Mobile robot localization using laser range scanner and omnicamera

Transcription

1 Mobile robot localization using laser range scanner and omnicamera Mariusz Olszewski Barbara Siemiatkowska, * Rafal Chojecki Piotr Marcinkiewicz Piotr Trojanek 2 Marek Majchrowski 2 * Institute of Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska 21, Warsaw, Poland bsiem@.ippt.gov.pl Warsaw University of Technology Institute of Automatic Control and Robotics sw. Andrzeja Boboli 8, Warsaw, Poland Warsaw University of Technology Institute of Control and Computation Engineering Nowowiejska, 15/19, Warsaw, Poland Abstract. In this paper a method of mobile robot localization in an unknown indoor environment is presented. The robot is equipped with a single omni-directional camera and a laser range nder. The data of the 2D scanner is used to detect walls in the robot environment. The images taken from omnicamera allow to detect texture on the walls. The robot's position can easily be estimated by combining information taken from the camera and from the laser scanner and this data can be used to follow the robot's path. The method has been tested with the use of mobile robot ELEKTRON R1 in a real oce environment. 1 Introduction Autonomous mobile robot has to be able to determine its position and orientation while moving and the most fundamental part of navigation systems is self-localization. The pose of a robot is denoted by a triple (x, y, θ), where (x,y) is the position of the robot and θ is its orientation. Until now numerous localization methods have been proposed[17][18][4][6][7][9]. The most widely used is odometry but error in determining the position of the robot increases proportionally to the distance traveled by the vehicle. In order to improve localization additional methods should be used. The methods belong to one of two classes: Relative - the current pose p t of the robot is determined relative to the previous one p t 1. Global - the position and orientation of the robot is computed within a priori given exact map or a known scene. 1

2 In this paper relative localization technique is considered but proposed techniques can be used for absolute and topological localization. Usually, an on-board laser range nder is used in order to trace the position of a robot. If the robot moves along a corridor the orientation of the robot and its displacement in the direction perpendicular to the wall can be compute very accurately but it is dicult to determine the displacement of the vehicle paralelly to the walls. In order to improve the localization technique additional sensor should be used. In our experiments the mobile platform is equipped with the omni-directional camera with hyperbolic mirror. The main advantage of omni-directional sensors is that they give 360 degrees view of the robot's environment and they simplify the interpretation of a scene. Based on images taken from an omnicamera the angular information about position of the object relatively to the robot is available immediately but the distance can be estimated after calibration of the sensor is performed. In our approach the calibration is performed using the method described in [15]. Figures 1a), 1b) present the readouts of the laser range nder taken in the corridor in two dierent positions. The displacement of the robot equals 40cm. Figure 2a), 2b) present the images taken from the omnicamera. Analysis of the images allows to determine the displacement of the robot pararelly to the walls. Figure 1. Laser readings The method presented in this paper is a development of the algorithm proposed in [15] and consists of following steps: 1. The omnicamera sensor is calibrated. The method of calibration is described in [15]; 2. Readings from laser range nder and omni-camera images are collected; 3. 2D map of an environment based on laser readings is build. The map is represented as a set of segments. 4. The images taken from omni-camera sensor are analysed. The images of the walls are transformed. 5. The displacement along the wall is computed. 2

3 Figure 2. Image of the wall taken from omnicamera 2 Wall detection The method of building 2D map of environment is described in [17]. The method of walls detection based on laser scanner readings consists of two stages: rstly the modication of Hough transform is used in order to built sets of collinear points. A line segment is described using normal notation: x cosα + y sinα = c (2.1) where c is the distance from the origin to this line computed along a normal, and α is the orientation of the normal with respect to the X axis. For points (x i, y i ), which belong to the same line, the parameters (α, c) are the same. In order to improve the precision of computed values of parameters we look for c and α which minimize the error: δ = N (R i cos(α φ i ) c) 2 (2.2) i=0 where N is the number of collinear readings, R i is the distance to the nearest obstacles in direction φ i. The straight line is indicated by the pair of parameters (c, α ) for which the value of δ is minimal. The method described above allows of determining the orientation of the robot and its displacement in direction perpendicular to the wall. When the robot acts in the corridor the error of detrming the robots orientation do not increase 0.3 o and the error of determining the displacement in the direction perpendicular to the wall 0.2cm. The error does not increase in time. 3 Cosine transform The discrete cosine transform (DTF) is a technique for converting a signal into elementary components. It is widely used in image compression. It was developed by Ahmed, 3

4 Natarajan and Rao [2]. Chen and Pratt [8] started to use DTF for images compression. 1D sequence of length N is dened by equation: N 1 C(u) = α(u) x=0 f(x)cos( π(2x + 1)u ) (3.1) 2N for u = 0, 1,2,...,N-1. α(u) is dened as: 1 α(u) = N for u = 0 (3.2) 2 N for u 0 The inverted cosine transform is dened by: f(x) = N 1 n=0 α(u)c(n)cos( π(2n + 1)x ) (3.3) 2N When cosine transform is applied to an input signal, it yields a vector of weighted values corresponding to how much of each basis function is present in the original signal. For most cases, much of the signal energy lies at low frequencies, so higher frequencies can be neglected with little distortion. 4 Detecting displacement along the wall The positions of observed walls are acquired by the laser scanner. Inverse perspective transform [1] can be used to nd texture of wall based on omnidirectional image. The angular image coordinates (ψ, β) are transformed to wall coordinates (w, h). where w - horizontal position, h - vertical position. Transformation is given by w = d (4.1) tg(ψ) tg(β) h = (4.2) d 2 + w 2 where d is distance to wall measured by laser scanner. Figure 4a) presents the fragment of the image taken from the omnicamera. Figure 4b) presents transformed image of the wall. The features from the walls are projected onto horizontal edges. For each vertical line of the wall the 1D cosine transform is performed. The weighted values of the cosine transform describe a texture of a line and they are the features which are projected. The lines of similar texture correspond to similar weighted values. In our experiment 8 values are used. Considering transformed images of the walls for two dierent positions of the robot we can determine the robot displacement along the wall by comparing the position of the areas of similar texture. 4

5 To gure out best t movement along the wall, one should nd minimum of the error given by following formulae: E(x, y) = [i 1 (ˆx) i 2 (x + ˆx)] 2 (4.3) M 1 ˆx=0 i - is a vector of feature of a line ˆx. M is the number of vertical lines in the image of the wall. When omnicamera sensor is used the resolution depends on the distance between the center of the camera and the observed region. In order to reduce an impact of errors we are searching for minimum of a function: E(x) = M 1 ˆx=0 a i [i 1 (ˆx) i 2 (x + ˆx)] 2 (4.4) where coecient a i qualify reliability of camera readings. The values are computed during calibration process. In our approach the value of a i is described by formulae a i = 1 + Ri 2 (4.5) Where R i is the distance between corresponding point on the wall and the robot position. a) Figure 3. Transormation of the image 5 Experimental results The robot ELECTRON 1 is used in our experiments 5. The robot was developed in the Institute of Automatic Control and Robotics and Institute of Control and Computation Engineering of Warsaw University of Technology. The six wheels mobile platform is equipped with on-board Biscuit PC computer (Celeron 650 MHz). Communication 5

6 between the robot and the host computer is done via wireless Ethernet. The robot is powered by two reversible DC motors. It can move with an approximate maximum speed of 0,2m/s. The vehicle is equipped with odometry sensors, 18 optical distance sensors, SICK LMS 200 laser scanner and a panoramic camera. The omni-directional sensor is composed of C-MOS color camera pointed upwards at the vertex of the hyperbolical mirror. The optical axis of the camera and the optical axis of the mirror are aligned. Figure 4. The mobile robot ELECTRON 1 1) catadioptric sensor, 2) camera, 3) laser scanner, 4) robot Experiments were performed in the corridor. The error of determining the robot displacement along the wall depends not only on the distance between the robot and the wall but also on the texture of the wall. The method is useless when there are not any characteristic area on the wall. The result depends also on the distance between the robot and characteristic places on the wall. Figures 5-6 present the result of our experiment. The task for the robot is to determined its distance to the center of the door. Error of determining robots position was computed for three dierent paths of the robot. In the rst situation approximated distance between the robot and the wall equals 0.5m, in the second one the distance equals 1m and in the last one 1.5m. 6 Conclusion The main motivation of the work presented in this article was to built the system for mobile robot localization. The environment is represented as 2D map of walls. Each wall is described using linear cosine transform. Values of coecients of cosine transform are 6

7 Figure 5. The path of the robot Figure 6. Error of determining the position of the robot the features which are traced. The performed experiments proved the eciency of the proposed method as a tool for local navigation. Presented method can be used not only as a localization technique but also as a tool for 3D map building. Bibliography [1] Adorni G., Cagnoni S., Mordonini M., Sgorbissa A.: Omnidirectional stereo systems for robot navigation. I EEE Workshop on Omnidirectional Vision (in conjunction with CVPR), June 2003 [2] Ahmed N., Natarajan T., Rao K. R. On image processing and a discrete cosine transform. I EEE Transaction on Computers C-23(1), pp [3] Aihira H., Iwasa N., et. al., Memory-based self-localization using omnidirectional images, I nternational Conference on Pattern Recognition, Silver Spring, pp

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