Enhanced SLAM for Autonomous Mobile Robots using Unscented Kalman Filter and Neural Network

Transcription

1 Indan Journal of Scence and echnology, Vol 8(0), DOI:0.7485/jst/05/v80/5470, August 05 ISSN (Prnt) : ISSN (Onlne) : Enhanced SLAM for Autonomous Moble Robots usng Unscented Kalman Flter and Neural Networ Omd Panah, Amr Panah,5*, Amn Panah 3 and Samere Fallahpour 4 Department of Computer, Ayatollah Amol Branch, Islamc Azad Unversty, Amol, Iran; o.panah@auamol.ac.r Department of Computer and I, Hadaf Hgher Educaton Insttute, Sar, Iran; amr.panah00@gmal.com 3 Department of Computer, Yazd Branch, Islamc Azad Unversty, Yazd, Iran; amn.panah00@gmal.com 4 Mazandaran Unversty of Medcal Scences, Sar, Iran; samere.fallahpour@gmal.com 5 Young Researchers and Elte Club, azvn Branch, Islamc Azad Unversty, azvn, Iran Abstract he novel method of moble robot Smultaneous Localzaton And Mappng (SLAM), whch s mplemented by optmzed Unscented Kalman Flter (UKF) Va a Radal Bass Functon (RBF) for autonomous robot n unnown ndoor envronment s proposed. For atone the Unscented Kalman Flter based SLAM errors ntrnscally caused by ts lnearzaton process, the Radal Bass Functon Networ s composed wth Unscented Kalman Flter. A moble robot localzes tself autonomously and maes a map smultaneously whle t s tracng n an unnown envronment. he offered approach has some benefts n handlng a robotc system wth nonlnear movements because of the learnng feature of the Radal Bass Functon. he smulaton results show the powers and effectveness of the proposed algorthm comparng wth a Standard UKF. Keywords: Hybrd Flter, Moble robot, RBF, SLAM, UKF. Introducton A eyword requste for a correctly autonomous robot s that t can localze tself and carefully map ts surroundngs smultaneously. Many algorthms have been offered for solvng SLAM obstacles, for example partcle flter, Kalman Flter (KF), Extended Kalman Flter (EKF) and an Unscented Kalman Flter (UKF). he UKF SLAM mang a Gaussan nose supposton for the robot observaton and ts movement. he UKF encourage calculaton values analogous to the ones of EKF but does not requrement the lnearzaton of the fundamental model. he UKF uses the unscented transform to lnearze the movement and measurement models 3. RBF, adaptve to the change of envronmental data flowng through the networ durng the process, can be combned wth an UKF to atone for some of the dsadvantages of an UKF SLAM method 4. Amr Panah 5 solved the SLAM problem wth a neural networ based on an Unscented Kalman flter. Accordng to the research results, the UKF SLAM based on Neural Networ, shows better performance than the Standard UKF SLAM. Stubberud et al. 6 extended an adaptve EKF composed wth neural networs, wth a neuroobserver to learn system uncertantes onlne. he offered system boost the performance of a control system comprse uncertantes n the stateestmator s model. In ths artcle, we descrbe a Hybrd way usng RBF networ and UKF based SLAM for declne uncertanty n compare to SLAM usng Standard UKF. we do, consder the power of UKF based RBF algorthm to handle nonlnear attrbutes of a moble robot. We started by ntroducng some related algorthms on SLAM are explaned n secton, and the Hybrd algorthm s presented n secton 3. he detaled descrpton of the smulaton and expermental results s shown n Secton 4 and fnally n Secton 5 summarzes the results and gves an outloo on future research actvtes. * Author for correspondence

2 Enhanced SLAM for Autonomous Moble Robots usng Unscented Kalman Flter and Neural Networ. Related Algorthms for SLAM. Radal bass Functon Neural Networ he dea of Radal Bass Functon (RBF) Networs derves from the theory of functon approxmaton. he RBF networ s a threelayer feedforward networ. Input layer nput layer has one neuron for each predctor varable. Input neurons standardzes the lmted area of the values by reduce the medan and dvdng by the nterquartle range. hen the nput neurons requre the values to each of the neurons n the hdden layer. Hdden layer has an unlmted number of neurons that the optmal number s decded by the tranng process. he out comng value s transmtted to the output layer. Output layer he value of a hdden layer that come to ths layer s multpled by a weght assocated wth the neuron and transmtted to the output whch adds up the weghted values and presents ths sum as the output of the networ. hat generally uses a lnear transfer functon for the output unts and a nonlnear transfer functon (normally the Gaussan functon) for the hdden unts. he nonlnear transfer functon (Gaussan functon) s appled to the net nput to produce a radal functon of the dstance. he output unts mplement a weghted sum of the hdden unt outputs 7. he structure of Radal Bass Functon shows n ( Fgure ). two steps of Networ tranng: frst, determnng the weghts from the nput to the hdden layer; then, the weghts from the hdden layer to the output layer are determned 8. Fgure. A Radal Bass Functon Neural Networ Structure.. Unscented Kalman Flter UKF ntroduced by Uhlmann and Juler n 997 for the frst tme. hs flter structure s based on unscented transformaton. hs flter s bult based on transformaton as unscented transformaton. In the UKF, there s no need to calculate Vol 8 (0) August 05 Jacoban matrx. Snce, the processng nose n ths system s accumulatve; therefore the augmented state vector s used to mplementaton ths approach. In ths approach, the mean and covarance estmaton are calculated wth consderng the second order of the aylor seres. Assume that a random varable x wth covarance P X and mean μ s defned and also a random varable z as wth x s assocated: z=f(x). In unscented transformaton, to gan the covarance and mean random varable z, sgma ponts that are set of weghted ponts are used. hs ponts should be selected so that have a covarance P X and mean μ. Calculate the set of + sgma ponts from the columns of the matrx ( n+ l) P x : l X0 = m, W0 = () n+ l ( ( ) ) l X = m+ n+ l Px, W = ( n+ l ) () l X+ n= m ( n+ l) Px, W+ n= (3) n+ l ( ) ( ) l= a ( n+ b) n (4) n number of state varables are added. In the above, W s the weght whch s dependent wth the th pont and also s used for adjustng the flter more correctly 9. he UKF maes use of the unscented transform descrbed above to gve a Gaussan approxmaton to the flterng soluton of nonlnear optmal flterng problems of form, but restated here for convenence: x = f x, u, e (5) ( ) z = hx (, u, d ) (6) Where x s state vector and u s control nput and ε δ, are the system nose and the measurement nose, respectvely. In the frst phase of mplementng ths flter, the augment state vector wll become as the followng form: éx (7) X = e ê d ú ë û In contnue of ths paper, all the formulas that are used n the UKF n whch t ncludes of two man from sectons: Measurement update and me update 0. he me Update X = f( X, u, e ) (8) wx = 0, = é 0, m é, m = m = å (9) P å w ë X ûë X (0) û Indan Journal of Scence and echnology

3 Omd Panah, Amr Panah, Amn Panah and Samere Fallahpour z = hx (, u, d ) z () å wz () he Measurement Update Px x = å w é 0 z, z éz, z = ë ûë û (3) P x y = å w é X z z 0, m é = ë ûë, û (4) K = P P (5) xy xx ( ) m = m + K z z (6) P = PKP xxk (7) x y Where X, m, P, z, z, Px, Px and K, are movement model, predcted mean, observaton model, predcted observaton, novaton covarance, cross correlaton matrx and Kalman gan. 3. SLAM Algorthm usng Hybrd Flter A Hybrd flter s proposed n ths part, a RBF supplemented for actng as an observer to learn the system completely onlne. he mean, μ whch s extracted from values (x y θ ε δ) usng the RBF algorthm, use for the predcton step, as shown n ( Fgure ). 3. me Update (Predct) he Hybrd flter usng landmars as a robot s poston and specfcatons. A confguraton of the robot wth a state equaton X a = (x y θ ε δ), has the form of Equaton (8) snce t s supposed that the robot s equpped wth exteroceptve sensors and encoders. X éx éx + v tcos( q) y y + v tsn( q ) ê ú ê ú ê q q ú q v tsn( L ) = = + ê ú e e êd ú ê d ú ë û ë û (8) u = v + N(0, M ) (9) v s velocty of wheels, L s the wdth between the robot s wheels, and t s the samplng perod. Fnally, M depcts the covarance matrx of the nose n control space. he state equaton for landmars, combned wth the robot poston. (0<<c) éx (0) Y = = (xy qed m,xm,ys 00) ê m ë úû he state transton has the form of Eq. (): X = f( X, u ) + N(0, e ) () ε s the process nose, f shows the nonlnear functons, and u s control nput. For the aylor development of functon, f ts dervatve s used wth respect to X, as shown n Equaton (). (, ) u ( X u ) f, ' f X u = X () f s approxmated at u and μ he lnear extrapolaton s acheved by usng the gradent of f at u and μ as shown n Equaton (3). ' f X, u = f m, u + f m, u X m ( ) ( ) ( )( ) Fgure. he Archtecture of the Hybrd Flter SLAM Man Basc nputs are covarance, mean whch are computed by prevous nput, u, and present nput, u. n a predcton step, he robot computes the prevous mean and covarance and then, n observaton step, t computes a Kalman gan, present mean and covarance and defned features. RBF neural networ can execute as a fast and correct means of approxmatng a nonlnear mappng based on observed data. (3) Wth the exchange values ganed from equatons,, 3, 4, 5, prevous covarance and mean have the followng form of: m = a å (4) wx =0, a a =, m =0, m P å w [X ][X ] (5) As demonstrated n Equaton (6), the observaton model, z contans of the nonlnear measurement functon h and the observaton nose δ. Vol 8 (0) August 05 Indan Journal of Scence and echnology 3

4 Enhanced SLAM for Autonomous Moble Robots usng Unscented Kalman Flter and Neural Networ é r z = hy ( ) + N( 0, d) = = êë Æ úû é ( ) ( ) mx, x + my, y m N(0, ) y, y + d (6) æ ö tan q çmx, x êë è ø úû m = m m (7) ( ) x y z = å wz =0 (8) 3. he Measurement Update (Correct) o obtan the values P xy and P xy, t s necessary to computex μ z z that are compute n equatons 8, 4, 6, 8, wth replacement of these values. o compute the Kalman gan K, we need to compute P xy and P xy n the featurebased maps. we wll have the followng equatons: Pxx =å w [ ][ ] = 0 z, z z, z (9) a Px y = å w[ X, m ][ z, z] (30) = 0 K P P = x y x x (3) Consderng Hybrd algorthm n contnuous. RBF algorthm s ncluded wth tran through nput data and measurement values. In the tranng process, weghts are determned based on the communcaton of nput and each hdden layers. RBF requre hgher weght to am value on the hgher relatons between poses and headng angle wth comparng to measurement. In addton, the second weght, ω 0,equals zero because the output offset s zero. herefore, new estmated mean, can be descrbed as n Equaton (3) (0 j J ) æ æ j j j j j j j j j j m d ö ö 0 0 ( ) ( 0 ( )) 0 exp m = w + åj= w j m = x åj= j m = x åj= j ç è èç ( t ) ø ø (3) d j s the center of the jth bass functon wth the same dmenson of the nput vector and μ s an ndmensonal nput vector. τ explan the wdth of the bass functon, N s j j the number of hdden layer s nodes, m d explans the j Eucldean norm of showng the dstance between m and, d j j and j ( x) means the answer of the jth bass functon of the nput vector wth a maxmum value at d j. m = m + K z z (33) ( ) xx P= P KP K (34) 4. Smulatons o showng the effectveness of offered algorthm, we used the amend Matlab code that was developed by Baley. he smulaton was carry out by a robot wth maxmum speeds of 3[m/sec] and wheel dameter of [m]. speed and the maxmum steerng angle are 5[ /sec] and 5[ ] respectvely. For observaton step, the number of arbtrary features around wayponts was used. In the observaton step, a range bearng sensor model and an observaton model were used to measure robot pose and the feature poston, whch ncludes [ ] n bearng and a nose wth level of 0.[m] n range. he sensor range s 5[m] for small areas and 5[m] for large areas. In ths paper, two navgaton cases of the robot are surveyed: a Crcular navgaton, and Wdespread navgaton. 4. Navgaton on Crcular Map In crcular navgaton, the standard UKF based navgaton and proposed flter based navgaton are shown n (Fgure 3). Bold blac lne s Robot path and the dashed lne, show the paths of robots should traverse, based on data descrbed by the actual odometry. In (Fgure 4), the bold gray lne (RBFUKF) and the dashed blac lne (UKF) are the x, y, and θ errors n the case of UKF SLAM and proposed flter SLAM, and n able. see Mean Square Error of t. Fgure 3. Navgaton result on crcular map. able. Mean Square Error mse UKFSLAM RBF UKFSLAM x y θ Vol 8 (0) August 05 Indan Journal of Scence and echnology

5 Omd Panah, Amr Panah, Amn Panah and Samere Fallahpour able. Mean Square Errorr mse UKFSLAM RBF UKFSLAM x y θ Fgure 4. Navgaton Errors on Crcular Map. 4. Navgaton on Wdespread map In ths case, the UKF based navgaton and proposed flter based navgaton are shown n (Fgure 5). he bold blac lne s Robot path and the dashed lne, show the paths of robots should traverse. (In Fgure 6.), the dashed blac lne (UKF) and the bold gray lne (RBFUKF) are the x, y, and θ errors n the case of UKF SLAM and Hybrd flter SLAM wth RBF algorthm, respectvely and n able. see Mean Square Error of t. 5. Concluson In ths contrbuton, a new approach proposes UKF SLAM based on RBF Networ method for a moble robot. he RBFUKF SLAM on a moble robot, to mae up for the UKF SLAM error nherently caused by ts nose assumpton and lnearzaton process. he proposed algorthm contans of two steps: the UKF algorthm and the RBF Neural Networ. he smulaton results for two dfferent navgaton cases show that the mprovement of the proposed flter based on RBF as compared wth the standard UKF SLAM and t also shown that algorthms has good results n wder envronment but we requre to use long range sensors. o defne the robustness of the proposed algorthm, smulaton n Matlab s performed. Based on the smulaton results, Standard UKF SLAM has more errors than proposed flter. 6. References Fgure 5. Navgaton result on wdespread map. Fgure 6. Navgaton Errors on Wdespread map. Baley. Moble robot localsaton and mappng n extensve outdoor envronments [degree of Doctor of Phlosophy]. Australan Centre for Feld Robotcs Department of Aerospace, Mechancal and Mechatronc Engneerng the Unversty of Sydney; 00 Aug.. Cho KS, Lee SG. Enhanced SLAM for a moble robot usng extended alman flter and neural networs. Internatonal Journal of Precson Engneerng and Manufacturng. 00; (): Frese U. A dscusson of smultaneous localzaton and mappng. Autonomous Robots. Netherlands: Sprnger Scence, Busness Meda, Inc; Ranjan N, Nheraol A, Navelar G. Navgaton of autonomous underwater vehcle usng extended alman flter. rends n Intellgent Robotcs. 00. p Panah A, Faez K. hybrd flter based smultaneous localzaton and mappng for a moble robot. 6th Internatonal Conference on Image Analyss and Processng; 0 Sep 4; Italy. 6. Chang HH, Ln SY, Chen YC. SLAM for ndoor envronment usng stereo vson. Second WRI Global Congress on Intellgent Systems DurrantWhyte H, Baley. Smultaneous localzaton and mappng: part I. IEEE Robotcs & Automaton Magazne. 006; 3():99 0. Vol 8 (0) August 05 Indan Journal of Scence and echnology 5

6 Enhanced SLAM for Autonomous Moble Robots usng Unscented Kalman Flter and Neural Networ 8. Wolf DF, Suhatme GS. Moble robot smultaneous localzaton and mappng n dynamc envronments. Autonomous Robots. 005; 9: Ip YL, Rad AB, Wong YK. Effectve method for autonomous smultaneous localzaton and map buldng n unnown ndoor envronments. In: Kols S, edtor, Moble Robots: Percepton and Navgaton; 007 Feb. p ISBN: Page SF. MultpleObject sensor Management and optmzaton [PHD thess]. Faculty of Engneerng, Sc ence and mathematcs School of Electroncs and Computer scence; Ca X, Zhang Z, Venayagamoorthy G, Wunsch G II. me seres predcton wth recurrent neural networs traned by a hybrd psoea algorthm. Neurocomputng. 007;70: Baley. Avalable from: edu.au/tbaley 6 Vol 8 (0) August 05 Indan Journal of Scence and echnology