COLLISION DETECTION AMONG MOVING OBJECTSIN MACHINING PROCESS SIMULATION

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Fast collision detection among multiple moving spheres

This paper presents an event-driven approach that efficiently detects collisions among multiple ballistic spheres moving in the 3D space. Adopting a hierarchical uniform space subdivision scheme, we are able to trace the trajectories of spheres and their time-varying spatial distribution. We identify three types of events to detect the sequence of all collisions during our simulation: collision, entering, and leaving. The first type of event is due to actual collisions, and the other two types occur when spheres move from subspace to subspace in the space. Tracing all such events in the order of their occurring times, we are able to avoid fixed time step simulation. When the size of the largest sphere is bounded by a constant multiple of that of the smallest, it takes O(n¯_c log n+n¯_e log n) time with O(n) space after O(n log n) time preprocessing to simulate n moving spheres, where n¯_c and n¯_e are the number of actual collisions and that of entering and leaving events during the simulation, respectively. Since n¯_e, depends on the size of subspaces, we modify the collision model from kinetic theory for molecular gas to determine the subspace sizes for the space subdivision scheme, that minimize simulation time. Experimental results show that collision detection can be done in linear time in n over a large range     

一种基于速度的移动对象轨迹简化算法

目前对移动对象轨迹简化问题分为离线简化和在线简化。以往的简化方法中许多依赖轨迹的几何特性,而针对移动对象的速度这一重要特征没有足够的关注。本文基于速度研究移动对象轨迹的离线简化新方法,提出了移动对象轨迹离线简化的动态规划算法、基于广度优先搜索的轨迹简化算法及其优化算法、时间复杂度更低的近似算法。并通过大量实验验证本文提出的算法比基于方向的简化算法和基于位置的简化算法具有更好的简化效率。     

An expert fuzzy system for predicting object collisions. Its application for avoiding pedestrian accidents

Collision among moving objects in space is one of the most common risks in daily life. In this context, we have developed an abstract model that allows to detect the presence of risk of future collisions among objects from the video content analysis. Our proposal carries out several stages. First, a camera calibration process calculates the real location of object in scene. Then, we estimate the object speed and their future trajectory in order to predict possible collisions. All the information of the objects is described in an ontology. Using the properties of objects (such as location, speed, trajectories), we have defined a fuzzy rule that permits to identify whether an object is in danger because another could hit him. The use of fuzzy logic results in two points: the collision detection is gradual and the model can be adjusted through membership functions to fuzzy concepts. Furthermore, the proposed model is easily adaptable to any situation and can be applied on various fields. With the aim of testing our proposal, we have focused on pedestrian accidents, a case of special interest since a lot of pedestrians die or are injured in traffic accidents daily. We have developed an application based on our model that is able to predict, in real time, the traffic accidents where a vehicle could run over a pedestrian. The obtained results in the experimental stage show a high performance of the system.     

基于轨迹结构的移动对象热点区域发现

针对现有热点区域发现算法难以从轨迹数据集中准确识别活动热点的问题,提出了基于轨迹结构的热点区域发现框架（TS_HS）。TS_HS由候选区域发现（CHSD）算法和热点区域过滤（HSF）算法组成。首先,使用基于网格相对密度的CHSD识别空间上的轨迹密集区域作为候选热点区域;然后,利用HSF根据候选区域中轨迹的活动特征和时间变化特征,筛选出移动对象活动频繁的热点区域。在Geolife数据集上进行的实验表明,与基于全局密度的热门区域发现算法（GD_HR）以及移动轨迹时空热点区域发现算法（SDHSRD）相比,TS_HS能更有效地解决多密度热点区域的识别问题。实验结果表明,TS_HS能够根据轨迹的活动特征准确发现移动对象的活动热点区域。     

iBTC:一种基于独立森林的移动对象轨迹聚类算法

移动对象轨迹聚类在城市规划、公共空间设计、移动对象行为预测等领域具有重要的理论指导意义和实际应用价值。针对传统聚类算法(如k-means,DBSCAN)在移动对象轨迹方面聚类效果不佳的问题,提出一种新的轨迹聚类算法iBTC。该算法首先对轨迹进行分段,根据最小描述长度原理,将轨迹分段问题转换为求无向图的最短路径问题,使用Dijkstra算法求得轨迹的最佳分段;然后将轨迹聚类问题转换为一种特殊的异常检测问题,并基于独立森林的思想,使用细分-合并过程对轨迹数据进行聚类;最后在模拟数据集和监控视频记录的行人轨迹公开数据集上进行实验,结果表明该算法能够取得较好的聚类效果。     

移动对象轨迹时空相似性度量方法

在分析移动对象行为时,移动对象轨迹因包含大量的信息而具有重要的作用。在实际应用中移动对象常受限于空间网络而无法利用现有欧氏空间中轨迹及其距离处理技术。分析了道路网络空间轨迹相似性性质,提出一种移动对象轨迹建模的时空表示方法,能有效地将轨迹从道路网络空间转化到欧氏空间;同时提出了一种基于兴趣点POI（Points Of Interesting）距离的轨迹间相似性测量方法,有效地对轨迹进行化简并减少轨迹中节点的数目,从而降低算法时间复杂度。该方法不仅可以用于搜索相似轨迹,还可方便地应用到轨迹聚类的相关工作中。     

基于大数据分析的移动对象轨迹预测方法

对移动对象的轨迹预测将在移动目标跟踪识别中具有较好的应用价值。移动对象轨迹预测的基础是移动目标运动参量的采集和估计,移动目标的运动参量信息特征规模较大,传统的单分量时间序列分析方法难以实现准确的参量估计和轨迹预测。提出一种基于大数据多传感信息融合跟踪的移动对象轨迹预测算法。首先进行移动目标对象进行轨迹跟踪的控制对象描述和约束参量分析,对轨迹预测的大规模运动参量信息进行信息融合和自正整定性控制,通过大数据分析方法实现对移动对象运动参量的准确估计和检测,由此指导移动对象轨迹的准确预测,提高预测精度。仿真结果表明,采用该算法进行移动对象的运动参量估计和轨迹预测的精度较高,自适应性能较强,稳健性较好,相关的指标性能优于传统方法。     

A review of moving object trajectory clustering algorithms

Clustering is an efficient way to group data into different classes on basis of the internal and previously unknown schemes inherent of the data. With the development of the location based positioning devices, more and more moving objects are traced and their trajectories are recorded. Therefore, moving object trajectory clustering undoubtedly becomes the focus of the study in moving object data mining. To provide an overview, we survey and summarize the development and trend of moving object clustering and analyze typical moving object clustering algorithms presented in recent years. In this paper, we firstly summarize the strategies and implement processes of classical moving object clustering algorithms. Secondly, the measures which can determine the similarity/dissimilarity between two trajectories are discussed. Thirdly, the validation criteria are analyzed for evaluating the performance and efficiency of clustering algorithms. Finally, some application scenarios are point out for the potential application in future. It is hope that this research will serve as the steppingstone for those interested in advancing moving object mining.     

Visually exploring movement data via similarity-based analysis

Data analysis and knowledge discovery over moving object databases discovers behavioral patterns of moving objects that can be exploited in applications like traffic management and location-based services. Similarity search over trajectories is imperative for supporting such tasks. Related works in the field, mainly inspired from the time-series domain, employ generic similarity metrics that ignore the peculiarity and complexity of the trajectory data type. Aiming at providing a powerful toolkit for analysts, in this paper we propose a framework that provides several trajectory similarity measures, based on primitive (space and time) as well as on derived parameters of trajectories (speed, acceleration, and direction), which quantify the distance between two trajectories and can be exploited for trajectory data mining, including clustering and classification. We evaluate the proposed similarity measures through an extensive experimental study over synthetic (for measuring efficiency) and real (for assessing effectiveness) trajectory datasets. In particular, the latter could serve as an iterative, combinational knowledge discovery methodology enhanced with visual analytics that provides analysts with a powerful tool for “hands-on” analysis for trajectory data.     

Variational sphere set approximation for solid objects

We approximate a solid object represented as a triangle mesh by a bounding set of spheres having minimal summed volume outside the object. We show how outside volume for a single sphere can be computed using a simple integration over the object’s triangles. We then minimize the total outside volume over all spheres in the set using a variant of iterative Lloyd clustering that splits the mesh points into sets and bounds each with an outside volume-minimizing sphere. The resulting sphere sets are tighter than those of previous methods. In experiments comparing against a state-of-the-art alternative (adaptive medial axis), our method often requires half as many spheres, or fewer, to obtain the same error, under a variety of error metrics including total outside volume, shadowing fidelity, and proximity measurement.     

New computer vision based Snakes and Ladders algorithm for the safe trajectory of two axis CNC machines

Multi-axis machine production process optimization, automation and intelligence are the key codes of today’s scientific community. Rapid decision and intelligence are becoming more important for precise and safe virtual and real production. Multi-axis CNC production is a high speed machining process that demands less human intervention and high intelligence, to deal with any uncomfortable situation regarding collisions. Current CAM softwares as well as CNC machines are able to detect collisions but are unable to avoid these collisions automatically. This paper aims to make the CAD-CAM/CNC multi-axis safe trajectory generation process optimal, intelligent and automatic, using vision based image processing by the Snakes and Ladders game analogy. Applying the Snakes and Ladders analogy on machine virtual scene (trajectory preparation) and real scene (during production) images gives promising methodology for safe and efficient trajectory generation while avoiding collisions named Snakes and Ladders Analogy for Production Trajectory (SLAPT). Our Rectangular Enveloped Safe and Efficient Trajectory (RESET) algorithm, based on the same principle of the SLAPT methodology is also discussed in this paper. Results include some applications of algorithms on virtual and real machine scene images for the safe and optimized trajectory of tools. This paper focuses on intelligence and optimization of 2D non-functional transversal trajectories of 2-axis machines for production and preparation processes as an initial effort towards the complex safe trajectory generation process (mill-turn).     

Speed Planning for a Maneuvering Motion

Collision-free motion among moving objects is an on-going research topic. Based on the concept of a modified path-velocity decomposition and application of the interface propagation method, a strategy for trajectory planning is proposed in this paper. In the proposed method, the global navigation paths for robots are assumed to have already been planned without any static obstacle crossing their paths. Each subtask along the global path of each controlled object contains a desired goal position and desired arrival time for reaching the position. Based on the information about each subtask, Space/Time Graphs (STGs) for the robots are created. By shifting the speed path from corresponding forbidden regions on the STG, potential collisions can be avoided. Optimal speed paths with least velocity alterations for controllable objects are derived automatically by applying the interface propagation method in the STGs. The applicability of the proposed approach is demonstrated and the results show that controllable and uncontrollable moving objects can work together in a shared environment by avoiding collisions.     

边界约束的非相交球树实体对象多维统一索引

针对现有空间索引剖分结构复杂、节点重叠率高及对多维实体对象检索及运算支撑较弱等问题,构建了一种边界约束的非相交球实体对象多维统一空间索引;利用球的几何代数外积表达,提出了基于求交算子的直线-平面和直线-球面的相交判定与交点提取方法,建立了多维实体对象体元化剖分方法及包含边界约束的非相交离散球实体填充算法,实现了实体对象空间均匀、非重叠的分割,并在填充球的个数、重叠率以及对象逼近近似度等约束条件上获得了较好的平衡.定义了最小外包球生成与更新的迭代算法与包含球体积修正的批量Neural Gas层次聚类算法,在尽可能保证球树各分支平衡性的前提下,实现了索引层次体系的稳健构建.利用几何代数下球对象间几何关系计算的内蕴性与参数更新的动态性,实现了索引结构的动态生成与更新,进而设计了实体对象表面及其内部任意位置及区域的检索策略及基于实体索引的空间关系计算方法.基于不同实体对象的模拟实验显示,基于几何代数的实体对象索引可以有效实现多维实体对象表面及其内部任意位置及区域的快速检索,并能在有限时间内以较高的精度实现多维实体对象最近邻距离和动态实体对象相交状态的检索.相对于常用球树索引,所提出的索引方法在填充率、节点重叠率、填充误差、体元个数、层次球个数、体积百分比和时间占用等方面均具有明显优势,且不同分辨率剖分条件下的索引结构及空间关系计算精度具有更高的稳健性,可运用于具有较强时间约束下复杂多维动态场景中对象检索与空间关系计算.     

Evaluation of the Visibility of Vessel Movement Features in Trajectory Visualizations

There are many visualizations that show the trajectory of a moving object to obtain insights in its behavior. In this user study, we test the performance of three of these visualizations with respect to three movement features that occur in vessel behavior. Our goal is to compare the recently presented vessel density by Willems et al. [ [WvdWvW09] ] with well‐known trajectory visualizations such as an animation of moving dots and the space‐time cube. We test these visualizations with common maritime analysis tasks by investigating the ability of users to find stopping objects, fast moving objects, and estimate the busiest routes in vessel trajectories. We test the robustness of the visualizations towards scalability and the influence of complex trajectories using small‐scale synthetic data sets. The performance is measured in terms of correctness and response time. The user test shows that each visualization type excels for correctness for a specific movement feature. Vessel density performs best for finding stopping objects, but does not perform significantly less than the remaining visualizations for the other features. Therefore, vessel density is a nice extension in the toolkit for analyzing trajectories of moving objects, in particular for vessel movements, since stops can be visualized better, and the performance for comparing lanes and finding fast movers is at a similar level as established trajectory visualizations.     

A new moving target interception algorithm for mobile robots based on sub-goal forecasting and an improved scout ant algorithm

It is difficult to make a robot intercept a moving target, whose trajectory and speed are unknown and dynamically changing, in a comparatively short distance when the environment contains complex objects. This paper presents a new moving target interception algorithm in which the robot can intercept such a target by following many short straight line trajectories. In the algorithm, an intercept point is first forecasted assuming that the robot and the target both move along straight line trajectories. The robot rapidly plans a navigation path to this projected intercept point by using the new ant algorithm. The robot walks along the planned path while continuously monitoring the target. When the robot detects that the target has moved to a new grid it will re-forecast the intercept point and re-plan the navigation path. This process will be repeated until the robot has intercepted the moving target. The simulation results have shown that the algorithm is very effective and can successfully intercept a moving target while moving along a relatively short path no matter whether the environment has complex obstacles or not and the actual trajectory of the moving target is a straight line or a complex curve.     

Efficient k-nearest neighbor search on moving object trajectories

With the growing number of mobile applications, data analysis on large sets of historical moving objects trajectories becomes increasingly important. Nearest neighbor search is a fundamental problem in spatial and spatio-temporal databases. In this paper, we consider the following problem: Given a set of moving object trajectories D and a query trajectory mq, find the k nearest neighbors to mq within D for any instant of time within the lifetime of mq. We assume D is indexed in a 3D-R-tree and employ a filter-and-refine strategy. The filter step traverses the index and creates a stream of so-called units (linear pieces of a trajectory) as a superset of the units required to build the result of the query. The refinement step processes an ordered stream of units and determines the pieces of units forming the precise result. To support the filter step, for each node p of the index, in preprocessing a time-dependent coverage function C _p (t) is computed which is the number of trajectories represented in p present at time t. Within the filter step, sophisticated data structures are used to keep track of the aggregated coverages of the nodes seen so far in the index traversal to enable pruning. Moreover, the R-tree index is built in a special way to obtain coverage functions that are effective for pruning. As a result, one obtains a highly efficient kNN algorithm for moving data and query points that outperforms the two competing algorithms by a wide margin. Implementations of the new algorithms and of the competing techniques are made available as well. Algorithms can be used in a system context including, for example, visualization and animation of results. Experiments of the paper can be easily checked or repeated, and new experiments be performed.     

Motion anomaly detection and trajectory analysis in visual surveillance

Motion anomaly detection through video analysis is important for delivering autonomous situation awareness in public places. Surveillance scene segmentation and representation is the preliminary step to implementation anomaly detection. Surveillance scene can be represented using Region Association Graph (RAG), where nodes represent regions and edges denote connectivity among the regions. Existing RAG-based analysis algorithms assume simple anomalies such as moving objects visit statistically unimportant or abandoned regions. However, complex anomalies such as an object encircles within a particular region (Type-I) or within a set of regions (Type-II). In this paper, we extract statistical features from a given set of object trajectories and train multi-class support vector machines (SVM) to deal with each type of anomaly. In the testing phase, a given test trajectory is categorized as normal or anomalous with respect to the trained models. Performance evaluation of the proposed algorithm has been carried out on public as well as our own datasets. We have recorded sensitivity as high as 86% and fall-out rate as low as 9% in experimental evaluation of the proposed technique. We have carried out comparative analysis with state-of-the-art techniques to benchmark the method. It has been observed that the proposed model is consistent and highly accurate across challenging datasets.     

Roadmap-based motion planning in dynamic environments

In this paper, a new method is presented for motion planning in dynamic environments, that is, finding a trajectory for a robot in a scene consisting of both static and dynamic, moving obstacles. We propose a practical algorithm based on a roadmap that is created for the static part of the scene. On this roadmap, an approximately time-optimal trajectory from a start to a goal configuration is computed, such that the robot does not collide with any moving obstacle. The trajectory is found by performing a two-level search for a shortest path. On the local level, trajectories on single edges of the roadmap are found using a depth-first search on an implicit grid in state-time space. On the global level, these local trajectories are coordinated using an A/sup */-search to find a global trajectory to the goal configuration. The approach is applicable to any robot type in configuration spaces with any dimension, and the motions of the dynamic obstacles are unconstrained, as long as they are known beforehand. The approach has been implemented for both free-flying and articulated robots in three-dimensional workspaces, and it has been applied to multirobot motion planning, as well. Experiments show that the method achieves interactive performance in complex environments.