Synthetic 2D LIDAR for Precise Vehicle Localization in 3D Urban Environment

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1 2013 IEEE International Conference on Robotics and Automation (ICRA) Karlsruhe, Germany, May 6-10, 2013 Synthetic 2D LIDAR for Precise Vehicle Localization in 3D Urban Environment Z. J. Chong 1, B. Qin 1, T. Bandyopadhyay 2, M. H. Ang Jr. 1, E. Frazzoli 3, D. Rus 3 Abstract This paper presents a precise localization algorithm for vehicles in 3D urban environment with only one 2D LIDAR and odometry information. A novel idea of synthetic 2D LIDAR is proposed to solve the localization problem on a virtual 2D plane. A Monte Carlo Localization scheme is adopted for vehicle position estimation, based on synthetic LIDAR measurements and odometry information. The accuracy and robustness of the proposed algorithm are demonstrated by performing real time localization in a 1.5 km driving test around the NUS campus area. I. INTRODUCTION Mobile robot localization is the problem of determining the pose of a robot relative to a given map of the environment [28]. It is a fundamental requirement to realize vehicle autonomy. This problem has been well solved for indoor robots on a planar surface. However, there are still many challenges to get an accurate, robust while low-cost approach for vehicle localization in an outdoor 3D urban environment. Together with localization comes its concomitant problem of mapping. A map is an abstract representation of the environment, which usually serves as a prior for robot localization. How to map the 3D environment and what representation to use are additional questions that must be addressed. This paper introduces a novel idea of synthetic LIDAR, which constructs synthetic 2D scan from 3D features, and solves the localization and mapping problem in a 2D manner. The algorithm is developed under the idea of minimal sensing, using only one tilted-down single-layer LIDAR, and odometry information. The fusion of Global Positioning System (GPS) and Inertial Navigation System (INS) to estimate vehicle position has been the most popular localization solution in recent years [18], [21], [4]. This solution works well in open areas; however, it is not suitable for dense urban environment where GPS signals severely suffer from satellite blockage and multipath propagation caused by high buildings [14]. Road-matching algorithms are then proposed to alleviate this problem, where a prior road map is used as either additional motion constraint or observation to update the localization estimation[6], [7]. While this solution achieves good global localization, it is not designed for precise estimation relative to the local environment, an ability that is highly desirable in many cases. 1 Z. J. Chong, B. Qin, M. H. Ang Jr. are with the National University of Singapore, Kent Ridge, Singapore {chongzj, baoxing.qin, mpeangh} at nus.edu.sg 2 T. Bandyopadhyay is with the Singapore-MIT Alliance for Research and Technology, Singapore tirtha at smart.mit.edu 3 E. Frazzoli and D. Rus are with the Massachusetts Institute of Technology, Cambridge, MA., USA frazzoli at mit.edu, rus at csail.mit.edu Map-aided algorithms are proposed for high precision localization using local features. In [9], single side curb features are extracted by a vertical LIDAR to build a boundary map to improve vehicle localization. This map is learned beforehand in the form of line segments. In [26], lane markers serve as local features, which are extracted from reflectivity values of LIDAR scans. A digital lane marker map is used as prior. The performance of the algorithm is similar to those in [9]. While these algorithms reduce lateral localization error considerably, they help little in the longitudinal direction. Levinson et al. in [16], [17] utilize road surface reflectivity for precise localization. A particle filter is used to localize the vehicle in real time with a 3D Velodyne LIDAR. The algorithm first analyses the laser range data, and extract those points cast on the ground. Then reflectivity measurements of these points are correlated to a map of ground reflectivity to update particle weights. One assumption underlying this algorithm is that road surfaces remain relatively constant, which may undermine the performance in some cases. Besides, the need for costly 3D LIDAR sensor limits its usage. Baldwin et al. in [2] utilizes accumulated laser sweeps as local features. The algorithm first generates a swath of laser data by accumulating 2D laser scans from a tilteddown LIDAR. Then the swathe is matched to a prior 3D survey by minimizing an objective function. This algorithm demonstrates its accuracy and robustness in GPS-denied areas. Although the algorithm proposed does not require an accurate 3D model of the environment, we argue that an accurate and consistent prior is always desired when the localization is integrated with other navigation functions. Similarly in [31], [15], a 3D point cloud of the environment is obtained by servoing a 2D LIDAR, and a reduced 2D feature is used to perform localization. This algorithm has been shown to work well in an indoor environment with a well structured ceiling features. In [5], a microwave radar sensor is used to perform SLAM. While the radar has the ability to see through obstacles, association of radar targets is a complex task and SLAM processing is done offline. This paper proposes a novel notion of synthetic LIDAR to solve the 3D localization problem in a 2D manner. The synthetic LIDAR is constructed in real time with interest points extracted from a 3D rolling window. The basic assumption is that many surfaces in the urban environment are rectilinear in the vertical direction. The interest points are extracted from the rectilinear surface, and then projected on a virtual horizontal plane to form a synthetic LIDAR. The synthetic LIDAR serves as a bridge between the real /13/$ IEEE 1554

2 world 3D environment and the virtualized horizontal 2D plane. With the idea of synthetic LIDAR, algorithms for 2D localization can be easily adapted to the 3D problem. This paper develops a Monte Carlo Localization algorithm with the notion of synthetic LIDAR, and demonstrates its accuracy and robustness through experiments. The rest of the paper is organized as follows. Section II discusses the idea of projecting 3D world to 2D plane, and gives an overview of the localization system. Section III introduces the construction of synthetic LIDAR. The localization algorithm is shown in Section IV, while experimental results and analysis are presented in Section V. II. LOCALIZATION ON A VIRTUAL PLANE A. Projecting 3D world to 2D plane Robot localization on a planar surface has been studied for decades and many algorithms have been proposed. The 2D scan-matching algorithm may be the most popular choice due to its accuracy and robustness [27]. However, it cannot be directly applied for vehicles moving in the 3D world. Since outdoor road can be very hilly at times, laser points from a planar LIDAR may cast on the road surface, rather than the desired vertical objects, as discussed in [2]. Our previous research in [22] utilizes a tilted-down LIDAR to extract road boundary features on urban road, and then uses these features for vehicle localization. Actually, there are many other salient features in urban environment that can benefit localization. What features to extract, how to extract them, and how to feed them into the localization scheme are questions to be further addressed. 3D range data is usually desired to extract features for robot navigating in the 3D world [20]. In this paper, we use a tilted-down LIDAR to generate 3D point cloud of the environment in a push-broom configuration. Rather than directly apply 3D scan-matching with the raw data [2], we try to extract features from the 3D point cloud, and use the vertical features for localization. The assumption of our method is that urban environment is rich in vertical surfaces, such as curbs, wall of buildings, and even vertical tree trunks. The vertical world assumption is actually a popular assumption used in many works in the literature. Harrison et al. in [8] propose a method to generate high quality 3D laser range data while the robot is moving. By exploiting the assumption of vertical world, useful information (e.g., roll and pitch angles) can be inferred. Kohlbrecher et al. [13] achieve 2D SLAM and 6DOF pose estimation with only a single 2D LIDAR and an IMU. Although not explicitly explained, the underlying assumption in the work is that the environments contains many vertical surfaces. Weingarten et al. in [30] uses this assumption to realize fast structured environment reconstruction. In this paper, since outdoor environments may have more arbitrary-shape objects other than structural environments, a classification step has to be taken before using the vertical assumption. In the classification procedure, laser points cast on the vertical surfaces are extracted based on surface normal estimation. When the tilted-down LIDAR sweeps the environment, some vertical surfaces will be swept from bottom to up in consecutive laser scans. If we take a bird-view for this scanning process and project the vertical features on to a virtual horizontal plane, it is exactly the same as a robot with a horizontal LIDAR moving on a 2D surface. From a mathematical point of view, the vertical surface constrains how laser points at different height should match with each other. With the above intuition, the idea of synthetic LIDAR is proposed. A synthetic LIDAR is a planar 2D LIDAR on the projected virtual plane, where the end points of its laser beams are the projected points from vertical surface in the 3D environment. The idea of synthetic LIDAR helps to solve the 3D localization problem on a 2D plane. Although a vehicle is moving in the 3D world with 6DOF, generally speaking, ground based vehicle is mostly interested in its 2D pose vector (x, y, yaw). By projecting the 3D vertical features onto a virtual plane, 2D occupancy grid map can be used by marking those vertical features. This way, an a-priori map can be obtained using SLAM with the idea of synthetic LIDAR. It should be clarified that our algorithm only applies to an environment with only one vertical traversable level. For cases with more traversable levels, some other 2.5D or full 3D algorithms may be used, for example [12]. B. System Overview The localization system mainly consists of two parts, 3D perception to extract key feature points, and 2D localization to solve the localization on the horizontal plane. The synthetic LIDAR serves as a bridge to connect the 3D world and the 2D virtual plane, as shown in Fig. 1(a). The system uses an IMU and a wheel encoder to provide 6DOF odometry information, a 2D tilted-down LIDAR to provide laser scans, and an occupancy grid map serving as a prior for localization. A simple dead reckoning is used to obtain the odometry information. Assuming the distance measured by a wheel encoder at n-th time step is r n, and the rotation is given by a pitch θ and a yaw Ψ, the change in position of the vehicle is given by: x n y n z n = cos(θ n ) cos(ψ n ) cos(θ n ) sin(ψ n ) sin(θ n ) ( r n r n 1 ) (1) The 3D perception assumes that odometry system is accurate enough in a short time period, and accumulates the laser scans for 3D range data. A classification procedure is then applied to extract interest points from the accumulated data. The extracted laser points are then projected onto a virtual horizontal plane (by ignoring their z values), and a synthetic 2D LIDAR is constructed. The 2D localization fuses odometry information from odometry and measurements from the synthetic 2D LIDAR in a Monte Carlo Localization scheme. With a prior map of vertical features generated beforehand, localization on the 2D horizontal plane is achieved. III. 3D PERCEPTION One of the requirements of the synthetic LIDAR is excellent adaptability that fits with different types of environment 1555

3 obsolete Tilted-down LIDAR IMU + Encoder Prior Map projected (x, y, yaw) 2D scan odometry 3D perception Rolling Window Updating Points Classification 2D Synthetic LIDAR 2D localization Monte Carlo Localization (a) Localization flow chart Fig. 1. rolling ahead scan accumulation β window size, ω (b) 3D rolling window Localization system overview in urban scenario. We achieve this by properly extracting interest points from a reconstructed environment model, before the synthetic LIDAR is built. To be able to recognize features that are perpendicular to the ground, an accurate model of the world is necessary. There are numerous ways that allow building an accurate environmental model, which includes nodding LIDAR and Velodyne. As introduced in section II-A, a fixed, tilted down single planar LIDAR enables the reconstruction of the environment accurately by sweeping across the ground surface. This is an attractive solution since it is low cost and only requires rigid mounting of the sensor. It also allows optimization to be done that allows real-time computation of feature extraction that is unique to this configuration. A. 3D rolling window The reconstruction uses rolling window sampling to maintain high probability of reflecting more recent samples by the ranging sensor. As such, a 3D rolling window is used to accumulate different scans recorded in a short distance. The size of the window is flexible and the rolling window forms a local map of the 3D environment, i.e., it rolls together with the vehicle, where new incoming scans will be added into the window, and the old samples get discarded. More specifically, given the window size w, the points p in n-th scan, P n is accumulated according to P n = k=n w {p k,..., p n } n > w (2) As shown in Fig. 1(b), w is used to control the number of accumulated scans such that the size of the window would not grow unbounded. Also, a new scan is only inserted when a sufficient distance, β is achieved. This has two effects, a small β will have denser points but the overall window size will become shorter and vice versa. The rolling window works in the odometry frame of the system, where each scan from a physical LIDAR is projected based on the odometry information derived from IMU and wheel encoder as discussed in Section II-B. B. Point Classification To extract features that are perpendicular to the ground, estimation of surface normal is used. While many method exists [11], we used normal estimation proposed by [3]. It is based on first order 3D plane fitting, where the normal of each point in the space is approximated by performing leastsquare plane fitting to a point s local neighborhood P K [25]. The plane is represented by a point x, its normal vector n and distance d i from a point p i P K, where d i is defined as d i = (p i x) n (3) By taking x = p = 1 k k i=1 p i as the centroid of p k, the values of n can be computed in a least-square sense such that d i = 0. The solution for n is given by computing the eigenvalue and eigenvector of the following covariance matrix C R 3x3 of P K [24]: C = 1 k (p i p) (p i p) T, C v j = λ j v j, j {0, 1, 2} k i=1 (4) Where k is the number of points in the local neighborhood, p as the centroid of the neighbors, λ j is the j th eigenvalue with v j as the j th eigenvector. The principal components of P K corresponds to the eigenvectors v j. Hence, the approximation of n can be found from the smallest eigenvalue λ 0. Once the normal vector n is found, the vertical points can then be obtained by simply taking the threshold of n along the z axis, e.g This can vary depending on how noisy the sensor data is. To find the local neighborhood points efficiently, KDtree [19] is built from all the points obtained from the rolling window and perform a fixed radius search at each point. Although the surface normal can be calculated as a whole, performing normal calculation at each point in the rolling window can be very expensive. To further reduce the computation complexity, two successive rolling windows are maintained, where P φ n+1 = P φ n Φ(Pn+1 \ P n ) (5) Where Φ can be any points classification function, P φ consists of the processed points and P contains the raw points. This way, surface normal calculation is only required for the much smaller rolling window P n+1 \ P n. In other words, this ensures that classification will only perform on the newly accumulated point cloud and the processed points from the previous instance can be reused. C. Synthetic LIDAR construction The result from the classified points consist of collection of interest points in 3D. For the construction of synthetic LIDAR, the interest points in 3D is projected into virtual horizontal plane (z=0). It can be seen that this synthetic LIDAR has a very special feature: the ability to see through the obstacles. This is possible since interpretation of points is done in 3D. The construction of synthetic LIDAR is completed by placing the virtual sensor at the base of the vehicle and perform transformation of all the interest points from odometry to the vehicle s base. 1556

4 LIDAR accumulation with 3D rolling window Synthetic LIDAR Construction Surface Normal Calculations Point Classification Interest Points Fig. 2. Construction of synthetic LIDAR In many applications where a standard LIDAR is desired (equally spaced angle increment), the synthetic LIDAR can be further reconstructed to fulfill this constraint. This would involve performing ray tracing at each fixed angle increment to obtain minimum range value from the possible end points. The overall 3D perception can be summarized in Figure 2. The 3D perception is done with the PointCloud library [23] which provides many of the operations described in this section. A. MCL Localization IV. ONLINE LOCALIZATION This paper adopts the Monte Carlo Localization (MCL) scheme in [1] to estimate the vehicle pose. MCL is a probabilistic localization method based on Bayes Theorem and Monte Carlo idea [28]. The core of MCL is a particle filter, where the belief of vehicle position is maintained by a set of particles. MCL mainly consists of three steps, prediction, correction, and resampling. For the motion model which is required for the prediction step, Pseudo-3D odometry motion model from our previous work [22] is used. The choice of measurement model is discussed in the following. B. Virtual LIDAR Measurement Model To incorporate the measurement into localization, a measurement model is needed for the synthetic LIDAR. The likelihood model is adopted for the synthetic LIDAR. Since the end points of virtual beams are the projection of interest points from vertical surfaces, it is possible that different points from different vertical surfaces may have the same angle. In other works, there exist two laser beams with the same angle while having two different range values. For this reason, synthetic 2D LIDAR is a peculiar LIDAR that only detects vertical surfaces, and can also see through these surfaces. In light of this, the likelihood model which only requires the end points of laser beams is well suited for the synthetic LIDAR. A. Experiment Setup V. EXPERIMENTS Our test bed is a Yamaha G22E golf cart equipped with various types of sensors. The hardware configuration is shown in Fig. 3. The tilted-down LIDAR mounted in the upper-front is a SICK LMS-291 LIDAR for localization. A 4-layer LIDAR, SICK LD-MRS is mounted at the waist level for obstacle detection. Both rear wheels of the golf cart are mounted with encoders that provide an estimate of the distance traveled. An Inertial Measurement Unit (IMU) MicroStrain 3DM-GX3-25 is mounted at the center of the real axle to provide orientation information of the vehicle. The localization algorithm is tested in the Engineering Campus of National University of Singapore, where the road is up-and-down and many high buildings exist off the road. A prior map is first generated with graph SLAM techniques by using the synthetic LIDAR as the input. To perform pose optimization, [29] is used as front end to detect loop closure. Then, the fully optimized pose is recovered using optimization library from [10]. To evaluate the quality of the recovered map built from synthetic LIDAR, the map is projected onto a satellite map, as shown in Fig. 5. The map shows consistency with good correlation with the satellite map, with an area of about 550 m 487 m. Although there are discrepancies towards the left side of the map due to uniform logitudinal features along the road, the overall topology is maintained. This shows that the map can be used for accurate localization. B. Experimental Results The synthetic LIDAR is able to perform at a rate of 50 Hz output on a laptop with Core i7 processor, showing that the synthetic LIDAR can be used to perform a real time localization. The localization results are shown in Fig. 6. Judging from the prior map, the localization result from our algorithm always aligns with our driving path where a parallel line with the road boundary is clearly shown in the long stretch of road. Since our algorithm does not rely on GPS, our estimation still performs well near areas crowded by tall buildings. Note that in the experiment, a rough initial position is given and hence localization is mostly concerned with pose tracking. However, the system is able to cope with small kidnapping problems, e.g. brief data error from the LIDAR since the odometry system is still able to provide information. Should a large kidnapping occur, e.g. the vehicle was moved in between placed without turning on the localization module, a rough initial position may be provided to speed up the convergence rate. Fig. 4 shows localization variance vs driving distance. 1557

5 (a) angle variance Fig. 3. Vehicle testbed The angle estimation variance is generally less than 1, as shown in Fig. 4(a). Fig. 4(b) shows position estimation variance vs driving distance in longitudinal and lateral direction relative to the vehicle. It is shown that during the whole test, variance in both directions remain small. The worse variance occur longitudinally, at a value about 0.2 m. This suggests the localization algorithm has high confidence about its pose estimates. At the same time, it is also seen that the lateral variance is generally smaller than the longitudinal one. This is inline with the fact that in an urban road environments, features in the lateral direction are much richer than those from the longitudinal direction, as discussed in our previous work [22]. This proposed method has since been used to perform autonomous navigation similar to [22]. To show that the localization results is consistent, two autonomous runs are performed as shown in Fig. 7. The golf cart is given a path to follow with the direction from A to E. To validate the precision of the localization, 5 checkpoints are selected where per-pixel absolute difference between 2 grayscale images captured from each autonomous run is performed. To ensure the same lighting condition, the two autonomous runs were performed consecutively on the same day. 5 smaller images from Fig. 7 are the results of the visual validation. The sharp edges of the images provide strong evidence that the localization system is able to provide precise position repeatedly. Do note that the dark spots present at images B, C and E are the natural results from moving objects. This shows that precise navigation can be achieved with only a single 2D LIDAR. VI. CONCLUSIONS AND FUTURE WORK This paper proposes the use of synthetic LIDAR to achieve precise localization in 3D environment. Through experiments, we show that the proposed method can handle localization on a large environment. Vehicle position estimation is conducted in a Monte Carlo Localization scheme, based on synthetic LIDAR measurements and odometry information. We demonstrate the accuracy and robustness of our localization algorithm in a driving test. Future work will look into more generic framework that allows multiple sensor modalities in order to achieve robust navigation for vehicle autonomy. Fig. 5. Fig. 4. (b) position variance Localization variance results Mapping of the NUS engineering area ACKNOWLEDGMENT This research was supported by the National Research Foundation (NRF) Singapore through the Singapore MIT Alliance for Research and Technology s (FM IRG) research programme, in addition to the partnership with the Defence Science Organisation (DSO). We are grateful for their support. REFERENCES [1] ROS AMCL. [2] I. Baldwin and P. Newman, Road vehicle localization with 2d pushbroom lidar and 3d priors, in Proc. IEEE International Conference on Robotics and Automation (ICRA2012), Minnesota, USA, May [3] J. Berkmann and T. Caelli, Computation of surface geometry and segmentation using covariance techniques, Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 16, no. 11, pp , nov [4] H. Carvalho, P. DelMoral, A. Monin, and G. Salut, Optimal nonlinear filtering in GPS/INS integration, IEEE Transactions on Aerospace and Electronic Systems, vol. 33, no. 3, pp , [5] P. Checchin, F. Gérossier, C. Blanc, R. Chapuis, and L. Trassoudaine, Radar scan matching slam using the fourier-mellin transform, in Field and Service Robotics. Springer, 2010, pp

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