NAFIPS 2005 - 2005 Annual Meeting of the North American Fuzzy Information Processing Society

Autonomous Navigation ofA Underwater RobotUsing Fuzzy Logic

Kyoung-Youb Kwon, Jeongmok Cho, Bong-Soo Yoo, Joongseon Joh*Dept. ofControl & Instrumentation Eng.

Changwon National University#9 Sarim-dong, Changwon, Kyungnam, 641-773, Korea

*Corresponding author: e-mail: jsioh@sarim.changwon.ac.krTel: +82-55-279-7555Fax: +82-55-262-5064

Abstract - A fuzzy logic for autonomous navigation ofunderwater robots is proposed in this paper. The VFF (VirtualForce Field) method, which is widely used in the field of mobilerobots, is modified for application to the autonomous navigationof underwater robots. This Modified Virtual Force Field (MVFF)method using fuzzy logic can be used for track keeping and/orcollision avoidance. The collision avoidance algorithm has theability to handle multiple static obstacles. Results of simulationshow that the proposed method can be efficiently applied tocollision avoidance and track keeping of the underwater robots.

I. INTRODUCTION

Nowadays, as the development of ocean resourcesbecomes very active, the demands for underwater workincrease rapidly. Accordingly, underwater robots for thegeneral inspection of ocean environment and resources emergeimportant subjects of research and development [1, 2].

Especially, autonomous navigation with obstacleavoiding ability is a very important subject and it has to beconsidered in order to prevent damages of the underwaterrobots due to collision with the hazardous objects [3, 4].

The autonomous navigation with obstacle avoidingability is also very important subject to mobile robotresearchers. One of the famous algorithms is the so-calledvirtual force field (VFF) algorithm. It has been applied to themobile robots very actively and outstanding results have beenreported in the literature [5-8].

The authors modified the VFF (MVFF) using fiuzzy logicin order to make the algorithm more sophisticated and appliedto the autonomous navigation of a ship [9]. This paper is anextension of the MVFF to the underwater robots. The 2Dproblem is extended to 3D and the fuzzy logic became moresophisticated. This paper handles multiple static obstacles.

Collision avoiding navigation of underwater robots isdivided into two consequent stages, which are keeping thepredefined reference track and collision avoidance behaviour.The proposed algorithm modified the VFF method to providetrack keeping capability in conjunction with collisionavoidance in the presence of multiple static obstaclesintelligently. Fuzzy logic is adopted to implement export'sknowledge. Four linguistic variables are used in the premisepart to include many cases of possible collisions.

In this paper a fuzzy logic for collision avoiding

navigation of underwater robots is proposed. In section 2 ofthis paper we will briefly discuss about the dynamicsmodeling of the underwater robots. Section 3 discusses aboutthe proposed MVFF. A fuzzy logic for collision avoidance andtrack keeping is presented in Section 4. Section 5 is thesimulation results for behavior of the underwater robots.

II. DYNAMICS OF UNDERWATER ROBOTS

The underwater robot is assumed to be a freelyswimming rigid body. A rigid body in 3-dimensinal space has6 degrees of freedom. In addition to the rigid body dynamicsand gravitational forces, an underwater robot is influenced byhydrodynamic forces like added inertia forces, hydrodynamicresistance, and buoyancy [10]. In [11] and [12], the equationsof motion for a 6 DOF underwater robot is formulated as

(1)

where Mq 7(q) is the inertia matrix including both rigid-bodymass and added mass, C7(v, 7) is the Coriolis and centripetalmatrix including rigid-body mass and added mass, D7(v,17) isthe total hydrodynamic matrix that includes radiation-inducedpotential damping, linear skin friction, wave drift damping anddamping due to vortex shedding, gq (q) contains the restoringterms formed by the underwater robot's gravitational andbuoyancy terms and r. includes the control forces and

moments. q = [x, y, z, 0, 9, V]T denotes the position andorientation vector with coordinates in the earth-fixed frame,V = [u,v,w,p,q,r]T denotes the linear and angular velocityvector with coordinates in the body fixed frame. It is assumedthat the behaviour of the underwater robot is controlled byhorizontal fin (or stern plane) and vertical fin (or rudder). Thetwo fins operate independently of each other. In this paper, theauthors designed a simple submarine-type underwater robotjust mathematically for this research using [12], so thedynamic behaviour may not be good. It was enough, however,for this research since the purpose of the research was thefeasibility study of the proposed algorithm.

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III. MODiFiED ViRTUAL FORCE FiELD METHOD

The basic concept of the VFF algorithm which is appliedto the mobile robots comes from the Coulomb's law. The goalattracts the mobile robot while the obstacle repels it, as in thecase of electric charges [5-8]. Figure 1 and equation (2) showthe concept of VFF. It can be seen that it has no function oftrack keeping, i.e., the mobile robot just goes to the goal fromthe present position.

GOAL

IFF

ROBOT

Fig. 1. The concept of the VFF method.

R=Fa+Fr (2)where F0 is the attractive force heading the goal, Fr is therepulsive force against the obstacle, and R is the resultant ofall forces. The magnitude of F0 and F. are constants or simplefixed functions. There usually exists predetermined track(usually the shortest path between neighboring points), whichthe underwater robot has to follow as precisely as possible forsome special applications. The operation of searching the seabottom may be the example. The original VFF method,however, fail to offer the flexibility and robustness needed toaddress this concern, which is important in the navigation ofunderwater robots. Consequently, we offer a modified VFF,which is capable of operating in either 'track keeping' or'collision avoidance'.The MVFF adds one more force vector, i.e., Fp, to the

equation (2) which plays track keeping role. Figure 2illustrates the concept of MVFF.

whereFa: attractive force heading next waypoint,

Fr, Frg repulsive force against obstacles, i = 1, 2, ..., n,

F.: perpendicular force returning to the predefined track,

R: resultant of all forces.

One of the novel ideas of the MVFF is in determination ofthe force terms in the equation (3). Equation (4) shows theway of determining the force terms in the MVFF algorithm.

Fa =ae

Fp = (p (4)

Fr = Teri+ er2 + * * + erz)where Ja is the unit vectors directed towards the next waypoint, ep is orthogonal to predefined track and is directed

towards the predefined track. "rHI 'r2 and ei, are unit vectorsdirected away from the given obstacles. a, Ai, and y areparameters which determine the magnitudes of each forceterms. Sophisticated fuzzy logics determining the parametersare devised to handle various situations which can be facedduring autonomous navigation ofunderwater robots.

IV. Fuzzy LOGIc FOR TRACK KEEPiNG AND COLLISIONAVOIDANCE

In this paper, the gains a, /1, and y for vector F, Fp,

and Fr are obtained from the fuzzy logic. These algorithmshave the ability to handle track keeping and collisionavoidance in various obstacles environment.The proposed algorithm modifies the VFF method to yieldMVFF method. The MVFF method consists of two majormodes in order to accomplish track keeping and collisionavoidance.

A. Fuzzy Logicfor Track keeping

Z tFig. 2. The concept ofMVFF.

The concept of the MVFF can be represented as

R=F +Fp +Fr =Fa+Fp+(Fr+Fr2+---+Fr) (3)

a and f8 are constants which are determined fromcorresponding fuzzy rules. Properly designed set of fuzzyrules for a and , provides efficient track keeping of theunder water robot to the desired track from its deviatedlocation.

S B

Fig. 3. Termn set for da

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Fig. 4. Term set for v.

c Z* 1I

9

a.

C.8A

t S]E/R~~~~~~a 0

Fig. 5. Term set for a

TABLE IRULE TABLE FOR a

Va S M B

da _

Z B B BS S S Su

B Z Z Z

Figure 3 represents the term set for the linguisticvariableda. It consists of {Z(ero), S(mall), B(ig)1. Figure 4represents the term set for the linguistic variable va . Itconsists of {S(mall), M(edium), B(ig)}. Figure 5 representsthe term set for the linguistic variable a . It consists of{Z(ero), S(mall), B(ig)). Table I shows rule table fora .

C~~~~~~.= I

a.S.a.0:22)

B

0 0 ~~~~~~~~~~~~~~~~~~~1Fig. 8. Term set for f/

TABLE IIRuLE TABLE FOR /3

e~\ N Z BAefi-

N B S ZZ S Z BB Z S B

Figure 6 represents the term set for the linguisticvariableep. It consists of {N(egative), Z(ero), P(ositive)}.Figure 7 represents the term set for the linguistic variable Aefi .It consists of {N(egative), Z(ero), P(ositive) }. Figure 8represents the term set for the linguistic variable 13. Table IIshows rule table for 13.

B. Fuzzy Logicfor Collision Avoidance

Basically, the VFF method yields good collisionavoidance performance. However, collision situations forunderwater robots are generally complicated. The originalVFF is not so flexible to handle these complicated situations.The proposed MVFF method introduces the concept of thevector of collision avoidance Pr . It is illustrated Figure 2.

.'oN ~Z P.u I

.2I-

a l 0 1

Fig. 6. Term set for X

§N ~ ~Z PES,

2

0Fig. 7. Term set for Aefi

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L

9z '-,1 I

Fig. 9. Term set for D

assumed that the real time position of the obstacles can besensed.

Figure 12 shows the ability of the MVFF algorithm fromthe view point of track keeping accuracy over the so-calledVFF algorithm which has been used widely in the field ofautonomous navigation of mobile robots. It can be seen easilythat the well-designed MVFF outperforms the conventionalVFF algorithm.

.0 NB NS ZR PS PB

XX lE

cI ~~~0 1Fig. 10. Tern set for AD,,

S M B VB

Quo iFig. 11. Term set for y

TABLE IRULE TABLE FOR V

NB NS ZR PS PB

Z VB VB VB VB VBS VB VB VB VB BM VB B M S ZB B M S Z ZVB M S Z Z Z

Figure 9 represents the term set for the linguisticvariableD7. It consists of {Z(ero), S(mall), M(edium), B(ig),V(ery)B(ig) }. Figure 10 represents the term set for thelinguistic variable AD, It consists of {N(egativ)B(ig),N(egative)S(mall), Z(e)R(o), P(ositve)S(mall),P(ositve)B(ig)}.Figure 11 represents the term set for the linguistic variable y.It consists of {Z(ero), S(mall), M(edium), B(ig), V(ery)B(ig)}.Table III shows rule table for y.

A1S

E --30_s~

Start Waypointl

Fixed eqauation

a t

-100

yarnj(a) 3D plot of track keeping performance

<ao £ bsiac1eAioundayzagion +: *3YIT 4 ±c<j X * X * 'N *.-50 _ _ _ _ _ _ _ _ _

100 150 200 250 300 350 400 450 500 5atmi

(b) 2D plot in xy-plane

V. SIMULATIONSIn this paper, an extensive simulation study is performed

to verify the validity of the proposed algorithm. It is assumedthat the underwater robot is following the predefined trackwhich is made by connecting two adjacent waypoints.Multiple obstacles are placed around the track. It is also

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, -i ' -. - - Fixed equationFuzzy logic

F~~~~~~~~1

0

olW.S.

I04.0

L

.aypoi*tl Constant-150 _~SF X z . s ~ ~ Fixed equation

Fuzzy logic

450 ... 4..~~.......

KARYp4iftz -

100 150 20 250 300 350 400 45 50 S5

(c) 2D plot m xz plane

*~~~~~~~~~ IN

Constant- - - Fixed equation

.200 Fuzzy logic

-300

3450

_ 00--- ,..40.- A, + +w

*: ,4TaypoihtiStart l/

650 500 450 400 -350 -300 -20 -200 460-100 -50ylm]

(d) 2D plot in yz-planeFig. 12. Performance comparison of the MVFF and VFF algorithm

-450

Wagintl

Obstacle boun4ary

200

250D

3,50-400

-300-2150.

4100

450x[m]

(a) Avoiding two obstacles

-300~~~ ~ ~ ~ ~~~~~0-300 ,... 400

.400~~~~~~~0y[m] 5J 2

(b) Avoiding three obstaclesFig. 13. Collision avoidance of the MVFF algorithm in presence of multiple

obstacles

Figure 13 illustrates the ability of the MVFF algorithm inavoiding multiple static obstacles. It shows the MVFFalgorithm avoids any number of obstacles nicely whilekeeping the predetermined track as close as possible.

VI. CONCLUSION

An algorithm for collision avoiding autonomousnavigation of underwater robots is proposed in this paper. TheMVFF(Modified Virtual Force Field) method is newly devisedto yield the track keeping and collision avoidance.

The novel idea of using three parameters a, f8, and ywith sophisticated fuzzy logic provides great flexibility inhandling more complicated situations of autonomousnavigation of underwater robots. Multiple static obstacles canbe avoided with the proposed algorithm. Various simulationresults are presented to verify the validity of the proposedalgorithm. It can be extended to include multiple movingobstacles and will be the theme of the next paper.

ACKNOWLEDGMENT

This work was supported by the Machine Tool ResearchCenter at Changwon National University.

REFERENCES[1] Jeen-Shing Wang; Lee, C.S.G., "Self-adaptive recurrent neuro-fuzzy

control of an autonomous underwater vehicle Robotics andAutomation," IEEE Transactions on, Vol. 19, Issue. 2, pp. 283 - 295,April 2003

[2] Ishii, K., Nishida, S., Watanabe, K, Ura, T., "A collision avoidancesystem based on self-organizing map and its application to anunderwater vehicle Control," Automation, Robotics and Vision, 2002.ICARCV2002. 7th International Conference on, Vol. 2, 2-5 Dec. 2002.

[3] Sayyaadi, H., Ura, T., Fujii, T., "Collision avoidance controller for AUVsystems using stochastic real value reinforcement learning method,"

544

EN

'Ei

Proceedings of the 39th SICE Annual Conference. Intermational SessionPapers, pp. 165 - 170, 26-28 July 2000.

[4] Xuemin Liu, Liang Peng, Jiawei Li, Yuru Xu, "Obstacle avoidanceusing fuzzy neural networks Underwater Technology," 1998.Proceedings of the 1998 International Symposium on, pp. 282 - 286,15-17 April 1998.

[5] A. A. Masoud and M. M. Bayoumi, "Robot navigation using the vectorpotential approach," Proc. of IEEE international Conference onRobotics andAutomation, vol. 1, pp. 805-811, 1993.

[6] Kwang-Young Im, Se-Young Oh, "An extended virtual force field basedbehavioral fusion with neural networks and evolutionary programmingfor mobile robot navigation," Evolutionary Computation, 2000,Proceedings of the 2000 Congress on, Vol. 2, pp. 1238 - 1244, 16-19July 2000.

[7] Kwang-Young lim, Se-Young Oh, Seong-Joo Han, "Evolving a modularneural network-based behavioral fusion using extended VFF andenvironment classification for mobile robot navigation EvolutionaryComputation," IEEE Transactions on , Volume: 6 , Issue: 4 , pp. 413-419, Aug. 2002.

[8] J. Borenstein, "Real-time obstacle avoidance for fast mobilerobot,"IEEE Transactions on Systems, Man and Cybernetics, Vol. 19,No. 5, pp. 117 9-1187, Sept./Oct., 1989.

[9] Joongseon Joh, Kyung-Yup Kwon and Sang-Min Lee, "CollisionAvoiding Navigation of Marine Vehicles Using Fuzzy Logic,"International Journal ofFuzzy Logic and Intelligent Systems, Vol. 2, No.2, pp. 100-108, June 2002.

[10] Donald P. Brutzman, "A Virtual World for an Autonomous UnderwaterVehicle," dissertation, Naval Postgraduate school, Monterey California,1994.

[11] T. I. Guidance and Control ofOcean Vehicles, John Wiley & Sons Ltd,Chichester, 1994.

[12] A. J. Healey, and D. Lienard, "Multivariable sliding mode control ofautonomous diving and steering of underwater vehicles," IEEE JournalofOcean Engineering, OE-18,3, pp.327-339, 1993.

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