North Carolina A&T State UniversityAbstractSoft Computing-based Design and Control for Mobile Robot Path TrackingAbdollah HomaifarNASA ACE CenterDepartment of Electrical EngineeringNorth Carolina A&T State UniversityGreensboro, NC 27411Daryl Battle Lucent Technologies67 Whippany RoadWhippany, NJ 07981Edward TunstelJet Propulsion LaboratoryCalifornia Institute of TechnologyPasadena, CA 91109AbstractA variety of evolutionary algorithms, operating accordingto Darwinian concepts, have been proposed toapproximately solve problems of common engineeringapplications. Increasingly common applications involveautomatic learning of nonlinear mappings that govern thebehavior of control systems. In many cases where robotcontrol is of primary concern, the systems used todemonstrate the effectiveness of evolutionary algorithmsoften do not represent practical robotic systems. In thispaper, genetic programming (GP) is the evolutionarystrategy of interest. It is applied to learn fuzzy controlrules for a practical autonomous vehicle steering controlproblem, namely, path tracking. GP handles thesimultaneous evolution of membership functions and rulebases for the fuzzy path tracker. As a matter ofpracticality, robustness of the genetically evolved fuzzycontroller is demonstrated by examining the effects ofsensor measurement noise and an increase in the robot'snominal forward velocity.1. IntroductionIn recent years, increased efforts have been centered ondeveloping intelligent control systems that can performeffectively in real-time. These include the developmentof non-analytical methods of soft computing such asevolutionary computation and fuzzy logic. Thesemethods have proven to be effective in designingintelligent control systems and handling real-timeuncertainty, respectively [1, 2]. In this paper, our effortsare focused on combining these paradigms to developpath tracking controllers for autonomous vehicles such asmobile robots and automated guided vehicles (AGVs).Specifically, we employ genetic programming (GP) foroff-line learning of path tracking rules to be implementedin a fuzzy logic controller. Genetic programming [3] has recently beendemonstrated to be a viable approach to learning fuzzylogic rules for mobile robot control and navigation [4, 5].Herein, we address the simultaneous design of fuzzy logiccontrollers (FLCs) using GP, i.e. evolution of both theinput membership functions and the rule base. Inaddition, we extend the evolutionary influence of GP byincorporating the random selection of fuzzy logicconnectives (t-norms) into the learning process. Finally,we examine the robustness of the evolved controllers bycorrupting sensory data used by the path following robot,and by increasing the nominal forward velocity of thevehicle. This provides an indication of how well GP canevolve practical solutions that also retain the tolerance ofimprecision and uncertainty characteristic of FLCs.2. Overviews of Fuzzy Control and GPA FLC is an intelligent control system that smoothlyinterpolates between rules, i.e. rules fire to continuousdegrees and the multiple resultant actions are combinedinto an interpolated result. A fuzzy set may berepresented by a mathematical formulation known as amembership function. That is, associated with a givenlinguistic variable (e.g. speed) are linguistic values orfuzzy subsets (e.g. slow, fast, etc.) expressed asmembership functions which represent uncertainty,vagueness, or imprecision in values of the linguisticvariable. These functions assign a numerical degree ofmembership to a crisp (precise) number. More precisely,over a given universe of discourse (relevant numericalrange) X, the membership function of a fuzzy set, denotedby (x), maps elements x  X into a numerical value inthe closed unit interval, i.e. (x): X  [0, 1]. Implementation of a fuzzy controller requires assigningmembership functions for inputs and outputs. Inputs to afuzzy controller are usually measured variables,associated with the state of the controlled plant, that arefuzzified (assigned membership values) before beingprocessed by an inference engine. The heart of thecontroller inference engine is a set of if-then rules whoseantecedents and consequences are made up of linguisticvariables and associated fuzzy membership functions.Consequences from fired rules are numerically aggregatedby fuzzy set union and then collapsed (defuzzified) toyield a single crisp output as the control signal for theplant. For detailed introductions to fuzzy control, fuzzyset operations, and concepts of fuzzification, inference,aggregation, and defuzzification see one of [2, 6]. In the GP paradigm, a population is comprised ofcomputer programs or procedures (individuals) that arecandidate solutions to a particular problem. Theseindividuals participate in a simulated evolution processwherein the population evolves over time in response toselective pressure induced by the relative fitness ofindividuals in the problem domain. In our approach, eachprogram executes condition-action statements, whichcollectively serve as a rule base to be embedded in afuzzy controller. To preserve diversity among populationsand vital genetic information among individuals, geneticoperators are applied to create new individuals forsucceeding generations. When the algorithm finallyconverges or satisfies its termination criteria, it isanticipated that the best (most fit) individual will berepresentative of an optimum or near optimum solution. In the next section, we introduce the autonomousvehicle control problem, followed by discussion of FLCdesign issues to be considered when employing GP.3. Mobile Robot Path Tracking ProblemThe control problem examined in this paper is a pathtracking problem, which was formulated by Hemami et al[7, 8] for a class of low speed (less than 2 m/s) tricycle-model vehicles. Essentially, the