (x,@,0) at each iteration of the backkg process. The produced fuzzy rules are Similiir to those of Wang-Mendel FLC and the fuzzy rule matrix is shown in Table

lCcrrhrlg~x=10~=90 I

x =o X=B

1 of the Appendix. We used a two-input single output three layers (input, hidden, and output) backpropagation neural network with a log- sigmoid nonlinear function. The following parameters were used: number of processing elements in the hidden layer = 20, error goal = 0.001, learning rate = 0.02, and momentum constant = 0.9. The neural network needed more than 50000 epochs to converge to its goal.

Figure 1. Diagram of simulated truck and loading zone.

4. A Comparative simulation The truck moves backwards by a fixed unit study of the responses distance in every stage. For simplicity, we assume enough clearance between the truck and the The truck model and the controllers were loading dock such that y does not have to be simulated using the considered as an input. The task here is to design MATLAB/SIMULINK package [7]. Several a control system, whose inputs are @ [-go", 2'j'O"I and x [0,20] and whose output is the steering

hitia1 states (&@> were used to test the controllers. The response of the controller (0)

angle 0 ~-400 , 400 I, such that the final states will be (xf, $f) = (10, 90"). For simulation purposes, the following approximate kinematics were used:

x(t+l) = x(t) + cos[$(t)+€I(t)] + sin[8(t)]sin[$(t)]

and the truck variables (x and @) from initial state (x = 13, Q = 30" ) is shown in Figure 2-a, b, and c, respectively. We can see that the fuzzy and the neural controllers successfully drive the truck to the desired position starting from this initial state. .

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We simulated the controller for other initial truck Dositions and observed the same results. I (4

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---- ...........................................................

- NNC

____ FLC

-40' ' 0 5 10 15 20 25 30 35 40

time(sec) (C)

0 20 40 time(sec) time(sec)

Figure 2. Time responses of the controllers for the initial state (13, 30" ). (a) the steering angle 8, (b) x-axis position, and (c) the truck angle +.

From the resulted simulations we could see that the control response of the neural network (e) has a smoother characteristics than that of the fuzzy controller. From the time response point of view, both controllers seem to have the same settling time, and it is clear that the neural controller is more stable than the fuzzy one. This is justified since the later oscillates around the desired states (e = Oo, @ = 90°, x = 10). This result was rather unexpected since the neural controller which has been trained using data pairs generated from the fuzzy controller outperformed the same fuzzy controller. The oscillatory response of the fuzzy controller is due to the property of its sets such as the shapes and the amount of overlapping between the sets. The performance of the fuzzy-controlled truck is further investigated after increasing the overlapping between the sets (each set is overlapped with 50% of the sets of its neighbors). Figure 3 illustrates the response of the modified fuzzy controller compared to the Wang-Mendel fuzzy controller and the neural controller. From this figure we could observe that the modified fuzzy controller outperformed the Wang-Mendel one and that reflects the effect of the amount of overlapping between the sets.

(4 I

-2011 NNC

- FLC

.____

7"

0 5 10 15 20 25 30 35 40

I I 2001 I (d (b) time(sec)

- mFLC . - mFLC ... NNC - FLC

100.

50

0 20 40 0 20 40 time(sec) time(sec)

Figure 3. Time responses of the modified fuzzy logic controller (mFXC) compared to the responses of the NNC and the FLC controllers for the initial state (13, 30" ).

To complete the comparison we studied the effect of the absence rules (empty cells in the fuzzy rule matrix shown in Table 1) on the performance of the controller when faced with a state that fires the non existed rule. Figure 4 shows the response of the controller when x = 13 and @ = -65.

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mFLC . ."

-40 0 5 10 15 20 25 30 35 40

time(sec) (C) (b)

0 20 40 0 20 40 time(sec) time(sec)

Figure 4. Time responses of the modified fuzzy logic controller (mFXC) compared to the responses of the NNC for the initial state (13, -65" ).

It is clear that the fuzzy controller didn't respond to this initial state which has no corresponding rule to deal with, and that led to the shown unacceptable response. However, the neural controller succeeded in backing-up the truck and

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that is a good indication of the generalization property of the neural network over the fuzzy one.

5. Conclusions

Fuzzy controllers can be easily designed using heuristic rules and/or numerical data pairs, whereas the neural nets can only be designed using sufficiently large set of training samples and the encoding of these training samples in the dynamical system by repetitive learning cycles. In the neural and fuzzy control of the truck backer- upper system, it is apparent that both controllers the NNC and the FLC, successfully backed-up the truck but the neural controller outperformed the fuzzy controller designed by Wang and Mendel even it has been trained by using data obtained from this controller. The amount of overlapping between the fuzzy sets highly affects the stability of the fuzzy controller. We showed that the response of the fuzzy controller became smoother after increasing the amount of overlapping. Completeness of the fuzzy rules affects the characteristic of the fuzzy controller. The controller may respond in an unacceptable manner if there are no rules dealing with states within the operating regions. The generalization capability of the neural controller is much better than the fuzzy one. A good trained neural network will work well with any states inside its input regions. The NNC computational operation operations involved multiplication, addition and taking the exponential of a vector, whereas the FLC operations involved only multiplication and summation of vectors. In order to determine whether a neural or a fuzzy is better suited to a particular application, the nature of the problem and the availability of reliable numerical structural data must be assessed.

6. Appendix

The modified fuzzy logic controller: The domain interval of the truck angle ($) is divided into seven membership regions (fuzzy sets), the domain region of the position (x) is divided into five regions, and the domain interval of the steering angle (0) is divided into seven regions. The shape of each membership function is triangular; one vertex lies at the center of the

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region and has a me:mbership value of unity. The other two vertices lie at the centers of the two neighboring regions, respectively, and have membership values equal to zero. The fuzzy sets corresponding to each fuzzy variables are given as the following (lalbel, left point, center point, right point): Truck angle (@): (S3, -115, -65, 0), (S2, -65, 0, 52.5), (Sl, 0, 52.5, go), (CE, 52.5, 90, 127.5), (Bl, 90, 127.5, 180)., (B2, 127.5, 180, 245), (B3, 180,245,295). Truck position (x): (32, -1000, 1.5,7), (Sl, 1.5, 7,10), (CE, 7, 10, 13), (Bl, 10, 13, 18.5), (B2, 13, 18.5, 1000). Where (S) stands for small, (B) stands for big, and (CE) stands for center set. The sets S2 and B2 of x are deliberately left 'open' by specifying a very large edge value. The fuzzy rules are given in Table I, where the tables' entries are the centers of the steering angle l(0) fuzzy sets.

Table I. Fuzzy Rule Assignment Matrix.

-40 -40 CE - -40

-40 B2

7. References

Bart Kosko, "Neural Network and Fuzzy Systems", Prentice-Hall, 1992. David J. Holloway et. al., " A Comparison of Neural Network and Fuzzy Logic Control Systems", ACCA"3. pp 2291-2294,1992. D. Nguyen and B. Widrow, "The Backer-Upper System: An Example of Self Learning in Neural Network, "IEEE Conltrol System Society Magazine,

Li-Xing Wang and Jerry Mendel, "Generating Fuzzy Rules by Learning from Examples", IEEE Transaction on System, Man, and Cybernetics, Vol. 22, No. 6, Novembermecember, 1992. Abdulla Ismail, Saeed Al-Dhaheri, S. Aly, and Emadeddin Abu-Khcusa, " Fuzzy Analogical Gates Control of Truck Backer-Upper System", WAC96 ,Montpellier, France. May, 1996. Togai Infralogic, Inc., "TILGen User's Manual", 1991. The Math Work, Inc. "SIMULINK User's Guide", March 1992

Vol. 10, NO. 3, pp. 18-23, 1990.