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

A Modular Neural-Fuzzy Controller forAutonomous Reactive Navigation

James L. Overholt, Gregory R. HudasU.S. Army RDECOM-TARDEC

Intelligent Vehicle Research TeamWarren, Ml

(im.overholt or greg.hudas})us.army.milAbstract - Fuzzy systems are modular by definition but lack

the trainability of neural networks. We will introduce amodular, neural-fuzzy system called Threshold Fuzzy Systems(TFS). A TFS has two unique features that distinguish it fromtraditional fuzzy logic and neural network systems; (1) therulebase of a TFS contains only single antecedent, singleconsequence rules (called a Behaviorist Fuzzy Rulebase (BFR))and (2) the fuzzy inference mechanism is modified to incorporatea highly structured adaptive node network (called a RuleDominance Network - RDN). Each rule in the BFR is a directmapping of an input sensor to a system output. Connectionnodes in the DN occur when rules in the BFR are conflicting.The nodes of the DN contain functions that are used to suppressthe output of other conflicting rules in the BFR. Severaldifferent approaches to tuning the unknown parameters of thedominance function can be used; including supervisory trainingmethods, self-organizing and evolutionary-based exploration.For the supervisory training approach, a unique gradient-matrixerror back-propagation algorithm (GMEBA) has been developedand will be discussed.

1. INTRODUCTION

Hierarchical systems contain multiple objectives that needto be satisfied in order for the overall system to perform itsdesigned function. These tasks will each have an associatedpriority, which is used to properly place the emphasis of thesystem control. The control policy created for this type ofhierarchical structure must strive to accomplish all of the tasksaccording to the order dictated by the relative priorities. Inactuality, the priority listing of each task is not fixed but willchange based on factors such as the current state(s) of theplant and the magnitude of the control (called a varying or"dynamic" priority hierarchy).

In addition, these priority changes will occur with verylittle (if any) forewarning (Figure 1). Perhaps the biggestconcern is that with the shifting priorities of the system, if alower priority task is accomplished it may result in the systembecoming unstable. Hierarchical systems control policiesneed to incorporate a structure, which tries to anticipate andhandle priority changes in the multiple tasks of the system.

The field of mobile autonomous robots must dealprecisely with the varying priority issues as stated above.Although a mobile robot can have a myriad of possible usesthe ability to change or alter its immediate goal, in the face of

K. C. CheokElectrical and Systems Engineering Department

Oakland UniversityRochester, Ml

cheok@oaklandedu

new or unexpected conditions, is one of the most desirabletraits that designers strive for.

Figure 1: Task Priority Listings

In his seminal paper, "A Robust Layered Control Systemfor a Mobile Robot" [2], Rodney Brooks proposes a layeredcontrol approach where the control strategies are built uponfundamentally simple control behaviors (e.g. avoid objects).While the system is running, all of the layers are processinginformation without the benefit of any central control. Whena conflict occurs, the system will default to a lower layerprocess. Brooks called this de-centralized, layer-based controlthe subsumption architecture. Outputs can be inhibited (bythe outputs of other layers) and inputs to the layers can besuppressed. This is the mechanism in which higher-levellayers subsume the role of lower levels. Brooks' subsumptionarchitecture allows simple insect-like mobile robots tomaneuver and navigate in an instinctual way.

II. THRESHOLD FUZZY SYSTEMS

Neuro-fuzzy systems are defined by the integration ofneural network structures into the mechanics of fuzzy systems[3]. We now introduce a new modular, neural-fuzzy systemcalled Threshold Fuzzy Systems (TFS). A TFS has twounique features that distinguish it from traditional fuzzy logic[4]; (1) the rulebase of a TFS contains only single antecedent,single consequence rules (called a Behaviorist Fuzzy

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Rulebase (BFR)) and (2) a highly structured adaptive nodenetwork (called a Rule Dominance Network (RDN)) isadded to the inference engine. Each rule in the BFR is adirect mapping of an input sensor to a system output.Connection nodes in the RDN occur when rules in the BFRare conflicting. The nodes of the RDN contain functions thatare used to suppress the output of other conflicting rules in theBFR. Supervised training is used to find the optimalparameters of the suppression functions.

-, " .- - .--,l .-l; |area of triangle =contribution of rule 21Figure 3: Geometric Interpretation ofRule Contribution and De-fuzzification

Normalized rule contribution is defined as the ratio ofthe rule contribution to the maximum allowable rulecontribution.

Figure 2 shows the components of a TFS. Besides thecommonly known components of a fuzzy logic system(fuzzification and de-fuzzification layers, inference engineand rulebase) it also contains the new RDN structure. Xrepresents the crisp inputs into the system, Y is the crispoutputs of the system, C is the contribution of each individualrule and D is the dominated contribution of each rule.

The two most important concepts of threshold fuzzysystems involve the definition of rule contribution and thenotion of rule conflict. The next sub-sections describe theseconcepts in greater detail.

III. RULE CONTRIBUTION DEFINITION

Rule contribution is used to compute the crisp output of afuzzy logic system [4]. The rule contribution is a measure ofhow much each rule in the rulebase is influencing the finaloutput. In geometric terms, the contribution of an individualrule is measured as the area of the scaled triangle (i.e.membership function) that remains after the rule inferenceprocess (Figure 3).

Mathematically, the rule contributions are described as

follows;

Cl = fPA(X) s(y) dy =PA(X) ps(y) dy

C2 = fpB() rT(y) dy =(JF) fp, (y) dy

These concepts of rule contribution are based on a fuzzysystem using product inferencing [4]. If other inferenceengines were being utilized then the contributions (bothstandard and normalized) would be different.

IV. FUZZY RULE CONFLICT DEFINITION

Given the single-input, single-output structure of the rulesin a threshold fuzzy system, many of the rules will haveconsequence portions of their rules in direct conflict. Forexample, the following two rules are said to be in fuzyconflict because their consequences differ for the same controlvariable.

Rule 1: If the target is straight_ahead then the throttlecommand isfast.

Rule 2: If an obstacle is detected straight_ahead then thethrottle command is stop.

For this simple example, the control variable (for eachrule) is throttle command. In Rule 1, the throttle command isfast. In Rule 2, the throttle commnand is stop. A standardfuzzy system would combine the resulting contributions ofeach rule during the aggregation phase of the process [6].This would normally result in a throttle command somewherebetween stopping and the fastest speed possible. However,there may be situations (or regions) where you would like onerule to dominate the other. If an obstacle were detectednearby, directly in front of the vehicle, you would want theAVS to stop. If the obstacle detected were directly behind the

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JIIA(X)fl(Y)dY_yfcCma f'U'8 8(y) dy{<l}x |'UJ5(y) dy

6- C2 Jf(X)Jlr(Y)'dYC2 = = =iJr(Y){C2 m. f|U T(Y) dY

UA()

vehicle, then you would want the throttle command to be fast.A formal definition of fizzy conflict [5]:

The fuzzy conflict definition presented above does notinclude any restrictions on the input variables (in this case Xland X2) or the input antecedents (A and B). There are specialcase rules when conditions are placed on these parameters inorder for conflict to occur; however these caveats still producethe 3 conditions for fuzzy conflict. Also note that with thisdefinition, no rule can conflict with itself [5].

V. RULE DOMINANCE NETWORK DEFINITION

With the concept of rule contribution, we have an ideahow each rule contributes to the whole. With fuzzy conflict,we have a formal definition of the conflicting commands thatcould occur in a rule-based system. Threshold Fuzzy Systemsinclude an additional neural network -like structure that isused to modify the contribution of each rule in the BFR. Thisadditional inference engine is called the Rule DominanceNetwork.

An RDN is an adaptive node network where each nodehas 2 inputs; one is the contribution that is being dominatedand the second is the dominating contribution. Thiscorresponds to a conflicting pair of fuzzy rules from the BFR.Each rule contribution is altered as it passes through a seriesof nodes. The level of modification at each node is dictatedby a dominance function. It is the dominance functions,which determine the regions where one conflicting rule can

partially (or totally) dominate another rule. Each individualdominance function will use the conflicting normalized rulecontribution as its independent input variable.

Once the rule contribution has passed through all of thenodes along its contribution path, the final node output servesas the final dominated rule contribution (i.e. if the BFS has'k' rules, then Ci,k= Di). Figure 4 shows a K-Rule TFS withan RDN. The nodes with '1' represent the locations wherethere is either no conflict between rules or an individual rulecannot conflict with itself

A. Dominance FunctionsThe most commonly used dominance function is the

sigmoid function [3].

f (C )-- 11 + A-bs)

This sigmoid dominance function describes the scalingthat occurs when the jth rule dominates the i' rule. In order toobtain a desired response, it becomes necessary to shape theregion where the domination takes place by varying the valuesof mij (the slope of the sigmoid dominance function) and b1j(the mid-point locator of the sigmoid dominance fimction).We will use the sigmoid as the basis for all dominancefunctions in the RDN. The sigmoid is also commonly usedfor the activation and squashing functions associated withneural networks.

Another commonly used dominance function in thisresearch is a Dirac function [3] (Figure 5).

ci

C .~f

{ 0 if

Figure 5: Dirac Dominance Function

If the dominating rule has non-zero contribution then thedominance function annihilates the incoming contribution.Otherwise the incoming contribution passes unchanged.

VI. AVS MODELING

The AVS used for this research is based on a poweredwheel chair. The left and right rear wheels are individuallymotorized (allowing for skid-steer maneuvers) and the singlefront tire acts like a castor. The AVS also contains a series ofidealized sensors (Figure 6). There are 6 idealized proximityor "sonar' sensors placed around the vehicle as well as a

directional targeting beacon. The sonar sensors return a

distance from an obstacle (within each lobe) while thetargeting beacon returns the current angle to the target.

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Given the two behaviorist rules:

If X1 is A then Y is S and If X2 is B then Y is T

Then the rules are said to be in Fuzzy Conflict if all of thefollowing 3 conditions hold:1. The Output Variables are identical (i.e. the output

variable for each rule is Y).2. The Output Consequences are not identical (i.e. S . T).3. The Contributions of each rule are both non-zero.

Figure 6: Autonomous Vehicle System

A. AVSKinematics and SimulationThe final difference equations used for the kinematics of

the AVS were computed by Overholt [5] and are presented inthe following equations.

Xk+1 = Xk + Vk+l .Cos(l) -At

Yk1 = Yk + Vk+l .sin(0kl)eAt

k {k+sgn(AO)-K4.At, IA1>>k, AAt0k+l k+ 0=^| XA

VMAXI Vk,I > VMAXVk+l = Vk+A, VMZN SVk+V S VMAX

VMIN, Vk+i < VMIv

The new AVS velocity and heading angle are determinedby knowing the dynamic capabilities of the steering andthrottle systems. KE is defined as the maximum change inheading angle of the AVS, for one second of time. K, isdefined as the maximum change in velocity of the AVS, forone second of time. These maximums are determnined by thephysical and performance limitations of the AVS. AVSpower characteristics as well as steering kinematics may limitboth the speed and steer capabilities ofthe vehicle.

In addition, the AVS is governed at a maximum andminimum speed (vMux and vmN, respectively). These speedlimitations are based on performance requirements as definedin the rules of the International Ground Robotics Competition(IGVC) [6]. The IGVC is a yearly competition whereautonomous vehicles compete against each other in a series oftasks designed to showcase their capabilities in obstacleavoidance, path planning and trajectory tracking. Eachvehicle must be governed at a maximum forward speed (-5mph) and a maximum reverse speed (-1.5 mph). This robot isbeing built for participation in this competition.

B. Target and Obstacle KinematicsIn the simulation of the AVS, the target is known in terms

of the global coordinate system (GCS). The AVS is alsoknown in terms of the GCS. The angle to the target iscalculated as a relative position with respect to the local frame

of the AVS system. All sonars of the AVS are idealized, inother words they reflect directly back to the emitter base anddo not scatter. All sonars can also fire simultaneously (this isuniquely different from an actual sonar array, which fire in aspecific pattern in order to reduce the scatter and resultingfalse readings).

In the simulation of the AVS, the obstacle positions areknown in terms of the global coordinate system. The AVS isalso known in terms of the GCS. The vector to each obstacleis calculated as a relative position with respect to the localframe of the AVS system. Once the relative position vector toan obstacle is calculated, it can be determined if the obstacle isbeing detected (i.e. is db, < sonar detection threshold) andwhich sonar lobe (or lobes) the obstacle lies in. Knowing thisinformation allows the controller to make steer and throttledecisions based on localized observations.

The AVS is simulated and animated using MatlabTM. Inthe AVS simulation, the vehicle has 120 seconds to find atarget on a 150' x 150' field. The field is randomly strewnwith obstacles. If the cart center ever comes within 3 feet ofan obstacle the simulation ends unsuccessfully. Likewise, ifthe AVS comes within 3 feet of the target the run endssuccessfully (Figure 7).

Figure 7: Simulation Structure of the AVS, Target and Sonar Kinematics

VII. THE BFR AND COMPANION RDN OF THE AVS

The BFR for the AVS steering and throttle commandswere found subjectively based on the repeated usage of aninteractive simulation model of the robot moving throughrandomly generated obstacle courses (Figure 8). For thisresearch, we used 10 rules for the speed controller and 15rules for the steering controller. For the speed commands, thechoices of linguistic outputs were narrowed to 'reverse' (R),'stop' (ST), and 'forward' (F). For the steer commands, thechoices were narrowed to 'turn left' (L), 'straight' (S), and'right' (R).

One of the other advantages of the TFS approach is nowpresented. With the BFR chosen, the connection structure ofits companion RDN is automatically fixed. Figure 9 showsthe steer RDN. Each '*' in the RDN represents a conflicting

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pair from the Steer BFR.

o#t.(neg)ouLO.,(ng) -* us()(z 4 uo(1Q^4r(neg) -+ us(R) 41,.,.zr) -o u41t(5)

otar(-)+ u,(ST) Oir(PS) 4 u5t(R)Otor(z) -> u. (F) ol,(pos) "Ous(R)

u*u(5T) d1(c/) uouf?(R)o (nr) uo (R)Otbar(pos) ........(I)..........

d2(fr) -* u5w(F) c4(nr) -* u,,(R)d2Qip) -+ UVp(F) d2(c/) usl(L)

( ).......

4(c/) -* u.(5T) d3(nr) -L

uSt)d5(c/) - u,(R)

............................... ....................

d6(cI) -4 U"(L)Figure 8: Speed and Steer BFR

'=l ( (j=14.i __)__=__( )

Y15= k ( -(k Ak VPIt-"FS AP

L c IICiP11 f;j(CjP)i=l vvj=l,j;ti i=l

Using input-output training data, the slope (mij) andcenter (bij) of each dominance function can be iterativelyfound. The update equations (in matrix form) for m1j and bijare given as:

41mj(q+1)[ 1 IL4ilj(q) 0

=C,PDP.(y1P ;(Cf)). ( F21, j ~~~~~~~~(VP)2

11

1 * * *1 * * ** 1 * *

* * 1 1* * I 1

'* *

'* *

* *

.1 1

,1 1

'tI1 * *'

* *

.* 1 I

'.** 1 1',

11

* *

* *

* *

*

*

*

1

1 l* **** .**1 *~1.**j1

.. .. .. .. .. ... ... ...

1 1 * * *.*-*1 1 **.1 1.*

:1*****1

11***'**.1 1 **~~~~~~~~~~~~~~..'1......

....* ...* ... ...... ...

11 ,1 1 1 1'

-4

-> 4

-044->D4-4

4041

-42-+43-44-45

Figure 9: AVS Steer RDN Fill Pattern

VIII. UPDATING mij AND b,ij

A gradient matrix error back-propagation algorithm(GMEBA) [5] (along with an interactive simulation used foracquiring training data [7]) is implemented to fmd theparameters of each dominance function of the speed and steerRDN.

The update equations for the slopes and centers of thesigmoid require finding a closed form expression for theoutput of the TFS when (a) product inferencing is used as themain production engine and (b) a CAD technique [4] is usedfor the de-fuzzification scheme. The superscript 'p' in theexpressions refers to the ph exemplar from the training set.

a and ,B are learning rates for the GMEBA. The datafrom these simulations was used in the GMEBA to obtain thefinal dominance functions of the speed RDN (Figure 10) andsteer RDN (Figure 11). The derived parameters are found in[5].

d:,(cl) 4u(R)Q: d4(dl) u,,(ST'

R4 4,.(neg) - u,(R)P, :Ota(pos) -UP: d2(nr) -÷u(STR,: 0(r(n) +u,(ST)

ot,,(p) u,,(ST)Q: d,(fr) uv,(F)

plo: d, (np) u,p(F)

,1: znrg) u,,(L)

O.:q(pos) U,,(R)

R0: c§(cI) u,,(R)

,;d,(nr) U,ur(R)R: a(c/) U,,(L)

RV: d,(nr) o X(L'Ro d, (c/) -U-,,(R)

,R: d2(cl) U(L)83: d?(CI) + Uf,(ejR4 d,(nr) -4 u(t)P,!,: d,Or) > ,(R)

1 1

1 1

I I 1.I I I1I I 1.'I I 1:

1 1 1.

I I 1.1 1

11

11

1 1

0~ 1 1 1 1

) 1 1 0d, 1 1 1

od 1 1 1 1 ,6bq*-S ^t.... ..

f4,2 1 1 1 4,6

1 f5,2 1 1 1 f5,6)f6 1 1 f64 f65 1)f7,1 1 1 1 1

) f8.1 1 1 1 1 1

f9,4 f95 11 1 1 f4,4 f0,5 1

Figure 10: Final Speed RDN

1 46 f4, 1 1 f,01: 1 24.6 fz;7 fI 4f,fI,11: 1 1 1 1 4A3 439

1 1 fb46 4 7 1 1 4,1

1 1 1 ef5 f19 1

f64 1 1 1 4tg4f4 1 1 1 f9

1 f85 4f, 4,7 1 4,

415 4,6 4,7 1 49O

I0,41 1 1f4,, 1

41,5 41.6 f41,7 1 1 f4lUO

fl,7 f,.8 1 11 1 24,9 f2,101 1 1 1

1

1

1

f9,7

f10,7

41f3l.

611

f7S,

711

401I

od

1 1 0d 0d 1 0d

1, 1 1 1 1d 0d 1

1 1 1 0d 1 1 0d

1 1 1 1 1 0d od 1

Figure 11: Final Steer RDN

1

I

1

11

fg,8f4o,s

f4,9 f410f5,9 f5101 1

47,9 f7,10fs,9 f8Ao1 1

1 1

1 od I Od

Od od od Od

od 1 Od I

I oo I od01 I1 I

od 1 od 11 11 1

1 0d 1 0d

od 1 0d 1

0d 1 od I

IX. NEURALNETWORK (NN) RESULTS

The final TFS system was simulated and compared to theAVS using a neural network trained using the same data. TheTFS system consistently outperformed the NN system (Table1). The random parameters of the training simulation were setto 75 obstacles (-10% of the total playing field). The TFS

125

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continued to perform well when subjected to less clutteredconditions. The TFS success rate decreased with additionalobstacles, but it still continues to outperform the system usingthe NN system.

Table 1: AVS Simulation Results (160 runs)dx=150' dy=150' AVSw/TFS AVSw/NN

Obstacles Density Winning % Winning %

25 -3.0% -89.0 -10.0

50 -6.0% -77.0 -22.0

75 -9.5% -63.0 -36.0

100 -12.5% -54.0 -45.0

REFERENCES

[1]. Arkin, R., Behavior-Based Robotics, MIT Press, 1998[2]. Brooks, R., A Robust Layered Control System For A Mobile Robot,

IEEE Joumal ofRobotics And Automation, vol 2, No. 1, March 1986[3]. Hussoun, M., Fundamentals of Artificial Neural Network, MIT Press,

1995[4]. Wang, L., Adaptive Fuzzy Systems and Control: Design and Stability

Analysis, Prentice Hall, NJ, 1994[5]. Overholt, J. L., Threshold Fuzzy Systems: Concepts and Foundations, a

dissertation for the Degree of Ph.D. Oakland University, 1999[6]. http://www.igvc.org/[7]. Overholt, J. L., Cheok, K. C., Smid, G. E., A Reactive Navigation

Scheme for an Autonomous Skid-Steer Robot Using Threshold FuzzySystems, Proceedings of the 2001 IEEE Electro-InformationTechnologies Conference, May 2001

X. CONCLUSIONS

The TFS methodology shows great promise for use onsensor-based autonomous navigation platforms. It alsopotentially has significant advantages over classical neuralnetworks in training times, structure and modularity. Furtherresearch in these last areas is needed to support these claims.

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