虚拟装配中基于精确模型的碰撞检测算法

针对目前虚拟装配中由多边形模型引起的碰撞检测准确性低的问题,提出一种考虑公差信息的精确碰撞检测算法.首先进行分层的多边形碰撞检测,获得发生碰撞的多边形;然后基于层次图像数据将发生碰撞的多边形映射到零件相应的几何上;再依据几何的公差信息计算碰撞阈值;最后根据碰撞阈值进行精确碰撞判定.实例验证结果表明,文中算法在保证虚拟装配系统实时性的同时,提高了碰撞检测的准确性.     

Incremental algorithms for collision detection between polygonalmodels

Fast and accurate collision detection between general polygonal models is a fundamental problem in physically based and geometric modeling, robotics, animation, and computer-simulated environments. Most earlier collision detection algorithms are either restricted to a class of models (such as convex polytopes) or are not fast enough for practical applications. The authors present an incremental algorithm for collision detection between general polygonal models in dynamic environments. The algorithm combines a hierarchical representation with incremental computation to rapidly detect collisions. It makes use of coherence between successive instances to efficiently determine the number of object features interacting. For each pair of objects, it tracks the closest features between them on their respective convex hulls. It detects the objects' penetration using pseudo internal Voronoi cells and constructs the penetration region, thus identifying the regions of contact on the convex hulls. The features associated with these regions are represented in a precomputed hierarchy. The algorithm uses a coherence based approach to quickly traverse the precomputed hierarchy and check for possible collisions between the features. They highlight its performance on different applications     

Collision Detection for Animation using Sphere-Trees

The detection of collisions between moving polyhedral objects is one of the most computationally intensive tasks in the computer animation process. The use of object-oriented techniques to encapsulate data within the objects' structures compounds this problem through the requirement for inter-object message passing in order to obtain geometric information for collision detection. The REALISM system decreases the time for collision detection by using a three stage process. The first stage identifies objects in the same locality using a global bounding volume table. The second stage locates regions of possible collision using a sphere-tree data structure (a hierarchical tree of spheres based on octree-type spatial subdivision). The final stage finds intersections between polygonal faces of the objects that are contained within the intersecting pairs of leaf nodes. Hence the algorithm uses a spherical geometry approximation rapidly to locate regions of potential collisions and then uses a local intersection test with actual object geometry information. The system is therefore fast and accurate. Tests for various geometric objects support this and show performance improvements of jive times over traditional polyhedral intersection tests.     

On the accuracy of the direct discrete simulation of the Landau collision integral by the Boltzmann integral

The Landau (Fokker–Planck) integral of Coulomb collisions is an integral component of the physical and mathematical models of both laboratory and space plasma, in which the intermediate collisionality regime is important. This paper discusses the method for the direct statistical simulation of the Monte Carlo type for a kinetic equation with a nonlinear operator of the Landau–Fokker–Planck (LFP) Coulomb collisions. This method is based on the approximation of the Landau collision integral by the Boltzmann collision integral. The paper has two main objectives: firstly, to obtain numerical estimates of the order of approximation of the Landau collision integral by the Boltzmann integral and, secondly, to explore the possibilities of optimizing the algorithm for multiply charged ions. The results are illustrated by the calculations of the problem on the relaxation of the initial distribution to equilibrium for one and two components.     

虚拟维修中表面间碰撞检测问题研究

基于几何约束的虚拟样机中,表面间的碰撞检测是实现维修操作的必要条件.目前有一些公用的碰撞检测工具包,但这些碰撞检测工具包一般支持多面片模型,并没有利用CAD模型中的表面信息,无法确定发生碰撞的表面.该文针对虚拟维修操作的特点,提出了一种新的场景图数据结构.在该场景图下采用表面-三角面片映射和表面-对象映射,在通用的碰撞检测工具包的基础上实现表面间的碰撞检测.最后,描述了约束管理系统的结构,利用该系统可对碰撞检测系统中发生碰撞的表面进行约束识别和求解,从而有效地支持虚拟维修中的装配和拆卸操作.     

基于混合模型的虚拟装配关键技术研究

针对虚拟装配中采用多边形网格模型引起的组件定位困难和碰撞检测精度低等问题,提出一种采用精确几何模型及其对应的多边形网格模型的混合模型作为底层数据,支持精确装配的虚拟装配系统构造方法,并基于Parasolid和Vir-tools平台进行了实现。基于混合模型的碰撞检测能根据计算精度和时间要求自适应求解,在速度快的同时,满足高精度碰撞检测要求;基于混合模型的组件装配,采用离散采样点定义装配路径,通过装配几何约束交互式定义限制组件的运动范围,通过自由度规约、装配约束求解实现了零部件精确定位,通过四元数插值实现装配路径中零部件位姿的平滑过渡,能满足高精度的装配要求。该方法已经在开发的多个系统中得到验证和应用。     

Improving performance of rigid body dynamics simulation by removing inaccessible regions from geometric models

Rigid body simulations require collision detection for determining contact points between simulated bodies. Collision detection performance can become dramatically slow, if geometric models of rigid bodies have intricate inaccessible regions close to their boundaries, particularly when bodies are in close proximity. As a result, frame rates of rigid body simulations reduce significantly in the states in which bodies come into close proximity. Thus, removing inaccessible regions from models can significantly improve rigid body simulation performance without influencing the simulation accuracy because inaccessible regions do not come in contact during collisions. This paper presents an automated pair-wise contact preserving model simplification approach based upon detection and removing of inaccessible regions of a given model with respect to another colliding model. We introduce a pose independent data-structure called part section signature to perform accessibility queries on 3D models based on a conservative approximation scheme. The developed approximation scheme is conservative and does not oversimplify but may undersimplify models, which ensures that the contact points determined using simplified and unsimplified models are exactly identical. Also, we present a greedy algorithm to reduce the number of simplified models that are needed to be stored for satisfying memory constraints in case of a simulation scene with more than two models. This paper presents test results of the developed simplification algorithm on a variety of part models. We also report results of collision detection performance tests in rigid body simulations using simplified models, which are generated using developed algorithms, and their comparison with the identical performance tests on respective unsimplified models.     

遗传算法在曲线多边形近似中的应用

在平面数字曲线的多边形近似中,为克服顶点的检测只依靠部区域,缺 乏全局信息的弱点,文中把多边形近似问题作了寻找在满足一定的近似误差下使顶点数最少,或者使顶点数和近似误差都尽可能少的最优化问题来处理。     

Simultaneous remote haptic collaboration for assembling tasks

Stand-alone virtual environments (VEs) using haptic devices have proved useful for assembly/disassembly simulation of mechanical components. Nowadays, collaborative haptic virtual environments (CHVEs) are also emerging. A new peer-to-peer collaborative haptic assembly simulator (CHAS) has been developed whereby two users can simultaneously carry out assembly tasks using haptic devices. Two major challenges have been addressed: virtual scene synchronization (consistency) and the provision of a reliable and effective haptic feedback. A consistency-maintenance scheme has been designed to solve the challenge of achieving consistency. Results show that consistency is guaranteed. Furthermore, a force-smoothing algorithm has been developed which is shown to improve the quality of force feedback under adverse network conditions. A range of laboratory experiments and several real trials between Labein (Spain) and Queen’s University Belfast (Northern Ireland) have verified that CHAS can provide an adequate haptic interaction when both users perform remote assemblies (assembly of one user’s object with an object grasped by the other user). Moreover, when collisions between grasped objects occur (dependent collisions), the haptic feedback usually provides satisfactory haptic perception. Based on a qualitative study, it is shown that the haptic feedback obtained during remote assemblies with dependent collisions can continue to improve the sense of co-presence between users with regard to only visual feedback.     

Continuous penetration depth computation for rigid models using dynamic Minkowski sums

We present a novel, real-time algorithm for computing the continuous penetration depth (CPD) between two interpenetrating rigid models bounded by triangle meshes. Our algorithm guarantees gradient continuity for the penetration depth (PD) results, unlike conventional penetration depth (PD) algorithms that may have directional discontinuity due to the Euclidean projection operator involved with PD computation. Moreover, unlike prior CPD algorithms, our algorithm is able to handle an orientation change in the underlying model and deal with a topologically-complicated model with holes. Given two intersecting models, we interpolate tangent planes continuously on the boundary of the Minkowski sums between the models and find the closest point on the boundary using Phong projection. Given the high complexity of computing the Minkowski sums for polygonal models in 3D, our algorithm estimates a solution subspace for CPD and dynamically constructs and updates the Minkowski sums only locally in the subspace. We implemented our algorithm on a standard PC platform and tested its performance in terms of speed and continuity using various benchmarks of complicated rigid models, and demonstrated that our algorithm can compute CPD for general polygonal models consisting of tens of thousands of triangles with a hole in a few milli-seconds while guaranteeing the continuity of PD gradient. Moreover, our algorithm can compute more optimal PD values than a state-of-the-art PD algorithm due to the dynamic Minkowski sum computation.     

Reconstruction of opaque inclusions in objects with high refractive index

The problem of reconstruction of inclusions in rough diamonds occupies an important place in the entire technological process of extraction and cutting precious stones. Inclusions are foreign objects that are naturally formed in raw stock during the formation of diamond (see Fig. 1). The algorithm proposed in the present paper performs a full reconstruction of three-dimensional models of inclusions from photo images. Three-dimensional models of inclusions are based on a voxel representation. The algorithm performs the coloring of voxels and the segmentation of a voxel grid and constructs polygonal models of inclusions. Experiments carried out on real and synthetic data show that the algorithm can reconstruct three-dimensional models of medium- and large-size inclusions, which may serve as a first approximation for the methods of refinement of the shape of inclusions.     

Fast computation of optimal polygonal approximations of digital planar closed curves

We face the problem of obtaining the optimal polygonal approximation of a digital planar curve. Given an ordered set of points on the Euclidean plane, an efficient method to obtain a polygonal approximation with the minimum number of segments, such that, the distortion error does not excess a threshold, is proposed. We present a novel algorithm to determine the optimal solution for the min-# polygonal approximation problem using the sum of square deviations criterion on closed curves.Our proposal, which is based on Mixed Integer Programming, has been tested using a set of contours of real images, obtaining significant differences in the computation time needed in comparison to the state-of-the-art methods.     

适用于复杂场景的碰撞检测算法研究

创建虚拟场景不仅要进行静态建模，更重要的是进行动态建模。而且物体之间的实时碰撞检测是关键。首先对常用检测算法的检测效率进行了分析和比较。然后重点针对复杂虚拟场景中吉有大量物体的特点，提出了混合包围盒碰撞检测算法。该算法利用帧与帧之间的时间和几何相关性，把对（cn^2＋m）个对象的动态跟踪转化为它们在三个坐标轴上的投影的排序问题，把时间复杂度由O（n^2）降低为O（n）。并引入树的深度的概念，根据不同的应用场合合理控制检测深度以加快检测速度。理论分析和仿真计算都表明，该算法能够满足多达几百个运动物体的实时交互碰撞检测。     

基于线性规划的碰撞检测算法研究

介绍了虚拟环境中一种基于凸多面体面信息对偶线性规划模型(DualModel)的快速旋转和移动物体之间干涉碰撞实时检测方法。该文详细介绍了建模过程和求解步骤,物体由构成凸多面体的三角形面信息表示,而物体的运动由一组虚拟现实环境中的全局移动和旋转矩阵表示。这种数学编程方法具有数据结构简单、算法可靠和速度快等优点,同时能够很好地解决高速(运动帧)碰撞的问题。这一方法通过使用主-对偶(primal-dual)内点方法来解线性规划方程,具有很好的效果,能够检测多物体对之间的碰撞。实验结果表明,基于数学编程的方法相对两种著名的工具包I-COLLIDE和SOLID,具有速度快和稳定可靠的优点,而I-COLLIDE和SOLID工具包基于两种著名的算法:LinCanny(LC)最近特征算法和GJK算法(EnhancedGilbertJohnsonandKeethialgorithm)。     

An efficient energy-conserving numerical model for the electron energy distribution function in the presence of electron-electron collisions

An efficient algorithm to calculate the contribution of electron-electron collisions in the Boltzmann equation for free electrons, in the two-term approximation is presented. The electron-electron collision term must be energy-conserving, while, due to non-linearity, commonly used algorithms do not satisfy this requirement. The efficiency of the algorithm make feasible the use of a non-linear iterative solver to conserve electron energy in electron-electron collisions.The performance of the proposed algorithm has been compared with standard numerical schemes obtaining: 1) considerable gain in computational time; 2) the conservation of the total electron energy density in e-e collisions under the required tolerance.     

Minimum-Time Aggregation Scheduling in Duty-Cycled Wireless Sensor Networks

Aggregation is an important and commonplace operation in wireless sensor networks. Due to wireless interferences, aggregation in wireless sensor networks often suffers from packet collisions. In order to solve the collision problem, aggregation scheduling is extensively researched in recent years. In many sensor network applications such as real-time monitoring, aggregation time is the most concerned performance. This paper considers the minimum-time aggregation scheduling problem in duty-cycled wireless sensor networks for the first time. We show that this problem is NP-hard and present an approximation algorithm based on connected dominating set. The theoretical analysis shows that the proposed algorithm is a nearly-constant approximation. Simulation shows that the scheduling algorithm has a good performance.     

An online collision-free trajectory generation algorithm for human–robot collaboration

The premise of human–robot collaboration is that robots have adaptive trajectory planning strategies in hybrid work cell. The aim of this paper is to propose a new online collision avoidance trajectory planning algorithm for moderate dynamic environments to insure human safety when sharing collaborative tasks. The algorithm contains two parts: trajectory generation and local optimization. Firstly, based on empirical Dirichlet Process Gaussian Mixture Model (DPGMM) distribution learning, a neural network trajectory planner called Collaborative Waypoint Planning network (CWP-net) is proposed to generate all key waypoints required for dynamic obstacle avoidance in joint space according to environmental inputs. These points are used to generate quintic spline smooth motion trajectories with velocity and acceleration constraints. Secondly, we present an improved Stochastic Trajectory Optimization for Motion Planning (STOMP) algorithm which locally optimizes the generated trajectories of CWP-net by constraining the trajectory optimization range and direction through the DPGMM model. Simulations and real experiments from an industrial use case of human–robot collaboration in the field of aircraft assembly testing show that the proposed algorithm can smoothly adjust the nominal path online and effectively avoid collisions during the collaboration.     

Efficient global penetration depth computation for articulated models

We present an algorithm for computing the global penetration depth between an articulated model and an obstacle or between the distinctive links of an articulated model. In so doing, we use a formulation of penetration depth derived in configuration space. We first compute an approximation of the boundary of the obstacle regions using a support vector machine in a learning stage. Then, we employ a nearest neighbor search to perform a runtime query for penetration depth. The computational complexity of the runtime query depends on the number of support vectors, and its computational time varies from 0.03 to 3 milliseconds in our benchmarks. We can guarantee that the configuration realizing the penetration depth is penetration free, and the algorithm can handle general articulated models. We tested our algorithm in robot motion planning and grasping simulations using many high degree of freedom (DOF) articulated models. Our algorithm is the first to efficiently compute global penetration depth for high-DOF articulated models.     

Estimating collision probabilities for trains on railroad stations based on a Poisson model

We consider the problem of estimating the probability of collision between shunting trains and passenger trains on a railroad station. We assume that the flow of shunting trains is Poisson for every turnout switch on which side collisions are possible. The data for computations include the station’s topology, timetable of passenger trains, and possible routes of their passing through the station together with the intensities of shunting trains moving through nonisolated turnout switches where collisions are possible, and also mean values of train lengths and their velocities. The proposed mathematical model of train motion can be regarded as a first approximation in modeling the collision process for trains on a railroad station. We also consider a real life example.