Trajectory Tracking Control for A Wheeled Mobile Robot Using Fuzzy Logic Controller

Transcription

1 Trajetory Traking Control for A Wheeled Mobile Robot Using Fuzzy Logi Controller K N FARESS 1 M T EL HAGRY 1 A A EL KOSY 2 1 Eletronis researh institute, Cairo, Egypt 2 Faulty of Engineering, Cairo University, Egypt Abstrat: A trajetory traking ontrol for a wheeled mobile robot using fuzzy logi ontroller (FLC) is presented in this paper The ontrol algorithm based on the errors in postures of mobile robot whih feed FLC, whih generates orretion signals for the left and right motor speeds The ontrol strategy is based on a feed forward veloity profile and the orreting signal in the veloity generated from the FLC aording to the postures errors Simulation and experimental results demonstrate the effetiveness of the proposed algorithm, whih proved the good traking results and showed the robustness of the algorithm against the unertainties in the system model Key-words:- veloity profile-trajetory traking-postures ontrol-fuzzy logi ontrol-and low-level ontrol system 1 Introdution Wheeled mobile robots (WMRs) are inreasingly present in industrial and servie robotis, partiularly when flexible motion apabilities are required, on reasonably smooth grounds and surfaes Several mobility onfigurations (wheel number and type, their loation and atuation, single or multi-body vehile struture) an be found in the appliation [5,6,8] The most ommon for single body robots are differential drive and synhro drive (both kinematially equivalent to a uniyle) Beyond the relevane in appliations, the problem of autonomous motion planning and ontrol of WMRs has attrated the interest of researhers in view of its theoretial hallenges In partiular, these systems are a typial example of nonholonomi mehanisms due to the perfet rolling onstraints on the wheel motion (no longitudinal or lateral slipping) [5] In the absene of workspae obstales, the basi motion tasks assigned to a WMR may be redued to moving between two robot postures and following a given trajetory The basi motion tasks that we onsider for a WMR in an obstale free environment are: Point- to- point motion: the robot must reah a desired goal onfiguration starting from a given initial onfiguration Trajetory following: a referene point on the robot must follow a trajetory in the Cartesian spae (ie, a geometri path with an assoiated timing law) starting from a given initial onfiguration Exeution of these tasks an be ahieved using either feed forward ommands, or feedbak ontrol, or a ombination of the two Indeed, feedbak solutions exhibit an intrinsi degree of robustness The design of feed forward ommands is instead stritly related to trajetory planning, whose solution should take into aount the speifi non-holonomi nature of the WMR kinematis Control of WMRs is generally divided into the following ategories: (1) Path Planning (PP) (2) Trajetory generation (TG) (3) Trajetory traking / Following (TT/TF) [2] PP problem of haraterizing the shortest path for a partile is by the determination of waypoints TG problem onsider the design of the robot motion trajetory as a funtion of a time, as well as generate orresponding referene inputs to the trajetory traking system (TT) the robot hene should move along a speified path The robot trajetory planning is the seond step after defining the waypoints of the robot travel (path planning), the purpose of trajetory planning takes into onsideration the system dynamis and different onstraints The trajetory planning and

2 generation onsists of rotation planning and translation planning In [4] a fuzzy ontroller is used to trak a path of a bi-steerable yberneti ar, also it takes the veloity planning "on-line planning" into onsideration in ontrol system Trajetory traking problem has been treated Several ontributors have disussed this problem Kanayama proposed that the mobile robot is ontrolled for running along speified path by a speed ommand inluding a feed-forward ontrol and feedbak ontrol [1], but the proposed tehnique does not take the veloity profile planning into onsideration Matthew disussed the problem of path traking problem-using feed forward and error based orretion signal for the angular veloity for the robot and a look ahead distane using PI ontroller [2], but the veloity planning is not taken into onsideration Luis Conde handled the problem of path traking of bi-steerable ar using FLC based on the look ahead distane, angle error, and urvature as inputs to the FLC without using feed-forward omponent [3,4] Hiroyuki presents PI ontroller using disturbane observer for trajetory traking problem in [6] Ti- Chung proposed a feedbak ontroller with linear and angular veloities onstraints in [8] In this paper the system omprises two suessive modules The first is off line planned veloity trajetories of left and right motors "differential steering" whih onsidered the approximate dynamis of the system in veloity planning during feed forward veloity trajetory generation The seond is the orretion signal extrated from the error deteted in the robot postures; FLC is proposed to overome the system dynami unertainties The veloity profile supplies the linear referene veloity, whih is onsidered as a feed forward ommand to the ontrol system, the errors in robot postures with respet to the planned path is ompensated by fuzzy feedbak ontroller The feedbak orretion ommand is added to the feed forward ommand to trak the given planned path The path-traking module uses the errors in robot postures as inputs to the fuzzy ontroller These errors inludes the errors in Cartesian oordinates (x, y) in loal oordinates system also, inlude the heading error The paper struture is as follows: setion 2 presents the ontrol system arhiteture, setion 3 presents kinematis model of the robot The veloity planned trajetories and path-traking ontroller are desribed in setions 4, and 5 respetively The simulation and experimental results and onlusion are presented in setion 6, and 7 respetively 2 Problem Formulation Models of mobile robot systems annot desribe exatly its performane due to system unertainties and shortage in parameter identifiation, so we proposed an intelligent ontroller to ompensate for these shortages without the need for extra validation of the proposed dynami model 21 Kinemati model The uniyle-modeled mobile robots onsidered in this paper are a lass of omputerontrolled vehiles whose motion an be desribed or transformed into the following model of onstrained movement in a plane [5]: x = v osθ, y = vsinθ, θ = ω (1) Where (x, y) are the Cartesian oordinates and θ is the angle between the heading diretion and the x-axis The non-holonomi onstraint for the model (2) is: y osθ xsinθ = 0 (2) It speifies the tangent diretion along any feasible path for the robot and briefly shows that a mobile robot with two independent drive wheels an be desribed using the uniyle model (1) We assumed that the referene point lies at the midpoint of the two drive wheels Let V L and VR denote the veloities of the left and the right wheel respetively The linear veloity V and the angular veloity ω of the mobile robot an be desribed as: v = ( vr + vl ) / 2 ω = ( v v ) / E R L (3) where E represents the distane between two drive wheels The urrent postures of the robot an be estimated as follows: x y = x + T vos( θ ) (4) = y + T vsin( θ ) (5) θ = θ + T ω (6) Where T is the sampling period 22 Veloity planning module The veloity-planning (VP) module estimates the linear referene veloity in whih the vehile should travel One main objetive taken into aount was to make the travel as omfortable as possible, ie to give the system the apability to fully ontrol the smoothness of the aeleration and deeleration profiles [5]

3 23 Path traking module In this researh the system omprises two suessive modules The first is off line planned veloity trajetories of left and right motors "differential steering" whih onsidered the approximate dynamis of the system in veloity planning during feed forward veloity trajetory generation The seond is the orretion signal extrated from the error deteted in the robot postures; FLC is proposed to overome the system dynami unertainties as well as problems generated due to line/irles representation of the trajetory The veloity profile supplies the linear referene veloity, whih is onsidered as a feed forward ommand to the ontrol system, the errors in robot postures with respet to the planned path is ompensated by fuzzy feedbak ontroller The feedbak orretion ommand is added to the feed forward ommand to trak the given planned path The path-traking module uses the errors in robot postures as inputs to the fuzzy ontroller These errors inludes the errors in Cartesian oordinates (x, y) in loal oordinates system also, inlude the heading error The path-traking module (PTC) is divided into path traking ontroller (high level ontrol system), and low-level ontrol system; the high-level path traker generates the speed ommands to the left and right motors, whih is exeuted by the low-level speed ontrol system The fuzzy logi ontroller is adopted as the path traker, whih generates the ommand signals for the low-level ontrol system The struture of the ontrol system for trajetory traking is shown in figure (1)The postures estimator blok estimates the postures of the mobile robot via the speed measurement of the right and left motor from the right and left shaft enoders, this estimation aording to equations (4-6) The errors of the postures in equation (7) is feed to the fuzzy logi ontroller, also the referene linear and angular speeds generated from the trajetory generator blok, V r and ω r, are feed to the fuzzy ontroller through whih, are onsidered the feed-forward signals The output of the fuzzy logi ontroller is the right and left ompensating signals that adapt the feed-forward signals aording to the dynamis and disturbanes onditions, then the modified linear and angular veloities feed to the veloity transformation blok to supply low level system with referenes for right and left motors The low level speed ontrol system bloks is responsible for traking the left and right speed profiles generated from the high level ontrol system xe = ( xr x )osθ + ( yr y ) sinθ ye = ( xr x )sinθ + ( yr y ) osθ θ e = θ r θ (7) The errors in equation (7) are the inputs to the fuzzy logi ontroller and the outputs of the ontroller are the orretion of the speed signals, whih modify the feed forward speed signals 3 Simulation and experimental results The MATLAB simulink tool is used for simulation Figure (2) shows the atual right and left speed trajetories aording to the planned veloity Low-level speed ontrol system + right motor Right shaft enoder Postures estimator Fuzzy ontroller Veloity transformation Trajetory generator Low-level speed ontrol system + left motor Left shaft enoder Fig(1) Simulated and experimental system desription

4 profiles for left and right motors using the FLC ontroller in low-level ontrol system The orresponding referene and atual trajetories of the robot motion is shown in figure (3), whih shows a good traking performane that uses the proposed path-traking algorithm desribed above The experimental verifiation of the proposed ontroller is under work now Figures (4,5,6,7) show the experimental referene and atual veloity profiles for the left and right motors using FLC ontrollers Referring to these figures we notie that the agreement of the atual with the referene veloity profile in left and right motor using FLC The appliation of high level proposed trajetory ontroller in the experimental verifiation is under work Fig 4 Experimental referene veloity profile of the left motor Fig2 Simulated atual linear speed trajetories of right and left motors in p u Fig 5 Experimental atual veloity profile of the left motor using FLC Fig 3 Simulated referene and atual trajetories using feed-forward and feed bak FLC Fig 6 Experimental referene veloity profile of the right motor

5 Referenes: Fig 7 Atual veloity profile of the right motor using FLC Fig 8 Experimental referene and atual veloity profile of 4 Conlusion the left motor using FLC A FLC for trajetory traking is proposed The FLC developed ompensates for system dynamis unertainties, and aordingly simplified the development of dynami model of the system Simulated and experimental results showed good agreement Simulation and experimental work demonstrate the effetiveness of the proposed algorithm with the two-wheeled mobile robot and proved that this method is haraterized by its robustness with unertainties in the system model [1]-Yutaka Kanayama "Mobile Robot Navigation Method" Patent Number , De17, 1991 [2]- Matthew J Barton "Controller Development and Implementation for Path planning and Following in an Autonomous Urban Vehile" A thesis submitted in partial fulfillment of the requirements for the degree of Bahelor of Engineering (Mehatronis) [3]- A Ollero, A Garia-Cerezo, J L Martinez, and A Mandow "Fuzzy Traking Methods For Mobile Robots" Chapter 17 of the book" Appliations of fuzzy logi: Towards high mahine intelligene quotient", Prentie Hall, 2004 [4]- Luis Conde Bento, Urbano Nunest, Abel Mendest, and Mihel Parent "Path Traking Controller of a bi-steerable Cyberneti Car using Fuzzy Logi" Proeedings of ICAR 2003, the 11th international Conferene on Advaned Robotis, Coimbra, Portugal, June 30-July3, 2003 [5] Danwei wang, Feng Qi "Trajetory Planning for a four-wheel-steering Vehile" Proeedings of the 2001 IEEE International Conferene on Robotis & Automation, seoul, Korea, May 21-26, 2001 [6] Hiroyuki kojima, Toshihiro Hashimoto, and Sadao shimoyama "Trajetory Traking Control of a Flexible Mobile Robot using Disturbane Observer" Proeedings of the 3rd International Conferene on Advaned Mehatronis, Okayama, Japan, Aug 1998, JSME [7] Sott Pawlikowski "Development of a fuzzy logi Speed and Steering Control system for an Autonomous Vehile" University of Cininnati, Master of Siene Researh Projet, Departement of Mehanial Engineering, Jan 10, 1999 [8] Ti-Chung Lee, Kai-Tai Song, Ching-Hung Lee, and Ching-Cheng Teng "Traking Control of Uniyle-Modeled Mobile robots using a Saturation Feedbak Controller" IEEE Transation on Control Systems Tehnology, Vol 9, No 2, Marh 2001