Neuro-fuzzy controller for mobile robot navigation with avoiding obstacles and reaching target behaviors.

Popescu, Cristina ; Paraschiv, Nicolae ; Cangea, Otilia 等

1. INTRODUCTION

In the latest work, the authors implemented on the Khepera III mobile robot a neuro-fuzzy controller which realizes the obstacle avoidance behaviour (Popescu et al., 2008). But in the navigation process of the robot, it is the possibility that the robot lets in a cycle which repeats continuously, so the authors proposed a neuro-fuzzy controller structure which implements reaching target behaviour beside the obstacles avoidance behaviour. The results are obtained by simulation, because the Khepera III robot has not the necessary sensorial system for implementing reaching target behaviour. To resolve this problem, one can be use a simple optical sensor with a rotate mirror or a global positioning system (GPS). Furthermore, the robot has to be equipped with a speed sensor to measure its current speed. In 2007, the same problem was studied by Zhu and Yang (Zhu and Yang, 2007) and they proposed an algorithm for robot navigation with target reaching behaviour. In this paper, the authors process this algorithm and adapt it for the mobile robot Khepera III.

Because the results are obtained by simulation, the authors intend to implement this neuro-fuzzy control structure on a real Khepera III robot.

2. MOBILE ROBOT CONFIGURATION

The mobile robot used for our experiments is Khepera III. This is an educational mobile robot that is ideal for artificial intelligent techniques implementation used for robot control. The sensorial system comprises an array of 9 Infrared Sensors for obstacle detection and 5 Ultrasonic Sensors for long range object detection (20 cm to 4 meters). The robot has an optional front pair of ground Infrared Sensors for line following and table edge detection (www.k-team.com). The robot motor blocks use very high quality DC motors for efficiency and accuracy.

3. SYNTHESIS OF A NEURO-FUZZY

CONTROLLER

The inputs of the neuro-fuzzy controller used for robot navigation are the distances from obstacles, obtained by left, front, right sensorial groups, like in figure 1, the robot speed and target direction.

[FIGURE 1 OMITTED]

For the Khepera III mobile robot the target direction 6d represents the angle between the movement direction of the robot and the line which connects the center of the robot with the target. The robot speed vs represents the current speed of the robot.

The outputs of the controller are represented by the two motor wheels accelerations, as and ad.

The inputs of the neuro-fuzzy controller have associated the following inputs variables: for distances to the obstacles - far and near, for robot speed - fast and slow, for target direction left, center and right. The outputs of the controller have associated the linguistic variables big positive, small positive, zero, small negative, big negative (Popescu et al., 2008).

The structure of the neuro-fuzzy controller is the one presented in figure 2, the respective design methodology following the known stages, which are: fuzzication, inference mechanism and deffuzification.

The fuzzification algorithm converts the real input values in fuzzy linguistic terms with membership values between 0 and 1. In order to realize this transformation, the authors proposed and defined in the Matlab(r) language the membership functions for the input variables and added these to the predefined list existing in the fuzzy toolbox of Matlab(r). The membership functions for the inputs are triangular, S type and Z type functions which were adapted for the existing situations. In figure 3 are illustrated the graphical representations of the membership functions of some inputs.

The membership functions of the outputs are singleton functions, with constant values.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

The adaptation process for membership functions stands on the learning algorithm with neural networks. To eliminate redundant rules which may appear, one used a separate algorithm (Godjevac, 1997). In different situations under the proposed control structure, the mobile robot can generate good trajectories to the target without "dead cycle" problem.

The inference system of the fuzzy controller is based on inference rules like the one described below:

If distance to the left from obstacle is near and distance to the front from obstacle is far and distance to the right from obstacle is far and direction to the target is right and robot current speed is slow

Then left wheel acceleration is positive big and right wheel acceleration is positive small.

The rule base for achieving the two behaviours, avoiding obstacles and reaching a target, consists of 48 rules formulated by the authors. Six of these rules are presented in table 1 with specification of the realized behaviour.

For the defuzzification algorithm the authors proposed the gravity center method (Wang, 1994). The output variables, respectively the wheel accelerations as and ad, are given by the following relations:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where [v.sub.k,1] and [v.sub.k,2] are the estimated values of the output which are made by the k rule, in respect to the membership functions centers of output variables; k is the rule numbers; [q.sub.k]=min{[p.sub.lkl], [P.sub.2k2], [P.sub.3k3], [P.sub.4k4], [P.sub.5k5]}; [P.sub.iki] is the membership range for the i input coresponding to k rule; i represents the number of input values.

[FIGURE 4 OMITTED]

It was obtained a minimal number of rules for the rule base by using a tuning parameters algorithm and deleting of redundant rules.This algorithm become expedient for the rule base with hundreds or thousands rules.

By simulation in the Matlab[R] language the authors observed that the robot gets to learn the two behaviours, obstacles avoiding and reaching a target, the final value of the error being very small, about 0,079, as presented in figure 4 (Popescu, 2008).

4. CONCLUSIONS

The actual trend for navigation of the mobile robots is the analysis of investigation techniques based on rules and neuro-fuzzy techniques based on rules. In this paper the authors proposed a neuro-fuzzy control structure which implements avoiding obstacles and reaching target behaviours, according to the main target of the robot which, generally, is to realise some predefine objects.

It was observed a good deportment of the robot in the navigation process with the rule base proposed by the authors, the main contributions of these being the implementation of the membership functions associated to the neuro-fuzzy controller inputs in the Matlab[R] language. These functions were introduced in the fuzzy toolbox of Matlab[R] beside those of the fuzzy inference system.

One can conclude that the problem of "dead cycle" which may appear during the robot navigation was solved only by simulation.

For future researches, the authors want to adapt or modify the sensorial system of the real Khepera III mobile robot in order to implement on it the neuro-fuzzy controller proposed in this paper which implement avoiding obstacles, reaching target behaviors and some predefined objective.

5. REFERENCES

Godjevac, J. (1997), Neuro-Fuzzy Controllers Design and Application, Presses Polytechniques et Universitaires Romandes, ISBN 2-88074-355-9, Lausanne

Popescu, C., Bucur, G., Popescu, C., Neuro-fuzzy Control for Khepera III Mobile Robot, Proceedings of The 19th International DAAAM Symposium, "Intelligent Manufacturing & Automation: Focus on Next Generation of Intelligent Systems and Solutions", pp. 1117-1118, ISSN 1726-9679, Trnava, Slovakia, October 2008

Popescu, C. (2008), Neuro-Fuzzy Control for Mobile Robot, PhD Thesis, Ploiesti, Romania

Zhu, A., Yang, X.S. (2007), Neuro-Fuzzy Based Approach to Mobil Robot Navigation in Unknown Environments, IEEE Transactions on Systems, Men and Cybernetics, Part C: Applications and Reviews, vol. 37, issue 4, pp. 610-621, ISSN 1094-6977, july, 2007

Wang, L.X. (1994), Adaptive Fuzzy Systems and Control Design and Stability Analysis, Prentice Hall, ISBN: 0-13099631-9, Upper Saddle River, NJ, USA

*** (2008) http://k-team.com--K-Team Corporation, Khepera III Documentation, Accesed on 2008-05-10

Tab. 1. A part of rule base

 Input

Rule [D.sub.s] [D.sub.f] [D.sub.d] [[theta].sub.d] [v.sub.s]

1 far far far left small
2 far far far left fast
3 far far far center slow
4 far far far center fast
9 far far near center slow
10 far far near center fast

 Output

Rule [a.sub.s] [a.sub.d] Behaviour

1 positive small positive big reaching target
2 negative small zero reaching target
3 positive big positive big reaching target
4 zero zero reaching target
9 zero positive small avoiding obstacles
10 negative small zero avoiding obstacles