Wheeled Mobile Robot Path Control in a Complex Trajectory using HybridMethods

Transcription

1 Wheeled Mobile Robot Path Contol in a Complex Tajectoy using HybidMethods MOHAMMED A H ALI 1,a, MUSA MAILAH 2, WAN AZHAR B YUSSOF 1, ZAMZURI BIN HAMEDON 1, ZULKILI B M YUSSOF 1 1 Faculty of Manufactuing Engineeing, Univesiti Malaysia Pahang 266Pekan, Pahang MALAYSIA a mohalihashim@gmailcom 2 Faculty of Mechanical Engineeing, Univesiti Teknologi Malaysia 8131 Skudai, Joho B MALAYSIA Abstact A obust contol algoithm fo tacking the mobile obot in a pe-planned path duing passing though complicated envionments such as in oundabout is pesented in this pape The poposed algoithm is deived fom the kinematic and dynamic of 3wheeled Non-holonomic mobile obot motion The contol scheme is pefomed using Resolved Acceleation Contol, Active Foce Contol stategy o mixed of them in Simulink-MATLAB, which ae compaed with each othe in the matte ofenabling the obot to follow the pedefined path while applying distubances Results show the capability of this contolle to tack the obot on the pe-defined path and emove the effect of the distubances Key-wods: Non-holonomicWheeled Mobile obot, Lagang-Eula Equation, Resolved Acceleation Contol, Lase Simulato, Active Foce Contol Stategy, Fuzzy Logic 1 Intoduction Nowadays, mobile obots ae a common use in many applications that epesent a hazadous, complex, high accuate o had tasks in woldwide fields, like aeospace, unde-wate, militay, medicine, inspection, mining etc Usually the obot is supposed to navigate autonomously eithe in stuctued o non-stuctued envionments; both need high obust contol to detemine its path within teain and avoiding obstacles In some conditions like oad envionments, it is impotant to contol obustly the obot in the pe-planned path; othewise it will cash cas o people Complex tajectoy is occued when thee ae open spaces aeas in the path of the obot such as in oundabout The path planning in such aea is esticted to the oad oles, undetectable aea in by sensos and choosing the ight banch to get out fom oundabout This path needs a high accuate contol system to be pefomed; othewise it can cash othe vehicles o collide with the oad s infastuctue [1] Diffeent methods and techniques have been investigated to solve the poblems of mobile obot motion contol; some of them depend only on the kinematics of the mobile obot; othes on the dynamics, o combination between them A wheel contolling with feed-fowad compensation of dynamics is used fo sevo contol of an autonomous mobile obot [2], which is adaptive to vaiations of movement using the ecusive least squae method fo online paametes estimato Fuzzy logic contolle with efeence speed deived fom the cuvatue of the detected tajectoy by camea and image pocessing is used fo contol of mobile obot [3] Fuzzy logic contolle is pefeed based on some popeties like non-linea natue of the FLC, a fast dynamic esponse, which esulted by an accuate dynamic model of system [4]An adaptive method using a kinematic and toque contolle based on Fuzzy Logic easoning is used fo intelligent contol of an autonomous Mobile Robot [5] Neual netwoks contolle is utilized fo contolling the motion of mobile obot [6] though using one laye to define the elationship between the linea velocities and the eo positions of mobile obota coss-coupling method [7] is used in diffeential dive fo contolling the velocity of both motos, in which the contol loop of each moto uses the position eos of the othe one Fuzzy logic contolle [8] is implemented fo contolling a wheeled mobile obot ISBN:

2 motion in unstuctued envionments with obstacles and slopes A stable tacking contol system [9] is used fo adjusting the linea and otational velocities of mobile obot using a Liapunov function, which depends on lineaizing of kinematics model with feedback contol An appoach based on feedback sliding mode contol [1] is used fo stabilizing of non-holonomic mobile obot Sliding-mode contol method [11] is utilized fo stabilization and tacking of non-holonomic mobile obots using kinematics in pola coodinates The back-stepping contol appoach with integation of a kinematic and a toque contolle [12] has been used fo contol of non-holonomic mobile obots contolle has been poposed by [13] and expeimentally implemented with a lot of mobile manipulato dynamics system, which esulted by high obust contol to the system especially with existence of distubances [14] In this pape, thee contolle has been used fo obot path contol namely;,, and a combination - is common used fo contoling the position and oientation eos duing movements howeve the is useful to be utilized with dynamic distubances The - contol system scheme consists of two feedback loops: extenal and intenal loop The extenal loop is used fo contolling the kinematics paametes by the Resolved Acceleation Contol and the intenal loop is used fo contolling the dynamics paametes and distubances of obot by contolle The contol of mobile obot in a complix path in some dangeous aeas such as in oundabout duing path execution still a complicated poblem in obot eseaches,since it needs to maintain the tack eos at zeo level [1] Hee in this pape, it is suggested to use ou lase simulato appoach fo path planning in oundabout, which is emaked as a complex envionments and still not modeled yet The obust contol stategy is applied to execute the path in the oundabout envionments; which is the contibution of this pape 2 Modeling of Non-Holonomic Wheeled Mobile Robot Lase The obot is assumed to be moved in a flat plane whee the motion can be descibed in x and y diection using thee wheels; two diffeential wheels and Casto as in Fig 1 The movement is geneated by motos, which switch the ight wheeled by angula velocity θ and switch the left one with θ l The heading diection ϕ detemines the otation of mobile obot in counte clockwise The obot motion can be descibed in two coodinate systems: global coodinate system X, Y axis and Local coodinate system W,V as in Fig 1 In the global coodinate system, the motion can be obtained in thee axises q [xc, yc, ϕ ] T as in Fig 1, wheeas the local coodinate system has only two axisesw,v The cente of Non-holonomic mobile obot has some constaints to its movements, due that the wheels ae assumed to be moved with pue olling, without slipping on the gound and it can move only in the nomal of the axis of diving wheels (no movement in sidewise) This constaints can be witten as in Eq 1 sin( ϕ) A( q) q Whee, L -: Length of the obot, :Distance between the two wheels, : Radius of the diving wheels ( both wheels ae with same adius), d :Displacement between the diving wheel shaft and the mass cente c of the mobile obot Fig 1 illustate mobile obot dimension with global and local coodinate system 21 Robot Kinematics and Dynamics The mobile obot is diven by two diffeential wheels with caste wheel in ea as in Fig 1 The ight wheel is led by velocity equal to V θ and the left wheel by Vl θl Theefoe the velocity of mobile of mobile obot can be witten as in Eq 2: V + V V l 2 - d sin( ϕ) - b sin( ϕ) b θl 2 2 T [ x y ϕ θ θl ] θ 2 θl (1) θ (2) ISBN:

3 The angula velocity of the heading otation is then the diffeence between the angula velocity of ight wheel and the left wheel, which can be calculated as in Eq 3: V Vl θ θl θ - θl ϕ (3) The velocity of the obot in a global coodinate can be descibed in local coodinate system by the means of angula velocity θ and θl as in Eq 4: d x - sin( ϕ) 2 d + y sin( ϕ) 2 ϕ 22 Mobile Robot Dynamics d + sin( ϕ) 2 d θ sin( ϕ) 2 θl - The dynamic equations of mobile obot can be detemined using Newton's law o Eula-Lagang equation In this eseach, the lagang equation is used to deive the dynamics equations of the obot: k k T (5) τ i A (q)λ dt qi qi whee k is the kinetic enegy and q is the coodinate system τ i is the exeted toque on the obot, A T (q) is the constiats of obot movement By deiving the Lagange equation, the total Lagange equation can be witten as in Eq 6: (4) 2 2m ωd ϕ sin( ϕ) 2 2m cos( ) ωd ϕ ϕ λ1 V ( q, q) λ λ2 λ3 τ τ τ l A T (q)tanspose of the constaints equation A(q) as in Eq 1 m : total mass of Mobile Robot mc + 2mw, mc : the mass of the platfom without the diving wheels and DC motos, mw: the mass of the diving wheels and the DC motos, I: total moment of inetia of mobile obot Ic+ 2mw (d 2 + b 2 ) + 2Im, Ic: the moment of inetia of the body of obot without the diving wheels and the motos about axis passed though P, Iw: the moment of inetia of each wheel and the moto oto about the wheel axis, Im: the moment of inetia of each wheel and the moto oto about the wheel diamete, τ : the toque exeted τ l : the toque on wheel axis by ight moto, exeted on wheel axis by left moto, λ: the Lagange multiplie coefficient 3 Design of Contolle The path of mobile obot is contolled using Resolve Acceleation Contol, Active Foce Contol and acombination of them - stategy In -, thee ae two feedback loops in the contol scheme, extenal and intenal loop as in Fig 2; the extenal loop is used fo contolling the kinematics paametes by the and the intenal loop is used fo contolling the dynamics of obot by contlle Tansfomation in Fig 2 is effeed to the elation between the global and local coodinate systes as in Eq 4 T M ( q) q+ V ( q, q) τ A ( q)λ (6) Whee: m 2mωdsin( ϕ) m - 2mωdcos( ϕ) M ( q) 2m dsin( ) - 2m dsin( ) I ω ϕ ω ϕ Iw Iw Fig 2: Illustate the - contol Scheme ISBN:

4 31 Contol Stategy This contolle poposed by [16] to contol the hand gippe This contolle is woking based on minimizing of the position and oientation eos to zeo, which needs to apply suitable toque o foces to the system Eqs 7-9 descibe this contolle (7) xact xef + Kd( xef xact ) + Kp( xef xact ) constant, we choose φ as the input fo FL, which is fuzzed to a fuzzy set with suitable linguistic vaiables as following: φ{vey low, Low, Medium, High, Vey High} In othewise, the output of FL is fuzzed into two output sets with suitable linguistic vaiables, which can be witten as following INR/INL{ Vey small, Small, Medium, Lage, Vey lage} yact yef + Kd( yef yact ) + Kp( yef yact ) (8) VS 1 8 S M L VL ϕ act ϕ ef + Kd( ϕ ef ϕ act ) + Kp( ϕef ϕact ) (9) Degee of membeship Whee suscipts ef and act efe to input and output espectively, Kd and Kp ae the diffeential and popotional gains espectively Fig2 show this contolle 32 Stategy contolle has been poposed by [12] and expeimentally implemented with seveal dynamic systems, which obustly eliminate the effects of distubances [13-15,17,18] It is the inne loop in the poposed contolle and it depends on the angula acceleation of the of wheels motos In eal-wold envionment, contolle consists of actuatos that apply toque to the diving wheels and sensos that measue the angula acceleation of wheels The measued acceleation with estimated Inetial matix is compaed with applied toque as in Eq18 By estimating the Inetial matix using Atificial Intelligence methods, the contolle can vey apidly and effectively compensate the distubances In simulation, these measuements ae assumed to be pefectly known The equation that estimated the distubance can be witten as in Eq 1: * (1) τ τ θ d IN * Whee τ d is the estimated toque distubance effected on the wheelsτ is the toque of actuato, which can be calculated in DC motos using the following equation: τ K t I, I is the cuent of DC moto IN is the estimated inetial matix The estimated Inetia matix foboth expeiments has been calculated using fuzzy logic appoach with following membeships as in Fig 5 Depending on that, the inetial Matix M(q) in Eq 9, can change only egading to (φ) and the othes values ae Degee of membeship 2 b 25 INR c INL Fig 5: Membeship functions of system input and output: (a) input (φ) (b) output INR (c) output INL In this simulation, the fuzzy infeence system is done using Mamdani type as follows: 1 If (phi is M) then (INR is MR)(INL is ML) 2 If (phi is VL) then (INR is VSR)(INL is VLL) 3 If (phi is L) then (INR is SR)(INL is LL) 4 If (phi is H) then (INR is LR)(INL is SL) 5 If (phi is VH) then (INR is VLR)(INL is VSL) 4Path contol Simulation Results and Discussion The simulation is done using Matlab/simulink fo the above-metioned pe-defined path with discete values simulation with the following paametes: Integation algoithm: ODE3 (Bogacki-Shanpine) Simulation type: Fixed step Fixed step size: Auto WMR Paametes: 15 m, b 75 m, d 3 m, m 31 kg, m w 5kg, I15625 kgm 2, I w 5kgm 2 Contolle Paametes: Kpx 2/s 2, Kpy 2/s 2, Kpφ 2/s, Kdx 1, Kdy,Kdφ 1 (fo the pat) Kt hi VSL SL ML LL VLL a Degee of membeship VSR SR MR LR VLR N/A (obtained fom catalogue of ISBN:

5 suitable DC moto fo pat) Distubance Models Paametes: Seveal constant toque distubances and Hamonic toque distubances wee applied to the contol system We have implemented thee types of contolles and compae them with efeence tajectoy: - based kinematic contolle - based dynamic contolle - - contolle Fig 3 bellow shows the actual tajectoy of all contolles without distubance fo the pedefined path of mobile obot pesents eckoning eos that incease incementally duing tacking the path with high tack eos in x(3mm) and y(35mm) Howeve the diffeence between the efeence and actual path of, - ae two small and theefoe they ae ovelapped each othe; whee the tack eos in the powe of 1-2 mm we can notice that a big shoots at the beginning of contolle will be occued because thee still no output fom contolle loop, wheeas at and -, thee was no oveshoot due to the effect of kinematic contolle at the beginning Ymm Refeence - Y eo mm Fig 3: Illustate the esult of and - contolle simulationwithout distubance (a) the tajectoy of mobile obot (b) y tack eos fo, and - (c) y tack eosfo and - (d) x tack eos fo, and - (e)x tack eosfo and - Fig 4 bellow shows the actual tajectoy of all contolles with constant distubance τd [ 1 1] T applying to the pedefined path of mobile obot pesents big deviation eos duing tacking the path with high tack eos in x(5mm) and y(6mm) Howeve the diffeence between the efeence and actual path of, - still two small and theefoe they ae ovelapped each othe; whee the tack eos in the powe of 1-2 mm at x and y diections 3 Eo in Y diection (d) - X eo mm (f) Eo in X diection X mm (a) 25 2 Refeenc - 5 Eo in Y diection 5 Eo in X diection y mm 15 1 Y eo mm X eo mm x mm (a) (b) (c) ISBN:

6 y eo mm Eo in Y diection (b) Fig 4: Illustate the esult of, and - contolle simulationwith distubance 1 Nm (a) the tajectoy of mobile obot (b) x tack eos(c) y tack eos 4 Conclusion - x eo mm The, and - contolles have been used to tack the obot on the pe-defined tajectoy The paametes of the contolles ae deived fom kinematics and dynamics equations that descibe the obot motion with non-holonomics constaints The fuzzy logic easoning is implemented to find the inetial matix fo the calculation of the applied toque Fom simulation esults, it has seen that, thee is no diffeence between the efeence and actual path without distubance fo and -, howeve thee was a sizable daft in When applying a constant distubance, thee was a big deviation between the efeence and actual tack in, but it doesn t affect to o - contolle In geneal, and - contolles pesent the capability to eliminate the effect of distubances on the system Refeences [1] Mohammed A H Ali, Autonomous Mobile Robot Navigation and Contol in the Road Following and Roundabout Envionments Incopoating Lase Range Finde And Vision System PhD Thesis UTM, 214 [2] K C Koh' and H S Cho Wheel Sevo Contol based on Feedfowad Compensation fo an Autonomous Mobile Robot Technical Repot, Depatment of Pecision Engineeing & Mechatonics School of Mechanical Engineeing KAIST, Koea [3] M Gunes, F Baba Speed And Position Contol Of Autonomous Mobile Robot On Vaiable Tajectoy Depending On Its Cuvatue Jounal of scientific and industial eseach vol 68 June 29, pp Eo in X diection (c) [4] T H Lee, F H F Hung P K S Tam Position Contol fo Wheeled Mobile Robots Using a Fuzzy Logic Contolle The Hong Kong Polytechnic, Univesity, Hung Hom, Kowloon, Hong Kong [5] L Astudillo, O Castillo, P Melin, A Alanis, J Soia, L Aguila Intelligent Contol of an Autonomous Mobile Robot using Type-2 Fuzzy Logic Division of Gaduate Studies and Reseach in Tijuana Institute of Technology, Mexico [6] JasminVelagic, Nedim Osmic, and BakiLacevic Neual Netwok Contolle fo Mobile Robot Motion Contol Wold Academy of Science, Engineeing and Technology [7] J Boensteinand Y Koen, Motion Contol Analysis of a Mobile Robot Tansactions of ASME, Jounal of Dynamics, Measuement and Contol, Vol 19, No 2, pp [8] GyulaMeste Intelligent Mobile Robot Motion Contol inunstuctued Envionments ActaPolytechnicaHungaica Vol 7, No 4, 21 [9] Y Kanayama, Y Kimua, F Miyazaki T Noguchi, A Stable Tacking Contol Method Fo a Non-Holonomic Mobile Robot, Poc IEEE/RSJ Int Wokshop on Intelligent Robots and Systems, Osaka, Japan, pp , 1991 [1] A BlochS Dakunov stabilization of a nonholonomic system via sliding modes Poceedings of the 33 d Confeence on Decision and Contol Lake Buena Vista, FL - Decembe 1994 [11] D Chwa Sliding-Mode Tacking Contol of Nonholonomic Wheeled Mobile Robots in Pola Coodinates IEEE tansactions on contol systems technology, vol 12, no 4, july 24 [12] R Fieo and F L Lewis Contol of a Nonholonomic Mobile Robot: Backstepping Kinematics into Dynamics Jounal of Robotic Systems 14(3), (1997) [13] Hewit, J R and Budess, J S (1981) Fast Dynamic Decoupled Contol fo Robotics using Active Foce Contol Tans Mechanism and Machine Theoy, 16(5), [14] Hewit, J R and Maouf, K B (1996) Pactical Contol Enhancement via Mechatonics DesignIEEETansIndustial Electonics, 43(1), ISBN: