GLOBAL LOCALIZATION USING DEAD-RECKONING AND KINECT SENSORS FOR ROBOTS WITH OMNIDIRECTIONAL MECANUM WHEELS

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1 Journal of Marine Science and Technology, Vol., No. 3, pp (4) 3 DOI:.69/JMST GOBA OCAIZATION USING DEAD-RECKONING AND KINECT SENSORS FOR ROBOTS WITH OMNIDIRECTIONA MECANUM WHEES Ching-Chih Tsai, Feng-Chun Tai, and Yu-Cheng Wang Key ords: dead-reconing, extended Kalan filter, global localization, KINECT sensor, lo-cost. ABSTRACT This paper presents a lo-cost global pose localization ethod using least-squares ethod and extended Kalan filter (EKF) for an anthropoorphous dual-ar obile robot (ADAMR) driven by onidirectional Mecanu heels in indoor environents. This ethod is developed by fusing easureents fro the KINECT sensor and four encoders ounted on the onidirectional Mecanu heels. The KINECT sensor is used to recognize landars in the oring environents of the robot, and then obtain the aziuth angles and distances beteen these landars and the robot. Based on these easured inforation, a static global pose initialization algorith using least-squares ethod is applied to estiate both unnon start-up position and orientation of the robot. Once the initial pose has been roughly deterined, an EKF approach is proposed to fuse the odoetric easureents fro the four encoders and the aziuth angles and distances fro the KINECT sensor to corresponding landars. Siulations are conducted to sho perforance of the proposed ethod. Experiental results are used to illustrate that the proposed ethod provides accurate static estiation of both unnon initial poses of the robot. I. INTRODUCTION The self-localization capability of an autonoous obile robot is very iportant for path tracing control and planned navigation in any given environent [, 8, ]. The global localization capability of an autonoous obile robot is Paper subitted 6/7/; revised //; accepted 9/9/3. Author for correspondence: Ching-Chih Tsai (e-ail: [email protected]). Departent of Electrical Engineering, National Chung Hsing University, Taichung, Taian, R.O.C. critical for its navigation issions at its prespecified environents [4-6, ]. Global pose initialization and pose tracing are the to ain probles in the global localization technology. The global pose initialization proble deterines the robot s initial pose ith respect to soe reference frae, using no priori or a priori ap or landar inforation, hile the pose tracing proble is concerned ith, given initial robot pose fro the user, ho to continuously aintain the robot s pose using internal and external sensors. Pose initialization is considered crucial for planned or autonoous navigation of the robot because it is relevant not only at start-up, but also during operation for recovery in case of pose localization failures [9]. The dead-reconing ethod, hich is based on the encoded or odoetric inforation fro the heels, has extensively been utilized to calculate the current location of an autonoous obile robot. Hoever, this ethod suffers fro the accuulation errors that are caused by heel slippage or by echanical tolerances and surface roughness. Hence, the robot ay fail to eep trac of its true location over long distances. The odoetric errors can be reduced by fusing landar observations using external sensors. Many sensors, such as sonar sensors [], laser range finders [], and caeras [7], have been used to detect landars and obtained the required easureents. Ultrasonic sensors have idely been applied to develop the useful and econoical external sensing systes for localization of autonoous obile robots [3]. Hoever, sonar sensors and laser range finders introduce several riss: the outbound energy ay affect the very characteristics that the sensor is attepting to easure. Furtherore, an active sensor ay suffer fro interference beteen its signal and signals beyond its control. Vision is our ost poerful sense, providing us ith an enorous aount of inforation about the environent and enables rich, intelligent interaction in dynaic environents. It is therefore not surprising that a great deal of effort has been devoted to providing achines ith sensors that iic the capabilities of the huan vision syste []. Recently, KINECT has been idely utilized for robot localization due to its lo cost [3].

2 3 Journal of Marine Science and Technology, Vol., No. 3 (4) V r V V V r V =Jo V o () V y Y V x V 3 V 3r V 4r X ω z V 4 4 here V = [ V V V3 V4] T R is the velocity vec- 3 tor in Cartesian coordinates; [ ] T V = vx vy ωz R is the heel velocity vector corresponding to the angular velocity. Moreover, l (a) (b) Fig.. Anthropoorphous To-Ared Robots ith Onidirectional Mecanu Wheels. (a) Its siplified geoetry ith respect to the oving frae; (b) a laboratory-built exaple of ADAMR ith Onidirectional Mecanu Wheels. Extended Kalan filter has been proposed for the pose estiation of autonoous obile robots to obtain better accuracy of pose initialization and pose racing using KINECT [4]. Hoever, the proposed ethod in [4] has not been experientally verified yet. The objectives of this paper are to apply the least-square ethod and the EKF approach to a lo-cost localization ethod for an ADAMR by fusing dead-reconing and KINECT easureents, and to deonstrate ho the proposed ethod achieves the better perforance of the robot localization. This technique is expected to be useful in iproving accuracy and robustness of the ADAMR s position and orientation estiates, and to provide a lo-cost global localization ethod for heeled obile robots. The reainder of this paper is outlined as follos. Section II briefly introduces the ineatics odel in the orld frae and dead-reconing odel of the syste. Section III presents the landar detection algorith of the KINECT sensor. This section ill utilize Hough transfor ethod to extract the landars fro the iage obtained by KINECT, thus achieving landar detection. Section IV shos a leastsquares pose initialization algorith to achieve global localization. Section V briefly introduces the extended Kalan filtering ethod. Section VI introduces the localization using natural landars. Coputer siulations and experiental results are respectively reported in Sections VII and VIII to sho the erit of the proposed ethods for global pose initialization and pose tracing of the ADAMR. Section IX concludes this paper. II. SYSTEM AND DEAD-RECKONING MODE. Kineatics Model in the World Frae Fig. shos the siplified geoetry of the ADAMR ith Onidirectional Mecanu heels. The inverse ineatics of its base in the oving frae is described by: ( l+ + ( l+ ( l+ + ( l+ 4 3 J = R () is a transforation atrix; the to paraeters l and are depicted in Fig.. To forulate inverse ineatic odels of the ADAMR in a global frae, e define that the vector T x y θ denotes the position and orientation of the vehicle in the orld frae, and let the oving and orld fraes have the rotational atrix expressed by x cosθ sinθ v x y sinθ cosθ = v y θ ωz Thus, the inverse ineatics odel of the MWOR is then expressed by V x = J( θ ) y θ sin( θ) cos( θ) ( l+ cos( θ) sin( θ) ( l+ here J ( θ ) = cos( θ) sin( θ) ( l+ sin( θ) cos( θ) ( l+ Since the transforation J(θ ) exists its pseudo inverse atrix, J (θ ) such that J(θ ) + J(θ ) = I 3, the forard ineatics of the ADAMR in the orld frae becoes here θ = θ + π /4 J ( θ ) x y = J ( θ ) V θ sin( θ) cos( θ) cos( θ) sin( θ) cos( θ ) sin( θ ) sin( θ ) cos( θ ) 4 + l + l + l + l = (3) (4) (5)

3 C.-C. Tsai et al.: Global ocalization Using Dead-Reconing and KINECT Sensors for OMWR 33. Dead-Reconing The purpose of the dead-reconing of the ADAMR is, given a correct initial pose, to continuously eep trace of its correct poses ith respect to the orld frae. Dead-reconing is the real-tie calculation of the robot s position fro heel encoder easureents. The dead-reconing proble of the ADAMR can be easily solved by using the nuerical approach, the velocity inforation fro the encoders ounted on the driving heels and the forard ineatical odel in (5). To find the continuous poses of the robot fro (5), any existing nuerical approaches, such as the Euler s forula, the Runge-Kutta ethod and so on, can be eployed according to the required nuerical accuracy and the step size. One of the siplest dead-reconing ethods is based on the second-order Runge-Kutta forula hich approxiates the pose differentiation of the robot by the folloing equation. x( ) x( ) + + ( ( ( )) ( ) ( ( )) ( )) y( ) θ θ y( ) J V + J V = + T θ( ) θ( ) (6) here T is the sapling period and sufficiently sall; x(), y() and θ() denote respectively the present easureents of x(t), y(t) and θ(t) at the th sapling instant. Notice that Eq. (6) gives the recursive forula to approxiately obtain the robot s position and orientation at the next sapling instant. Worthy of ention is that the accuracy of the dead-reconing ethod increases as the sapling period decreases. Hoever, if the sapling period T is fixed and not significantly sall, then the accuracy of the dead-reconing ethod can be iproved by using the fourth-order or higherorder Runge-Kutta nuerical Method. Thus, this ind of dead-reconing ethod can often be used as a useful pose tracing approach for the robot over short traveling distances. This is because, no atter hat ind of the nuerical ethod is used, the proposed dead-reconing ethod alays suffers fro unavoidable accuulation errors caused by slippage, surface roughness, surface friction and even the echanical structure of the ADAMR. RGB Iage Color Inforation of andars andar Color Selection No andar in the Iage Depth Iage Yes START Matching Iage ith All andar Colors Iage Binarization Hough Edge Detection andar Existance END No Yes Getting Iage Coordinates of the andar s Center No Fig.. Flo diagra of KINECT sensing. αi, λi. KINECT Calibration This subsection describes a calibration ethod converting the KINECT disparity into the corresponding distances. Acquiring the depth iage of KINECT is based on the light coding technology [4]. The coded light is captured by the IR caera in order to produce the KINECT disparity atrix. The relationship beteen the disparity and actual depth value for a noral stereo syste is given by, b f z = (7) d here z is the depth, b is the horizontal baseline beteen the caeras, f is the focal length of the caeras in pixels, and d is the disparity. Hoever, a zero KINECT disparity does not correspond to infinite distance, so the KINECT disparity is related to a noralized disparity by the subsequent relation III. KINECT SENSOR KINECT is a otion sensing input device used by Microsoft for video gaing console. This sensor offers a natural interface using physical gestures and spoen coands for users to control the gae ithout touching the controller. This sensor is equipped ith an RGB caera and a pair of depth sensors. The KINECT sensor has the spatial (x/y) resolution of 3 at distance fro sensor, hile its effective operation range is about ith the resolution of c at distance fro the sensor. In this paper, a KINECT sensor is ounted on the robot as shon in Fig. (b), and the height of the KINECT is arbitrarily set. d = ( doff dinect ) (8) 8 here d off is an offset value for a given KINECT device, and d inect is the KINECT disparity hich provides 48 levels of sensitivity in VGA resolution ith -bit depth. The factor /8 is used due to the fact that d inect is in /8 pixel units. Hoever this calibration results ay slightly differ fro one sensor to another. Therefore each sensor should be calibrated separately before using it for depth estiation.. andar Detection Using KINECT Fig. depicts the detailed flochart of the proposed

4 34 Journal of Marine Science and Technology, Vol., No. 3 (4) Table. The degree value of H ith respect to its color. Degrees Color Red Yello Green Blue Magenta landar detection algorith for the circular artificial landars. In the algorith, the HSI color space is adopted because its representation of colors is siilar to ho the huan eyes sense. The HSI odel represents every color ith three coponents: hue (H), saturation (S), and intensity (I). The H coponent utilizes an angle beteen [,36] degrees, as shon in Table. The S and I coponents utilize a real nuber beteen [,] separately. The value I = eans blac and eans hite. The value of S represents ho uch the color is ixed ith hite color. In the easureent update step, the ADAMR detects landars around it to estiate its pose. In this section, circles ith different colors are used as landars. The RGB iages and their depth values are obtained by the KINECT sensor. Hough transfor filters are utilized to detect landars in the RGB iage. The landars are distinguished fro each other by HSI color odel. The aziuth angle α i ith respect to the heading direction of ADAMR and the distance λ i to the i th landar i ( x, y, ) i z i at tie can be calculated using the i KINECT easureents. The value of the easureent function can be deterined by y y tan i θ α i x x Zi = i λ = (9) i ( x ) ( ) ( x + y ) i y + z i z i IV. POSE INITIAIZATION This section presents a hardare configuration and a static pose initialization approach for localization of the robot using KINECT easureents. Suppose that landars are installed at the non positions denoted by = (x, y, z ) T, = (x, y, z ) T,, (x, y, z ) T, respectively and the robot pose is denoted by (x, y, z, θ) T. The KINECT data fro the landars to the robot can be converted into their corresponding distances fro the landars to the robot. et r, r,, r denote the distances fro the landar positions (x, y, z ) T, (x, y, z ) T,, (x, y, z ) T to the robot, respectively. Then one obtains the folloing set of equations ( x x) + ( y y) + ( z z) = r ( x x) + ( y y) + ( z z) = r ( x x) + ( y y) + ( z z) = r () hich give the folloing atrix equation for the robot position (x, y, z). here A X= B () ( x x ) ( y y ) ( z z ) A = ( xxp) ( y yp) ( zzp) ( x3 x) ( y3 y) ( z3 z), r r ( x x) ( y y) ( z z) r r3 ( x x3) ( y y3) ( z z3) B = rp r ( xp x) ( yp y) ( zp z) In (), the least-squares ethod can be used to solve for the robot position (x, y, z) T, i.e. T T =( ) = [ x y z] X A A A B () if the atrix A has a full ran. Note that if the atrix A is not of full ran, then the pseudo inverse ethod ill be adopted to solve for the robot position in (). Once the robot position (x, y, z) T has been calculated via (), the robot heading is then found by θ y y αi (3) i = tan i= xi x As a result, the initial static pose (position and orientation) of the robot can be uniquely deterined using () and (3). V. POSE TRACKING This section is dedicated to elucidating the EKF ethod used for the pose estiation of the ADAMR. Although researchers have verified that particle filter (PF) get ore accurate results than the extended Kalan filter (EKF) does [3], but hen the ethod be extended into 3D space, PF ill consue too uch calculation resource so that it ill cause control delay. In order to avoid that, e used the EKF instead the PF. The initial pose estiate x is taen as the initialized pose in the previous section. The extrapolation steps of the filter are executed using the dead-reconing inforation. The state updating step ill be preceded only hen a landar is detected. Whenever a landar is not detected, the predicted state is taen as the state estiate for the next iteration of the filter, i.e. x + = x. + In this paper, the process and easureent noises of the T

5 C.-C. Tsai et al.: Global ocalization Using Dead-Reconing and KINECT Sensors for OMWR 35 ADAMR syste are assued to be stationary Gaussian hite noise ith zero ean. As a result, the noise covariance atrices, Q, and R are considered diagonal [7]. Origin σ x N(, Q), Q = σ y σθ (4) A B Σ D C σ α v N(, R), R = σ λ (5) The process noise variances of (x, y) coordinates and orientation are represented by σ x, σ y, and σ θ respectively, hile σα and σ λ are the easureent noise variances. Consider the folloing nonlinear discrete-tie syste odel and easureent odel of the ADAMR: X = f( X, ) + (6) Z = hx (, ) + v (7) here f( ) and h( ) are nonlinear functions of the state X = [x() y() z() θ()] T, and tice differentiable. Note that both nonlinear functions, f( ) and h( ), can be found in (6) and (9). Thus, the proposed EKF hose prediction and estiation equations can be easily stated as follos: (i) One-step prediction x = f ( x, ) (8) + z = h ( x, ) (9) P =Φ P Φ + Q () [] [] T + (ii) Estiation (easureent update) x = x + K ( z z ) () + = A B + C D Fig. 3. The advantage of integral iages. VI. OCAIZATION AND MAPPING USING NATURA ANDMARKS This section is aied to develop a KINECT-based EKF approach using SURF for global localization and apping of the ADAMR navigating in partially non indoor environents. Since SURF algorith has been idely used to extract and atch features of objects of interests, it can be applied to detect features of natural landars in the indoor environents.. Feature Detection of Natural andars An essential part of establishing a ap of the environent ith iage features is the robust atching. This section is aied to briefly describe the procedure of iage feature detection and atching ith SURF algorith. SURF is a novel scale and rotation invariant detector and descriptor and is utilized to extract and atch features beteen to successive iages. The detector is based on the Hessian atrix because of its good perforance in scale invariant. More precisely, SURF replaces the tie-consuing coputation of deterinant of the Hessian atrix ith box filters and integral iages. The integral iages play a very iportant role in using box type of filters. It is defined as follos, T ( ) x y I ( xy, ) = Iij (, ) (4) i= j= here P = P P H ( H P H + R ) H P () [] T [] [] T [] + K = P H R (3) [] T + denotes the su of the pixels ithin a rectangular region of the iage, and the rectangular region is fored by origin and radius. Therefore, it taes only three additions to copute the su of pixels inside the region of any size, as shon in Fig. 3. The original Hessian atrix is defined as follos φ h Φ =, H =. [] [] x x= x x x x = xx ( x, σ) xy ( x, σ) H( x, σ ) = xy ( x, σ) yy ( x, σ) (5)

6 36 Journal of Marine Science and Technology, Vol., No. 3 (4) dx - + Σdx Σ dx Σdy + Σ dy - dy Fig. 4. Descriptor of the feature based on Haar. here ij ( x, σ ) express the convolution of iage and Gaussian second order partial derivative. In order to g( σ ) ij reduce the coputation, the approxiate deterinant of the Hessian atrix is used and defined as follos Fig. 5. Experient of detected interest points. det( H ) D D ( D ) approx = xx yy xy (6) here D ij is the approxiation for the ij, the second order Gaussian partial derivative in x-direction, y-direction and xy-direction, and is eight of the filter responses used to balance the expression for the Hessian s deterinant. Due to the use of box filters and integral iages, the scale space is analyzed by up-scaling the filter size rather than iteratively reducing the iage size as SIFT algorith. This aes better coputational efficiency. Subsequently the descriptor vectors of the detected feature are calculated. Each one is calculated by the feature itself and surrounding region centered around it. To build the descriptor, the size of feature descriptor region is set to pixels and divided into 4 4 sub-regions. For each square, the avelet responses are coputed fro 5 5 saples. Consequently the descriptor vector of a descriptive region has total = 64 eleents, as shon in Fig. 4. For each field, e collect the sus dx, dx ; dy, and dy, coputed relatively to the orientation of the grid Fig. 5 shos an experient of the detected interest points. In the atching stage, the trace of the Hessian atrix for the underlying interest point is included. Fig. 6 shos an experient of atching result of the fifty detected interest points.. EKF-Based Global ocalization and Mapping Algorith EKF is utilized to address the global localization and apping proble for global localization and apping proble of the ADAMR. This section is devoted to describing Fig. 6. Experient of feature atching in to sequential still iages. the EKF algorith and proposing a procedure of the global localization and apping. In doing so, the robot s dead-reconing ethod and the least-square pose initialization algorith are the sae to those proposed in sec. and sec. 5. Once an EKF-based global localization and apping is ipleented, e have to estiate the pose of the robot X and the features in the environent. The state vector is coposed by the pose of the robot and the positions of the atching features fro the environent, as shon by x x x x y x= and = l l l y y y z = z z z θ In the easureent update step, KINECT detects and atches features around it ith SURF to estiate the pose of the obile base. et α i be the aziuth angle ith respect to the heading direction of ADAMR, φ i be the elevation angle ith respect to the horizontal plane, and λ i be the distance fro the robot to the i th landar l i (x i, y i, z i ) at tie. Note that these three easureents can be calculated using the KINECT easureents.

7 C.-C. Tsai et al.: Global ocalization Using Dead-Reconing and KINECT Sensors for OMWR 37 Thus, the easureent vector function is forulated as belo; ( x x ) + ( y y) + ( zz ) y y tan θ λ x x α z z tan φ ( x x) + ( y y) Z = = λ ( x ) ( ) ( x + y y + z z) α y y tan φ θ x x z z tan ( x ) ( x + y y) (7) With (5), the proposed EKF-based global localization and apping can be easily stated as follos: Step : (i) Utilize the least-squares pose initialization algorith to find the global position and orientation of the ADAMR, i.e. (x, y, z, θ ). (ii) Utilize SURF to detect features SURF and calculate the 3D-location depth of the points ith respect to all pixels ithin the depth iage ith the initial pose of the obile base. (iii) Obtain the data coposed by the repeated points siultaneously appeared in and depth. Step : (i) One-step Prediction SURF = l l l ln (8) x = f ( x, ) (9) + P = F P F + Q (3) [] [] T + here f( ) represents the dead-reconing ethod, i.e. x( ) x( ) J ( ( )) V( ) J ( ( )) V( ) y( ) θ θ y( ) + = + T θ( ) θ( ) and F eans the Jacobian atrix ith respect to f. [] F f = x [] x= x (ii) Use SURF to detect features SURF and atch ith SURF. Obtain the data coposed by the location of the atched features fro. (iii) Use to copute Step 3: z = h ( x, ) (3) here h( )denotes equation (7), i.e. ( x x) + ( y y) + ( z z ) y tan y θ λ x x α tan z z φ ( x x) + ( y y) Z = = λ ( x x ) ( y y ) ( z z ) + + α y y φ tan θ x x z z tan ( x x) + ( y y) (i) Estiation (Measureent Update) x = x + K ( z z ) (3) + P = P P H ( H P H + R ) H P (33) Where [] T [] [] T [] + K = P H R (34) [] T + [] H eans the Jacobian atrix ith respect to h. H [] h x =. x= x (ii) Calculate and update the 3D-position of the points depth ith respect to all pixels ithin the depth iage ith the update pose of the obile base. (iii) Update the data given by the repeat points appeared in and depth. SURF (IV) Replace SURF to SURF. Step 4: Repeat step and step 3. Fig. 7 shos the flochart of the Step. And Fig. 8 shos the iteration of Step and Step 3.

8 38 Journal of Marine Science and Technology, Vol., No. 3 (4) RGB Iage Depth Iage START Global ocation Initialization Ref. Si. EKF Predict Features Detection Mapping.5 SURF (The points siultaneously appeared in SURF and Depth Iage) END Fig. 7. Flochart of the proposed global localization and apping algorith at the start-up phase Fig. 9. Siulation results of the proposed pose initialization and posture tracing ethod. Encoder START Prediction of Robot Pose ex () SURF and RGB Iage Depth Iage SURF Detection ( SURF ) and Matching (coposed by the location of the atched features) Update the Robot Pose Mapping Update SURF to SURF Update the data given by the repeat points appeared in SURF and Depth Iage. ey () eth (deg.) Saple END Fig.. The errors of pose tracing in siulation. Fig. 8. Deployent of the four landars in the second experient. VII. SIMUATION AND DISCUSSION In this section, one siulation result is perfored to exaine the perforance of the proposed EKF-based global localization algoriths of ADAMR using artificial landars, four encoders and KINECT sensor. This siulation is done using Matlab/Siulin codes. In the siulation, the pose localization algorith is only verified hen the ADAMR oves in the flat environents.. The Proposed Pose Tracing Method To do the siulation of the proposed pose initialization and tracing, the second siulation sets up the size of environent as 4 3, installs telve circle landars hose positions and color are non. All the landars are fixed at the sae height. In the beginning of pose initialization, four landars are given in front of the ADAMR. Then, a rounded-corner trajectory is set in Fig. 9, here there is a clearance of.5 against the all. After these steps, each distance beteen to localized points is.5. Fig. 9 and Fig. depict the siulation results and the pose tracing errors. The siulation results reveal that the proposed pose initialization and continuous pose tracing ethods are capable of giving accurate pose estiates for position and orientation of the ADAMR.. The Proposed Pose Tracing Method To do the siulations of the proposed global localization and apping, one sets up the size of environent as 3 3. In the beginning of pose initialization, four ovable circle landars hose positions and color are non are given in front of the robot. Then, a circular trajectory ith the radius of is set as the otion trajectory of the robot, as shon in Fig.. The velocities of the four heels of the obile base are set as follos; V.47 V.489 = V 3.47 V4.489 sec (35)

9 C.-C. Tsai et al.: Global ocalization Using Dead-Reconing and KINECT Sensors for OMWR 39 3 Ref. Si. EKF Predict andar Fig.. Siulation results of the global siulation and apping ethod. Error of theta (degree) Error of x (c) Error of y (c) Siulation of global localization and apping Saple nuber Fig.. The errors of pose tracing in siulation. Fro the siulation results in Fig., the average of the errors equals [.38 c.4 c.4 ] T. As can be seen in Fig., those landars are recognized and their calculated positions are alost the sae to their true ones. Through the siulations, the proposed localization and apping algorith has been shon to find accurate locations of unnon natural landars and give accurate pose estiates for position and orientation of the ADAMR. VIII. EXPERIMENT RESUTS AND DISCUSSION This experient is devoted to exploring the erit of the proposed pose initialization using the lease-squares ethod, and the second experient focuses on the effectiveness of the proposed EKF-based tracing algoriths of the ADAMR. Worthy of ention is that the pose initialization and tracing Fig. 3. Deployent of the four landars in the second experient. pixel RGB Iage Fro KINECT ocallization Result: (-.5983, -3.78, ) (c) Orientation =.8393 (deg) (.6847, -.695) (.4333,.7367) (.446,.36647) (Distance =.63, Aziuth = rad) pixel (Iage size: 64 48) Fig. 4. Coputed global position and orientation of the KINECT in the orld frae using the four distances and aziuths of the four landars. algorith are tested using only four circle landars ith distinct colors. The initial pose of the KINECT got started at the posture, i.e. [x y y θ ] T = [. c. c 58 c deg.] T and the four landars ere located at the corresponding four positions [3.4 c 57.5 c 74.4 c] T, [.3 c 6. c 7.8 c] T, [63.8 c 47.6 c 73. c] T, and [4. c. c 9.3 c] T. Fig. 3 shos the deployent of the four landars in the experient, and the four distances and aziuths of the four landars are depicted, thereby obtaining the global position and orientation of the KINECT in the orld frae in Fig. 4, In coparison ith the true distance and aziuth of the yello landar, the errors are [.6 c.65 deg.] T. Furtherore, in coparison ith the true position and orientation of the KINECT, one can find the errors are [.5983 c 3.78 c c.8393 deg.] T in Fig. 5. Through the experient results, the proposed pose initialization ethod has been shon capable of giving initial pose localization ith acceptable accuracy for position and orientation of the ADAMR. The experient result reveals that the average of the errors equaled [ c.955 c ] T in three axes. The above-entioned results indicate that the proposed

10 33 Journal of Marine Science and Technology, Vol., No. 3 (4) Error of x (c) Error of y (c) Error of theta (degree) Experient of static localization. Average of errors: ( , ) (c) Orientation = (deg) Saple nuber Fig. 5. Errors of pose tracing in experient. continuous pose tracing ethod is capable of giving accurate pose estiates for position and orientation of the ADAMR for the static case. IX. CONCUSIONS This paper has developed a global localization approach for the ADAMR based on the least-square estiate ethod using KINECT, a KINECT-based detection algorith of artificial landars, and an EKF-based localization algorith by fusing the inforation fro the odoetric encoders and the KINECT sensor in indoor environents. Accuulation errors of the dead-reconing ethod can be significantly reduced by fusing the KINECT inforation. By fusing the KINECT data and odoetric easureents, the proposed EKF-based pose estiation ethod using the artificial landars has been shon capable of eeping trac of the continuous poses of the robot navigating on a flat terrain at slo speeds. The siulation results for both pose initialization and continuous pose tracing have verified that the proposed ethods provide ore accurate pose estiates for the obile ADAMR. The experiental results for static pose localization have confired the effectiveness and perforance of the proposed global localization ethod. It is orthhile to note that the proposed localization syste can be installed at several distinct and pre-specified location ithin the robot s oring space, in order to calibrate the robot s poses. Except the static experient, the authors are conducting experients on obtaining EKF-based pose estiation of the ADAMR hile navigating around its oring environent. ACKNOWEDGMENTS The authors gratefully acnoledge financial support fro National Science Council, the Republic of China, under contract NSC -8-E REFERENCES. Adachi, N., Fuao, T., and Naagaa, H., Adaptive tracing control of a nonholonoic obile robot, IEEE Transactions on Robotics Autoation, Vol. 6, No. 5, pp ().. Dellaert, F., Burgard, W., Fox, D., and Thrun, S., Monte carlo localization for obile robots, Proceeding on IEEE International Conference on Robotics and Autoation, Vol., pp (999). 3. Ganganath, N. and eung, H., Mobile robot localization using odoetry and inect sensor, IEEE International Conference on Eerging Signal Processing Applications (ESPA), pp (). 4. Graf, B., Hans, M., and Schraft, R. D., Mobile robot assistants, IEEE Robotics and Autoation Magazine, Vol., No., pp (4). 5. Jensen, B., Froidevaux, G., Greppin, X., orotte, A., Mayor,., Meisser, M., Rael, G., and Siegart, R., The interactive autonoous obile syste Robox, IEEE/RSJ International Conference on Intelligent Robots and Syste, Vol., pp. -7 (). 6. Ki, G., Chung, W., Han, S., Ki, K. R., Ki, M., and Shinn, R. H., The autonoous tour-guide robot Jinny, IEEE/RSJ International Conference on Intelligent Robots and Syste, Vol. 4, pp (4). 7. Kiriy, E. and Buehler, M., Three-state extended Kalan filter for obile robot localization, Technical Representative, McGill University, Montreal, Canada (). 8. Masarov, D. and Durrant-Whyte, H., Mobile vehicle navigation in unnon environents: a ultiple hypothesis approach, Proceeding on Institute Electric Engineering - Control Application Theory, Vol. 4, No. 4, pp (995). 9. Maybec, P. S., Stochastic Models, Estiation, and Control, Vol., Acadeic Press, Ne Yor (979).. Siegart, R. and Nourbahsh, I. R., Introduction to Autonoous Mobile Robots, The MIT Press.. Thrun, S., Benneitz, M., Burgard, W., Creers, A. B., Dellaert, F., Fox, D., Hahnel, D., Rosenberg, C., Roy, N., Schulte, J., and Schulte, D., MINERVA: a second-generation useu tour-guide robot, IEEE International Conference on Robotics and Autoation, Vol. 3, pp (999).. Triggs, B., Model-based sonar localisation for obile robots, Robotics and Autonoous Syste, Vol., Nos. 3-4, pp (994). 3. Tsai, C. C., in, H. S., and Hsu, J. C., Ultrasonic localization and pose tracing of an autonoous obile robot via fuzzy adaptive extended inforation filtering, IEEE Transactions Instruent Measureents, Vol. 57, No. 9, pp (8). 4. Tsai, C. C. and Wang, Y. C., Global localization using dead-reconing and KINECT sensors for anthropoorphous to-ared robots ith onidirectional ecanu heels, Proceedings of National Syposiu on Systes Science and Engineering, Keelung, Taian ().