An acquisition of operator's rules for collision ... - Semantic Scholar

280

IEEE TRANSACTIONS ON FUZZY SYSTEMS,VOL. 3, NO. 3, AUGUST 1995

An Acquisition of Operator’s Rules for Collision Avoidance Using Fuzzy Neural Networks Ichiro Hiraga, Takeshi Furuhashi, Member, IEEE, Yoshiki Uchikawa, Senior Member, IEEE, and Shoichi Nakayama, Member, IEEE

Abstract-The procedure for acquiringcontrol rules to improve the performance of control systems has received considerable attention recently. This paper deals with a collision avoidance problem in which the controlled object is a ship with inertia which must avoid collision with a moving object. It has proven to be difficult to obtain collision avoidance rules, i.e., steering rules and speed control rules, which coincide with the operator’s knowledge. This paper shows that rules of this type can be acquireddirectly from observational data using fuzzy neural networks ( F N ” s ) . This paper also shows that the FNN can obtain portions of the fuzzy rules for the inferences of the static and dynamic degrees of danger and the decision table based on the degrees of danger to avoid the moving obstacle.

I. INTRODUCTTON

M

ANY procedures for improving the performance of control systems based on the control strategies of human operators have already been published [ 11-[8]. Sawaragi et al. 111 proposed an algorithm for analyzing an operator’s control action sequence based on AI techniques. Hammer and Hara [2] and Shimada er al. [3] proposed methods to describe operator’s recognition rules for avoiding collision of ships using fuzzy logic. A great deal of work is required to acquire the operator’s knowledge when these methods are used. Maeda and Yamanaka 141 proposed an automatic method for acquiring a collision avoidance strategy for a mobile robot directly from data generated by operator performance using the cerebellar model arithmetic computer (CMAC). The CMAC acquires a decision table for deciding the direction of avoidance from degrees of danger; the degree of static danger a and that of dynamic danger /3 are obtained using fuzzy inference [ 5 ] . It is not clear, however, whether the obtained avoidance knowledge coincides with the operator’s knowledge, since the decision table was obtained indirectly through the degrees of danger. The dynamics of the robot, moreover, were not considered in these papers. The present authors have already described a method for the automatic acquisition of control strategy and tactics from operator-generated data using fuzzy neural networks (FN”s) [6]-[8]. The F ” ’ s are capable of identifying fuzzy rules and tuning membership functions automatically, and the knowledge obtained by the F ” ’ s is described via clear fuzzy

rules 191-[ 131. Hayashi [ 141 and Fu [ 151 proposed methods to interpret neural network knowledge in symbolic form. These methods acquire crisp rules from a neural network which is specially designed to handle confirming rules. The input space is divided crisply a priori. For a control use where the fuzzy division of the input space is an important problem, these approaches for acquiring crisp rules can not be applied. This paper studies knowledge acquisition for avoiding collision of ships using the F ” ’ s and shows that the operator’s “rules” can be acquired directly from a combination of observables and operator-generated data. Two FNN’s are used for the knowledge acquisition process, one to acquire the operator’s steering rules and the other to generate the speed control rules. It is also shown that the FNN for the steering operation can be used to obtain portions of a fuzzy rule base for the inference of static and dynamic degrees of danger and the decision table based on them [4]. In Section 11, the basic structure of the F” is explained. The simulation conditions for the collision avoidance problem are described in Section 111, and the procedures whereby the steering control rules are acquired as well as simulation studies are described in Sections IV-VI. Procedures for the acquisition of speed control rules used for more complex control are described in Section VII. Finally, conclusions are provided in Section VIII. 11. FUZZYNEURALNETWORK

This paper will use the “Type I” F” described in [9]-[ 121 and shown here in Fig. 1. The figure shows the case where the F” has two inputs 2 1 ~ x 2and one output y* and three membership functions in each antecedent. The symbols “box” and “circle” in the figure denote units of the neural network and wc,w g ,wb, and 1, -1 denote connection weights. The F” realizes a simplified fuzzy inference written as follows

Ri: If

21

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is

y = bi

j = l,2)

Manuscript received September 21, 1993; revised September 16, 1994. I. Hiraga, T. Furuhashi, and Y. Uchikawa are with the Department of Information Electronics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-01, Japan. S. Nakayama is with Fujitsu VLSI Limited. IEEE Log Number 9410134. 10634706/95$04.00 0 1995 IEEE

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0 1 . A N ACQUISlTION OF OPERATOR'S RULES FOR COLLISION AVOIDANCE USING FUZZY NEURAL NETWORKS

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A----1

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Fig. 3. Pseudo-trapezoidal membership function in antecedent.

(e)

(E) (C) (D) (FfiF)

algorithm of the FNN is based on the BP method as follows:

Antecedent Consequence Fig. 1. Fuzzy neural network.

(4) k

iy)

'-1

L 4-0.5L 0- L0.5-

where t j is the teaching signal of the jth unit. o:?) and are the output and the input of the jth unit in (n)-layer. f'(.) denotes the derivative of the inner function of the unit. is the weight between the kth unit in (n 1)-layer and the jth unit in (n)-layer. The input-output relationship of the units in (E)-layer is given by

wG+"~)

1

Fig. 2. Membership function in antecedent.

where Riis the ith fuzzy rule, Aill, Ai22 are linguistic terms, bi is a constant, n~ is the number of fuzzy rules, ij denotes the type of membership function for the input xj of the ith fuzzy rule, mj is the number of membership functions for the input zj, pi is the truth value of Ri, ,hi is the normalized truth value so that the sum of ,& is unity, and y* is the inferred value. The F" realizes the inference in (1) and (2) in the neural network structure. The connection weights of the network wc, w g, Wb corresponding to the parameters of fuzzy inference are updated via the backpropagation (BP) learning algorithm. The units in (C)-layer have sigmoid functions as their inner functions. The output of the unit in (C)-layer O(") is given by

O(C)

1 1 +exp{-wg(zj

+ wc))'

(3)

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The inner functions of these units have multi-inputs. The algorithm for these units is

Since multiplications are done in the succeeding layer, the following algorithm is used in (D)-layer

The connection weights w,,wg determine the positions and gradients of the sigmoid functions, respectively. Fig. 2 shows the membership functions in the antecedent (8) Alj(zj), Azj(zj), Asj(zj) realized in (AXD)-layers. Each The connection weights are modified using (4H8)and the membership function consists of one or two sigmoid functions. The pseudo-trapezoidal membership function Azj is made following with two sigmoid functions as illustrated in Fig. 3. The dotted w!"'"-l)(m + 1) = w;;'"-')(m) + qsj(n) oi(n-1) (9) 32 lines are the sigmoid functions. The outputs of the units in (D)-layer are the grades of the membership functions. The where m means the mth sequence to update the connection products of the grades are fed to the units in (E)-layer and weights and 17 is called learning rate. The modification of the outputs of the units are normalized truth values in the the connection weight wg in the antecedent part is greatly antecedent j&. The output of the unit in (F)-layer is the sum influenced by the outputs of the units in (B)-layer. It is better of the products of the connection weights Wb and ,hi. The to normalize the modifying amount as follows: connection weights Wb correspond to the singletons in the wj;,n-')(m + 1) = w(.""-"(m) 3' + q6j")1wj;'"-')(m)I consequences (the bi). The output in (F)-layer is, therefore, the inferred value y*. . o!"-l). (10) The F" tunes the membership functions in the antecedents " -this ~ ) equation means the input and identifies the fuzzy rules by adjusting the connection The term . ~3 2( . ~ ' ~ - ~ ) ( m ) o !in of the unit in (C)-layer. At the occasion w g is updated, the weights w,, w g and Wb, through the BP algorithm. The F" identify the fuzzy rules and tune the membership derivative of the sigmoid function in (C)-layer has a certain functions by modifying the connection weights. The learning value. This means that the input of the unit in (C)-layer is

282

IEEE TRANSACI’IONS ON FUZZY SYSTEMS, VOL. 3, NO. 3, AUGUST 1995

goal

north

other ship

20’

t

Fig. 4. Simulation parameters.

in a certain range regardless of the amount of oin-l). Using (lo), wg is modified with moderate influences from greatly varying oinpl). Sun [ 161 proposed methods of modeling a fuzzy inference system using an adaptive network. This paper contains a nice description of the adaptive network which is very similar to Type I1 F” in [lo]-[12]. It is recommended to refer these papers for further understanding of the F”’s.

operator’s ship starting point

Fig. 5. Simulation on CRT.

111. STEERING OF A SHIP WITH INERTIA Data for the simulation is gathered from the actions of an operator who steers a ship while observing other ships on a CRT screen. The operator is obliged to consider inertia as the maneuvers are executed. The equations below are taken to be a reasonable approximation of the ship’s dynamics [l], [8] dw T -dt

starling point

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(b)

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O(t) =

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dt

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dt

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(11)

Fig. 6 . Track of ships. (a) 22.5 degrees,

head on.

(12)

The simulation, for example in Fig. 5, is started with such initial conditions as the operator’s ship is directed to the goal (the goal is north), i.e., O(0) = 0, w ( 0 ) = 0; the speeds of the operator’s ship IV1 and the other ship IVol are constant. Fig. 5 shows the case where the other ship comes from 20 degrees to the left. In Fig. 5, the ship takes 30 secs from the start point to the goal if the operator does nothing. If he does not avoid the other ship, however, the ships probably collide with each other. The time constant T is five secs.

where T is the time constant of the first-order system, V is the velocity of the operator’s ship and /VI is the speed, U is the steering angle, w is the angular velocity, 6’ is the angular deviation from true north, and x,y is the position of the ship. Fig. 4 shows the terms used to describe the position of the operator’s ship relative to another ship and the goal. The distance between the ship and the other ship is denoted by IV. ACQUISITIONOF AVOIDINGRULES D. The angle between the direction of the operator’s ship We begin by examining collision avoidance using only the and the direction of the other ship viewed from the operator’s steering angle; thus, the single manipulated variable of the ship is denoted by So. In the same way, the angle between operator’s ship is the steering angle U . The tracks of the ship the direction of the operator’s ship and the direction of the obtained from the simulations shown in Fig. 6 are used to train goal viewed from the operator’s ship is SG. VR is the relative the F”.Fig. 6(a) shows the case where the other ship comes velocity of the operator’s ship (moving at V ) with respect to from 22.5 degrees to the left; (b) shows the case where the another ship (moving at VO).The angle formed by VRand the other ship approaches the operator’s ship head on. We also direction vector of the operator’s ship will be referred to as 4; simulated the cases where the other ship comes from five, when 4 is near zero the other ship is approaching the operator’s 10, 15, 30, 45 degrees to the left and to the right. Once the ship nearly head on, when 4 is positive the other ship should operator has successfully avoided the other ship, he steers his pass in front of the operator’s ship, and when 4 is negative the ship directly toward the goal. other ship should pass behind the operator’s ship. As the other The relative distance D, the relative angle So,the angle 4, ship approaches the operator’s ship 4 approaches 90 (or -90) and the relative angle SG are considered to be observed by the degrees; once the two ships have reached maximum proximity operator and are used as the inputs of the F”.The teaching their positions begin to diverge, the value of 4 increases (or signal used for the learning of the F” is given as decreases), and the relative distance D is assigned a negative SR = O(t + T ) - 6(t) value. (14)

HIRAGA et al.: AN ACQUISlTION OF OPERATOR’S R U L E FOR COLLlSION AVOIDANCE USlNG FUZZY NEURAL NETWORKS

283

TABLE I AVOIDING Fuzzy RULESIDENTIFIED BY FNN (RULESFOR DIRECTION COMMAND)

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0

Far

3I

Direction bo Direction b o Left Fore Right’ @ Left Fore Riglit 31 Lflft 34 15 9 31 Left -33 -31 -31 -4 -T 1 0 0 0 6c:lRight -9 -27 -23 6clRight 31 34 33 Directioii b o Direction bo Direction b o Left Foic Riglit Left Fore right^' @ ‘Left Foro Riglit 0 O 0 3 Left 0 0 0 f Left - 2 i -8 -18 5 0 - 3 6 Forc 0 0 0 6 Fore -1 0 2 0 0 0 , 6~; Riglit 0 0 -1 6~; Riglit 18 4 2i

Dilcctioii b o ’Left For(’ Riglit 31 Left 0 0 0

0

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SclRight

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3

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’

’

Left 6 Fore 6~Right

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0.5

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n

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0

400

800

Distance D ( h t ) Rear

Approach

n y30-2-10 0

10 20 30 Direction S o (&I

-40 -20 0 20 40 -6-4-20 2 Direction Camand SR (deg) AngJler Velocity w

4

6

(des/sx)

Fig. 8. Membership functions of FNN for steering command.

Fore

0.5 n

-30-20-10 0 10 20 30 Relative Angle C (des)

-30-20-10

0 10 20 30

Goal FG (deg)

Fig. 7. Membership functions of FNN for direction command.

+

where O ( t ) is the current position of the ship and O(t T) is the position of T seconds later. T is the time constant in (1 1). The positions e(t T) are obtained from the track of the ship. The F” was trained 500 times. In one training cycle, each of the input-output training pairs is used once. Three membership functions were used for each input term, with three being considered the minimum necessary for adequate resolution. Fig. 7 shows the membership functions for each input variable. The dotted lines show the predefined membership functions and the solid lines show the membership functions derived by application of the FNN. The unit of the distance between the ships is defined here to be a dot on the CRT screen. There are 720 dots between the starting point of the ship and the goal. Note that the F” can be used to fine tune the membership functions in the antecedents as well as to identify the fuzzy rules via BP learning. For the rough definition of the membership functions shown by the dotted lines, the F” was also used, because appropriate universe of discourse nor shapes of membership functions were not known a priori. The elements of the universe of discourse were roughly initialized, and only the connection weights on

e@), +

the consequent side (the Wb) were adjusted via BP while the elements of the universe of discourse were adjusted stepwise until minimum error values were achieved. The FNN was then trained to tune the w,,w g in the antecedent side as well as Wb via BP. This method of learning was used to avoid generating seriously deformed membership functions which might otherwise result due to the fact that the F” operates with many degrees of freedom. The acquired fuzzy rules are shown in the Table I. The labels of the membership functions in Figs. 7 and 8 are used in the table. The values of the table are the amounts of connection weights Wb in the FNN corresponding to the bi in (l), and also are the direction commands of the ship SR (deg) in each fuzzy subspace. The positive sign means the right hand side direction and the negative sign means the opposite. In the subspace where the distance is “gone” means that the value of 4 is over 90 degrees or under -90 degrees. The rules in the tables can be read as, for example, if the other ship is ‘‘(D=) Near” and it is “( 4 =) Approaching” the operator’s ship to the “(SO =) Right” and goal is seen to the “(SG =) Fore” then steer to the “(SR =) Right” (19 degrees). V. ACQUIRED AVOIDING RULES

Table I can be divided into nine parts; we shall refer to these parts as “rule tables.” There are cases where the other ship is far from the operator’s ship (0, @, near the

a),

284

IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 3, NO. 3, AUGUST 1995

(@,a,

a),

operator’s ship @), or gone (0, @, and the cases where the other ship passes to the rear of the operator’s 0. @ approaches I), the operator’s ship (0,0, @), ship (0, or passes to the fore of the operator’s ship (0, @, 8).These various rule tables are applied appropriately with the progress of the avoidance procedure; in Fig. 6, for instance, it can be seen that the rule table progression is Let us provide a bit more detail for the sake of clarity. When the other ship is far away, the operator will initiate avoiding procedures only if the other ship is approaching from the fore (rule table @). When the other ship is near, he steers his ship to the left when the goal is fore and the other ship is coming This leftward steering is continued from the left (rule table 0). as long as the other ship is approaching and the goal is to the right (rule table 0).The other ship then passes to the fore of the operator’s ship and rule table @ is activated because the goal is now to the right, the ship is steered to the right. Finally, as the other ship reaches “gone” status, rule table @ takes effect and the ship makes a final leftward adjustment to @, 0, and @, head directly toward the goal. Rule tables 0, which are nearly empty, apply essentially vacuously because they reflect essentially impossible or irrelevant situations (in the case of rule table @, the impossible situation that the other the ship is both approaching and gone; in the case of 0-0, situation that the other ship is passing to the rear, in which case no operator adjustments are required). The acquired fuzzy rules coincide well with the operator’s image of avoiding operations. Maeda and Yamanaka [4] defined the static degree of danger Q using fuzzy inference from D and SO. and the dynamic degree of danger /3 using the fuzzy inference from VR and 4. The basic rules are: when the other ship is near and in front of the operator’s ship, a is large; when the relative velocity is large and the other ship is approaching the operator’s ship, p is large. In the Table I, therefore, a small a is implicit in @, 0, and a large one in @. Maeda and rules 0, Yamanaka did not define a situation corresponding to the one where the other ship is “gone:” presumably, such situation (0, 0, and correspond to those with a small a. Similarly, in rule tables @-@ p would be large, while in the other rule tables of Table I p would be small. Maeda and Yamanaka [4] derived a relationship between the degrees of danger (a and p) and the avoiding direction using the CMAC. The decision table acquired by the CMAC indicates that when both Q and p are large, the ship starts to avoid the collision. Moreover, depending on the value of V R ,a decision is made to pass either in front of or behind the other ship. Rule table 0in Table I corresponds to the situation in which both a and p are large; furthermore, this rule table directs collision avoidance by steering the operator’s ship to the back of the other ship. The FNN, therefore, has acquired the same rules described in the decision table using a and p in [4].

TABLE I1 FUZZY CONTROL RULESIDENTIFIED BY

lrft

straight

F”

riglit

@-@-@-a.

(Left) - -stcering

allgle

I I (deg)-

+ (Riglit)

the FNN were the angular velocity of the ship w and the relative angle SR from the track. The teaching signal was the steering angle U. The relative angle SR corresponds to the direction command which the operator is supposed to have in mind. The membership functions for the angular velocity w were three (left, straight, right) and for the relative angle SR, also three (left, fore, right). The angular velocity w could take as maximum value the maximum steering angle of the ship, but the actual maximum is taken to be half that value for smooth steering. The universe of discourse for the membership functions for w was set to be the range of the actual angular velocity. The learning procedure was the same as that in Section IV. The universe of discourse were determined first. Fig. 8 shows the membership functions in the antecedent before learning (dotted line) and after learning (solid line). The membership functions for the direction command SR were fairly heavily modified because the universe of discourse was only roughly determined. The crossing point of the membership functions for SR were greater than 0.5 for smooth change of the steering angle U with varying SR. Table I1 shows the obtained control rules. The values in the table correspond to the steering angle U. A positive value indicates that the ship should be steered to the right and a negative value indicates that the ship should be steered to the left. It is a bit more difficult to interpret the rules implicit in this table, so the input-output surface of the F”is shown in Fig. 9. The axes on the horizontal surface are the angular velocity w and the relative angle 6 ~ The . vertical axis U* is the output of the F”. The input-output surface around the origin (SR = 0 , w = 0) shows that the obtained control rules work as a fuzzy PD controller. The absolute values of the control angle Ju*),however, become the largest where the signs of the direction of the ship SR and the angular velocity w are the same. This is because the operator steered his ship smoothly, so only a small number of training data in these extreme regions were gathered. A fuzzy controller is made with one FNN having the avoiding control rules commanding the direction of the ship and another FNN having the control rules for steering the ship to follow the command as shown in Fig. 10. This fuzzy controller performs its collision avoidance task very well. The results are shown in Fig. 11. The first two cases (a) and (b) were cases for which the controller was specifically trained, while the second two cases (c) and (d) were cases for which the VI. FUZZYCONTROLLER controller was not specifically trained. These studies show that Control rules mediate the interface between the operator’s the controller could successfully steer the ship to pass behind steering data and the actual path the ship is directed to take. the other ship except when the other ship approached from an These rules will be described in this section. The inputs of angle of four degrees to the left. This is because four degrees

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a)

HIRAGA

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al.: AN ACQUISITION OF OPERATOR'S RULES FOR COLLISION AVOIDANCE USlNG FUZZY NEURAL NETWORKS

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a' 3 3 '

-40

0 E .-m U

b'+

70 _

-10

0 Left

10

Right

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Fig. 9. Input-output surface of FNN for steering command.

Fig. 10. Configuration of fuzzy controller.

to the left is on the border of the left and fore directions for So and the controller could not decide which way to steer.

VII. ACQUISITION OF AVOIDING RULE USING STEERING AND SPEED CONTROL

When the other ship approaches from the far left or the far right direction, the operator is more likely to avoid collision by controlling the speed of the ship than by controlling its direction. Thus, when the relative velocity VRis large, it may be necessary to slow the ship down, while when the relative velocity is small it may be necessary to speed the ship up. The operator, then, uses steering mainly when the other ship comes from the fore, and uses acceleration or deceleration when the other ship comes from the left or right. This section discusses the acquisition of this more sophisticated control mechanism. The inputs to the FNN which was expected to learn directional command were the relative distance D ,the relative angle SO, the relative velocity VR,the relative angle of the relative velocity 4, and the relative angle SG. The output signal was SR from the track, and the FNN was trained 500 times. Five membership functions were used for SO, while three membership functions were used for each of the other parameters. Four input variables were used for the other FNN (the one used to determine the velocity of the operator's ship): D,So,VR,and 4.The output signal was dV which was the difference between the speed of the operator's ship and its initial value V(0) (= 40, 40 corresponds to 24 dots/sec in this paper), and the FNN was trained lo00 times. The velocity of the ship was obtained as the output of the first-order system with a time constant T = 5 (sec). The input of the system was dV V ( 0 ) .For VR,two membership functions were used, and for others, three were used. There was a dead point in deciding whether to accelerate or decelerate, and the operator steered the ship to avoid a collision at the dead point. After the learning process was finished, we constructed the multiple fuzzy controllers with the FNN's as shown in Fig. 12. One F" determined the direction command SR, another F"

+

(C)

(d)

Fig. 1 1 . Results of simulations (steering control). (a) Head on (mned); (b) 22.5 degrees (trained); (c) 18 degrees (untrained); and (d) 4 degrees (untrained).

Ship

speed control

Fig. 12. Configuration of fuzzy controller with steering and speed control.

controlled the speed of the ship, and a third was used to give the steering angle U to the ship. Fig. 13 shows results of simulations. In Fig. 13(a), the controlled ship avoided the collision using the steering control only, and in (b), only the speed control was used. In Fig. 13(c), the angle 60 was borderline relative to a decision about what kind of control to use in the avoidance procedure, and so input from both controllers was required. As a result, the deviation of the track was smaller than that in Fig. ll(b). Finally, in Fig. 13(d), the relative velocity VR was at the dead point of the speed control. In this case, the ship succeeded in collision avoidance using the steering control. Table I11 shows the portions of the control rules acquired by the FN"s. Table IU-A corresponds to rule table @ in Table I; when the other ship comes from the medium left, fore, or medium right, control is via steering adjustments like the one shown in Fig. 13(a); when the other ship comes from the left or right, control is primarily via speed adjustments rather than by steering adjustments, and the absolute values of the steering adjustments are small. Table 111-B shows the speed control rules which apply to cases like the one shown in Fig. 13(b). When the other ship approaches from the left or right and the

286

E E E TRANSACTIONS ON FUZZY SYSTEMS. VOL. 3, NO. 3, AUGUST 1995

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TABLE III-C AVOIDING FUZZY RULESIDENTIFIED BY F”(RULES FOR DIRECTION COMMAND AND SPEED CONTROL)

o is -.Approaching” L AIL (C) (d) Fig. 13. Results of simulations (steering and speed control). (a) Head on; (b) 22.5 degrees (Left); VR is S; (c) 18 degrees; and (d) four degrees (Left), L’R is M.

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F AIR R

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expected that the methods described in this paper will be able to acquire the rules necessary to operate under these more complex conditions. The authors also plan to investigate knowledge acquisition for avoidance procedures when multiple moving objects must be avoided and when each of the moving objects has their own avoidance procedures in operation. REFERENCES

+(Right)

relative velocity VR is small, the controlled ship increases its own speed to escape from the collision. Table In-C shows the rules which apply to cases like the one shown in Fig. 13(d). When the other ship comes from the side (So is L or R) and the relative velocity V, is on the dead point, the avoiding operation is made using steering control only. VIII. CONCLUSION This paper has demonstrated that avoidance rules which correspond well to an operator’s knowledge can be acquired by F ” ’ s using data from operator manipulations. Furthermore, it was demonstrated that a FNN could generate fuzzy rules which correspond to the degrees of danger and their use in a decision table as described by Maeda and Yamanaka [4]. In real maritime operations, certain priorities need to be considered; these priorities depend on the relative directions and/or the sizes of the ships involved in the decisions. It is

[I] T. Sawaragi, 0. Katai, and S. Iwai, ‘Tuning knowledge for intelligent fuzzy controller by analyzing a history of control operations,” Trans. SICE, vol. 26, no. 8, pp. 854-861, 1990. [2] A. Hammer and K. Hara, “Knowledge acquisition for collision avoidance maneuver by ship handling simulator,” in Proc. MARSIM 4-ICSM ‘90, 1990, pp. 245-252. [3] K. Shimada, S. Mabuchi, and K. Hara, “Identification of operators’ judgement rules of danger in collision avoidance maneuvering of ships,” in Pmc. 7rh F u u y Sysr. Symp., Japan, 1991, pp. 509-512. [4] Y. Maeda and T. Yamanaka, “Fuzzy obstacle avoidance control with the strategy of operator obtained by the CMAC learning,” in Proc. 6th F u u y Sysr. Symp.. Japan, 1990, pp. 531-534. [5] Y. Maeda, “Fuzzy obstacle avoidance method for a mobile robot based on the degree of danger,” in Proc. NAFIPS ’90, vol. 1, 1990, pp. 169-172. [6] T. Furuhashi, S. Horikawa, Y. Uchikawa, and S. Nakayama, “An acquisition of strategic and tactical control rules using fuzzy neural networks,” in Proc. 2nd IEEE lnt. Workshop AMC, 1992, pp. 383-390. [7] S. Nakayama, S. Horikawa, T. Furuhashi, and Y. Uchikawa, “Knowledge acquisition of strategy and tactics using fuzzy neural networks,” in Pmc. IJCNN ’92-BALTIMORE, vol. 2, 1992, pp. 751-756. [8] S. Nakayama, T. Furuhashi, S. Horikawa, and Y. Uchikawa, “Knowledge acquisition of control strategy and tactics using fuzzy neural networks,” J. Japan Soc. Fuzzy Theory Syst., vol. 4, no. 5, pp. 929-941, 1992. [9] S. Horikawa, T. Furuhashi, S. Ohkuma, and Y. Uchikawa, “A fuzzy controller using a neural network and its capability to learn expert’s

HIRAGA et nl . AN ACQIJISITTON OF OPERATORS RULES FOR COLLISION AVOIDANCE USING FUZZY NEURAL NETWORKS

[lo] [ 111

[ 121

[13] [I41

[15] [ 161

control rules,” in Proc. Int. Con$ Fuuy Logic Neural Networks, 1990, pp. 103-106. S. Horikawa, T. Furuhashi, S. Ohkuma, and Y. Uchikawa, “Composition methods of fuzzy neural networks,” in Pmc. Con$ Rec. IEEWlECON’90, 1990, pp. 1253-1258. S. Horikawa, T. Furuhashi, and Y. Uchikawa, “On fuzzy modeling using fuzzy neural networks with the backpropagation algorithm,” IEEE Trans. Neural Networks, vol. 3, no. 5 , pp. 801-806, 1992. __ , “Composition methods and learning algorithms of fuzzy neural networks,” J. Japan Soc. Fuzzy Theory Syst., vol. 4, no. 5 , pp. 9 6 9 2 8 , 1992. L.-X.Wang and J. M. Mendel, “Backpropagation fuzzy system as nonlinear dynamic system identifiers,” in Proc. IEEE Int. Con$ F u u y S y ~ t . ,1992, pp. 1409-1418. Y. Hayashi, “A neural expert system with automated extraction of fuzzy if-then rules and its application to medical diagnosis,” in Advances in Neural Information Processing System. San Mateo, CA: Morgan Kaufmann, 1990, vol. 3. L. Fu, “Rule generation from neural networks,” IEEE Trans. Syst.. Man, Cybern., vol. 24, no. 8, pp. 11141124, 1994. C.-T. Sun, “Rule-base structure identification in an adaptive-networkbased fuzzy inference system,” IEEE Trans. Fuzzy Systems, vol. 2, no. 1, pp. 6 4 7 3 , 1994.

Ichiro Hiraga was born in Yamaguchi, Japan, in 1969. He received the B.E. degree in mechanical engineering from Nagoya University, Japan, III1993. His current research interests are in knowledge acquisition using the fuzzy reasoning.

Takeshi Furuhashi (S’83-M’85) was born in Shizuoka, Japan, in 1954. He received the B.E., M.E., and Ph.D. degrees in electrical engineenng from Nagoya University, Japan, in 1980, 1982, and 1985, respechvely. He was with Toshiba Corporation from 1985-1988. From 1988-1990, he was with the Department of Electrical Engineering of Nagoya University as an Assistant Professor. From 1990-1994, he was with the Department of Electronic-Mechanical Engineering of Nagoya University as an Associate Professor. Since June 1994, he has been an Associate Professor of the Department of Information Electromcs of Nagoya University. His current research interests are in fuzzy theory, genetic algonthm, complex systems, and soft computings.

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Yoshiki Uchikawa (SM’93) was born in Aichi, Japan, III 1941. He received the B.E., M.E., and Ph.D. degrees in electrical engineering from Nagoya University, Japan, in 1964, 1966, and 1971, respectively. From 1969-1977, he was with the Department of Electrical Engineering of Nagoya University as an Assistant Professor. From 1978-1984, he was with the Department of Electromc-Mechanical Engmeering of Nagoya University as an Associate Professor. From 1985-1994, he was with the Department of Electronic-Mechanical Engineering of Nagoya Umversity as a Professor. Since June 1994, he has been a Professor of the Department of Information Electromcs of Nagoya University. His current research interests are in neural network, fuzzy theory, genehc algorithm, immune systems, autonomous decentralized system, and electron microscopy.

Shoichi Nabziyama (M’91) was born in m e , Japan, in 1968. He graduated from the electncal engineermg of Ise mdustnal h g h school, Japan, in 1986 He has worked for Fujitsu VLSI Lirmted, Japan, since 1986. He has been engaged in the areas of the system development around the sermconductormanufactunng process at Fujitsu VLSI Linuted. From Apnl 1991-May 1993, he was with the Department of Electromc-Mechmcal Engineenng of Nagoya Umversity as a research student, where he engaged in a research of applications of the fuzzy neural network