PROBABILISTIC LOCALIZATION AND MAPPING OF MOBILE ROBOTS IN INDOOR ENVIRONMENTS WITH A SINGLE LASER RANGE FINDER

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1 nd International Congress of Mechanical Engineering (COBEM 3) Noveber 3-7, 3, Ribeirão Preto, SP, Brazil Copyright 3 by ABCM PROBABILISTIC LOCALIZATION AND MAPPING OF MOBILE ROBOTS IN INDOOR ENVIRONMENTS WITH A SINGLE LASER RANGE FINDER Sith Washington Arauco Canchuuni Marco Antonio Meggiolaro Pontifical Catholic University of Rio de Janeiro, Gávea - Rio de Janeiro, RJ - Brasil saraucoc@uni.pe eggi@puc-rio.br Abstract. Undoubtedly, due to the recent advances in robotics, robots are increasingly autonoous. Therefore, for a robot, to have the ability to ove within an environent without the assistance of a huan being, it is required to have knowledge of the environent and its location within it at the sae tie. In any robotic applications, it is not possible to have an a priori ap of the environent. In those situations, the robot needs to build a local ap of its environent while executes its ission and, siultaneously, deterine its location. A typical solution for the Siultaneous Localization and Mapping (SLAM) proble priarily uses two types of sensors: i) an odoeter, which provides inforation of the robot's oveent, and ii) a range easureent, which provides perception of the environent. In this work, a solution for the SLAM proble is presented using a DP-SLAM algorith purely based on laser readings, focused on structured indoor environents. It considers that the obile robot only uses a single D Laser Range Finder (LRF), and the odoetry sensor is replaced by the inforation obtained fro the overlapping of two consecutive laser scans. The Noral Distributions Transfor (NDT) algorith of the scan atching is used to approxiate a function of the ap overlapping. To iprove the perforance of this algorith and deal with lowquality range data fro a copact LRF, a scan point resapling is used to preserve a higher point density of high inforation features fro the scan. A differential evolution algorith is presented to optiize the overlapping process of two scans. During the developent of this work, the obile robot "irobot Create", assebled with one LRF "Hokuyo URG-4LX", is used to collect real data in several indoors environent, generating D aps presented as results. The techniques, described in this work, enable a obile robot, with a D laser scanner, to obtain precise aps of indoor environents, which can be useful in search and reconnaissance issions, e.g. in warehouses, production plants, and other industrial areas. Keywords: SLAM, Scan Matching, Evolution Differential, Robot Mobile, Laser Range Finder. INTRODUCTION Recently, significant advances have been ade in Mobile Robotics, allowing sophisticated robotics systes to be able to perfor copletely autonoous tasks. Basic tasks such as path planning, localization, and navigation are well understood and have been solved in a high degree. These coponents enable the robot to perfor a variety of tasks with no huan intervention or supervision. Several robotic systes need to have a fairly coplete knowledge of the world, along with a reasonable ap of the environent. This ap, in addition to being accurate, should be fairly coplete covering all the places that the robot can reach in its exploitation. In the robotics counity, the proble to build a local ap of its environent while executing its ission and, siultaneously, deterining its location, is known as Siultaneous Localization and Mapping (SLAM). SLAM has been a challenge to autonoous robots. The probles of localization and apping appear as two distinct challenges but, in fact, probles are intricately intertwined. For a robot, to update the ap correctly, it is necessary to know its location when the observations are ade. However, in order to track the location of the robot, it is essential to have a good ap to copare with the observations. Thrun and Burgard (6) reviewed the existing techniques to solve the SLAM proble, such as axiu likelihood estiation, expectation axiization, extended Kalan filter (EKF), or extended inforation filters (EIF). Besides these ethods, the FastSLAM algorith can be used to approxiate the posterior probabilities of particles (Biber and Straber, 3), while the DP-SLAM algorith is purely based on laser readings, which plays an iportant role in D apping (Eliazar, 5). Most algoriths that solve the SLAM proble have sensors to perceive the environent (such as a range easureent) and sensors for capturing the displaceents of the obile robot (such as an odoeter). However, such sensors are subject to significant noise, and there are any objects that norally cannot be detected directly (Herrera ). In this paper, a solution for the SLAM proble is presented using a DP-SLAM algorith applied to the obile robot irobot Create, assebled with a single D Laser Range Finder (LRF) and without an odoeter. This LRF, odel Hokuyo URG-4LX, allows the robot to collect real data in several indoor environents, while the odoetry sensor is

2 S.W.A. Canchuuni, M.A. Meggiolaro Probabilistic Localization and Mapping of Mobile Robots in Indoor Environents with a Single Laser Range Finder replaced by the inforation obtained fro the overlapping of two consecutive laser scans (Scan Matching) by the Noral Distributions Transfor (NDT) algorith. Figure. Hokuyo URG-4LX Laser Range Finder. This paper is organized as follows. Section introduces the atheatical structure of the estiation-theoretic SLAM proble. Section 3 then provides an overview of the scan atching algorith, and Section 4 describes the experients and presents the results of the analysis using real data collected fro the irobot Create in indoor environents. Finally, Section 5 suarizes the work.. THE ESTIMATION-THEORETIC SLAM PROBLEM The SLAM proble is best described as a probabilistic Markov chain. This section establishes the atheatical fraework eployed in the study of the SLAM proble. The Bayes rule plays a proinent role in the area of probabilistic robotics (and probabilistic inference, in general). Suppose one wants to learn about a quantity (ap) or (pose) based on easureent data. As in the SLAM process, there are two different types of data: sensor easureents z t and control outputs u t. Here, superscripts are used as an index of tie for the discrete data in the tie period. Then the Bayes rule says that the proble can be solved by ( ) - ( ) - () where and refer to data leading up to tie, and is a noralizer of Bayes Rule. Note that Bayes rule is recursive, that is, the posterior probability ( ) is calculated fro the sae probability of an earlier tie. The initial probability in tie is ( ) ( ). In Equation (), there are two iportant probability distributions: - and. Both are generative odels of the obile robot and its environent.. Motion odel The probability - is referred to as otion odel, and specifies the control effect on the state. This odel describes the probability that the control output, if executed in the state, can lead to state. The ain purpose of a otion odel is to capture the relationship between the control effort of the obile robot and changes in its position. Instead of using odoetry sensors for displaceent inforation of the robot, the proposed algorith uses Scan Matching to extract this inforation.

3 nd International Congress of Mechanical Engineering (COBEM 3) Noveber 3-7, 3, Ribeirão Preto, SP, Brazil. Measureent odel The probability is referred to as the easureent odel, which describes the process of foration through which the easureents of the sensors are generated in the physical world. In probabilistic ters, it describes how the sensor easureents are generated for different positions in the environent. The Measureent Model accounts for the uncertainty in the robot's sensors. In practice, it is often ipossible to odel a sensor with high accuracy. The recent developent of Laser Range Finders (LRF) at reasonable prices quickly turned the into a doinant sensor to be used in the apping proble. 3. SCAN MATCHING Most obile robots require soe knowledge of their location in the environent. Scan atching approaches for localization are based on overlaying two scans, without aking any assuption about their shape nor searching features. In other words, scan atching approaches rely on the raw data provided by range sensors, such as the LRF. Scan Matching is the proble of finding the roto-translations ( ) between a scan input and a scan reference obtained fro a device such as a LRF which axiizes the overlap between the parts of the environent represented by and. A definitive solution does not exist because scan atching is used in a vast range of operative conditions (Burguera and Gonzalez, 8). Biber and Straber (3) proposed a ethod called Noral Distributions Transfor (NDT) that does not need correspondences of points. Thus, NDT akes an occupancy grid and subdivides the D plane into cells. To each cell, it assigns a noral distribution, which odels the probability of easuring an obstacle in such cell. The result of the transfor is a piecewise continuous and differentiable probability density, that can be used to atch another scan using Differential Evolution (DE). 3. Scan atching algorith The Scan Matching algorith for NDT can be outlined in the following steps: i) build the NDT of the to deterine the probability function associated with ; ii) initialize the estiate for the roto-translations ( ); iii) for each saple of the and, for each point, deterine the spatial transforation in the coordinate syste of the according to the paraeters ( ); iv) evaluate each resulting point in the probability function associated with ; and v) optiize the paraeters ( ) to obtain a axiu overlapping of the and. 3. Differential evolution for scan atching Differential Evolution (DE), like Genetic Algoriths, belongs to the faily of Evolutionary Coputation. It is an optiization technique that uses an exceptionally siple evolution strategy, which is significantly fast and robust, with a high likelihood to find a function s true global optiu (Pricel and Storn, 5). The use of DE is robust and useful to estiate the roto-translations ( ) between scans. These three displaceent values are the variables to be codified; thus, one chroosoe is coposed as ( ), which are represented by real nubers. The fitness function is given by the probability function associated with the NDT algorith. The stopping criterion used in this paper for the optiization is given by two values. The first is the fitness value. Thus, the optiizations stop if the fitness value is less than a value acquired epirically. The second stopping criterion is based on a axiu nuber of generations. 3.3 Scan filtering A crucial proble in Scan Matching is how to select points of scans that are useful for atching. Each scan contains hundreds of points, and any of the could be redundant, especially when the environent is so siple. Furtherore, redundant points of scans affect the efficiency and accuracy of the Scan Matching algorith. The scan density strongly depends on paraeters such as robot speed or the aterial of the obstacle (Toono, 5). To avoid this proble, it is necessary to resaple the scan. In this paper, scan filtering is perfored with the goal of preserving iportant scan points and discarding redundant scan points, so points with low saliency inforation are eliinated. The Saliency-based Scan Point Resapling ethod calculates the saliency of each scan point according to the aount of inforation the scan point has, or the length of the line segent on which the scan point lies. This approach is able to resaple a scan with a inial loss of inforation, with very low coputational requireents. Figure exeplifies the effect of the resapling step.

4 S.W.A. Canchuuni, M.A. Meggiolaro Probabilistic Localization and Mapping of Mobile Robots in Indoor Environents with a Single Laser Range Finder y y Features outstanding x x Figure. Set of laser readings before resapling (left) and after resapling (right). Figure shows results for a scan acquired in a corridor. The nuber of scan points is originally 68 per scan. But, after resapling, the nuber of points reduces to 34. As it can be seen in the figure, all the points around the corners are preserved as salient point and points on the walls are resapled alost uniforly, iniizing eory requireents without losing significant inforation about the ap walls. 4. EXPERIMENTS Indoor experients are conducted in buildings fro the Pontifical Catholic University of Rio de Janeiro. An irobot Create obile robot is eployed, which is a two-wheeled obile robot. A Hokuyo URG-4LX LRF is then ounted on it, with a scan range of 4, angular resolution.35 degrees, and angular range between 4 and 4 degrees. Figure 3. Mobile robot irobot Create coupled with the Laser Range Finder.

5 nd International Congress of Mechanical Engineering (COBEM 3) Noveber 3-7, 3, Ribeirão Preto, SP, Brazil Data sets, gathered in seven different environents fro the University, have been used. These environents consist of corridors and hallways with parallel walls, corners, doors and soe features. In order to obtain the solution for the SLAM proble, a single LRF sensor is used to get inforation on the location of the obile robot and perfor environent apping along as the robot oves. First, the Scan Matching algorith is used to replace the odoetry inforation. Then, it is applied to solve the SLAM proble, while the DP- SLAM algorith is used to iprove the solution. The NDT algorith for Scan Matching was ipleented and tested in experients perfored with the paraeters shown in Table. This table presents the size of the grid (grid resolution) used in the NDT algorith, and the population size, nuber of generations, scaling factor and crossover constant associated with the Differential Evolution algorith to axiize the overlapping between two consecutive scans. Table. Scan Matching paraeters. Algorith Paraeters Value NDT Grid resolution Nuber of Generations 5 Differential Evolution Population Size Crossover.95 Scaling factor. Figure 4 shows two consecutive scans obtained fro the LRF, followed by a figure with the atching and overlapping between the. By successfully overlapping both scans, it is possible to estiate the obile robot displaceent. In this exaple, the environent has distinctive features such as pillars, doors, corners and other characteristics, resulting in a low overlay error Y Y X X Figure 4. Scan atching in environents with special distinctive features, showing the first scan (left), second scan (iddle) and the atching and overlapping between the, used to estiate the obile robot displaceent (right). In a few of the experients carried out, parts of the environent have few features, such as plain corridors with parallel walls. In this case, the scan atching algorith presents a greater difficulty to find the overlay between two consecutive sensor readings, resulting in a poor estiate of the obile robot displaceent. Figure 5 shows this case, where two sensor readings are taken in an environent with parallel walls. Such overlay errors can be seen in the dashed region in the right iage of Figure Y Y X X Figure 5. Scan atching in environents with special distinctive features, showing the first scan (left), second scan (iddle) and the atching and overlapping between the, used to estiate the obile robot displaceent (right). It is found that the SLAM proble can be solved with the Scan Matching algorith, without the need for odoeters. It is shown that it is possible to obtain the displaceent ( ) between the positions of two

6 S.W.A. Canchuuni, M.A. Meggiolaro Probabilistic Localization and Mapping of Mobile Robots in Indoor Environents with a Single Laser Range Finder consecutive sensor readings. Perforing a coordinate transforation for all sensor readings in accordance with the displaceent of two successive scans, one can obtain the trajectory of the obile robot and the ap where it oves. Figure 6 shows the resulting aps fro experients. The location of the obile robot is represented in red dots and the detected environent in blue dots. Note that these environents basically present two parallel walls, with few distinctive features, which akes it ore difficult to perfor scan atching. Nevertheless, the generated ap of the environents provides a reasonable outline of the real aps Figure 6. Maps generated by the obile robot, showing the identified walls (in blue) and the estiated robot trajectory (in red) without the use of odoeters. Figure 7 shows another environent and the resulting ap. This hallway presents several corners and perpendicular corridors, which results in a ap with iproved accuracy due to such distinctive features. Note that, during the oveent of the obile robot in this environent, the robot passes twice along the sae part of the ap, but it is able to distinguish both tours Figure 7. Map building and localization by scan atching.

7 nd International Congress of Mechanical Engineering (COBEM 3) Noveber 3-7, 3, Ribeirão Preto, SP, Brazil These aps are then iproved by using a representation of the occupancy grid, provided by the DP-SLAM algorith. Furtherore, DP-SLAM can be used to reduce the errors produced by the Scan Matching algorith (Eliazar, 4). Figure 8 shows the hallway for the sae environent of the botto ap fro Figure 6. In this ap, one can observe ore clearly the contours of coluns, doors, elevators, trash cans, aong other characteristics, resulting in a better ap representation. Siilarly, Figure 9 shows the representation using the DP-SLAM algorith of the environent shown in Figure 7. Here, the perpendicular ways and other features of the environent are clearly observed. Figure 8. Resulting ap after the application of DP-SLAM on the data fro the botto ap fro Figure 6. Figure 9. Resulting ap after the application of DP-SLAM on the data fro Figure CONCLUSIONS This paper proposed a ethod to iprove the perforance of the NDT Scan Matching using Differential Evolution for the axiization of the overlap between scans fro a laser range finder (LRF), applied to the solution of the SLAM proble. The inforation obtained fro the Scan Matching algorith is useful to replace odoetry sensors and create accurate aps using the DP-SLAM algorith. The fraework developed in this work allows a low cost obile robot with a single D LRF to obtain accurate aps of indoor environents without the need for odoetry sensors.

8 S.W.A. Canchuuni, M.A. Meggiolaro Probabilistic Localization and Mapping of Mobile Robots in Indoor Environents with a Single Laser Range Finder 6. REFERENCES Biber, P. and Straber W., 3 The Noral Distributions Transfor: A New Approach to Laser Scan Matching. In IEEE-RSJ International conference on Intelligent Robots ans Systes. Las Vegas, Nevada, USA. Burguera, A. and Gonzalez, Y., 8. On the use of likelihood fields to perfor sonar scan atching localization. In IEEE-RSJ International conference on Intelligent Robots ans Systes. Edonton, Alberta, Canada. Eliazar, A., 5. DP-SLAM. Ph.D. thesis, Departent of Coputer Science Duke Univerdity. Eliazar, A. and Parr, R., 3. DP-SLAM: Fast, Robust Siultaneous Localization and Mapping Without Predeterined Landarks. In Proceedings 8 th International Joint Conference on Artificial Intelligence, (IJCAI). Eliazar, A. and Parr, R., 4. DP-SLAM.. In IEEE International Conference on Robotics and Autoation (ICRA). Herrera, L.E.Y.,, Mobile robot Siultaneous localization and apping using DP-SLAM with a single laser range finder. MSc. thesis, Departent of Mechanics Engineering Pontifical Catholic University of Rio de Janeiro. Pricel, K.V. and Storn, R.M., 5. Differential Evolution: A Practical Approach to global Optiization. Springer, New Jersey. Thrun, S. and Burgard, D.F., 6. Probabilistic Robotics. The Mit Press Cabridge, Massachusetts, London, England. Toono, M., 5. Efficient global scan atching using Saliency-based Scan Point Resapling. In IEEE-RSJ International conference on Intelligent Robots ans Systes. Nice, France. 7. RESPONSIBILITY NOTICE The authors are the only responsible for the printed aterial included in this paper.