Heuristic fuzzy-neuro network and its application to reactive navigation of a mobile robot

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Heuristic fuzzy-neuro network and its application to reactive

navigation of a mobile robot

Kai-Tai Song

∗;1

_{, Liang-Hwang Sheen}

2

Department of Electrical and Control Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan, ROC Received July 1996; received in revised form November 1997

Abstract

A novel pattern recognition approach to reactive navigation of a mobile robot is presented in this paper. A heuristic fuzzy-neuro network is developed for pattern-mapping between quantized ultrasonic sensory data and velocity commands to the robot. The design goal was to enable an autonomous mobile robot to navigate safely and eciently to a target position in a previously unknown environment. Useful heuristic rules were combined with the fuzzy Kohonen clustering network (FKCN) to build the desired mapping between perception and motion. This method provides much faster response to unexpected events and is less sensitive to sensor misreading than conventional approaches. It allows continuous, fast motion of the mobile robot without any need to stop for obstacles. The eectiveness of the proposed method is demonstrated in a series of practical tests on our experimental mobile robot. c 2000 Elsevier Science B.V. All rights reserved.

Keywords: Pattern recognition; Fuzzy navigation; Fuzzy-neuro network; Mobile robots

1. Introduction

Reactive obstacle avoidance is one of the most de-sirable characteristics of an autonomous mobile robot. It is the ability to free-range in an unknown envi-ronment relying only on sensory information. Fig. 1 shows a block diagram of such a motion planning and control system. In the robot navigation system, a local motion-planning module is responsible for gen-erating steering commands in response to onboard sensory data. It is important for the robot to respond

∗_{Corresponding author. Fax: 886-3-5715998.} E-mail address: ktsong@cc.nctu.edu.tw (K.-T. Song)

1_{This work was supported by National Science Council of the}

ROC under grants NSC-84-2212-E009-029.

2_{Liang-Hwang Sheen is now with Phoenixtec Power Co., Ltd.,}

Taipei, Taiwan, ROC

promptly to its surroundings, for instance, to avoid unexpected obstacles and continue traveling toward the target. However, available sensors are not good enough to provide accurate recognition of the envi-ronment. Very often, the measured data contain un-certainties that cause motion errors. It is therefore dif-cult for the mobile robot to navigate in an unknown and dynamically changing environment.

One reactive navigation approach employs the po-tential eld or vector force eld concepts [1, 4], in which a two-dimensional Cartesian grid is utilized for obstacle representation. The target exerts a virtual at-tractive force on the mobile robot, and the obstacles exert repulsive force. The robot-motion reaction is determined by the resultant virtual force. The short-coming of these methods is that they require a lot of calculation. Recently, considerable work has been

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Fig. 1. System block diagram of sensor-based navigation.

reported concerning the application of articial neural networks (ANN) and fuzzy logic for reactive control. An incremental supervised learning scheme has been proposed for reactive navigation of a mobile robot [12]. In [10], a reinforcement learning scheme was employed to train a neural network for obstacle avoid-ance. The advantage of this approach is the learn-ing capacity of the neural network, however, learnlearn-ing convergence is very slow and generalization is not always satisfactory. On the other hand, fuzzy logic concepts was employed to handle the uncertainty prob-lems in environmental map-building [11]. The con-structed fuzzy maps from ultrasonic sensors were then used to plan a collision-free path. Several methods exploiting fuzzy control schemes have been proposed for avoiding unexpected obstacles [6, 8, 9, 14]. A rule table was established in these methods according to heuristic experience. In [8], 155 rules were employed for avoiding static and moving obstacles along a pre-planned path. In [14], a fuzzy navigation controller was combined with virtual concepts for a mobile robot to navigate in an unknown environment. There were 81 rules for each right-fuzzy-logic controller and left-fuzzy-logic controller. It is noticed that there are a great many rules and some of them might not be acti-vated during navigation. The redundant rules will in-crease the complexity of fuzzy inference.

In this paper, we present a novel design approach to building a rule table for reactive navigation ex-ploiting fuzzy-neuro control. Satisfactory navigation performance can be achieved using reduced numbers of rules. The basic idea is to let the IF-part of a rule be the obstacle-conguration class and the THEN-part

be the reference velocity values. A resultant velocity command to each wheel motion controller is generated through fuzzy Kohonen clustering network (FKCN) instead of by conventional fuzzy inference. FKCN is a fuzzy neural network normally used for pat-tern clustering. In this study this patpat-tern-recognition structure is extended to local motion planning and control. The developed method is fast, ecient and free of the problems mentioned above. Moreover, in order to make the system robust and exible, we adopted a behavior-based architecture for the mobile robot [5]. Consequently, the mobile robot has several ways of producing steering commands using dierent behavior modules. The rest of this paper is organized as follows: Section 2 describes the development of the reactive navigation algorithm based on the FKCN structure. In Section 3, we introduce a design for obstacle avoidance of an experimental mobile robot. Relevant simulation results are presented in Section 4. Section 5 illustrates practical experiments in an indoor environment. We conclude the paper in Section 6. 2. Prototype pattern assignment

To achieve real-time reactive navigation, a good strategy would be to construct a perfect mapping between input sensor data and appropriate control actions. The relation, however, is very complicated and highly nonlinear. In the rst place, dierent types of sensors have dierent measurement characteristics. It would be dicult to estimate the spatial param-eters using onboard sensors in order to determine the conguration relationships between the mobile robot and its immediate surroundings. On the other hand, it is well recognized that articial neural networks have impressive capacity for nonlinear mapping and pattern-recognition applications [2]. In this paper useful heuristics are combined into a fuzzy neural network to achieve the desired pattern-recognition results. The structure of the proposed reactive nav-igation system is illustrated in Fig. 2. It consists of two major parts: the lower is a fuzzy neural network and the upper is responsible for velocity calculation. The FKCN structure [7] was adopted for the desired pattern-recognition function. FKCN is a three-layered, pattern-clustering network. Once it is trained, there is a prototype pattern associated with each cluster.

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Fig. 2. The proposed heuristic FKCN for reactive navigation.

Consequently, every prototype pattern characterizes a cluster. In the neural network, all these prototype patterns are set to the weights in the distance layer. However, we do not apply the unsupervised learning algorithm of the original FKCN. The weights in the distance layer are assigned instead of being trained. There are two reasons for doing it this way. One is for simplicity and consequently a reduction in com-putation time. The other reason is that the clusters are known in advance in our application. The prototype patterns learned by the unsupervised learning algo-rithm might not be better than the assigned patterns derived from actual experimental data and human experience.

In the following, we describe the method for deter-mining the distance and similarity between an input pattern and the prototype patterns. As shown in Fig. 2, the distance layer is responsible for comparing an in-put pattern with the prototype patterns. Outin-put dijof

node j in the distance layer equals 0 when the in-put pattern Xi perfectly matches the prototype pattern

Wj. The output of the distance layer is computed as

follows:

dij= kXi− Wjk2= (Xi− Wj)T(Xi− Wj); (1)

where Wj is the jth prototype pattern.

Formula (1) is a 2-norm equation. The larger the dierence between Xi and Wj is, the faster dij will

increase by powers of 2. The membership layer is provided to map the distance dijto membership values

uij. If an input pattern does not match any prototype

pattern, then the similarity between the input pattern and each individual prototype pattern is represented by a membership value from 0 to 1. The determination

of the membership value is given in [3] and can be summarized by the following equations:

uij=

1 if dij= 0,

0 if dik= 0; (k 6= j; k¿0; j6c − 1), (2)

where c denotes the number of prototype patterns, otherwise uij= c−1 X l=0 dij dil !−1 : (3)

The larger the uijis the more input pattern Xiis similar

to some prototype pattern Wj. Since each prototype

pattern is associated with a rule, the membership value represents the degree of activation of a rule. The sum of the outputs of the membership layer equals 1.

In this study, ultrasonic range sensors are employed for obstacle detection. This type of sensor is simple and ecient for measuring distances to obstacles. Sixteen ultrasonic transducers were xed in a ring on our experimental mobile robot. A detailed discus-sion on the system will be found later. In practice, we can get sonar vectors from these sensor readings corresponding to each dierent obstacle-conguration class. For example, the vector Wj = {w1; w2; : : : ; wp}

is the sonar vector for the jth obstacle-conguration class; where wi is the ith sensor reading, and p

transducers are used to construct the sonar map. Using the concept of pattern recognition, we view each sonar vector as a pattern. Hence, we can deter-mine several prototype patterns corresponding to var-ious obstacle-conguration classes. These prototype patterns are then assigned to be the weights of the neural network. After the network weights have been assigned, they can be recalled on-line when the sen-sory input data are provided during navigation. The recall procedure is described brie y below.

Step 1: A quantized sonar vector (input pattern) constructed from current ultrasonic sensor readings is presented to the neural network input.

Step 2: The distances between the input pattern and every prototype pattern are computed using (1).

Step 3: The similarities between the input pattern and every prototype pattern are calculated using (2) and (3). The similarities are represented by member-ship values from 0 to 1, according to their distance values.

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Fig. 3. Grouping of ultrasonic sensors.

Our experimental mobile robot is equipped with two independent drive wheels. Its course is determined by the relative velocities of the left and right wheels. Therefore, in this design, each prototype pattern is as-sociated with a pair of reference wheel velocities. This association is determined in a preset manner. In other words, we have to provide a rule table for this map-ping (see Fig. 2). The number of rules equals that of prototype patterns. Notably, it will be shown that sat-isfactory reactive navigation results can be obtained employing a considerable reduced number of rules compared with using a conventional fuzzy logic con-troller. In this manner, the mobile robot can perform on-line obstacle avoidance using onboard ultrasonic sensors. The complete navigation design is presented in the next section.

3. Design for obstacle avoidance

The proposed navigation scheme was developed for an experimental mobile robot. Sixteen ultrasonic sen-sors are mounted in a circle on the robot 22:5◦_apart,

alternating in height at 30 cm or 75 cm to cover more detection space. It takes 150 ms to complete an updat-ing cycle of all sixteen sensors [15]. Only eight sen-sors mounted on the front of the mobile robot were used in this study. Those on the back side were not included because backward motion commands were beyond the scope of the current experiments. These eight sensors were divided into ve groups, as shown in Fig. 3. Only one sensor in group 1 and another in group 5 were used to detect obstacles at the left or right side of the mobile robot, leaving two sensors in

each of the other three groups. In these three groups, the smaller of the two transducer readings was used in each sampling instant. These ve sensor-group val-ues were quantized before sending into the neural net-work. The quantization formula for groups 1, 2, 4 and 5 is as follows: xi=        1 for 0¡di6100 cm, 2 for 100 cm¡di6150 cm, 3 for 150 cm¡di6200 cm, 4 for di¿200 cm, (4) where di is the sensor value of the ith group.

The two sensors in group 3 were responsible for detecting head-on obstacles. The quantization of this group sensor data must take into account the response time for preventing from collision:

xi=        1 for 0¡d36150 cm, 2 for 150 cm¡d36200 cm, 3 for 200 cm¡d36250 cm, 4 for d3¿250 cm, (5) where d3 is the sensor value of the 3rd group.

Too many grades of quantization would have resulted in a complicated rule table, but too few grades would have led to unclear representation of the obstacle-conguration classes. Quantized sensory data are used in the FKCN and uij; j = 0 ∼ c − 1 is

calculated according to (1)–(3). The mobile robot is always trying to reach the assigned target. Therefore, the target direction is also taken into account during the reactive navigation (see Fig. 2). The target direc-tion is dened relative to the heading of the mobile robot. It is divided into 5 levels as shown in Fig. 4. The details of this division are as follows:

t =            1 for 180◦_¡6270◦_; 2 for 120◦_¡6180◦_; 3 for 60◦_¡6120◦_; 4 for 0◦_¡660◦_; 5 otherwise, (6)

where is the direction of the target with respect to the current heading of the mobile robot. In (6), the range in each level aects the stability of navigation in avoiding an obstacle in a long corridor. This phenomenon has been examined in experiments.

Nine typical obstacle-conguration classes were considered in this study as depicted in Fig. 5. Through fuzzifying and combining these nine classes in the

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Fig. 4. Quantization of target direction.

Fig. 5. Obstacle-conguration classication used in this design.

heuristic FKCN, we practically had no need to con-sider other obstacle conguration. This is the main purpose of the membership layer. Consequently, the number of the prototype patterns can be kept few. This resulted in considerable fewer control rules than otherwise employed in conventional fuzzy control methods. We take the rst obstacle-conguration class in Fig. 5 as an example to illustrate the idea of forming control rules. In this case, there is an obstacle in front of the mobile robot and the corresponding prototype pattern is

Wj= {4 4 1 4 4}:

The corresponding rule can be set in the following manner: For t = 1; IF Wj= {4 4 1 4 4}; THEN vlj= 2:0 cm=s; vrj= 10:0 cm=s; or For t = 2; 3; IF Wj = {4 4 1 4 4}; THEN vlj= 3:0 cm=s; vrj= 10 cm=s; or For t = 4; 5; IF Wj = {4 4 1 4 4}; THEN vlj= 10:0 cm=s; vrj= 3:0 cm=s;

where vlj and vrj are the output (reference) left and

right wheel velocities, respectively. The rule table was constructed exploiting the representative prototype patterns and heading levels. We employed altogether 16 rules in the present study as shown in Table 1. Notably, the elements of prototype patterns Wj are

mostly of quantized value 1 or 4. This is because it would be benecial if the obstacle-conguration classes could be represented as sharply as possible. The quantized values 2 and 3 are only used to repre-sent special conguration classes.

The algorithm for generating velocity commands is described below. First of all, if an input pattern is iden-tical to one of the prototype patterns (dij∗= 0), then

the ring of the corresponding rule to this input pat-tern is equal to one. The generated velocity command will be equal to the reference velocities of the ex-cited rule. However, in most situations, the calculated smallest distance dij∗ is only less than a pre-dened

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Table 1

Implemented rule table

Rule IF-part THEN-part reference velocity

prototype pattern t = 1 t = 2 t = 3 t = 4 t = 5 No. vl vr vl vr vl vr vl vr vl vr 1 4 4 1 4 4 2.0 10.0 3.0 10.0 3.0 10.0 10.0 3.0 10.0 3.0 2 3 4 1 4 3 2.0 10.0 3.0 10.0 3.0 10.0 10.0 3.0 10.0 3.0 3 4 4 4 1 4 3.0 10.0 5.0 10.0 5.0 10.0 5.0 10.0 5.0 10.0 4 4 1 4 4 4 10.0 5.0 10.0 5.0 10.0 5.0 10.0 5.0 10.0 3.0 5 1 1 1 4 4 10.0 3.0 10.0 3.0 10.0 3.0 10.0 3.0 10.0 3.0 6 4 4 1 1 1 3.0 10.0 3.0 10.0 3.0 10.0 3.0 10.0 3.0 10.0 7 1 4 4 4 1 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 8 1 4 4 1 1 8.0 10.0 8.0 10.0 8.0 10.0 8.0 10.0 8.0 10.0 9 1 1 4 4 1 10.0 8.0 10.0 8.0 10.0 8.0 10.0 8.0 10.0 8.0 10 4 4 4 4 4 3.0 10.0 5.0 10.0 10.0 10.0 10.0 5.0 10.0 3.0 11 4 1 1 4 4 10.0 3.0 10.0 3.0 10.0 3.0 10.0 3.0 10.0 1.0 12 4 4 1 1 4 1.0 10.0 3.0 10.0 3.0 10.0 3.0 10.0 3.0 10.0 13 1 1 4 4 4 10.0 8.0 10.0 8.0 10.0 8.0 10.0 5.0 10.0 3.0 14 4 4 4 1 1 3.0 10.0 5.0 10.0 8.0 10.0 8.0 10.0 8.0 10.0 15 4 4 4 4 1 3.0 10.0 5.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 16 1 4 4 4 4 10.0 10.0 10.0 10.0 10.0 10.0 10.0 5.0 10.0 3.0

value mindist for the current obstacle conguration. This means the input pattern is similar to one or more prototype patterns. Consequently, if dij∗6mindist for

an input pattern Xi, then only those neurons with

dis-tances dis’s not larger than maxdist are fuzzied

us-ing (3). In this case, the sum of the rus-ing of rules will still equal one. The velocity command is calcu-lated by the weighted sum of all ring rules. Here, the parameter maxdist is employed to reduce the in- uence of less important prototype patterns. For a dij

greater than maxdist, the input pattern is recognized as quite dierent from the prototype pattern. On the other hand, when an input pattern does not match or similar to any prototype pattern, i.e., dij∗ (the

small-est dij) ¿ mindist, then it is treated as a special

pat-tern that cannot be recognized. The velocities will not change in this situation. The threshold values mindist and maxdist are determined by experimental observa-tion. The algorithm is summarized in Table 2.

In the present study, we implemented two behaviors for local navigation, namely obstacle avoidance havior and danger behavior. Obstacle avoidance be-havior was designed using the fuzzy-neuro network described above. Danger behavior is activated when the mobile robot is either trapped in a cul-de-sac, or the mobile robot is navigating in a special obstacle conguration that temporarily cannot be resolved by the ultrasonic sensors. A rule was designed to deal

with such circumstances [13]. It instructs the mobile robot to spin around until it nds a direction in which to escape from the unfavorable situation. The direc-tion of spin is determined according to the onboard sensory data. However, when obstacle avoidance behavior and danger behavior are triggered simulta-neously, the latter has priority.

4. Simulation results

In order to verify the eectiveness of the proposed method, we set up a simulation program on a per-sonal computer. The ultrasonic sensors were modeled by taking into consideration the characteristics of wide beam-angle and specular re ections [13]. The sam-pling period for ultrasonic sensor data updating was 0.5 s in the simulation. The velocity commands to the motor controller were assumed to be perfectly exe-cuted. Motion errors due to wheel slippage, surface irregularities, etc., were not considered.

Figs. 6–9 present several simulation results of the proposed fuzzy-neuro navigation algorithm. In these gures, the label ‘S’ denotes the start point and the la-bel ‘T’ denotes the target position. The mobile robot is represented by a circle in proper proportion to the environment. The executed navigation route is de-picted with a sequence of circles, where the positions

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Table 2

The navigation algorithm Dene: mindist = 5; maxdist = 12 dij∗= min (d_i0; d_i1; : : : ; d_i(c−1)); c = 16 IF dij∗= 0 THEN uij∗= 1 uij= 0; j 6= j∗; (j = 0 ∼ 15) vl= vlj∗; vr= vrj∗

where vl: left wheel velocity command

vr: right wheel velocity command

vlj∗: the left reference velocity of the j∗th rule

vrj∗: the right reference velocity of the j∗th rule

ELSE IF 0¡dij∗6mindist THEN uij= P s ⊂ S _d ij dis !−1 ; j ⊂ S dij∗6d_is6maxdist (7)

S: the set of neurons satisfying (7) vl= P s ⊂ S vlsuis (8) vr= P s ⊂ S vrsuis (9) ELSE vl= vl∗; vr = v∗r; where v∗

l the left velocity command of previous sample instant

v∗

r the right velocity command of previous sample instant

of the mobile robot was plotted for every four sam-pling periods. A darker-colored circle was plotted for every 40 sampling periods to enable easier determi-nation of velocity proles. The darker line-segment in each circle denotes the heading of the mobile robot. The size of the outside rectangle area shown in Figs. 6–8 is 12 m×12 m. Fig. 6 presents the robot’s ability to avoid obstacles directly in front of it. Fig. 7 illustrates a situation where a local minimum would be faced using the potential eld method, thus trapping the robot. As shown in the gure, the current design can handle this situation if the rectangles are not so wide. The robot will not move into the concave region and therefore navigate successfully to the target. However, for deeper traps or a closer target position to the obsta-cle as shown in Fig. 8, the mobile robot will move into

Fig. 6. Simulation result of avoiding head-on obstacles.

Fig. 7. Simulation result of navigating in an environment where a local minimum exists.

the concave region and be trapped. In such situations, the danger behavior will come into action and bring the robot out of the trap (see Fig. 8). A wall-following behavior can be added to the navigation system, allow-ing the mobile robot to travel along obstacle’s contour for escaping from the trap [9]. Fig. 9 presents the sim-ulation result of navigating in a long corridor. In this case, the surrounding area was 40 m × 40 m, an ex-ample of our laboratory environment. This simulation

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Fig. 8. Simulation result of encountering a trap.

Fig. 9. Simulation result of navigation in a long corridor.

depicts that the mobile robot can explore an unknown environment exploiting onboard sensory information. 5. Experimental results

Practical navigation experiments were conducted employing a self-constructed mobile robot. It is of

Fig. 10. Experimental result of obstacle avoidance.

cylindrical shape with a diameter about 60 cm. Two drive wheels are placed at the ends of its central axis, and there are two free casters at the front and rear for balance. Motion control is accomplished by dierential-velocity steering using the independent drive wheels. This motion control method has two advantages. One is that the robot can spin 360◦ _in

place; the other is that we can control the robot simply by velocity commands to the two drive wheels. The robot has a maximum travel speed of Vmax = 43 cm=s.

An industrial personal computer AT-486 is carried onboard for navigation control. Two HCTL-1100 mo-tion control chips from Hewlett-Packard are used for motor servo control. The merit of employing these chips is that they accept velocity commands, decreas-ing the computation burden of the onboard computer. The specied traveling speed in these experiments was 20 cm/s and the sampling time was 250 ms. It takes less than 1 ms for obstacle avoidance behav-ior calculation in the current implementation. In the experiments, only the start and target positions were specied. The mobile robot had to nd a collision-free path to the target employing onboard sensory information.

Fig. 10 presents an experimental result in which the navigation path depicts two occasions of turning away from walls and avoidance of a rectangular carton. The recorded trajectory reveals that the robot can avoid

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Fig. 11. Recorded wheel velocities of the experiment of Fig. 10.

obstacles safely and in an ecient manner. Fig. 11 presents the recorded velocity proles of both wheels in this run. They can be used to check the maneuvering of the robot navigation as it encounters obstacles. We see that the danger behavior was not activated in this case. Consequently, a smooth trajectory was executed in obstacle avoidance and traveling to the target.

Fig. 12 presents the experimental result of explo-ration in a long corridor. As in the simulation, only the target position was specied in this experiment; the mobile robot had to explore in an unknown en-vironment employing its onboard sensors. We see in the gure that the recorded route deviates from the actual locations in the corridor. This discrepancy is mainly due to wheel slippage which causes accumu-lated errors in the onboard odometer. Notably, the mobile robot explored the environment safely in this long journey without any collision. The experimen-tal result in Fig. 12 reveals more velocity variations than the simulation result shown in Fig. 9. This is because that there are doors and extinguisher-boxes along the corridor wall, which are concave and con-vex regions for the ultrasonic sensors. Moreover,

Fig. 12. Experimental result of exploration in a long corridor.

actual ultrasonic sensor data contain measurement errors caused by specular re ections and wide beam-opening angle; this also causes velocity variation during navigation. It should be mentioned that this

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method is good for local reactive navigation, the mo-bile robot is controlled by perceptual sensors. For practical applications, a global path planner should be provided for optimal performance.

6. Conclusion

A pattern-recognition approach to reactive navi-gation based on real-time sensory information has been developed and successfully implemented on an autonomous mobile robot. Through the process of prototype-pattern assignment, the proposed fuzzy neural network can be adapted for reactive motion control. By employing a small number of rules, satis-factory performance has been achieved. The amount of computation is therefore reduced a great deal and this enhances the real-time performance of reactive control. Furthermore, this method oers a straightfor-ward mapping between control rules and human-like heuristics. The mobile robot can therefore demon-strate human-like tendencies for continuous motion without stopping for obstacles. Many aspects of this method are worth further investigation in the future. On the one hand, other sensors such as CCD cam-eras can be used for better detection of obstacles. Although the present design can cope with moving as well as stationary obstacles, more accurate perception sensors are required for more complex environmental congurations. On the other hand, optimization of the prototype-mapping can be made to play a more important role in the algorithm.

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