Ky yfai H^i thto ICT.rda'06 Proceedings of ICrr.rda'06 Hanoi May 2' DESIGNING FUZZY BEHAVIORS FOR AUTONOMOUS ROBOT NAVIGATION SYSTEIM Thiet ke cac hanh vi mcr cho he dan dircrng robot tu hanh Ngo Thanh Long, Pham The Long, Nguyen Hoang Phuong Abstract Robot navigation using fuzzy behavior is suited in unknown and unstructured environmen in which each behavior have an individual task This paper deals with an approach ii designing fuzzy behaviors including collision avoidance, wall-following, reach target Thi proposed hierarchy of fuzzy behaviors is used to fuse the command in which each behavioi being fuzzy inference system and undertaking individual task Its inputs are informatior fused from sensors using fuzzy directional relationship The simulation results with somt statistics show that the system works correctly Keywords: robot navigation, fuzzy directional relation, fuzzy inference system, fuzzy behavior, hierarchy of behavior Tom tdt Ddn dudng robot sir dung cdc hdnh vi md phir hgp cdc mdi truang phi cdu true vd khdng rd rdng, mdi hdnh vi ddm nhdn mgt nhiem vu rieng Bdi bdo de xudt mgt phuang phdp thiet ke cdc hdnh vi md bao gom Irdnh chuang nggi vgt, theo-tuong, diin dich Mgt kien triic cua cdc hdnh vi ciing dugc de xudt de Idng hgp lenh dieu khien ciia cdc hdnh vi, mdi hdnh vi Id mgt he suy dien ma Ddu vdo ciia chiing Id thdng tin dugc tdng hgp tit sensor dua tren quan he hudng ma cita hai ddi tugng Cdc kit qud md phong vd mgt sd thdng ke dugc sir dyng de kiem chiing tinh dn djnh cua phuang phdp TH khda: ddn dudng robot, quan he huang ma, hi suy dien ma, hdnh vi md, kiin true hdnh vL INTRODUCTION Fuzzy behaviors with capable of making inferences are well suited for mobile robot navigation because of uncertainty of the environment The hierarchy of behaviors is a widely applied-methodology to divide the system into several smaller subsystem in which each subsystem is a fuzzy behavior, The partitioning may guarantees real-time performance with a large rule-base by reducing the complicated level of inference system Recently, there are many approaches to design a hierarchy of behaviors applied in robotics applications Brooks [1] proposed an approach to built behavior control paradigm ^^^^^ ° " decomposing the problei autonomous control by task E Petriu proposed the hierarchy of behaviors neuro-fuzzy controller by using sonar se to detect obstacles The command modi fusion fuses the output of fuzzy infe systems of behaviors and then defuzzi obtain the crisp value Thongchai [3] behaviors to execute individual tasks an output of them is fused command based o priority degree of each behavior John Ye proposed the approach to fuse the oi fuzzy set of behaviors into a final fuzz' ^^^ defuzifymg to get the crisp comn valueThe paper deals with an approacl designing fuzzy behaviors for mobile n j C y y ^ HQi Uito ICT.rda'06 Proceedings of ICT.rda'06 Hanoi May 20-21, 2006 navigation based-on fuzzy directional fuzzy if-then rules and aggregation of outpu relationship Behaviors are built as collision sets and defiizzifieation We generally have A avoidance, wall-following, reach-target, turn-fuzzy "IF-THEN" niles, where the /* nile ha; around in which each behavior is a fiizzy the form: inference system Collision avoidance /?': IF X, is A|' AND X2 is A2' ANE behavior is used to avoid obstacles detected jCpisA/THEN>'isB' (1) by robot Wall-following behavior is used to where jr, e A^ (/ = 1,2, , p) be universes, j navigate the robot moving along to the wall Reach-target is used to locate and to navigate Y are linguistic variables representing fo the robot reaching the target Tum-around input set, A/S, B ' are fuzzy subsets, having only is used in cace robot be not able moving membership functions be p^ (^)» MY {y)' o So rule-base is enough smaller to implement antecedent and consequent sets, respectively the task in real time The extended fiizzy The rule represents fuzzy relation between th( directional relationship computed from range input space Xi x A'2 x x Xp and the outpu sensors [5, 6] is one of inputs of ftizzy space Y behaviors Because of modeling the crisp environment using information from range input sensors and fiizzy directional relationship, Fuzzifier Inference > Defuzzifier may be there are many entities of the same ^€Y ) n type of fuzzy behaviors (in case there are many obstacles) at the time Authors have Rules developed idea in designing the hierarchy of ( fiizzy behaviors to fuse command from many entities of individual behaviors The hierarchy has two layers The first is used to fiise Figure The structure of fuzzy logic system command from entities of the same type And The fuzzier maps the crisp input into the three outputs corresponding three types of fuzzy set being input of inference engine Th( behaviors are fused by the second fusion inference engine combines rules and gives < layer The output of the second fusion layer is mapping from fuzzy input sets into fuzz) defiizzified to achieve the crisp value for output sets Multiple antecedents in rules ar( navigating robot connected by the t-norm operatoi (corresponding to intersection of sets) af The paper is organized as follows: following: Section introduces fuzzy inference process, 1 1 1 t 1 an overview on behavior-based mobile robot navigation, the extended fiizzy directional relationship Section introduces the proposed approach to design the hierarchy of behaviors for robot navigation Section shows some simulation results and section is conclusion and future works BACKGROUND 2.1 Fuzzy Inference System A fuzzy inference system essentially defines a nonlinear mapping of the input data vector into a scalar output, using fuzzy rules The mapping process involves input/output niembership fimctions, fuzzy logic operators, Mi,:{y) = Mx,.x, x,^Ay) 1 1 t 1 (2) = A^rM ° [^.r, U ) ° Z*^, (^2) - /') (3) where • is t-conorm operator beinj maximum operator The defuzzifier produces a crisp outpui from the fuzzy set that is the output ol inference engine There are many methods ol Ky y^u HQi thao ICT.rda'06 Proceedings of lCT.rda'06 Hanoi May defiizification such as centroid, maximumdecomposition, center of maxima or height defuzzification 2.2 Behavior-based robot navigation Behavior models have been widely used in advanced robotic system opoating in uncertainty dynamic envinnunent, combining information fiom many sens(MS Behavior hierarchy, has developed to navigiite robot more flexibility, involves many ordered behaviors The main components of this aichitectiue are behavior entity that is respcmsible fra- only a very narrow task of robot navigation Each behavior only receives the information needed for its task Fuzzy inference systems (FIS) is used to construct behaviors There are some approach^ command from fuzzy outputs ([2], and almost of approaches are base methods: fusing command from f before defuzzification or fusing > from crisp values after Jefuzzificatic 3) See that two methods fusing i have results being different 2.3 Extended fuzzy directional rela Fuzzy directional relation has devel Keller and Matsakis [5,6,7] from ide relation of position between two area Fuzzy directional relationship of A, B is computed based on the truth v proposition like "A is in direction a There are many proposed approach to c truth value of the above proposition as network [6], angle histogram [8] Behniotl JL histogram [5] These approaches ComAAnd Defiixa&ition Beh entities (n > 0, m > 0) based on the number ol detected obstacles The first fusion layer is used to fuse command from the same behaviors, so there are two command fuser; for collision-avoidance behaviors and wall following behaviors The second fusion layei fuses commands from entities of the firs Ky ylu HQi thao ICT.rda'06 layers The crisp command control is output of the defuzzification layer that has the input being the output of the second fusion layer The tum-around behavior is used to control robot in case impossible moving CoUicion Proceedings of ICT.rda'06 Hanoi May.' "^ -1 4)8 4)6 -0.4 41.2 02 04 0.6 Fig Membership functions of FDR li variables Figure The hierarchy of behaviors to fuse command 3.2.1 Collision avoidance behavior This is most important behavior of a mobile robot The behavior is built based on fuzzy inference system using the modeled information of environment The collision avoidance behavior uses two inputs being the extended fuzzy directional relationship [9] and range to the obstacle The fiizzy rule of the behavior has the form as following: \?FDR is A, MiD Range isBilVEtiAoD is C, where Ai, B|, C| are fiizzy subsets of linguistic variables The fiizzy directional relation has six linguistic values^ (Negative Large-NL, Negative Medium-NM, Negative Small-NS, Positive Small-PS, Positive Medium-PM and with membership Positive Large-PL) functions in figure The range from robot to obstacle is divided in three subsets: Near, Medium and Far with membership functions in figure The output of fuz^ if-then is a linguistic variable representing for angle of deviation, has six linguistic variables the same the fuzzy directional relation with the difTerent membership fimctions in figure The rule-base and membership functions of linguistic variables are described more detail in table Figure Membership functions ofRa linguistic variables Mjige 40 -30 KlteSiir" NS!-«i P S - PUeshirc -20 -10 Fig S.Membership function for DoD lingt variables Table Rule base of FLC for collis avoidance behavior FDR NS Range N AoD PL FDR PS Range N NS NS M F PM PS PS PS M F NM NM NM N M F PM PM PS PM PM PM N M F NL NL NL N M F PM PS PS PL PL PL N M F ] 3.2.2 Wall-following behavior The wall-following behavior is als fiizzy inference system with the fiizzy i having the form as following: :::3!^ HQi thAo ICT.rda'06 Proceedings of ICT.rda'06 Hanoi May 20-21.2006 IF the obstacle is Ai AND Range is B, THEN Angle of Deviation is C/ The position relation between the robot and obstacles is computed from obstacles built by Si, S2, Sg and S9 sensors The mentioned position relation, that is lefi or right, is fuzzy spatial relationship between the robot and the obstacle (more detail in [5, 6]) So rule base of wall-following behavior is as following: Left Range Medium Medium Near Right Near FDR Left Right Angle of deviation Positive Small Negative Small Positive Medium Negative Medium The membership fimctions of the linguistic variables are described as following: Le^ 3.2.2 Reach-target behavior The reach-target behavior is a fiizzy inference system with the fuzzy rule having the form as following: IF the obstacle is A, THEN AoD is B, The positive relation between obstacles has three linguistic values (Left, Small, Right) with membership fiinction described in figure 10a The angle of deviation also has three linguistic values (Left, Small, Right) with membership function described in figure 10a The output is angle of deviation having three fuzzy subsets vnih membership function in figure 10c Left LSmag H 180 -30-20 >1.0 "Snwl u Ri^ 20 30 180 a> Tlw fuzz}' spatinl reUnouhip -0.5 small negative stnal \ 0,5 I a) The fuzzy spatial relationship 1.0 • / II small ,2 positive small / -0.2.0.10.10 2.0 b) The anfle of dn-iatioii Figure 10 Membership functions of fuzzy subset of linguistic variables So the rule base of reach-target behavior is described as following: b) Range NMe4