Soft computing paradigms for hybrid fuzzy controllers: experiments and applications

Soft Computing Paradigms for Hybrid Fuzzy Controllers: Experiments and applications* M. R. A kbarzadeh-T., E. Tunsteli K. KumblaQ M. Jamshidi NASA Center for Autonomous Control Engineering (ACE) University of New Mexico, Albuquerque, NM 87131, USA E-mail: [email protected] Abstract Neural Netw orks (NN), Genetic A lgorithms (GA ), and G enetic Pro g ram s ( G P) are o ften aug m ented w ith fuzzy logic-based schemes to enhance artificial intelligence of a given system. Such hybrid combinations are expected to exhibit added intelligence, adaptation, and learning ability. In this paper, implementation of three hybrid fuzzy controllers are discussed and verified by experimental results. These hybrid controllers consist of a hierarchical NN-fuzzy controller applied to a direct drive motor, a GA -fuzzy hierarchical controller applied to a flexible robot link, and a GP-fuzzy behavior-based co ntro ller applied to a mo bile ro bo t navigatio n task. It is experimentally show n that all three architectures are capable o f significantly impro ving the system response. I Introduction Trad itio nal metho d s w hich ad d ress ro bo tics co ntro l issues rely upo n stro ng mathematical mo d eling and analy sis. The v ario us ap p ro aches p ro p o sed to d ate are suitable for control of industrial robots and automatic guided vehicles w hich operate in strzlctzlred enviro nments and perfo rm simple repetitive tasks that require o nly end -effecto r po sitio ning o r mo tio n alo ng fixed paths. How ever, operations in unstructured environments require robots to perform more complex tasks for w hich analytical models for control can often not be determined. In cases w here models are available, it is questionable w hether or not uncertainty and imprecisio n are sufficiently acco unted fo r. Und er such co nd itio ns fuzzy lo gic co ntro l is an attractive alternative *This work was supported in part by Waste Education and Research Consortium grand under award #WERC/NMSU/DOE Amd 35 and by NASA contract # NCCW-0087 t Currently with Jet Propulsion Laboratory, Pasadena, CA. tcurrently with Kirtland Airforce Base in Albuquerque, New Mexico. 0-7803-4863-X/98 $10.0001998 IEEE that can be successfully implemented on real-time complex systems. Fuzzy controllers and their hybridization w ith other paradigms are robust in the presence of perturbations, easy to design and implement, and efficient fo r systems that deal w ith co ntinuo us variables. The co ntro l schemes described in this paper are examples of approaches that augment fuzzy logic w ith other soft computing techniques to achieve the level of intelligence required of complex robotic systems. Three so ft co mputing hybrid fuzzy parad igms fo r auto mated learning in ro bo tic systems are briefly d escribed and experimentally verified . The first scheme concentrates on a methodology that uses NNs to adapt a fuzzy lo gic co ntro ller (FLC) in manipulato r co ntro l tasks. The seco nd parad igm d evelo ps a tw o -level hierarchical fuzzy co ntro l structure fo r flexible manipIt inco rp o rates GA S in a learning schem e ulato rs. to ad ap t to v ario us env iro nm ental co nd itio ns. The third paradigm employs GP to evolve rules for fuzzybehavio rs to be used in mo bile ro bo t co ntro l. Experimental results of fuzzy controllers learned w ith the aid of these soft computing paradigms are presented. 2 Neuro-Fuzzy S y s t e m Neural netw orks exhibit the ability to learn patterns of static o r d ynamical systems. In the fo llo w ing neurofuzzy appro ach, the learning and pattern reco gnitio n of NN are exploited in tw o stages: first, to learn static response curves of a given system; and second, to learn the real-time dynamical changes in a system to serve as a reference model. The neuro-fuzzy control architecture uses the tw o neural netw orks to modify the parameters o f an ad aptive FLC. The ad aptive capability o f the fuzzy controller is manifested in a rule generation mechanism and automatic adjustment of scaling factors or shapes of membership functions. The NN functions as a classifier o f the system’ s tempo ral respo nses. A multi-layer perceptron NN is used to classify the tem- I1200 r PC Memory Storage Figure 1: Block Diagram of the A daptive Neuro-Fuzzy Co ntro ller po ral respo nse o f the system into d ifferent patterns. Depend ing o n the type o f pattern such as ‘Vesponse w ith o versho o t” , “ damped respo nse” , “ o scillating respo nse” etc. the scaling factor of the input and output membership functio ns are ad justed to make the system respond in a desired manner. The rule generation mechanism also utilizes the tempo ral respo nse o f the system to evaluate new fuzzy rules. The non-redundant rules are appended to the existing rule base during the tuning cycles. This co ntro ller architecture is used in real-time to co ntro l a d irect d rive mo to r. Figure 1 illustrate the architecture of the Neuro-fuzzy controller w here the tw o NNs and the fuzzy control architecture are integrated for adaptive control of nonlinear systems PI . 2.1 Real-Time Adaptive Control of a Direct Drive Motor In o rd er to perfo rm real-time co ntro l, it is necessary that the co ntro ller to stand alo ne w ith the so le task of calculating the output needed to control the object system. This means the task o f co mmunicating d ata for storing as w ell as acquiring co ntro ller parameters (if the controller is adaptive) should be performed by external pro cesso rs. In this w ay a real-time co ntro l can be achieved w ith required sampling rate for high band w id th o peratio n. The FLC algo rithm requires pro cessing o f several functionalities such as fuzzification, inferencing and defuzzificatio n. This means the co mputatio n time taken by the FLC itself does not leave any room for an adap- 1201 Intel 486 on LabWindows Display and User Interface Fig ure 2: H ard w are fo r Im p lem enting N euro -Fuz z y Controller for Real-Time Control of a Direct Drive Motor Using a Digital Signal Processor tive algorithm such as rule generation, calculating the scale facto r o f the membership functio n, o r NN algo rithms. In order to implement all these functionalities, a m ulti-p ro cessing architecture is need ed . This can be achieved by combining a sufficiently fast processor specifically designed for real-time processing, such as a TMS320C30 d igital signal pro cesso r (DSP) co mbined w ith a PC Intel p ro cesso r (Pentium o r 486). Fig ure 2 show s the hardw are built to interface and control a direct drive motor. The d ynamics o f a d irect d rive brushless DC Mo to r exhibits no nlinear characteristics. This is evid ent in the d ead -zo ne regio ns o f o peratio n and frequency lo ad characteristics. A digital to analog converter o f 12-bit resolution is used to interface to the DSP board through a memory mapped register I/ O port. The position of the motor is measured by an optical encoder (w hich generates 8000 pulses per revolution of the moto r). This is co nverted to d igital K&bit p o sitio n d ata by encoder circuitry. The DSP’s expansion memory is accessible to the PC with which the data communication is carried out using direct nternory access (DMA ). The experimental data as w ell as fuzzy controller pa- rameter and communication control data are sent back and forth using this DMA . Figure 3(a) show s the result of the experiment. Initially there are no rules in the fuzzy controller. Hence for the first tw o cycles w hen the motor w as commanded to go from +lOOO to -1000 enco d er read ings, there is no action and the motor is stationary (O-1000 sampling tim e; each cy cle co rresp o nd s to 500 sam p led d ata). Fig ure 3: Po sitio n Co ntro l Direct Driv e M o to r: Response A fter (a) First and (b) Final Trial Ho w ever, in the third cycle w hen the mo to r is co mmanded to go to +lOOO counts, the motor spins out of control clockw ise. This is because the rule generation mechanism has produced 4 new rules in the last tw o cycles and they are in actio n. These rules are unstable because the rules generated are not the right ones or may be insufficient to control the motor adequately. This unstable behavio r co ntinues until after the 8th tuning cycle (after 4000 sampling instant). The co rresponding motor command show s a bounded region., Figure 3(b) sho w s the stabilized respo nse. Here, the fuzzy controller has completely learned to control the direct drive motor. 3 Figure 4: GA -Based Learning Hierarchical Control A rchitecture : (1 ..--- f...&. Several issues sho uld be ad d ressed w hen d esigning a GA fo r o p tim iz ing fuz z y co ntro llers: the d esign o f a transfo rmatio n (interpretatio n) functio n, the method of incorporating initial expert know ledge, and the cho ice o f an appro priate fitness functio n. Each o f the above issues significantly influences the success of GA in find ing impro ved so lutio ns. These issues are briefly d iscussed belo w as they apply to d esign o f a GA -fuzzy controller for a flexible link. Application to Flexible Robot Control 1 i : j : 1” . .+......~ ,_.....L........t”““.v . .. . “ ..“ .. Figure 5: GA Simulatio n (a) Co mpariso n o f Simulatio n Respo nses (b) Plo t o f A verage Fitness (c) Initial Experimental Results GA-Fuzzy Systems for Control of Flexible Robots In this section, GA S are applied to fuzzy control of a single link flexible arm. GA S are guided probabilistic search ro utines mo d eled after the mechanics o f Darw inian theo ry o f natural evo lutio n [2]. Genetic algo rithms have demonstrated the coding ability to represent parameters of fuzzy know ledge domains such as fuzzy rule sets and membership functio ns [3] in a genetic structure, and hence are applicable to o ptimization of fuzzy rule-sets. 3.1 A Distributed Parameter System The GA -learning hierarchical fuzzy control architecture is sho w n in Figure 4. W ithin the hierarchical co ntro l architecture, the higher level mo d ule serves as a fuzzy classifier by determining spatial features of the arm such as straight, oscillatory, curved. This information is supplied to the low er level of hierarchy w here it is processed among other sensory information such as errors in position and velocity for the purpose of determining a d esirable co ntro l input (to rque). In [5] this control system is simulated using only a priori expert know ledge. In the given structure, a genetic algorithm fine tunes parameters of membership functions. The follow ing fitness function w as used to evaluate individuals w ithin a population of potential solutions, J tf i ness ft = t; 1 e2+r2+1 dt ’ w here e represents the error in angular position and y represents overshoot. Consequently, a fitter individual is an ind ivid ual w ith a lo w er o versho o t and a lo w er overall error (shorter rise time) in its time response. Here, results fro m previo us simulatio ns o f the architecture are applied experimentally. The metho d o f 1202 grtd-parenting [6] w as used to create the initial population. Members of the initial population are made up of mutation of the know ledgeable grandparent(sb. A s a result, a higher fit initial population results in a faster rate of convergence as is exhibited in Figure 5(a). Figure 5(a) show s the time response of the GA -optimized co ntro ller w hen co mpared to previo usly o btained results thro ugh the no n-GA fuzzy co ntro ller. The rise time is improved by 0.34 seconds (an 11% im p ro v ement), and the overshoot is reduced by 0.07 radians ( a 54% improvement). The average fitness of each generation is show n in Figure 5(b). A total of 10 generatio ns w ere simulated . Mutatio n rate fo r creating the initial population w as set at 0.1. M utatio n rate thro ug ho ut the rest of the simulation w as set to 0.01. Pro bability of crossover was set to 0.6. Initial experimental results demonstrate that the GA learned controller is able to co ntro l the actual experimental system as in Figure 5( c > . The hard w are used to implement the abo ve algo rithms is the same as w as explained in the previo us sectio n w ith few mo d ificatio ns pertaining to flexible robot control such as tip end position sensor and several strain gauges distributed evenly across the length of the flexible beam. 4 GP-Fuzzy Hierarchical Behavior Control The ro bo t co ntro l benefits to be g ained fro m so ft co m p uting -based hy brid FLCs is not limited to rigid and flexible manipulato rs. Similar benefits can be gained in applicatio ns to co ntro l o f mo bile ro bo t behavior. A uto no mo us navigatio n behavio r in mo bile ro bo ts can be d eco mp o sed into a finite number o f special-purpose task-achieving behaviors. A n effective arrangement of behaviors as a hierarchical netw ork of distributed fuzzy rule-bases w as recently proposed for auto no mo us navigatio n in unstructured enviro nments [8]. The proposed approach represents a hybrid control scheme incorporating fuzzy logic theory into the framew ork of behavior-based control. A behavior hierarchy that enco mpasses so me necessary capabilities fo r autonomous navigation in indoor environments is show n in Figure 6. It implies that goal-directed navigation can be decomposed as a behavioral function of goal-seeking and route follow ing. These behavio rs can be further decomposed into the low er-level behaviors show n, w ith d epend encies ind icated by the ad jo ining lines. Each block in Figure 6 is a set of fuzzy logic rules. The circles in the figure represent dynamically adjustable w eights in the unit interval w hich specify the degree to w hich 1203 Figure 6: Hierarchical d eco mpo sitio n o f mo bile ro bo t behavio r. low -level behaviors can influence control of the robot’s actuato rs. Higher-level behavio rs co nsist o f fuzzy d ecisio n rules w hich specify these w eights acco rd ing to goal and sensory information. Each low -level behavior co nsists o f fuzzy co ntro l rules w hich prescribe mo to r control inputs that serve to achieve the behavior’s designated task. The functionality of this hierarchical fuzzy-behavior control approach depends on a combined effect of the behavioral functionality of each low -level behavior and the competence of the higher-level behaviors w hich coo rd inate them. Perhaps the mo st d ifficult aspect o f applying the approach is the formulation of fuzzy rules for the higher level behaviors. This is not entirely intuitive, and expert kno w led ge o n co ncurrent co o rd ination of fuzzy-behaviors is not readily available. We have successfully addressed this issue in [9] using GP to computationally evolve rules for composite behaviors. In this sectio n, w e d escribe the genetic pro gramming approach to fuzzy rule-base learning. Next, w e present a representative experimental result of applying the behavior hierarchy’ to autonomous goal-seeking. 4.1 GP-Fuzzy approach The GP p arad ig m [lo] co mputatio nally simulates the Darw inian evolution process by applying fitness-based selectio n and genetic o perato rs to a po pulatio n o f individuals. Each individual represents a computer program of a given programming language, and is a candidate solution to a particular problem. The programs are structured as hierarchical compositions of functions (in a set F) and term inals (functio n arg um ents in a set T). The population of programs evolves over time in response to selective pressure induced by the relative fitnesses of the programs for solving the problem. For the purpose of evolving fuzzy rule-bases, the search space is contained in the set of all possible rule-bases that can be composed recursively from F and T . The set, F, co nsists o f co mpo nents o f the generic if-then ations rang ing fro m 10-15. In GP, g enetic d iv ersity remains high even fo r very small po pulatio ns d ue to the tree structure o f ind ivid uals [lo]. The experimental testbed is a custo m-built mo bile ro bo t d riven by a tw o-w heel differential configuration w ith tw o passive casters for support. The independent drive motors are geared DC motors. The robot stands about 75 cm tall and measures abo ut 60 cm in w id th. Range sensing is achieved using a layo ut o f 16 ultraso nic transd ucers; optical encoders on each driven w heel provide positio n info rmatio n used fo r d ead -recko ning. Its maximum speed w as limited to 0.3m/s. The vehicle is controlled using a 75MHz Pentium-based master processor (lapto p PC) and M o torola MC68HCll micro pro cesso r slaves for sonar processing and low -level motor control functio ns. In the current implementatio n, the cycle time of the control system is 0.15 seconds (7Hz). This includes time spent acquiring and preprocessing sonar and enco d er d ata, and co mmand ing the mo to rs. The o verall inference o f the behavio r hierarchy co nsumes abo ut 0.05 seconds of this time. That is, the hierarchy itself can run at a rate of 20Hz. rule and co mmo n fuzzy lo gic co nnectives, i.e. functions for antecedents, consequents, fuzzy intersectio n, rule inference, and fuzzy union [9]. The set, T, is made up of the input and output linguistic variables and the co rrespo nd ing membership functio ns asso ciated w ith the problem. A rule-base that could potentially evolve fro m F and T can be expressed as a tree data structure w ith symbolic elements of F o ccup y ing internal nodes, and symbolic elements of T as leaf nodes of the tree. This tree structure o f symbo lic elements is the main feature w hich distinguishes GP from GA S w hich use the numerical string representation. A ll rule-bases in the initial population are randomly created , but d escend ant po pulatio ns are created primarily by repro d uctio n and cro sso ver o peratio ns o n rule-base tree structures. Fo r the repro d uctio n o peration several rule-bases selected based on superior fitness are co pied fro m the current po pulatio n into the next, i.e. the new generation. The crossover operation starts w ith tw o parental rule-bases and produces tw o offspring that are added to the new generation. The operation begins by independently selecting one random node (using uniform probability distribution) from each parent as the respective crossover point. The subtrees subtended from crossover nodes are then sw apped betw een the parents to pro d uce the tw o o ffspring. GP cycles thro ugh the current po pulatio n perfo rming fitness evaluation and application of genetic operators to create a new population. The cycle repeats on a generation by generation basis until satisfaction of terminatio n criteria (e.g. lack o f impro vement, maximum generatio n reached , etc). The GP result is the best-fit rule-base that appeared in any generation. In the GP approach to evolution of fuzzy rule-bases, the same fuzzy linguistic terms and operators that comprise the genes and chromosome persist in the phenotype. Thus, the use o f GP allo w s d irect manipulatio n of the actual linguistic rule representation of fuzzy rulebased systems. Furthermore, the dynamic variability of the representation allow s for rule-bases of various sizes and different numbers of rules. This enhances population diversity w hich is important for the success of the GP system, and any evo lutio nary algo rithm fo r that matter. The dynamic variability also increases the potential for discovering rule-bases of smaller sizes than necessary for completeness, but sufficient for realizing desired behavior. 4.2 Real-time navigation GP was used to evolve fuzzy decision rules to be used fo r go al-seeking by a mo bile ro bo t. Po pulatio n sizes of lo-20 rule-bases w ere run fo r a number o f gener- During operation, the robot is not provided w ith an explicit map o f the enviro nment. Ho w ever, it is co gnizant of the notion of a tw o-dimensional Cartesian coo rd inate system. Its paths are no t pre-planned ; they are executed in response to instantaneous sensory feedback fro m the enviro nment. Therefo re, w e are essentially d ealing w ith a lo cal navigatio n pro blem as o pposed to a global navigation problem w hich relies on a global map that is either provided a priori, or is acquired via exploration. The experiment w as conducted in an ind o o r enviro nment co nsisting o f co rrid o rs and doors. The robot’s task is to navigate from one location to another on the same floor of the building. The result of the navigation task is show n in Figure 7 as the path traveled in a po rtio n o f the ind o o r test enviro nment w hich includ es the start and co mmand ed go al. The robot is displayed as an octagonal icon w ith a radial line indicating its heading. It was commanded to navigate from a start pose, (Z y S>T = (9.5m 22m 3.Onzd)* to a goal located at (21.5m, 37.5m). A s show n in Figure 7, the ro bo t successfully navigates in clo se pro ximity to the g o al w itho ut p rio r m ap -based info rm atio n. The fuzzy-behavior based motion control relied primarily on so nar and d ead -recko ning info rmatio n, bo th o f w hich are know n to be sources of uncertainty in mobile robot navigation. Throughout the navigation task, the fuzzybehavior hierarchy continuously modulates the w eights of low -level behaviors in order to appropriately coordinate their co ncurrent activity. The hierarchy of fuzzy-behaviors provides an efficient approach to synthesis of behavioral capabilities neces- 1204 References I 1 I 1 38- . . . . . i . .."...................._ i i/'.> . 36 _ 32 [l] K. K. Kumbla, ‘(A daptive Neuro-Fuzzy Controller fo r Passive No nlinear Systems,” Ph.D. Dissertation, University of New Mexico, A pril, 1997. ..*........... i ... .i ........ ..<........., i i . ....i.......@ .. .../............ i i i .................. i [2] D. E. Goldberg,“ Genetic A lg o rithm s in Searc h, Optimizatio n and Machine Learning,” AddisonWesley, MA , NY, 1989. 10 Fig u re 7: behaviors. 12 14 16 X (meters) 18 20 22 [3] A . H o m aifar & E. M c C o rm ic k, “ Sim u ltaneo u s Design o f Membership Functio ns and Rule Sets for Fuzzy Controllers Using Genetic A lgorithms,” IEEE SPransactions on Fuzzy Systems, Vol. 3, No. 2, pp.129, 1995. 24 [4] M . A . Lee and H . Takag i, “ Integ rating D esig n Stag es o f Fuz z y Sy stem s Using Genetic A lg o rithms,” Proceedings of the 1993 IEEE International Conference on Fuzzy Systems, San Francisco , CA , pp. 612-617. G o al- se e king nav ig atio n u sing fuzzy- sary for autonomous navigation by mobile robots. This hybrid control scheme incorporates fuzzy logic into the a behavior-based control framew ork for w hich coordination rules can be discovered using GP. For the purpose of evolving fuzzy rule-bases, GP has certain advantages. Namely, it facilitates manipulation of the linguistic variables directly associated w ith the problem, and it allow s for populations of rule-bases of various sizes. The navigatio n result d emo nstrates ro bustness of the fuzzy-behavior hierarchy to uncertainty in real w o rld senso r-based co ntro l o f mo bile ro bo ts. In ad dition, the result show s that the approach is useful in situations w here maps are not available, or are perhaps unreliable. [5] M.-R. A kbarzad eh-T. “ A Fuzzy Hierarchical Co ntro ller Fo r A Single Flexible Arm,“ Proceedings of the 1994 International Symposium on Robotics and Manufacturing, ISRAM’94, Maui, Haw aii. 1994. [6] M .-R. A kbarz ad eh-T. and M . Jamshid i, “ Inco rpo rating A Prio ri Expert Kno w led ge in Genetic A lgo rithms,” Proceedings of the 1997 IEEE Conference on Computational Intelligence in Robotics and Automation, pp.300-305, Mo nterey, Califo rnia, 1997. [7] E. H. Mamd ani, “ Tw enty Years of Fuzzy Control: Experiences Gained and Lesso ns Learnt” , IEEE Intb. Conf. on Fuzzy Systems, pp. 339-344, 1993. 5 Conclusion In this paper, three experiments illustrate the utility of soft-computing approaches in handling complex models and unstructured environments. Neuro-fuzzy, GAfuzzy, and GP-fuzzy hybrid paradigms are successfully implemented to solve three prominent robot control issues, namely: control of direct drive robot motors, control of flexible links, and intelligent navigation of mobile robots. In the future, as these paradigms mature, w e w ill gain more know ledge of their exact nature and advantages. This w ill allow us to combine soft computing paradigms for more intelligent and robust control. Not long ago, a hybrid combination of these paradigms could not be applied to a real-time system. How ever, as show n in this paper, w ith the current advances in increase of speed of processing and DSP parallel processors, various combination of hybrid soft computing paradigms are now realizable. [S] E. Tunstel, “ Mo bile Ro bo t A uto no my via Hierarchical Fuzzy Behavio r Co ntro l” , 6th Intl. Symp. on Robotics and Manufacturing, 2nd Wodd AUtomation Congress, pp. 837-842, May, 1996. [9] E. Tunstel, T. Lippinco tt and M. 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