TELK OMNIKA T elecommunication, Computing, Electr onics and Contr ol V ol. 19, No. 1, February 2021, pp. 327 338 ISSN: 1693-6930, accredited First Grade by K emenristekdikti, No: 21/E/KPT/2018 DOI: 10.12928/TELK OMNIKA.v19i1.16223 r 327 Maximum lik elihood estimation-assisted ASVSF thr ough state co v ariance-based 2D SLAM algorithm Heru Suw oy o 1 , Y ingzhong T ian 2 , W enbin W ang 3 , Long Li 4 , Andi Adriansyah 5 , F engfeng Xi 6 , Guangjie Y uan 7 1,2,4,7 School of Mechatronic Engineering and Automation, Shanghai Uni v ersity , Shanghai, China 2,4,7 Shanghai K e y Laboratory of Intelligent Manuf acturing and Robotics, Shanghai, China 1, 5 Department of Electrical Engineering, Uni v ersitas Mercu Buana, Jakarta, Indonesia 3 Mechanical and Electrical Engineering School, Shenzhen Polytechnic, Guangdong, China 6 Department of Mechanical, Aerospace, and Industrial Engineering, Ryerson Uni v ersity , T oronto, Canada Article Inf o Article history: Recei v ed Mar 31, 2020 Re vised May 19, 2020 Accepted Jul 6, 2020 K eyw ords: Adapti v e smooth v ariable structure filter Maximum lik elihood estimator Simultaneous localization and mapping State estimation Wheeled mobile robot ABSTRA CT The smooth v ariable structure filter (ASVSF) has been relati v ely considered as a ne w rob ust predictor -corrector method for estimating the state. In order to ef fecti v ely utilize it, an SVSF requires the accurate system model, and e xact prior kno wledge includes both the process and measurement noise statistic. Unfortunately , the system model is al w ays inaccurate because of some considerations a v oided at the be ginning. More- o v er , the small addicti v e noises are partially kno wn or e v en unkno wn. Of course, this limitation can de grade the performance of SVSF or also lead to di v er gence condition. F or this reason, it is proposed through this paper an adapti v e smooth v ariable struc- ture filter (ASVSF) by conditioning the probability density function of a measurement to the unkno wn parameters at one iteration. This proposed method is assumed to ac- complish the localization and direct point-based observ ation task of a wheeled mobile robot, T urtleBot2. Finally , by realistically simulating it and comparing to a con v en- tional met hod, the proposed method has been s ho wing a better accurac y and stability in term of root mean square error (RMSE) of the es timated map coordinate (EMC) and estimated path coordinate (EPC). This is an open access article under the CC BY -SA license . Corresponding A uthor: Heru Suw o yo School of Mechatronic Engineering and Automation Shanghai Uni v ersity Shanghai, 200444 China Email: heru.suw o yo@mercub uana.ac.id 1. INTR ODUCTION The presence of a map can be useful for a mobile robot to perform its na vig ation task. Un f ortunately , the consistent map is una v ailable at the be ginning [1]. Consequently , the system should be able to track the robot path and to b uild a map based on the robot measurement [2-4]. It can be done by kno wing the current pose when sensing a feature and locating the pose based on the around features [5]. Since these tasks should be addressed at the same time , the definition of simultaneous localization and mapping (SLAM) is stated [6- 12]. The SLAM-based mobile robot na vig ation has intensi v ely recei v ed attention because of some challenging f actors that need to be solv ed such as wide uncertainty , system comple xity , inaccurate system model, limited J ournal homepage: http://journal.uad.ac.id/inde x.php/TELK OMNIKA Evaluation Warning : The document was created with Spire.PDF for Python.
328 r ISSN: 1693-6930 prior information, noise statistics of the process and measurement, computational cost and filter di v er gence [13, 14]. Additionally , in the mobile robot application, the successful of solving SLAM problem can be v al- idated root mean square error (RMSE) [15-17] calculated based on the dif ferent of the estimated and true v alue. The continuosly gro wn uncertainty mak es the estimated v alues de viates from its base. F or this reason, the probability-based filtering method has been intensi v ely used. It has been frequently adopted to ef fecti v ely represent all the possibility related to the system [18]. The most popular one is e xtended kalman filter which has the basic task to update the state and co v ariance with an assumption all the related v ariable comply with Gaussian distrib ution. Generally , e xtended kalman filter [11, 19-23] is kno wn as an nonlinea r v ersion of its pre- decessor named kalman filter [18-20, 24-28]. The easiness to apply e xtended kalman filter mak es it has been widely used to solv e in man y dif ferent fields such as for the state and parameter estimation including SLAM, signal processing, f ault detection and diagnosis and tar get tracking [29]. Ne v ertheless, it has man y incompat- ibilities and dif ficulties such as the de viant solution from the state trajectory , less optimal state estimation and lar ge estimation error due to the linearization process and computational cost [14, 15, 17]. These limitations mak e its practical application becomes limited no w adays. Furthermore, man y researcher ha v e switched to use the similar method that might of fered better ro- b ustness rather than EKF such as unscented kalman filter (UKF) [20, 30-32], cubature kalman filter (CKF) [15, 16, 26] smooth v ariable structure filter (SVSF) [15-17, 33], etc. Their recorded successes ha v e been pro ving to ha v e significant impro v ement of EKF . Among of them, SVSF has been rapidly de v eloped. The SVSF is a relati v e ne w predictor -estimator , which is first in v ented in 2007 [15, 16]. Firstly , it w as deri v ed from a v ariable structure filter (VSF)[34] and e xtended v ar iable structure filter (EVSF) [13, 17, 35]. Then proceed with a pres- ence of ne w form by completing it with the error co v ariance matrix without af fecting its accurac y and stability [35, 36]. As a common filtering technique, it w as then enhanced by in v olving the time-v arying boundary layer width to replace its pre vious characteristic [36, 37]. Due to these de v elopments, SVSF becomes the popular method to ag ainst the uncertainty which is not only suitable for the linear b ut also nonlinear syst em [15-17]. Additionally , based on its characteristic, the SVSF can be combined with dif ferent methods in obtaining the optimal solution [15-17, 33, 34]. Ho we v er , lik e the other traditional filter methods, to apply SVSF the noise statistic is often predefined to be fix ed and constant for the whole estimation process. It often leads to di v er - gence and de gradation performance. Thus, traditional SVSF should at least be enhanced to partially estimating the noise statistic. Therefore, through this paper , SVSF is adapti v ely impro v ed. Firstly , the SVSF’ s error co v ari- ance matrix is mathematically deri v ed via maximum a lik elihood estimator [38]. It aims to recursi v ely update the process co v ariance matrix Q as well as the measurement error co v ariance matrix R . Since the prediction step of SVSF [15, 16, 33, 34] is totall y same as EKF , so that, the inno v ation error can be similarly computed. Consequentially , the deri v ation process of finding the compact formulation of Q and R is easy to be e v aluable [31, 38]. Additionally , since this algorithm is used to solv e SLAM problem, henceforth it is termed as ASVSF- SLAM algorithm in this paper . In case of kno wing the performance of this algorithm, the proposed algorithm is realistic simulated and compared with traditional SLAM algorithm. Based on the comparati v e results, it can be declared that the ASVSF-SLAM algorithm can significantly solv e the SLAM problem of wheeled mobile robot in term of RMSE for both estimated path coordinate and estimated map coordinate. The rest parts of this paper are arranged as follo ws. Section 2 presents a discussion of the ori ginal SVSF . Section 3 sequentially presents the mathematical deri v ation conducted to find the recursi v e error co- v ariance matrix of both the process and measurement noise statistic. Section 4 discuss an algorithm named ASVSF-SLAM algorithm with e xpansion of kinematic configuration and motion model, direct point-based ob- serv ation and, in v erse point-based observ ation. Finally , Section 5 presents a conclusion according to the result discussed in pre vious section 2. CLASSICAL SVSF Considering that the dynamic model of Gaussian nonlinear system is gi v en as follo ws ( x k = f ( x k 1 ; u k ) + ! k 1 z k = h ( x k ) + k (1) where k is discrete ti me inde x, x 2 R n is the state v ector , u is the control v ector and z 2 R m is the measurement TELK OMNIKA T elecommun Comput El Control, V ol. 19, No. 1, February 2021 : 327 – 338 Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA T elecommun Comput El Control r 329 v ector . While, ! 2 R n and 2 R m are small process, and measurement noise, respecti v ely . Whereas, f ( : ) and h ( : ) are the nonlinear function and measurement model, respecti v ely . The statistical characteristic of t his dynamic model is gi v en as follo ws 8 > < > : E [ ! k ] = 0 ; C ov [ ! k ; ! j ] = Q k k j E [ k ] = 0 ; C ov [ k ; j ] = R k k j E [ ! k ; j ] = 0 (2) where is Kroneck er delta function. Meanwhile, E [ : ] and C ov [ ; ] are mean and co v ariance term, respecti v ely . Then the complete formulation of SVSF can be chainned as follo ws ^ x k j k 1 = f ( ^ x k 1 j k 1 ; u k ) + q k 1 (3) P k j k 1 = F P k 1 j k 1 F T + Q k 1 (4) e z ;k j k 1 = z k h ( ^ x k j k 1 ) r k (5) A = j e z ;k j k 1 j abs + j e z ;k 1 j k 1 j abs (6)   = ( A 1 H P k j k 1 H T ( H P k j k 1 H T + R k ) 1 ) 1 (7) sat [   1 e z ;k j k 1 ] = 8 > < > : 1 ;   1 e z ;k j k 1 1   1 e z ;k j k 1 ; 1   1 e z ;k j k 1 1 1 ;   1 e z ;k j k 1 1 (8) K S V S F k = H + A sat [   1 e z ;k j k 1 ] [ e z ;k j k 1 ] 1 (9) ^ x k j k = ^ x k j k 1 + K S V S F k e z ;k j k 1 (10) P k j k 1 = ( I H K S V S F k ) e z ;k j k 1 e T z ;k j k 1 ( I H K S V S F k ) T + K S V S F k R k K S V S F T k (11) e z ;k j k = z k h ( ^ x k j k ) r k (12) j e z ;k 1 j k 1 j abs > j e z ;k j k 1 j abs (13) 3. ESTIMA TING THE NOISE ST A TISTIC T raditionally , SVSF has no ability to approximate the responsi v e noise statistic. Consequently , the possibility of di v er gence still high in case of either the realistic simulation or real application. Moreo v er , inaccurate modelled system might also increase the uncertainty that is precisely lead to de gradation of filter performance. F or this reason, an ef fort to complete SVSF with recursi v e noise statistic is proposed in this paper . This process can be done by estimating error matrix of the noise s tatistic by deri ving the predicted error co v ariance matrix of the state using MLE [31, 38]. First, by recalling the inno v ation sequence of SVSF and considering that the nonlinear system (1) is Gaussian. According to [38, 39] and [6], S k can also be alternati v ely calculated as ^ C k = k X j = k N +1 d j d T j (14) Maximum lik elihood estimation-assisted ASVSF thr ough state co variance-based... (Heru Suwoyo) Evaluation Warning : The document was created with Spire.PDF for Python.
330 r ISSN: 1693-6930 where d k is inno v ation sequence error as sho wn in (5), ^ C k is alternati v e form of S k , and the addition of P k j = k N +1 d j d T j is the mo ving windo w [40] for N refers to the windo w size. No w , by recalling as sho wn in (2) and assuming that the unkno wn parameter = f Q; R g , the adapta- tion process is done with assumptions that State v ector x is not depend on i.e @ x @ , F and H are independent of and time v ariant, k is white and er godic sequence within the estimation windo w , and S k is re g arded as the main k e y of adaption on depend parameters. Therefore, the probability density function of the measurements conditioned on the parameter at time k can be described as follo ws [31, 38] P ( z j ) k = (2 ) n j C k j 1 = 2 exp 1 2 k d k k 2 C 1 k (15) Then by taking its algorithm, and ignoring all the constants, the compact formulation of sho wn in (15) is J ( ) = k X j = k N +1 d T j C 1 j d j = min (16) Ne xt, by addopting tw o relations of matrix dif ferential calculus [38], (16) is deri v ed as follo ws J ( ) = k X j = k N +1 tr C 1 j @ C j @ d T j C 1 j @ C j @ C 1 j d j = min (17) At this point, it is clear that the adapti v e SVSF lies on the determination of C and its partial deri v ati v e with respect to . Additionally , the main interest is in R k and Q k instead of C [31, 41, 42] . Therefore, by sequentially referring to (6), first deri v ati v e of C with respect to , and a condition of P k 1 j k 1 in the steady state, (17) can be compactly e xpressed as follo ws k X j = k N +1 tr C 1 j C 1 j d j d T j C 1 j  H @ Q j @ H T + @ R j @ = 0 (18) At this point, the process of obtaining both the adapti v e estimation of the process noise and measure- ment noise co v ariance are presented. First, Q is assumed to be kno wn and independent of to obtain the e xplicit e xpression for R . Similarly , the process to g ain the e xpression for Q will also in v olv e the assumption that R is fix ed and independent of at the pre vious process. Both processes can be sequentially described at the follo wing subsection 3.1. Adapti v e co v ariance matrix of pr ocess noise statistic Gi v en R then (18) becomes k X j = k N +1 tr H C 1 j H T H C 1 j d j d T j C 1 j H T = 0 (19) Then by referring to (7) after replacing S k by C k , the alternati v e formulation of C 1 k is obtained as follo ws C 1 k H T =   1 AH + P 1 k j k 1 (20) Since,   1 AH + is g ain of SVSF on (9), and the saturation function on (8) is satisfied at the pre vious step, then it is clear to ha v e the follo wing form C 1 k H T = K S V S F k P 1 k j k 1 (21) Since (21) is formed then by substituting (21) into (19), it yields TELK OMNIKA T elecommun Comput El Control, V ol. 19, No. 1, February 2021 : 327 – 338 Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA T elecommun Comput El Control r 331 k X j = k N +1 tr P 1 j K S V S F j H P j K S V S F j d j d T j K S V S F T j P 1 j = 0 (22) where P j is P k j k 1 . By definition, it should be at least semi-definite positi v e matrix, thus P 1 j can be v anished. k X j = k N +1 tr K S V S F j H P j K S V S F j d j d T j K S V S F T j = 0 (23) As well-kno wn that the alternati v e formulation of (11) is P k j k = P k j k 1 H K S V S F k P k j k 1 , thus P k j k P k j k 1 = K S V S F k H P k j k 1 (24) No w , substituting (10) and (24) into (23), it yields k X j = k N +1 tr P + j P j ( ^ x + j ^ x j )( ^ x + j ^ x j ) T = 0 (25) Note that P + and P refer to P k j k and P k j k 1 , respecti v ely . Meanwhile, ^ x + and ^ x refer to ^ x k j k and ^ x k j k 1 , respecti v ely . Then by substituting (4) into (25), it yields k X j = k N +1 P + j F P + j F T Q ( ^ x + j ^ x j )( ^ x + j ^ x j ) T = 0 (26) Finally , the co v ariance matrix of process noise statistic is obtained ^ Q = k X j = k N +1 P + j F P + j F T ( ^ x + j ^ x j )( ^ x + j ^ x j ) T (27) Suppose that (24) alternati v ely represents the updated co v ariance of SVSF . It is totally same with Kalman Filter , then (26) can be approximately reformed as ^ Q = K S V S F k C k K S V S F T k (28) 3.2. Adapti v e co v ariance matrix of measur ement noise statistic Similarly , since Q is fix ed and independent of , then (18) becomes k X j = k N +1 tr C 1 j C 1 j d j d T j C 1 j  0 + I = 0 (29) It can also be simplified as k X j = k N +1 tr C 1 j C j d j d T j C 1 j = 0 (30) then by deri ving (30), it yields C k = 1 N k X j = k N +1 d j d T j (31) No w since 1 N P k j = k N +1 d j d T j is the w ay to calculate the e xpectation of d j d T j , which is also as sho wn in (2), then the recursi v e measurement error co v ariance matrix is ^ R = C k H P k j k 1 H T (32) Mathematical deri v ation abo v e sho wing that the adapti v e co v ariance matrix of measurement noise statistic seems able to be adopted from the v alue used at the pre vious iteration. Finally , both the process and measure- ment noise statistic are obtained already when their corresponding mean are considered to be zero. Maximum lik elihood estimation-assisted ASVSF thr ough state co variance-based... (Heru Suwoyo) Evaluation Warning : The document was created with Spire.PDF for Python.
332 r ISSN: 1693-6930 4. AD APTIVE SVSF-B ASED FEA TURE 2D SLAM ALGORITHM The proposed method is approached to address a feature-based SLAM problem of the wheeled mobile robot [14, 17]. The objecti v e is concurrently estimating the robot pose and feature in certain en vironment. It is assumed that by using the motion model the robot mo v es after e x ecuting the control command, and by using laser scanner -based measurement, it senses the features with distance and bearing as the g athered data [3, 4, 43, 44]. It is noted that all the prerequisites for a feature-based SLAM algorithm in [14] and [17], therefore, Algorithm 1 ASVSF-SLAM Algorithm 1. Loop 2. Prediction Step: If propriocepti v e data is a v ailable 3. Propag ate the state estimate ((3)) 4. Propag ate the co v ariance relati v e to the state ((4)) 5. Update Step: If the observ ation data is a v ailable 6. Compute the inno v ation sequence error ((5)) 7. Calculate Gain ((9)) 8. Update the State, and Co v ariance ((10) and (11)) 9. Compute the noise statistic ((28) and (32)) 10. endloop 5. RESUL TS AND DISCUSSION The proposed algorithm discussed abo v e is realistically simulated and applied for solving SLAM problem of wheeled mobile robot. Initially , the robot pose and co v ariance as well as all the completeness parameters for ASVSF are initialized as follo ws ^ x 0 = 2 4 0 0 35 180 3 5 ; P 0 = 2 4 0 0 0 0 0 0 0 0 0 3 5 ; = 15 e 2 ; e z ; 0 = 0 : 1 0 : 5 180 T (33) Note that all the parameters sho wn herein are adopted from the real robot platform, T urtlebot2, which equipped with laser scanner [4, 43, 14] in displacement d l s = 14 cm . By realistically measuring the distance between tw o separately po wered wheels, it is obtained W r = 33 cm . It assumed that this mobile robot is operated in planar indoor en vironment with the size and random point as described in Figure 1 that is serv ed as the reference path and map in this e xperiment. The v alidation is conducted based on RMSE of dif ferent algorithm in estimating the robot path and map. Figure 1. Reference trajectory and map TELK OMNIKA T elecommun Comput El Control, V ol. 19, No. 1, February 2021 : 327 – 338 Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA T elecommun Comput El Control r 333 The v alidation is conducted based on RMSE of dif ferent al g or ithm in estimating the robot path and map. There are tw o dif ferent condition of the initial noise statistic in order to see the consistenc y of the proposed algorithm as sho wn in T able 1. All the parameters presented in T able 1 aim to kno w the performance of the proposed algorithm when the initial process and measurement noise statistic are increased in type of additi v e white Gaussian noise. T able 1. The predefined noise statistic N o : ^ r 0 ^ R 0 ^ q 0 ^ Q 0 1 st Simulation 0 : 5 5 = 180 0 : 5 2 0 0 5 = 180 2 0 : 05 2 = 180 0 : 05 2 0 0 2 = 180 2 2 nd Simulation 0 : 8 8 = 180 0 : 8 2 0 0 8 = 180 2 0 : 1 8 = 180 0 : 1 2 0 0 8 = 180 2 All the parameters presented abo v e aim to kno w the performance of the proposed algorithm wh e n the initial process and measurement noise statistic are increased in type of additi v e white Gaussian noise. The scenario is in v olv ed to v alidate the stability of the proposed ASVSF-SLAM algorithm compared to con v en- tional SVSF-SLAM algorithm. Re g arding to these parameters and the reference path depicted in Figure 1 the follo wing results were obtained. It analogized that the robot mo v es based on all the command send to the odometers. It aims to track the reference path as well as locating ne w detected landmark in the en vironment then by applying tw o dif ferent algorithm which are SVSF-SLAM and Adapti v e SVSF-SLAM algorithm, the performance of the robot can be graphically e xpressed as sho wn in Figure 2. (a) (b) Figure 2. Performance of SVSF and ASVSF-SLAM algorithm for (a) 1st simulation and (b) 2nd simulation Figure 2 represents the performance of dif ferent SLAM algorithm. The y are attempted to estima te the path and map coordinate by respecting to the reference trajectory . According to dif ferent simulations, both SVSF and ASVSF-based SLAM algorithm sho w the con v er gence to track the reference. Additionally , the proposed method sho ws a smoother performance with a guaranteed stability when the no i se statistic is in- creased. Ho we v er ,it is quite dif ficult to kno w t he detail di v ersity of the SLAM algorithms through the graphical representation only . Therefore, to ease the v alidation and analysis, their estimated path and estimated map coordinate are compared in term of root mean square error . Figure 3 depicts the dif ference RMSE v alues for SVSF and ASVSF-SLAM algorithms. According to tw o dif ferent simulation, it is clear to see that the adapti v e SVSF gi v es smaller RMSE for the estimated robot path in which there is no much di v ersity to its reference. By using the same method and term, the estimated map of SVSF and ASVSF-SLAM algorithm is also compared. Maximum lik elihood estimation-assisted ASVSF thr ough state co variance-based... (Heru Suwoyo) Evaluation Warning : The document was created with Spire.PDF for Python.
334 r ISSN: 1693-6930 According to Figure 4 the stability and accurac y of ASVSF-SLAM is v alidated. There is no significant ef fect after increasing the initial noise statistic. Therefore, it can be stated that since no de gradation detected, ASVSF- SLAM algorithm is better than SVSF-SLAM algorithm. (a) (b) Figure 3. RMSE of estimated path coordinate for (a) 1st simulation and (b) 2nd simulation (a) (b) Figure 4. RMSE of estimated path coordinate (a) 1st Simulation and (b) 2nd Simulation Referring to all the graphical result abo v e, it might be dif ficult to see the dif ference. F or this reason, the follo wing T ables 2 and 3 are presented. In which, these tables are intended to gi v e detail v alues for all test as the w ay to v alidate the accurac y for each algorithm. T able 2. RMSE of dif ferent SLAM-based algorithm (first test) SLAM Alg. x-EPC (cm) y-EPC (cm) -EPC (rad) x-EMC (cm) y-EMC (cm) SVSF 6.4992 11.2050 0.1066 16.1687 20.0962 ASVSF 5.6514 2.6893 0.0991 11.1031 12.1210 T able 3. RMSE of dif ferent SLAM-based algorithm (second test) SLAM Alg. x-EPC (cm) y-EPC (cm) -EPC (rad) x-EMC (cm) y-EMC (cm) SVSF 11.3148 19.2975 0.7886 31.3384 38.7499 ASVSF 5.5325 6.4678 0.1109 24.9880 29.7186 6. CONCLUSIONS The main contrib ution of this paper is to equip the traditional SVSF with an approach termed as adapti v e filtering s trate gy . It utilizes the maximum lik elihood e stimation (MLE) used to approximate the error co v ariance matrices of noise statistic by conditioning the probability density function of measurement to an TELK OMNIKA T elecommun Comput El Control, V ol. 19, No. 1, February 2021 : 327 – 338 Evaluation Warning : The document was created with Spire.PDF for Python.
TELK OMNIKA T elecommun Comput El Control r 335 unkno wn parameter at one iteration. The output of this project is the enhancement of SVSF . It can recursi v ely calculate the co v ariance of the noise statistic based on the uncertainty condition of the pre vious process. In other w ords, the predetermined co v ariance of the noise statistic is e x ecuted once at the first iteration and the system continuously generates ne w co v ariances for the rest iteration. The proposed method is applied to solv e the feature-based SLAM problem of a wheeled mobile robot named ASVSF-based SLAM algorithm. The presence of adapti v e strate gy pre v ent the SVSF from de gradati o n and di v er gence condition under time inte gration when it is applied for the real case. Re g arding to all the comparati v e results, the accurac y , stability , and rob ustness of the proposed algorithm is guaranteed and satisfied. 7. A CKNO WLEDGMENTS Research w as supported by Special Plan of Major Scientific Instruments and Equipment of the State (Grant No.2018YFF01013101), National Natural Science F oundation of China (61704102), the IIO T Inno v a- tion and De v elopment Special F oundation of Shanghai (2017-GYHL W01037) and Project named “K e y T ech- nology Research and Demonstration Line Construction of Adv anced Laser Intelligent Manuf acturing Equip- ment” from Shanghai Ling ang Area De v elopment Administration, Shanghai Uni v ersity , Shanghai-China, and Uni v ersitas Mercu Buana, Jakarta-Indonesia. REFERENCES [1] R. Sie gw art, I. R. Nourbakhsh, and D. Scaramuzza, ”Introduction to autonomous mobile robots, ” MIT press , 2011. [2] H. Najjaran and A. Goldenber g, “Real-time motion planning of an autonomous mobile manipulator using a fuzzy adapti v e kalman filter , ” Robotics and Autonomous Systems , v ol. 55, no. 2, pp. 96–106, Feb . 2007. [3] W . Li, S. Sun, Y . Jia, and J. Du, “Rob ust unscented kal man filter with adaptation of process and measure- ment noise co v ariances, ” Digital Signal Processing , v ol. 48, pp. 93–103, Jan. 2016. [4] Y . T ian, Z. Chen, T . Jia, A. W ang, and L. Li, “Sensorless collision detection and contact force estimation for collaborati v e robots based on torque observ er , ” 2016 IEEE International Conference on Robotics and Biomimetics (R OBIO) , pp. 946–951, Dec. 2016, doi: 10.1109/R OBIO.2016.7866446. [5] F . K endoul, I. F antoni, and K. Nonami, “Optic flo w-based vision system for autonomous 3d localization and control of small aerial v ehicles, ” Robotics and Autonomous Systems , v ol. 57, no. 6-7, pp. 591–602, Jun. 2009. [6] T . Baile y and H. F . Durrant-Wh yte, “Simultaneous localization and mapping (SLAM): P art I, ” IEEE Robotic s and Automation Mag azine , v ol. 13, no. 2, pp. 108–117, Jun. 2006, doi: 10.1109/MRA.2006.1638022. [7] K. Berns and E. v on Puttkamer , “Simultaneous localization and mapping (SLAM), ” Autonomous Land V ehicles , pp. 146–172, 2010. [8] A. Chatterjee and F . Matsuno, “ A neuro-fuzzy assisted e xtended Kalman filter -based approach for si- multaneous localization and mapping (SLAM) problems, ” IEEE T ransactions on Fuzzy Systems , v ol. 15, no. 5, pp. 984–997, Oct. 2007,doi: 10.1109/TFUZZ.2007.894972. [9] M. W . M. G. Dissanayak e, P . Ne wman, S. Clark, H. F . Durrant-Wh yte, and M. Csorba, “ A solution to the simultaneous localization and map b uilding (SLAM) problem, ” IEEE T ransactions on robotics and automation , v ol. 17, no. 3, pp. 229–241, Jun. 2001, doi: 10.1109/70.938381. [10] T . Lemaire, S. Lacroix, and J. Sol ` a, “ A practical 3D bearing-only SLAM algorithm, ” 2005 IEEE/RSJ International Conference on Intelligent Robots and System s , pp. 2757–2762, Sept. 2005, doi: 10.1109/IR OS.2005.1545393. [11] A. Mallios, et al., “Ekf-slam for auv na vig ation under probabilistic sonar scan-matching, ” 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems.IEEE , pp. 4404–4411, Oct.2010, doi: 10.1109/IR OS.2010.5649246. [12] H. W ang, G. Fu, J. Li, Z. Y an, and X. Bian, “ An adapti v e ukf based sl am method for unmanned underw ater v ehicle, ” Mathematical Problems in Engineering , v ol. 2013, no. 4, pp. 1-2, No v . 2, doi: 10.1155/2013/605981. [13] D. Fethi, A. Nemra, K. Louadj, and M. Hamerlain, “Simultaneous localization, mapping, and path plan- ning for unmanned v ehicle using optimal control, ” Adv ances in Mechanical Engineering , v ol. 10, no. 1, pp. 1–25, Jan. 2018, doi: 10.1177/1687814017736653. Maximum lik elihood estimation-assisted ASVSF thr ough state co variance-based... (Heru Suwoyo) Evaluation Warning : The document was created with Spire.PDF for Python.
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