Normal Distribution Transform Research Articles

3D Environment Mapping with a Variable Resolution NDT Method

With the continuous development of the 3D LiDAR (Light Detection And Ranging) mapping algorithm and its application in various fields, the size of the point cloud map becomes a bottleneck that limits the 3D LiDAR mapping algorithm from running for a long time. In this paper, a 3D LiDAR mapping method based on scan-to-map and variable resolution NDT (normal-distributions transform) registration is proposed. When updating the global map, variable resolution processing can reduce the size of the global map and improve the accuracy of map construction. In addition, the size of the map created by the mapping algorithm is proportional to the size of the space and does not grow infinitely over time. The mapping experiments using a rotating LiDAR in the room, corridor, and outdoor environments show that the algorithm has higher mapping accuracy and smaller map size than without considering the variable resolution strategy. The experimental results of the map construction for a long time in an appropriate test area illustrate that the map built by the algorithm does not grow infinitely with time in the fixed space. In summary, by adjusting the map resolution adaptively according to the curvature of different areas in the 3D LiDAR mapping process, the proposed variable resolution strategy can maintain the size of the global map almost proportional to the size of the space. Moreover, the mapping accuracy can be improved as well.

Estimation of ship berthing parameters based on Multi-LiDAR and MMW radar data fusion

Achieving autonomous and safe berthing can reflect the intelligence level of unmanned ships, which is also an important manifestation to ensure the safe navigation of ships. As high-precision sensors, LiDAR (Light Detection and Ranging) and MMW Radar (millimeter wave radar) can provide environmental data for berthing. However, the use of one of them has certain shortcomings, and the fusion of the data from both sensors can provide more accurate and ample berthing information. Therefore, a novel data fusing method is proposed for assisting berthing. This method combines multi-solid-state LiDAR point cloud and MMW Radar data to obtain berthing parameters. Firstly, the collected data are pre-processed according to the characteristics of asynchronous sensors separately, and then the berthing parameters under the two sensors are obtained by the relative spatial position between the ship and the berth; In addition, the data-level fusion of multiple LiDARs point cloud is achieved by the point cloud registration-based 3D-NDT (Normal Distributions Transform) algorithm, and the decision-level fusion of berthing parameters acquired from the multi-LiDAR point cloud and MMW Radar data is performed by the weighted data fusion algorithm. Two sensors were used as perceptual devices to effectively monitor the berthing process of the experimental Ro-Ro ship at Pikou Port. The results demonstrate that the proposed method can make the data of the two sensors complement each other and effectively estimate model-free berthing parameters, which is important to assist in achieving efficient and safe berthing of ships.

Fourier변환을 갖는 Tempered Stable Lévy 프로세스(6모수 CGMY 모형)에 의한 옵션가격결정

In the real world, products in the stock market do not generally follow a normal distribution, but are known to follow a fat-tail distribution with high kurtosis and thick tails of skewness. Therefore, the purpose of this study is to analyze option pricing using a distribution in which random variables follow a stable and independent distribution and well represent the properties of the actual distribution. At this time, for the empirical analysis data, 252 daily KOSPI200 closing price indexes were used from November 15, 2019 to November 20, 2020. Call Options(Put options) were set as OTM(ITM) and ITM (OTM) and analyzed.
 In the research methodology of this paper, option pricing was performed by the CTS (or CGMY) model assuming a Tempered Stable Distribution that is capable of Furier transformation. In addition, the Black-Scholes model assuming a normal distribution and Fourier transformation, and the Fourier transformation were performed. The option pricing model using the Merton Diffusion Process and Variance-Gamma process was compared and analyzed.

A Spatiotemporal Calibration Algorithm for IMU-LiDAR Navigation System Based on Similarity of Motion Trajectories.

The fusion of light detection and ranging (LiDAR) and inertial measurement unit (IMU) sensing information can effectively improve the environment modeling and localization accuracy of navigation systems. To realize the spatiotemporal unification of data collected by the IMU and the LiDAR, a two-step spatiotemporal calibration method combining coarse and fine is proposed. The method mainly includes two aspects: (1) Modeling continuous-time trajectories of IMU attitude motion using B-spline basis functions; the motion of the LiDAR is estimated by using the normal distributions transform (NDT) point cloud registration algorithm, taking the Hausdorff distance between the local trajectories as the cost function and combining it with the hand–eye calibration method to solve the initial value of the spatiotemporal relationship between the two sensors’ coordinate systems, and then using the measurement data of the IMU to correct the LiDAR distortion. (2) According to the IMU preintegration, and the point, line, and plane features of the lidar point cloud, the corresponding nonlinear optimization objective function is constructed. Combined with the corrected LiDAR data and the initial value of the spatiotemporal calibration of the coordinate systems, the target is optimized under the nonlinear graph optimization framework. The rationality, accuracy, and robustness of the proposed algorithm are verified by simulation analysis and actual test experiments. The results show that the accuracy of the proposed algorithm in the spatial coordinate system relationship calibration was better than 0.08° (3δ) and 5 mm (3δ), respectively, and the time deviation calibration accuracy was better than 0.1 ms and had strong environmental adaptability. This can meet the high-precision calibration requirements of multisensor spatiotemporal parameters of field robot navigation systems.

Low‐cost solid‐state LiDAR/inertial‐based localization with prior map for autonomous systems in urban scenarios

AbstractA low‐cost and accurate positioning solution is significant for the massive deployment of fully autonomous driving vehicles (ADV). Conventional mechanical LiDAR has proven its performance, but its high cost hinders the massive production of autonomous vehicles. This paper proposes a low‐cost LiDAR/inertial‐based localization solution for autonomous systems with prior maps in urban areas. Instead of relying on the costly mechanical LiDAR, this paper proposes to utilize the solid‐state LiDAR (SSL) with the prior map to estimate the position of the vehicle by matching the real‐time point clouds from the SSL and the prior map using the normal distribution transformation (NDT) algorithm. However, the field of view (FOV) of the SSL is signifcantly smaller than the conventional mechanical LiDAR, which can easily lead to failure during the NDT map matching. To fill this gap, this paper proposes to exploit the complementariness of the inertial measurement unit (IMU) and the SSL, where the IMU pre‐integration provides a coarse but high‐frequency initial guess to the map matching. To evaluate the effectiveness of the proposed method in this paper, the authors collect the dataset in two typical urban scenarios through a pedestrian hand‐hold and a vehicle driving condition. The results reveal that the SSL‐only‐based localization is significantly challenged in dynamic scenarios. With the help of the IMU, the robustness of the proposed method is significantly improved, achieving an accuracy of within 0.5 m. To show the sensitivity of the SSL‐based map matching against the initial guess of the state, this paper also presents the convergence results of the map matching under different levels of accuracy in terms of the initial guess.

R-LIO: Rotating Lidar Inertial Odometry and Mapping

In this paper, we propose a novel simultaneous localization and mapping algorithm, R-LIO, which combines rotating multi-line lidar and inertial measurement unit. R-LIO can achieve real-time and high-precision pose estimation and map-building. R-LIO is mainly composed of four sequential modules, namely nonlinear motion distortion compensation module, frame-to-frame point cloud matching module based on normal distribution transformation by self-adaptive grid, frame-to-submap point cloud matching module based on line and surface feature, and loop closure detection module based on submap-to-submap point cloud matching. R-LIO is tested on public datasets and private datasets, and it is compared quantitatively and qualitatively to the four well-known methods. The test results show that R-LIO has a comparable localization accuracy to well-known algorithms as LIO-SAM, FAST-LIO2, and Faster-LIO in non-rotating lidar data. The standard algorithms cannot function normally with rotating lidar data. Compared with non-rotating lidar data, R-LIO can improve localization and mapping accuracy in rotating lidar data.

3D SLAM based on NDT matching and ground constraints for ground robots in complex environments

PurposeIn large-scale environments and unstructured scenarios, the accuracy and robustness of traditional light detection and ranging (LiDAR) simultaneous localization and mapping (SLAM) algorithms are reduced, and the algorithms might even be completely ineffective. To overcome these problems, this study aims to propose a 3D LiDAR SLAM method for ground-based mobile robots, which uses a 3D LiDAR fusion inertial measurement unit (IMU) to establish an environment map and realize real-time localization.Design/methodology/approachFirst, we use a normal distributions transform (NDT) algorithm based on a local map with a corresponding motion prediction model for point cloud registration in the front-end. Next, point cloud features are tightly coupled with IMU angle constraints, ground constraints and gravity constraints for graph-based optimization in the back-end. Subsequently, the cumulative error is reduced by adding loop closure detection.FindingsThe algorithm is tested using a public data set containing indoor and outdoor scenarios. The results confirm that the proposed algorithm has high accuracy and robustness.Originality/valueTo improve the accuracy and robustness of SLAM, this method proposed in the paper introduced the NDT algorithm in the front-end and designed ground constraints and gravity constraints in the back-end. The proposed method has a satisfactory performance when applied to ground-based mobile robots in complex environments experiments.

AUTOMATED GENERATION OF HIGH-QUALITY 3D POINT CLOUDS OF ANTLERS USING LOW-COST RANGE CAMERAS

Abstract. Three-dimensional imaging demonstrates advantages over traditional methods and has already proven feasible for measuring antler growth. However, antlers' velvet-covered surface and irregular structure pose challenges in efficiently obtaining high-quality antler data. Animal data capture using optical imaging devices and point cloud segmentation still require tedious manual work. To obtain 3D data of irregular biological targets like antlers, this paper proposes an automated workflow of high-quality 3D antler point cloud generation using low-cost range cameras. An imaging system of range cameras and one RGB camera is developed for automatic camera triggering and data collection without motion artifacts. The imaging system enables motion detection to ensure data collection occurs without any appreciable animal movement. The antler data are extracted automatically based on a fast k-d tree neighbor search to remove the irrelevant data. Antler point clouds from different cameras captured with various poses are aligned using target-based registration and the normal distribution transformation (NDT). The two-step registration demonstrates precisions of the overall RMSE of 4.8mm for the target-based method and Euclidean fitness score of 10.5mm for the NDT. Complete antler point clouds are generated with a higher density than that of individual frames and improved quality with outliers removed.

EVALUATION OF A COMPACT HELMET-BASED LASER SCANNING SYSTEM FOR ABOVEGROUND AND UNDERGROUND 3D MAPPING

Abstract. As a strategic resource, urban underground space can be used for rail transportation, commercial streets, which has high economic and social benefits, and is of great significance to sustainable city development. Due to denied Global Navigation Satellite System (GNSS) signal, traditional mobile mapping systems have difficulty collecting accurate 3D point clouds in urban underground space. Thus, a helmet-based laser scanning system, named "WHU-Helmet", is integrated in this paper to make up for the shortcomings of the existing traditional mobile mapping systems. "WHU-Helmet" is mainly equipped with four types of sensors: a GNSS receiver (optional), an IMU, a laser scanner, and a global shutter camera. "WHU-Helmet" is not relying on GNSS signal and has the advantages of low cost, small volume and easy operation. Using "WHU-Helmet", a multi-scale Normal Distributions Transform (NDT) based LiDAR-IMU SLAM is implemented to collect underground 3D point cloud in real-time. To validate the performance of "WHU-Helmet" in aboveground and underground 3D mapping, experiments were conducted in a typical urban metro station. The experiments show that the average and RMSE of HLS point errors of "WHU-Helmet" are 0.44 meters and 0.23 meters, respectively, showing great potential of "WHU-Helmet" in the application of aboveground and underground 3D mapping.

High-Precision and Fast LiDAR Odometry and Mapping Algorithm

LiDAR SLAM technology is an important method for the accurate navigation of automatic vehicles and is a prerequisite for the safe driving of automatic vehicles in the unstructured road environment of complex parks. This paper proposes a LiDAR fast point cloud registration algorithm that can realize fast and accurate localization and mapping of automatic vehicle point clouds through a combination of a normal distribution transform (NDT) and point-to-line iterative closest point (PLICP). First, the NDT point cloud registration algorithm is applied for the rough registration of point clouds between adjacent frames to achieve a rough estimate of the pose of automatic vehicles. Then, the PLICP point cloud registration algorithm is adopted to correct the rough registration result of the point cloud. This step completes the precise registration of the point cloud and achieves an accurate estimate of the pose of the automatic vehicle. Finally, cloud registration is accumulated over time, and the point cloud information is continuously updated to construct the point cloud map. Through numerous experiments, we compared the proposed algorithm with PLICP. The average number of iterations of the point cloud registration between adjacent frames was reduced by 6.046. The average running time of the point cloud registration between adjacent frames decreased by 43.05156 ms. The efficiency of the point cloud registration calculation increased by approximately 51.7%. By applying the KITTI dataset, the computational efficiency of NDT-ICP was approximately 60% higher than that of LeGO-LOAM. The proposed method realizes the accurate localization and mapping of automatic vehicles relying on vehicle LiDAR in a complex park environment and was applied to a Small Cyclone automatic vehicle. The results indicate that the proposed algorithm is reliable and effective.

A factor graph optimization mapping based on normaldistributions transform

This paper aims to achieve highly accurate mapping results and real time pose estimation of autonomous vehicle by using the normal distribution transform (NDT) algoritm. A factor graph optimization algorithm (FGO-NDT) is proposed to address the poor real-time performance and pose drift errors of the NDT algorithm. Smooth point cloud data are obtained by multisensor calibration and data preprocessing. NDT registration is then used for lidar odometry and feature matching. The global navigation satellite system (GNSS) data and loop detection results are added to the factor graph framework as the pose constraint factors to optimize the pose trajectory and eliminate the pose drift error generated during mapping. In addition, a sliding window method is used for map registration to extract a local map to shorten the map loading time. Thus, the real-time performance of creating point cloud maps of large scenes is significantly improved. Several experiments are conducted in different environments to verify the accuracy and performance of the FGO-NDT. The experimental results demonstrate that the proposed method can eliminate the pose estimation error caused by drift, improve the local structure, and reduce and root mean square error.

NDT-LOAM: A Real-Time Lidar Odometry and Mapping With Weighted NDT and LFA

The Lidar Simultaneous Localization and Mapping (Lidar-SLAM) processes the point cloud from the Lidar and accomplishes location and mapping. Lidar SLAM is usually divided to front-end odometry and back-end optimization, which can run parallelly to improve computation efficiency. The font-end odometry estimates the Lidar motion through processing the point clouds and the Normal Distributions Transform (NDT) algorithm is usually utilized in the point clouds registration. In this paper, with the aim to reduce the accumulated errors, we proposed a weighted NDT combined with a Local Feature Adjustment (LFA) to process the point clouds and improve the accuracy. Cells of the NDT are weighted according to the range’s values and their surface characteristics, the new cost functions with weight are constructed. In the experiments, we tested NDT-LOAM on the KITTI odometry dataset and compared it with the state-of-the-art algorithm ALOAM/LOAM. NDT-LOAM had 0.899% average drift in translation, better than ALOAM and at the level of LOAM; moreover, NDT-LOAM can run at 10 Hz in real-time, while LOAM runs at 1 Hz. The results display that NDT-LOAM is a real-time and low-drift method with high accuracy. In addition, the source code is uploaded to GitHub and the download link is <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/BurryChen/lv_slam</uri> .

Accuracy evaluation of surface registration algorithm using normal distribution transform in stereotactic body radiotherapy/radiosurgery: A phantom study

PurposeTo evaluate a feasibility of normal distribution transform (NDT) algorithm compared with the iterative closest point (ICP) method as a useful surface registration in stereotactic body radiotherapy (SBRT)/stereotactic radiosurgery (SRS).MethodsPoint cloud images using the 3D triangulation technology were obtained from a depth camera‐based optical imaging (OSI) system equipped in a radiosurgery room. Two surface registration algorithms, NDT and ICP, were used to measure and compare the discrepancy values between the reference and the current surfaces during the positioning of the patient. The performance evaluation was investigated by calculating the registration error and root‐mean‐square (RMS) values for the surface model, reposition, and target accuracy, which were analyzed statistically using a paired t‐test.ResultsFor surface model accuracy, the average of the registration error and RMS values were measured as 3.56 ± 2.20 mm and 6.98 ± 1.89 mm for ICP method, and 1.76 ± 1.32 mm and 3.58 ± 1.30 mm for NDT method (p < 0.05). For reposition accuracy, the average registration error and RMS values were calculated as 1.41 ± 0.98 mm and 2.53 ± 1.64 mm using ICP method, and 0.92 ± 0.61 mm and 1.75 ± 0.80 mm using NDT method (p = 0.005). The overall target accuracy using the NDT method reduced the average of the reposition error and overall RMS value by 0.71 and 1.32 mm, respectively, compared to the ICP method (p = 0.03).ConclusionsWe found that the surface registration algorithm based on NDT method provides more reliable accuracy in the values of surface model, reposition, and target accuracies than the classic ICP method. The NDT method in OSI systems offers reasonable accuracy in SBRT/SRS.

Setting Method of Downsampling Factor and Grid Factor for NDT Relocation Algorithm in Dynamic Environment

Normal Distribution Transform (NDT) algorithm plays the role of detecting the relative pose of the vehicle in high-precision map. In this paper, a method of setting downsampling factor and grid factor for NDT relocation algorithm in dynamic environment is proposed, which can solve the problems of excessive NDT relocation error and location loss caused by dynamic objects accounting for 1 % to 35 % of the volume of scanning point cloud in vehicle environment. To simulate a real dynamic point cloud environment, the single-frame LiDAR point cloud space is voxelized into a mesh. Each grid is assigned a random number evenly distributed between 0 and 1. The threshold value for whether to add a Gaussian noise point is also set. Seven representative dynamic objects on the highway are selected. The threshold value of probability distribution function of Gaussian noise object needs to be set. Then the volume content of the dynamic object in the single frame point cloud space is calculated according to the set threshold value by using the definite integral. By changing the content and volume of dynamic obstacles in a dynamic environment, the effects of the downsampling factor and the grid factor on the accuracy of the repositioning trajectory are obtained. The resampling and mesh coefficients are optimized based on the analysis of the repositioning trajectory accuracy. The results show that When the current sampling factor is fixed, the grid factor of the NDT algorithm is proportional to the RMSE factor. When the NDT grid factor is fixed and the down sampling factor is equal to the side length of the obstacle, the NDT relocation accuracy is the highest and reaches the local optimum.

SLAMDATMO in roadway and sidewalk environments by helmet-mounted LiDAR and IMU

This paper presents a method for simultaneous localization, mapping, detection, and tracking of moving objects (SLAMDATMO) using LiDAR and IMU set on a helmet of micro-mobility rider. An environmental obstacle map built by SLAMDATMO represents stationary objects, road boundaries and road surface conditions in roadway and sidewalk environments. This map can be used to active safety for micro-mobility, such as bicycles, e-bikes, and e-scooters. Distortion in the LiDAR scan data is corrected by estimating the helmet’s pose (three-dimensional position and attitude angle) based on the information from Normal Distributions Transform (NDT)-based SLAM and IMU. The road surface, boundary, stationary and moving-object scan data are classified from the corrected LiDAR scan data. The moving scan data are used for DATMO, whereas the stationary scan data are used for point-cloud mapping. The boundary scan data are used to detect obstacles, such as curbs, gutters, and steps. The road surface scan data from LiDAR are in conjunction with IMU, and potholes and humps, such as manhole cover and cracks, are detected to reduce the falling risk of micro-mobility. The experimental results in a road environment of our university campus show the effectiveness of the proposed SLAMDATMO method.

Realization of indoor and outdoor localization and navigation for quadruped robots

The quadruped robot has the advantages of flexible movement and large load because of the bionic leg structure. In order to improve their intelligence and autonomy in the complex environment, we build a highly integrated sensing system with lidar and an inertial measurement unit (IMU) on a quadruped robot. After the robot completes the construction of the map, point clouds are aligned using Normal Distribution Transform(NDT) registration to realize the localization of the robot. In the experimental part, we quantitatively tested the accuracy of outdoor localization and also completed indoor-outdoor navigation experiments for the quadruped robot. The experimental results validate the effectiveness of the perception system.

3D Dense Mapping with the Graph of Keyframe-Based and View-Dependent Local Maps

This article concerns the problem of a dense mapping system for a robot exploring a new environment. In this scenario, a robot equipped with an RGB-D camera uses RGB and range data to build a consistent model of the environment. Firstly, dense mapping requires the selection of the data representation. Secondly, the dense mapping system has to deal with localization drift which can be corrected when loop closure is detected. In this article, we deal with both of these problems, and we make several technical contributions. We define local maps which use the Normal Distribution Transform (NDT) stored in the 2D structures to represent the local scene with varying 3D resolution. This method directly utilizes the uncertainty model of the range sensor and provides information about the accuracy of the data in the map. We also propose an architecture that utilizes pose and covisibility graphs to correct a global model of the environment after loop closure detection. We show how to integrate the dense local mapping with the pose graph and keyframes management system in the ORB-SLAM2 localization. Finally, we show the advantages of the view-dependent model over the methods that uniformly divide the space to represent objects in the environment.

An Optimized FPGA-Based Real-Time NDT for 3D-LiDAR Localization in Smart Vehicles

Light detection and ranging (LiDAR) based normal distribution transform (NDT) is a popular localization algorithm in smart vehicles for its robustness and accuracy. To meet the requirement of higher speed of smart vehicles, LiDAR point clouds become increasingly large due to the increase of not only the number of laser channels but also their frame rates. However, previous NDT implementations fail to achieve real-time performance when handling large point clouds because they require an enormous number of search operations and perform intensive computations per search operation. To address this issue, we propose an optimized NDT algorithm and its FPGA implementation. First, we effectively speed up each search operation by proposing a new non-recursive and memory-efficient data structure, called occupation-aware-voxel-structure (OAVS). Second, we significantly reduce the number of search operations by removing redundant searches with an optimized semantic-assisted OAVS-based NDT algorithm (SEO-NDT). Third, we further improve the real-time and energy efficiency by proposing a streaming FPGA accelerator architecture for SEO-NDT. Compared with the state-of-the-art embedded CPU and GPU implementations, our FPGA implementation achieves up to 35.85x and 2.44x execution time speed up, respectively.

V2I based environment perception for autonomous vehicles at intersections

In recent years, autonomous driving technology has made good progress, but the noncooperative intelligence of vehicle for autonomous driving still has many technical bottlenecks when facing urban road autonomous driving challenges. V2I (Vehicle-to-Infrastructure) communication is a potential solution to enable cooperative intelligence of vehicles and roads. In this paper, the RGB-PVRCNN, an environment perception framework, is proposed to improve the environmental awareness of autonomous vehicles at intersections by leveraging V2I communication technology. This framework integrates vision feature based on PVRCNN. The normal distributions transform(NDT) point cloud registration algorithm is deployed both on onboard and roadside to obtain the position of the autonomous vehicles and to build the local map objects detected by roadside multi-sensor system are sent back to autonomous vehicles to enhance the perception ability of autonomous vehicles for benefiting path planning and traffic efficiency at the intersection. The field-testing results show that our method can effectively extend the environmental perception ability and range of autonomous vehicles at the intersection and outperform the PointPillar algorithm and the VoxelRCNN algorithm in detection accuracy.

Real-time high-precision location and mapping system based on NDT of the large scene

The traditional lidar registration algorithm has good stability and high precision when carrying out large-scale simultaneous localization and mapping. However, in complex and changeable environments such as outdoor, severe occlusion, or electronic interference, the signal is easily affected, and the positioning accuracy cannot be guaranteed. To solve the above problems, a high-precision localization method based on laser-point cloud NDT (Normal Distributions Transform) is proposed in this paper, which makes full use of the mean and variance characteristics of NDT registration of the midpoint cloud, and the proposed method is added into the complete framework of SLAM (Simultaneous Localization and Mapping). The algorithm proposed in this paper was verified on the “Wuling Electric Vehicle“ platform. The experimental results were showed that the proposed algorithm could effectively avoid the influence caused by signal weakening, which improved the positioning accuracy. It also had stronger robustness and better tracking performance.