fuzzy speed and steering control of an agv - control...

112 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 10, NO. 1, JANUARY 2002

Fuzzy Speed and Steering Control of an AGVK. R. S. Kodagoda, W. S. Wijesoma, and E. K. Teoh

Abstract—The development of techniques for lateral andlongitudinal control of vehicles has become an important andactive research topic in the face of emerging markets for advancedautonomous guided vehicles (AGVs) and mobile robots. In thisrespect there has been much literature published, although notso much on actual performance of such controllers in a practicalsetting. The primary focus in this paper is on the development andactual implementation of intelligent and stable fuzzy proportionalderivative–proportional integral (PD–PI) controllers for steeringand speed control of an AGV. The AGV used in this study is anelectrically powered golf car suitably modified for autonomousnavigation and control. The use of fuzzy logic for control lawsynthesis, among other things, facilitates the incorporation of con-trol heuristics, while guaranteeing stability, uncoupling steeringcontrol from speed control, and providing for easy incorporationof a braking controller. Through experimentation, the designedcontrollers are demonstrated to be insensitive to parametric un-certainty, load and parameter fluctuations and most importantlyamenable to real-time implementation. The performance of theproposed uncoupled direct fuzzy PD/PI control schemes for theparticular outdoor AGV is also compared against conventionalproportional integral derivative (PID) controllers. Experimentalresults demonstrate that the proposed fuzzy logic controllers,which are synthesized from a variable structure systems viewpoint, also outperform conventional PID schemes, particularlyin tracking accuracy, steady-state error, control chatter, androbustness.

Index Terms—Fuzzy control, fuzzy logic, intelligent control, mo-bile robots, vehicles, velocity control.

I. INTRODUCTION

T HE DEVELOPMENT of techniques for lateral and longi-tudinal control of vehicles has become an important and

active research topic in the face of emerging markets for ad-vanced autonomous guided vehicles (AGVs) and mobile robots.AGVs are characterized by highly nonlinear and complex dy-namics [1]. Extraneous forces, such as those due to head winds,turning and static friction, typical of harsh outdoor environ-ments, further complicate the modeling process and the deter-mination of model parameters. Even if the model and the param-eters are known accurately for an AGV, there are the road gradechanges and variations in the amount of cargo in the AGV thatneed be accounted for. Thus any control strategy to be usefulfor outdoor AGV control must be able to deal with the aboveeffectively.

The application of linear control methods has not been un-common as evident from the reported literature [2]–[4]. Mostcommonly used linear control techniques for AGV control are

Manuscript received January 10, 2000; revised November 17, 2000. Manu-script received in final form May 21, 2001. Recommended by Associate EditorK. Moore.

The authors are with the School of Electrical and Electronic Engineering,Nanyang Technological University, Singapore 639798, Singapore.

Publisher Item Identifier S 1063-6536(02)00086-6.

Fig. 1. The experimental system.

proportional integral (PI) [2], [3], proportional derivative (PD)[2], and proportional integral derivative (PID) [4]. In the litera-ture there are only a few instances where the results of the appli-cation of nonlinear methods such as variable structure systemstheory and fuzzy control have been reported [5]–[7]. However,the fuzzy controllers proposed and implemented lack theoreticalanalysis of stability. In this paper fuzzy controllers are designedfor stability from the perspective of variable structure systemstheory and hence ensure stability.

The complexity of the AGV dynamics, the difficulty of ob-taining the actual vehicle dynamic parameters, the variability ofcertain model parameters and the human-knowledge availableon speed and steering control motivates the use of a fuzzy logicapproach to control law synthesis. In Section II, the particularAckerman steered AGVs hardware architecture is described. InSection III, stable fuzzy logic controllers are synthesized usingvariable structure systems theory, followed by experimental re-sults for specific scenarios. Section IV concludes the paper.

II. THE EXPERIMENTAL SYSTEM

The experimental system shown in Fig. 1 was built using acommercially availableCARRYALL 1golf car. The actuationsystem for steering control is comprised of a permanent magnetdc motor (48 V, 650 W) coupled to the steer shaft by meansof a gear assembly (ratio 5 : 1). In the conversion no attemptwas made to alter the drive actuation system, which is com-prised of a dc series motor (48 V, 2300 W) and a gear assembly(ratio 12.28 : 1). This only provides for the application of posi-tive torques. Active deceleration is achieved by manipulating acable attached to the brake pedal of the golf car through the actu-ation of a stepper motor. This operation mimics human brakingaction. Outputs of each encoder mounted on the four wheelsof the AGV are used to calculate the speed of the vehicle. The

1063–6536/02$17.00 © 2002 IEEE

IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 10, NO. 1, JANUARY 2002 113

Fig. 2. Proposed control structure.

steering angle and angular speed is obtained similarly via an en-coder mounted on the steering shaft. A PII 450-MHz Pentiumprocessor-based industrial PC provides the required computingpower for all three systems.

III. FUZZY CONTROL

The proposed control structure is as shown in Fig. 2. It may benoted that the longitudinal (speed) and lateral (steer angle) con-trol are achieved through separate uncoupled fuzzy controllers.Further, longitudinal control is realized by means of a fuzzydriving controller for acceleration and cruising at a constantspeed while a fuzzy braking controller is used for active decel-eration. Using three separate direct fuzzy controllers instead ofa single fuzzy controller significantly reduces the complexity ofthe fuzzy system. The coupling effects between the drive andthe steering systems are not explicitly accounted for in the sep-arate uncoupled controllers. Should there be undesirable effectsdue to coupling the structure proposed provides for inclusion ofexplicit coupling rules.

A. Control Law Development and Stability

The vehicle dynamics for the above AGV can be expressedas follows [1]:

(1)

and represent the disturbances. The remaining parametersare defined in the Appendix. Now (1) can be arranged in theform

(2)

For this class of systems, it is possible to design a stable slidingmode controller (SMC) within a computed torque framework.For a detailed derivation of the SMC control law, please refer to[8]. The overall computed torque structure is

(3)

A suitable choice of is, , where repre-sents the desired value ofand is a diagonal matrixwith elements . The choice rep-resents the computed torque component, whereand areestimates of and , respectively. The term is used to re-move the effects of inexact decoupling as a result of model mis-match and bounded disturbances. Let us define theth switchingplane as

(4)

A condition for the intersection of switching planes, ,to be attractive can be derived by defining a quasi Lyapunovfunction

(5)


Fig. 3. Membership functions of FDC.

where is the positive definite inertia matrix. Now, thethcomponent of can be chosen as in (6) to ensure

so as to guarantee the asymptotic stability ofand hencethe tracking errors as follows:

(6)

In (6), and are positive constants whose magnitudesdepend on the extent of the model mismatches. It may be notedthat by choosing and sufficiently large, the need for thecomputed toque component of the control law (3) may be elim-inated. As seen from (6), the increase/decrease of magnitude of

causes the magnitude of control torque to increase/decrease.This SMC law (6) can befuzzyfiedto obtain a fuzzy slidingmode controller (FSMC) [9]. Further, an equivalent fuzzy PDcontroller can be synthesized using this FSMC [10]. This leadsto a diagonal rule base usually referred to as a standard rule tablein the literature. It can be shown that the fuzzy PD controllersdesigned using the diagonal rule table for the AGV dynamicsare stable if

(7)

where and are the magnitudes of the fuzzyPD (or PI with the switching planes defined appropriately)controller’s output and output of the SMC, respectively.is

the universe of discourse of the normalized sliding surface.Maintaining this stability condition (7), parameters of the fuzzyPD/PI controller can now be tuned as well as heuristic rulescan be added as required, in order to satisfy the performancecriteria.

B. Fuzzy Driving Controller (FDC)

1) Control Structure: One of the most important issues infuzzy controller design is the choice of inputs and outputs ofthe system. As shown in Fig. 2, the inputs to the FDC are speederror and integral of speed error. The controller output is drivingvoltage ( ). We use singleton fuzzification and Mamdani in-ference strategy. The crisp control output is obtained throughcenter-of-gravity (COG) defuzzification. Triangular member-ship functions are chosen for inputs and outputs as shown inFig. 3. These are simpler, easier to optimize and tune. It is to benoted that the normalized universe of discourse of the drivingvoltage is limited to the range [0, 1] as negative voltages donot provide negative torques in dc series motors. If a negativevoltage is applied, the series connected motor will maintain itssense of rotation. As a result the control strategy will not operatesatisfactorily since the vehicle, instead of braking, will graduallyreach a different speed. Under these conditions the vehicle witha zero input voltage will stop due to the rolling losses and the


Fig. 4. Rule base of FDC.

Fig. 5. Speed tracking performance of the FDC for an acceleration of 0.5ms .

motor/gearbox inertia and not due to a negative control voltage.The rule base for the FDC is as shown in Fig. 4. The body of thetable in Fig. 4 shows fuzzy implication in the form

IF is and is Then is

where

NEL, NVL, NL, NS, NVS, ZO, PVS, PS,

PL, PVL, PEL

ZO, PVS, PS, PL, PVL, PEL

2) Results: For the purpose of assessing the relative perfor-mance of the fuzzy drive controller a conventional PID con-troller was used. The gains of the PID controller were initiallyestimated based on a simplified model of the drive motor [11]without regard to the coupling effects. Thereafter, the gains werefine tuned manually to yield the best possible performance forthe chosen reference trajectories. We choose a speed trajectoryas shown in Figs. 5(a) and 6(a). It can be seen from Figs. 5 and6 that the FDC closely follows the trajectory while the PID con-troller does not. Further, the PID controller output has very high

Fig. 6. Speed tracking performance of the PID controller for an accelerationof 0.5 ms .

Fig. 7. Speed tracking performance at slower speeds. (a) FDC. (b) PID.

control chatter, large voltage output (5.87 V rms) and satura-tion [Fig. 6(b)]. This is highly undesirable as it causes wear andtear of the mechanical system and it also affects the lifetimeof the batteries and the motor. FDC output is always operatingbellow 6 V (3.86 V rms). The FDC and PID controller perfor-mance at slower speeds is given in Fig. 7. It is to be noted that thePID controller gives rise to oscillatory behavior at slower speedswhereas FDC does not. This shows the susceptibility of the PIDcontroller to the operating point (region) but not the FDC. Therobustness results of the controllers to parameter changes are


Fig. 8. Speed performance with 30% increase of the load. (a) PID. (b) FDC.

shown in Fig. 8. An increase of 30% in the vehicle load causedthe PID controller to perform badly, whereas FDC was unaf-fected.

C. Fuzzy Braking Controller (FBC)

1) Control Structure: It is to be noted that only accelerationor a constant speed of the AGV can be actively affected by con-trolling the voltage to the drive motor for the reasons given inSection III-B. Since no negative torques can be output for activedeceleration control of the AGV, an FBC is utilized. The mem-bership functions selected for the FBC are as shown in Fig. 9.The rule base as shown in Fig. 10 is designed to output a zerovoltage for most of the combinations in positive velocity errors.

The overall speed control of the actual AGV can be achievedby operating the FDC and FBC in unison as both controllers arerelated to speed error and its integral. The FDC was designedto provide an active torque (voltage) during most of the time,while the FBC is effective in the event of deceleration to a lowerspeed. However, one should be very careful with the design be-cause braking while accelerating can lead to higher consump-tion of the limited energy of the batteries, wear in the brakingsystem and jerky movements. One of the ways to overcome thisproblem is to incorporate a supervisory controller to oversee theswitching of FBC appropriately. The supervisory controller im-plements the following heuristics in our implementation. “TheAGV needs to brake if and only if the actual speed is greater thanthe requested speed.” If the driving controller can be designednot to overshoot whenever the AGV requires a higher speed,above statement can be further simplified as, “The AGV needsto brake whenever it is required to reduce speed or decelerate.”Therefore, the supervisory controller can be designed to detectany request for deceleration in the desired speed and switch theFBC “ON” accordingly. During this time, the FDC can be de-signed to output a very small positive or zero voltage.

2) Results: In this application, combination of driving withbraking provides for the longitudinal control of the AGV. We

Fig. 9. Membership functions of FBC.

Fig. 10. Rule base for the FBC.

choose the desired speed profile as shown in Fig. 11(a) to as-sess the longitudinal fuzzy controller (LOFC), which is a com-bination of FDC and FBC. The resultant tracking performanceis also shown in Fig. 11(a). It can be seen from Fig. 11(b) thatthe FDC and FBC are independently contributing to the finallongitudinal control of the AGV. Fig. 12 shows in the case ofover-braking how FDC and FBC are actively contributing toachieve their goals.

D. Lateral Fuzzy Controller (LAFC)

1) Control Structure: The lateral or the steering control ofa mobile robot is a very challenging nonlinear control problemdue to the complexity of the model, the uncertainty of the param-eters and coupling effects of the driving on the steering system.Other nonlinear effects such as gear backlash and road gradevariations can also render adverse effects.

The steering angle error (ae) and rate of change of steeringangle error (aed) are chosen as inputs to the LAFC as shown in


Fig. 11. FBC performance in a two-step speed reduction.

Fig. 12. Combined performance of FDC and FBC for a trapezoidal speedprofile.

Fig. 2, whereas the output is a voltage. Triangular membershipfunctions are used for the input and output in the normalized uni-verse of discourse as shown in Fig. 13. The rule base structure

Fig. 13. Membership functions of the LAFC.

Fig. 14. Rule base for the LAFC.

(Fig. 14) conforms to the diagonal form as this choice guaran-tees stability of the system (Section III-A).

2) Results: The PID controller and LAFC was tuned toyield a good performance for a reference trajectory of counterclockwise turn, followed by a clockwise turn as shown inFig. 15. Both controllers yielded good tracking accuracy. Thenthe controllers were given a different operating condition asshown in Fig. 16. It can be seen from the figures that the PIDcontroller performance is significantly degraded while LAFCis not, demonstrating the latter controller’s ability to copewithin a wider operating region. To assess the performance ofthe steering controller in the presence of road grade changes,the vehicle was initially moved along an equi-leveled surfaceand then down a 10downward slope. As shown in Figs. 17(a)and 18(a), both the PID and LAFC controllers perform wellunder flat and level road conditions. However, in the 10downward slope [Figs. 17(b) and 18(b)], the performance ofthe conventional PID controller degrades significantly while


Fig. 15. LAFC and PID controller tracking performance with a 15s rateof change of steer angle.

Fig. 16. LAFC and PID controller tracking performance with a 1s rate ofchange of steer angle.

Fig. 17. PID steer controller performance (a) in a leveled road and (b) in a 10downward slope.

the LAFC performance is not affected. This demonstrates theLAFCs robustness to road grade variations.

E. Simultaneous Operation of Longitudinal and LateralControllers

It is very interesting and important to investigate a more prac-tical case where the longitudinal and lateral controllers are op-erating simultaneously as this gives some indication of the cou-pling effects between the steering and drive systems. For thispurpose, reference speed and steer angle trajectories as shown inFigs. 19 and 20 were chosen. As is seen from the results shownin Figs. 19(a) and 20(a) both PID and fuzzy longitudinal con-trollers are not visibly affected by the coupling effects. However,Figs. 19(b) and 20(b) show that the PID steering (lateral) con-troller is unable to remove coupling effects due to the high-speedturning, a problem not evident in the LAFC performance.

IV. CONCLUSION

In this paper we have proposed a control structure for un-coupled longitudinal and lateral control of an AGV, which is aconverted, electrically powered golf car. Longitudinal control isachieved via two uncoupled fuzzy controllers,viz., a fuzzy drivecontroller and a fuzzy braking controller switched appropriatelyby a supervisory controller. The lateral controller is also synthe-sized using fuzzy logic. All of the fuzzy controllers are derivedfrom the perspective of variable structure systems theory thusguaranteeing stability and convergence of tracking errors. Theresulting rule structures for all controllers conform to a standard


Fig. 18. LAFC performance (a) in a leveled road and (b) in a 10downwardslope.

Fig. 19. PID drive and steer controllers performances at 2 ms.

rule table. Gains and membership functions are tuned to yieldthe desired performance based on trial and error and heuristics.

The performances of the three FLCs were experimentally as-sessed individually as well as simultaneously. The individual

Fig. 20. Fuzzy drive and steer controller performances at 2 ms.

assessments showed the proposed FLC schemes outperform theconventional PID schemes, particularly in tracking accuracy andsteady-state errors. Further, the results showed that the designedFLCs are robust to load changes, coupling effects, operatingpoint changes and road grade changes. The simultaneous oper-ations of LOFC and LAFC showed that the designed uncoupleddirect fuzzy controllers are capable of removing coupling ef-fects implicitly, unlike PID control. Simultaneous operation ofFDC designed for a dc series motor powered drive system andthe FBC designed for a stepper motor driven braking systemshowed smooth speed tracking performance with no jerking.

APPENDIX

Fig. 21 shows the schematic diagram of the experimentaltest-bed (see Fig. 22).

Parameter definitions of the vehicle modelVirtual steer angle.Speed of the vehicle.Heading angle.Driving torque.Braking torque.Steer torque.Coefficient of air drag force.Coefficient of turning friction.Coefficient of braking.Coefficient of rolling friction.Mass of the chassis of the vehicle.Mass of a wheel.Total mass of the vehicle.Width of a tire.Radius of a tire.Inertia of the chassis around the-axis.Inertia of the tire along the axel.


Fig. 21. Schematic diagram of the golf car.

Fig. 22. The experimental golf car.

Inertia of the tire perpendicular to the axel.and Terms are related to friction.

Related to inertias of the vehicle.and Defined in Fig. 21.

Further, and are the first partial derivatives of andwith respect to . Similarly, is the second derivative ofwith respect to .

REFERENCES

[1] D. Wang and G. Xu, “Full state tracking and internal dynamics ofnonholonomic wheeled mobile robots,” inProc. Amer. Contr. Conf.,Chicago, , June 2000, pp. 3274–3278.

[2] A. Kamga and A. Rachid, “Speed, steering angle and path tracking con-trols for a tricycle robot,” inProc. IEEE Int. Symp. Comput.-Aided Contr.Syst. Design, Dearborn, MI, Sept. 1996, pp. 56–61.

[3] Z. Zalila, F. Bonnay, and F. Coffin, “Lateral guidance of an autonomousvehicle by a fuzzy logic controller,” inIEEE Int. Conf. Syst., Man, Cy-bern., vol. 2, 1998, pp. 1996–2001.

[4] K. J. Hunt, J. Kalkkuhl, H. Fritz, T. A. Johansen, and Th. Gottsche, “Ex-perimental comparison of nonlinear control strategies for vehicle speedcontrol,” inProc. IEEE Int. Conf. Contr. Applicat., Italy, Sept. 1998, pp.1006–1010.

[5] J. K. Hedrick, D. McMahon, V. Narendran, and D. Swaroop, “Longitu-dinal vehicle controller design for IVHS systems,” inProc. Amer. Contr.Conf., vol. 3, June 1991, pp. 3107–3112.

[6] J. K. Hedrick, “Nonlinear controller design for automated vehicle ap-plications,” inProc. UKACC Int. Conf. CONTROL’98, vol. 1, 1998, pp.23–32.

[7] C. D. Lee, S. W. Kim, Y. U. Yim, J. H. Jung, S. Y. Oh, and B. S. Kim,“Longitudinal and lateral control system development for a platoon ofvehicles,” in Proc. IEEE/IEE/JSAI Conf. Intell. Transportation Syst.,ITSC’99, Tokyo, Japan, Oct. 1999, pp. 605–610.

[8] W. S. Wijesoma and R. J. Richards, “Robust trajectory following ofrobots using computed torque structure with VSS,”Int. J. Contr., vol.52, no. 4, 1990.

[9] W. S. Wijesoma, “Fusion of computational intelligence with slidingmode control for robot control,” inProc. IASTED Int. Conf. ArtificialIntell. Soft Comput., Aug. 1999, pp. 49–53.

[10] W. S. Wijesoma and K. R. S. Kodagoda, “Synthesis of stable fuzzyPD/PID control laws for robotic manipulators from a variable structuresystems standpoint,” inLecture Notes in Computer Science 1625. NewYork: Springer-Verlag, May 1999, pp. 495–511.

[11] T. K. Leong and Y. T. Men, “Design and implementation of drive systemfor outdoor AGV,” Tech. Rep., Nanyang Technol. Univ., Singapore,1998.

本文献由“学霸图书馆-文献云下载”收集自网络，仅供学习交流使用。

学霸图书馆（www.xuebalib.com）是一个“整合众多图书馆数据库资源，

提供一站式文献检索和下载服务”的24 小时在线不限IP

图书馆。

图书馆致力于便利、促进学习与科研，提供最强文献下载服务。

图书馆导航：

图书馆首页文献云下载图书馆入口外文数据库大全疑难文献辅助工具

http://www.xuebalib.com/cloud/

http://www.xuebalib.com/

http://www.xuebalib.com/cloud/


http://www.xuebalib.com/vip.html

http://www.xuebalib.com/db.php

http://www.xuebalib.com/zixun/2014-08-15/44.html


fuzzy speed and steering control of an agv - control...

Documents