Simulated Sensor Reading. Heading. Y [m] local minimum ; m. local maximum ; M. discontinuity ; D. connection ; c X [m]

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1 Localization based on Visibility Sectors using Range Sensors Sooyong Lee y Nancy. Aato Jaes Fellers Departent of Coputer Science Texas A& University College Station, TX 7784 fsooyong,aato,jpf938g@cs.tau.edu Abstract This paper presents a rapid localization ethod for obile robots. Localization, i.e., absolute position easureent, is an iportant issue since odoeter errors render it ipossible for any robot to precisely follow a specied trajectory, resulting in a growing dierence between the actual conguration and the calculated conguration as the robot travels. Periodic localization is required to correct these errors. In this paper, we propose a new localization ethod using range sensor data which is based on siple geoetric properties of the environent. In any coon situations, inforation regarding the environent is provided a priori for path planning. During processing, the ethod proposed here utilizes this inforation to partition the workspace into sectors using siple visibility coputations, and a sall identifying label is coputed for each sector. The localizer analyzes range sensor readings (distances) and extracts characteristic points, which are copared with the pre-coputed sector labels to localize the robot, rst to a sector, and then to a particular conguration within that sector. Advantages of this two step process are that it is coputationally very siple, and that it allows precise localization without any landarks fro any conguration in the environent. This localization ethod also provides opportunities for the global navigation procedure to analyze and select trajectories in ters of their tolerance to localization errors. Introduction Autoatic navigation by obile robots involves following a planned trajectory taking the robot fro a known start conguration to a goal conguration. The desired trajectory can be viewed as a collection of robot congurations, which describe the robot's location (x; y) and orientation This research supported in part by NSF CAREER Award CCR-96435, NSF Grants IIS-96985, EIA-98583, and EIA-98937, and by the Texas Higher Education Coordinating Board under grant ARP y Sooyong Lee is with Korea Institute of Science and Technology, Seoul, KOREA. He is currently visiting Texas A& University Figure : Coordinates () with respect to the world coordinate syste (see Figure ). Unfortunately, it is not possible for robots to precisely follow planned trajectories. This is due to unavoidable easureent errors which prevent the robot fro precisely deterining its current conguration. In particular, obile robots have encoders to accurately easure/control the rotation of their wheels. Based on its kineatics, the robot's conguration is calculated fro the encoder reading. However, the error between the actual conguration of the robot and the estiated conguration gets larger as the robot travels, ainly due to encoder errors caused by the slip between the wheel and the surface [6]. Since the robot cannot follow the given trajectory exactly, periodic localization (i.e., precise deterination of x; y; ), which resets the error to zero is necessary. uch work has been done on obile robot localization. A nuber of landark-based or ap-based approaches have been proposed which use ultrasonic range or sonar sensors. In [6], a position estiation ethod based on principal coponent analysis of laser range data is proposed. The structure of an environent is represented as a faily of surfaces in an eigenspace, which is constructed fro the principal coponents of a large nuber of range data sets. The Generalized Voronoi Graph (GVG) can be used for localization [] by coparing the coordinates of the current eet point (vertex of the GVG) with the coordinates of previously discovered eet points. If there is a atch, then the robot can locate itself on the partially explored GVG. The disadvantage of this approach is that localization is possible only at eet points. A fast localization algorith for dynaic environents is proposed in

2 [7]; it is based on the denition of a very sall landark, which is calculated fro the circular depth function using a sonar sensor. Sonar sensor data is used in [7] to build aulti-level description of the robot's surroundings. The resulting two-diensional aps are used for path planning and navigation. The localization ethod in [4] uses sensor data and the current odoetry reading to build a series of local perception grids, and then registers the local and the global grids. They assue the obile robot has a ap of its environent represented as an evidence grid (i.e., each grid cell is arked as either free or occupied). The basic principles of landark-based and ap-based positioning also apply to vision-based positioning which relies on optical sensors instead of ultrasonic range sensors and inertial sensors. Coon optical sensors include photoetric caeras using CCD arrays. Visual sensing provides a treendous aount of inforation about a robot's environent and it is potentially the ost powerful source of inforation aong all the sensors used on robots. Due to the wealth of inforation, however, extraction of visual features for positioning is not an easy task. The proble of localization by vision has received considerable attention and any techniques have been suggested. ost localization techniques using vision provide absolute/relative conguration of sensors. Techniques vary substantially, depending on the sensors, their geoetric odels and the representation of the environent. Sugihara [5] considered two cases of point location probles, and [] followed this approach and forulated the positioning proble as a search in a tree of interpretations. In [4], an algorith is proposed for localization based on ray angle easureent using a single caera, and then in [5], an odoetric sensor was added to landark-based ray easureents and an extended Kalan lter was used to cobine vision and odoetric inforation. A ethod was developed in [] that uses a stereo pair of caeras to deterine the correspondence between the observed landarks and the preloaded ap and to estiate the two-diensional location of the sensor fro the correspondence. A syste for navigation in a partially odeled environent is outlined in [8], and in [3], trinocular stereo and three-diensional line features are used for building, registering, and fusing noisy visual aps. ost of the vision-based approaches use landarks, whose locations are previously dened in world coordinates. Soe of the ap-based localization techniques only provide for localization in restricted regions of the environent (e.g., only at previously known or discovered landarks such as eet points). To our knowledge, no localization ethod has been proposed which exploits precoputable geoetric properties of (partially) known environents to enable localization at virtually any point in the environent using only range sensor data.. Our Approach In this paper, we propose a new localization ethod using range sensor data (i.e., distance easureents) which is based on siple geoetric properties of the environent. In any coon situations, inforation regarding the environent is provided a priori for path planning. Our goal is to utilize this inforation for localization. Our localization ethod is coputationally very siple and enables the robot to estiate its conguration at any place in the workspace. During preprocessing, the workspace is partitioned into sectors using siple visibility coputations, and a sall identifying label is coputed for each sector. The localizer analyzes the range sensor readings and extracts characteristic points, which are copared with the pre-coputed sector labels to localize the robot, rst to a sector, and then to a particular conguration within that sector. This two step process is coputationally very siple, and allows precise localization without any landarks (beacons). Another advantage of this localization ethod is that it provides opportunities for the global navigation procedure to analyze and select trajectories in ters of their tolerance to localization errors. The ethod as described in this paper is applicable to static, copletely known environents. We are working on extensions of the ethod so that it can be used in partially known environent which include unknown or oving obstacles. The paper is outlined as follows. Section describes visibility sectors, and localization based on visibility sectors is described in Section 3. The global navigator is outlined in Section 4. Preliinary experiental results are presented in Section 5, and soe conclusions are given in Section 6. Visibility Sectors To facilitate subsequent localization, it is convenient during preprocessing, to partition the environentinto sectors that are distinguished by the features of the environent that are visible fro the sector. We assue that a odel of the environent is provided a priori, that the portion of the workspace relevant for navigation can be considered to be planar, and that obstacles can be odeled by siple polygons. In particular, we assue that a description of the environent isavailable as an ebedded planar graph G = (V; E), jv j = n and jej =, which decoposes the plane into regions that are free (i.e., contain no obstacles) or blocked (i.e., lled with obstacles). The union of the free (blocked) regions of the environent iscalled the workspace (obstacle space) and is denoted by W (B). Two points p and p are visible if p p does not properly intersect B. The point visibility polygon V (p) is the set of all points visible fro p [3] (see Figure (a)). A visibility sector si Wis a axial region such that every point p si is visible fro the sae set of environent vertices Vs i V. Thus, the visibility sectors of W are the faces in the planar subdivision that is obtained by overlaying the point visibility polygons for all v V (see Figure (b)). While ore sophisticated ethods exist, it is sucient for us to use a less ecient algorith since the environents we consider are quite sall and these coputations

3 (a) (b) Figure : (a) A point visibility polygon, and (b) the visibility sectors. Sector labels for the environent of Fig- Table : ure (b). Sec. Label Dc Dc 3 4 cd 5 cd 6 DccD 7 DccD 8 DccD 9 DccD are perfored during preprocessing. In particular, we siply consider all pairs of vertices vi;vj V and deterine what contribution, if any, the line containing the akes to V (vi) orv(vj). After deterining all such segents, we add the to our description of the environent G =(V; E) to obtain a new graph G =(V; E ) (intersection points are not introduced yet). Finally, we use the LEDA [] routine to construct a planar ap, whose faces correspond to our visibility sectors, fro the graph G.. Visibility Sector Labels To aid the localization process, we copute, during preprocessing, a label for each sector that includes a coponent for each vertex and edge of the environent visible fro that sector. The coponent for each feature is classied as one of four types of characteristic points: a local axia (), a discontinuity (D), a local inia (), or a connection (c) point. The local axia represent the convex vertices of the environent visible fro the sector, while the discontinuity points are the concave environent vertices that inhibit the view of soe portion of the environent fro the sector. The Local inia of a sector are the visible concave vertices that are not discontinuity points or are points on edges which are perpendicularly visible fro a sector (i.e., if a perpendicular segent fro the edge can reach the sector without intersecting any obstacle). Finally, each discontinuity point D has a corresponding connection point c, which represents the partially visible edge whose visibility is blocked by D (i.e., c represents the `landing' point ofaray fro the sector through D). Note that if a point could be both a discontinuity oraconnection point and a local iniu or axiu, distinction as a discontinuity or connection point takes precedence. A sector's label is a string of ark characters (,, D and c), one for each characteristic point, which appear in the order the characteristic points are seen in a counterclockwise scan with an initial orientation of (i.e., eastern point rst). For exaple, Table shows the sector labels for the environent of Figure (b). 3 Localization Our localization ethod is actually a two-step process. First the robot is localized to a particular visibility sector, and then its precise position and orientation in that sector are coputed. Both these steps ake use of the visibility sector inforation coputed during preprocessing and are accoplished using only distance readings obtained by siple range sensors. To siplify the exposition, in this section we ake the following assuptions: (i) each visibility sector in the environent has a unique label, and (ii) the robot's range sensors provide at least three readings for each edge visible fro the robot's current position. While the rst assuption is in general not valid, the second ay be practically true for laser scanning sensors in certain environents. These assuptions are reoved in Section Range sensor data The `visibility' inforation required by our localization algorith can be obtained using siple, inexpensive range sensors. Ultrasonic range sensors or laser scanning sensors are coonly used for obile robots to easure the distance to nearby (visible) obstacles or to avoid collision. Laser scanning sensors provide distance easureents of radians with a very high sapling rate. Soe obile robots are equipped with a rotating table so that the ultrasonic sensor ounted on top gives radians sensor readings. Figure 3 shows an exaple of a siulated sensor reading. The center is the origin of the sensor coordinates. If easured N ties for radians, the resolution is N radians and the i-th sensor reading gives distance inforation (ri) at an angle (i) with respect to the sensor coordinates. We denote the set of N sensor readings by SD: SD = f(ri;i)jri R; i ; i N, g : ()

4 9 6 Sensor Reading c DISTANCE [] D Figure 3: Siulated Range Sensor Reading 3. Localization to a visibility sector To localize the robot to a particular visibility sector of the environent, we extract a label `R fro the distance data R scanned by the robot and atch this label with a label `vs for one of the environent's visibility sectors (recall in this section we assue each sector has a unique label). This is accoplished by extracting characteristic points fro the easured distance data, and then coposing the into a label. Figure 4 shows the easured distance data scanned fro to radians. If we scan these readings in sorted angular order, then the local inia and axia readings directly correspond to local inia and axia characteristic points and, respectively. The discontinuity and connection characteristic points D and c, respectively, can be found by a siilar scan. In this case, if two consecutive distance readings dier by soe predeterined threshold value "T, then the saller reading corresponds to D and the larger to c. This process is outlined in the pseudo-code below, where R = fr ;r ;:::;rn,g is the set of N distance readings sorted in angular order; all index arithetic is done odulo N, and denotes string concatenation. Construct Scan Label(R). `R := ;. for i := to N 3. if (ri, ri+ >"T)then `R := `R cd 4. elseif (ri+, ri >"T)then `R := `R Dc 5. elseif (ri, >ri and ri <ri+) then `R := `R 6. elseif (ri, <ri and ri >ri+) then `R := `R 7. endif 8. endfor The characteristic points identied by Construct Scan Label are arked in Figure 4, and Figure 5 shows the sensor reading apped into the workspace. In this case, a total of 8 saples are easured. The label constructed for this sensor reading is `R = DC where the initial orientation is = 5 direction in Figure 5). (note the heading Y [] ANGLE [rad] Figure 4: Sensor Data Analysis Siulated Sensor Reading local iniu ; local axiu ; discontinuity ; D connection ; c Heading X [] Figure 5: Characteristic Points Once the label `R is coposed fro the scan, it is then atched with a label `vs for one of the environent's visibility sectors. Our assuption that the range sensors provide at least three distance readings for all visible edges of the surrounding environent iplies that we will have a distance reading for each characteristic point visible fro the robot. However, since the orientation of the robot is not known, our atching of `R with the environent's sectors labels ust consider cyclic shifts of `R when perforing the atching. For exaple, in the exaple considered above, the label `R atches the label for visibility sector s, but only after cyclically shifting `R. 3.3 Localization in a visibility sector Once the visibility sector containing the robot is identied, we now ust deterine the position and orientation of the robot in that sector, i.e., we ust deterine its congu-

5 ration (xo; yo; o) (see Figure ). Note that we know the world coordinates of the vertices and edges visible in this sector. In addition, we have sensor readings for each visible edge, and oreover, after the label atching, we know the edge associated with each distance easureent. If our sensor readings corresponding to the local axia characteristic points exactly coincided with the corresponding vertices of the environent, then localization would be trivial. For exaple, let (X ;Y) and (x ;y) denote the coordinates of the scanned local axiu point in the world and the robot's local coordinate systes (X; Y ) and (Xr; Yr), respectively. Then, the robot conguration (xo; yo; o) denotes the linear transforation fro (X; Y )to(xr;yr) with translation (xo;yo) and rotation ( o), which can represented as shown in Equation : " # #, cos o sin o X, sin o, cos o Y #" x y = " xo In the above atrix representation, there are three unknown variables (xo;yo; and o), and two equations. Therefore, in order to solve for (xo;yo; o)we require the local coordinates of at least two environent vertices ( characteristic points). Unfortunately, due to the nite nuber of scans, our readings do not exactly coincide with environent vertices. However, we can use the readings to copute the local coordinates of (two) environent vertices, and then use these to copute (xo;yo; o) as described above. Consider the situation shown in Figure 6, where we have scans on the edges adjacent to the local axiu vertex =(x;y). In the gure, (Xr;Yr) yo () In practice, it is convenient to select two adjacent vertices so that the equations for only 3 lines need to be coputed, i.e., we use the edge between the vertices in both cases. 4 Global Navigation The global navigator includes the localizer and the path planner/updater odules, which both use the environent's visibility sector inforation. With the given start and goal congurations, and the known environent inforation, the global navigator plans the path, and outputs a trajectory for the obile robot. As the robot traverses the path, it (periodically) sends sensor readings to the localizer odule. Fro the sensor data, the localizer estiates the current conguration, and sends it to the path updater, which replans the path, if necessary, and outputs a new trajectory for the obile robot. Figure 7: Global Navigator If each sector in the environent has a unique label, then the localization procedure described in Section 3 is sucient to localize the robot to a sector. We note that in any situations, the labels of the visibility sectors will in fact be unique. For exaple, in the ore coplex oce environent shown in Figure 8, which contains 8 visibility sectors, each sector's label is unique. Figure 6: Coputing the local coordinates of fro scans on its incident edges. is the robot's local coordinate syste and (X; Y ) is the world coordinate syste. We can derive the equation for the line containing the left edge using the series of sensed (local) points Pi+; Pi+;Pi+3;Pi+4. Only two points are required to get the equation of the line, but ultiple points are used for a least square error ethod to reduce the error. Siilarly, the equation for the line through the right edge can be derived fro Pi;Pi,;Pi,;Pi,3. In principle, one could use any two convex environent vertices (local axia points) for the above calculations. Figure 8: Sectors for an Oce Environent However, there exist environents in which ultiple sectors have the sae label. To deal with this case safely,

6 the global navigator should plan the path carefully so that no abiguities will arise, or it should ask the robot to localize suciently often so that accurate localization is always possible. any researchers have developed algoriths that estiate the position uncertainty of a dead-reckoning robot [9, 6]. With this approach, each coputed robot position is surrounded by a characteristic error ellipse which indicates a region of uncertainty for the robot's actual position [, 6]. Typically, these ellipses grow with travel distance (Figure 9). Localizing with our ethod is not possible if an uncertainty ellipse intersects two sectors with identical labels. In order to avoid this situation, the global naviga- Figure : obile robot Figure 9: Uncertainty Ellipses and Abiguous Sectors tor should attept to plan the path and the relocalization points so that this does not occur. Deterining the iniu nuber of scans necessary for accurate localization is an iportant issue because iniizing the sensing tie will iniize the localization tie. A full description of the global otion planner and a ethod for deterining the iniu nuber of scans will be available in the full version of the paper. 5 Preliinary Experiental Results We are currently ipleenting our localization ethod with the obile robot shown in Figure. The robot has dual dierential drive with DC gear otors and encoders. Due to encoder errors caused by slip between the wheel and the surface, periodic localization is necessary. Three ultrasonic range sensors are ounted on the pan/tilt head so that each sensor gives readings of radians. The sensors have a iniu and axiu range of c and 3.5, respectively, with a resolution of %. For this initial test, we used environent identical to the running exaple used in the paper (Figure ), but in reduced scale (:54 :54 as opposed to ). Figure shows the robot sensing the environent fro sector s ; N = 6 sensor scans were obtained ( scans by each sensor). Figures and 3 show preliinary experient results. Note that the experiental data is very close to the siulated sensor readings shown in Figures 4 and 5. Due to crosstalk of signals, the easureent shows several incor- Figure : Experient rect readings, and postprocessing of the sensed inforation is currently being investigated. 6 Conclusion In this paper, we present a new localization ethod for obile robots. This ethod is based on range sensor data and soe siple preprocessing of the environent to partition it into visibility sectors. A strength of this localization ethod is that it can be applied fro any conguration in the environent (it does not need landarks). It is also very siple, requiring only a coparison of soe features easily extracted fro the sensor reading with siilar inforation coputed for each sector in the environent. This localization ethod also provides opportunities for the global navigation procedure to analyze and select trajectories in ters of their tolerance to localization errors. We believe this ethod is very proising, particularly in indoor environents for which good odels are often readily available. We will report ore coplete experiental results in the nal version of the paper. We are also working on extensions of the ethod so that it can be used in the presence of unknown (e.g., furniture) or oving (e.g., people) obstacles.

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