多样化实时刚体破碎模拟

目的 现有刚体破碎仿真模拟中,基于物理受力分析的方法往往难以应用在对实时性要求较高的场景中;而基于非物理方法的破碎模拟,破碎效果大多缺乏多样性。为了使得破碎模拟同时满足实时性和破碎效果多样化,提出了一种多样化实时刚体破碎模拟方法。方法 进行破碎模拟时首先由选定的种子点生成类型得到种子点集,采用Sweep Plane算法生成Voronoi图后基于Voronoi图信息对模型进行空间剖分;然后选择破碎时行为模拟方式,对物体破碎时所受外力进行模拟;最后对破碎时碰撞检测及碰撞后碎片的运动过程进行模拟并渲染显示。结果 通过组合不同的种子点生成类型和破碎时行为模拟方式,得到了多样化的刚体破碎效果。对单个刚体进行破碎模拟时,碎片数目不超过200个时帧率可以达到75帧/s,满足实时性的需求;对多个可破碎目标同时存在的复杂场景,破碎仿真模拟的平均帧率可以达到50帧/s,同样满足实时性要求;与现有方法对比的结果也验证了本文方法在计算效率和破碎效果多样性两方面达到了较好的平衡。结论 本文方法在满足实时性要求的同时,丰富了刚体破碎的效果,不同种子点生成类型和破碎时行为模拟方式的组合可以实现破碎效果多样性。     

Passivity-preserving splitting methods for rigid body systems

A rigid body model for the dynamics of a marine vessel, used in simulations of offshore pipe-lay operations, gives rise to a set of ordinary differential equations with controls. The system is input–output passive. We propose passivity-preserving splitting methods for the numerical solution of a class of problems which includes this system as a special case. We prove the passivity-preservation property for the splitting methods, and we investigate stability and energy behaviour in numerical experiments. Implementation is discussed in detail for a special case where the splitting gives rise to the subsequent integration of two completely integrable flows. The equations for the attitude are reformulated on \(\mathit{SO}(3)\) using rotation matrices rather than local parameterisations with Euler angles.     

刚性轮—土壤相互作用的多体动力学仿真研究*

车轮与松软地面相互作用的研究对越野车辆的设计、性能评价和行驶操作等至关重要。提出了一种新的多体系统大规模接触碰撞理论与地面力学理论相结合的车轮土壤相互作用仿真方法。基于自行开发的多体动力学仿真软件研制了车轮土壤相互作用模块并构建了单轮土槽多体仿真模型。对相同实验条件下得到的仿真与实验结果的对比分析表明,该仿真算法具有较高的工程实用性。     

Composite rigid body formalism for flexible multibody systems

The paper describes the extension of the composite rigid body formalism for the flexible multibody systems. The extension has been done in such a way that all advantages of the formalism with respect to the coordinates of large motion of rigid bodies are extended to the flexible degrees of freedom, e.g. the same recursive treatment of both coordinates and no appearance of O(n ³) computational complexity terms due to the flexibility. This extension has been derived for both open loop and closed loop systems of flexible bodies. The comparison of the computational complexity of this formalism with other known approaches has shown that the described formalism of composite rigid body and the residual algorithm based on it are more efficient formalisms for small number of bodies in the chains and deformation modes than the usual recursive formalism of articulated body inertia.     

A fast impulsive contact suite for rigid body simulation

A suite of algorithms is presented for contact resolution in rigid body simulation under the Coulomb friction model: Given a set of rigid bodies with many contacts among them, resolve dynamic contacts (collisions) and static (persistent) contacts. The suite consists of four algorithms: 1) partial sequential collision resolution, 2) final resolution of collisions through the solution of a single convex QP (positive semidefinite quadratic program), 3) resolution of static contacts through the solution of a single convex QP, 4) freezing of "stationary" bodies. This suite can generate realistic-looking results for simple examples yet, for the first time, can also tractably resolve contacts for a simulation as large as 1,000 cubes in an "hourglass". Freezing speeds up this simulation by more than 25 times. Thanks to excellent commercial QP technology, the contact resolution suite is simple to implement and can be "plugged into" any simulation algorithm to provide fast and realistic-looking animations of rigid bodies.     

Planning rigid body motions using elastic curves

This paper tackles the problem of computing smooth, optimal trajectories on the Euclidean group of motions SE(3). The problem is formulated as an optimal control problem where the cost function to be minimized is equal to the integral of the classical curvature squared. This problem is analogous to the elastic problem from differential geometry and thus the resulting rigid body motions will trace elastic curves. An application of the Maximum Principle to this optimal control problem shifts the emphasis to the language of symplectic geometry and to the associated Hamiltonian formalism. This results in a system of first order differential equations that yield coordinate free necessary conditions for optimality for these curves. From these necessary conditions we identify an integrable case and these particular set of curves are solved analytically. These analytic solutions provide interpolating curves between an initial given position and orientation and a desired position and orientation that would be useful in motion planning for systems such as robotic manipulators and autonomous-oriented vehicles.     

Investigation of a method for the three-dimensional rigid body dynamics inverse problem

The three-dimensional rigid body dynamics inverse problem is cast as a discrete optimal control problem and solved using dynamic programming. The optimal control problem uses a forward dynamic model to provide estimates of unknown forces while matching noisy measurement histories. An L curve analysis is used to objectively select the amount of smoothing by trading off the magnitude of the estimated unknown forces with the fit to the noisy measurements. The forward dynamic model is derived using finite-element methodology and accounts for the inertia and mass properties of rigid bodies with the use of natural coordinates. The advantages of this forward model are that the large displacements’ nonlinearities can be routinely represented in the inverse problem and that it also allows the use of an exact energy conserving method to numerically integrate the equations of motion. A numerical example of a large displacement three body model is included to demonstrate the performance of the methodology.     

A fast and stable penalty method for rigid body simulation

Two methods have been used extensively to model resting contact for rigid body simulation. The first approach, the penalty method, applies virtual springs to surfaces in contact to minimize interpenetration. This method, as typically implemented, results in oscillatory behavior and considerable penetration. The second approach, based on formulating resting contact as a linear complementarity problem, determines the resting contact forces analytically to prevent interpenetration. The analytical method exhibits expected-case polynomial complexity in the number of contact points, and may fail to find a solution in polynomial time when friction is modeled. We present a fast penalty method that minimizes oscillatory behavior and leads to little penetration during resting contact; our method compares favorably to the analytical method with regard to these two measures, while exhibiting much faster performance both asymptotically and empirically.     

Dynamic simulation of articulated rigid bodies with contact and collision

We propose a novel approach for dynamically simulating articulated rigid bodies undergoing frequent and unpredictable contact and collision. In order to leverage existing algorithms for nonconvex bodies, multiple collisions, large contact groups, stacking, etc., we use maximal rather than generalized coordinates and take an impulse-based approach that allows us to treat articulation, contact, and collision in a unified manner. Traditional constraint handling methods are subject to drift, and we propose a novel prestabilization method that does not require tunable potentially stiff parameters as does Baumgarte stabilization. This differs from poststabilization in that we compute allowable trajectories before moving the rigid bodies to their new positions, instead of correcting them after the fact when it can be difficult to incorporate the effects of contact and collision. A poststabilization technique is used for momentum and angular momentum. Our approach works with any black box method for specifying valid joint constraints and no special considerations are required for arbitrary closed loops or branching. Moreover, our implementation is linear both in the number of bodies and in the number of auxiliary contact and collision constraints, unlike many other methods that are linear in the number of bodies, but not in the number of auxiliary constraints.     

Dynamic simulation of water distribution systems

A review of full scale simulation of water distribution systems is made which reveals the computational problems associated with on-line applications. The paper then presents a generalised method for obtaining simplified dynamic models of complex water supply systems. The models obtained have been shown to be suitable for evaluation of and use in computer controlled operations. Validation tests have been performed on a typical water distribution system and the predicted results shown to give close agreement with measured data.     

Dynamic simulation of crankshaft multibody systems

General multibody system approaches are often not sufficient for specific situations in applications to yield an efficient and accurate solution. We concentrate on the simulation of the crankshaft dynamics which is characterized by flexible bodies and force laws describing the interaction between the bodies. The use of the floating frame of reference approach in our model leads to an index-2 DAE system. The algebraic constraints originate from the reference conditions and the normalization equation for the quaternions. For the time integration of this system, two aspects have to be taken into account: firstly, for efficiency exploiting the structure of the system and using parallelization. Secondly, consistent initial values also with respect to a related index-3 system have to be computed in order to compute missing initial velocities and to reduce transient phenomena. The work of C.B. Drab, J.R. Haslinger, and R.U. Pfau is supported by the “Bundesministerium für Wirtschaft und Arbeit” and by the government of Upper Austria within the framework “Industrielle Kompetenzzentren und Netzwerke”.     

Time-varying formation control with attitude synchronization of multiple rigid body systems

In this article, we study the leader-following formation control problem for a group of rigid body systems whose followers' motions are described by dual quaternion equations. A few features are as follows. First, we introduce an exosystem to generate the leader's trajectory as well as the formation configuration, which can produce a large class of time-varying signals so that we can achieve a variety of time-varying formations. Second, to overcome the communication constraint described by a digraph, we extend the distributed observer to estimate not only the desired attitude and angular velocity but also the leader's position and linear velocity. Third, a novel distributed control law is synthesized to furnish a rigorous performance analysis of the closed-loop system. The effectiveness of our design is illustrated by a numerical example.     

Moving-body simulations using overset framework with rigid body dynamics

The simulation of flow past bodies in relative motion is a challenging task due to the presence of complex flow features, moving grids, and rigid body movements under the action of external forces and moments. A generalized grid-based overset framework is presented for the simulation of this class of problems. The equations that govern the fluid flows are cast in an integral form and are solved using a cell-centered finite volume upwind scheme. The rigid body dynamics equations are formulated using quaternion and are solved using fourth-order Runge–Kutta (RK) time integration. The overset framework and the six degree of freedom (6-DOF) rigid body dynamics simulators are developed in a library form for easy incorporation into existing flow solvers. The details of the flow solver, the 6-DOF library, and the overset framework are presented in this paper along with the validation results of the developed system.     

Dynamic scheduling techniques for heterogeneous computing systems

There has been a recent increase of interest in heterogeneous computing systems, due partly to the fact that a single parallel architecture may not be adequate for exploiting all of a program's available parallelism. In some cases, heterogeneous systems have been shown to produce higher performance for lower cost than a single large machine. However, there has been only limited work on developing techniques and frameworks for partitioning and scheduling applications across the components of a heterogeneous system. In this paper we propose a general model for describing and evaluating heterogeneous systems that considers the degree of uniformity in the processing elements and the communication channels as a measure of the heterogeneity in the system. We also propose a class of dynamic scheduling algorithms for a heterogeneous computing system interconnected with an arbitrary communication network. These algorithms execute a novel optimization technique to dynamically compute schedules based on the potentially non-uniform computation and communication costs on the processors of a heterogeneous system. A unique aspect of these algorithms is that they easily adapt to different task granularities, to dynamically varying processor and system loads, and to systems with varying degrees of heterogeneity. Our simulations are designed to facilitate the evaluation of different scheduling algorithms under varying degrees of heterogeneity. The results show improved performance for our algorithms compared to the performance resulting from existing scheduling techniques.     

Comparing software prediction techniques using simulation

The need for accurate software prediction systems increases as software becomes much larger and more complex. We believe that the underlying characteristics: size, number of features, type of distribution, etc., of the data set influence the choice of the prediction system to be used. For this reason, we would like to control the characteristics of such data sets in order to systematically explore the relationship between accuracy, choice of prediction system, and data set characteristic. It would also be useful to have a large validation data set. Our solution is to simulate data allowing both control and the possibility of large (1000) validation cases. The authors compare four prediction techniques: regression, rule induction, nearest neighbor (a form of case-based reasoning), and neural nets. The results suggest that there are significant differences depending upon the characteristics of the data set. Consequently, researchers should consider prediction context when evaluating competing prediction systems. We observed that the more "messy" the data and the more complex the relationship with the dependent variable, the more variability in the results. In the more complex cases, we observed significantly different results depending upon the particular training set that has been sampled from the underlying data set. However, our most important result is that it is more fruitful to ask which is the best prediction system in a particular context rather than which is the "best" prediction system     

Closed-form time derivatives of the equations of motion of rigid body systems

Multibody System Dynamics - Derivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many...     

A comparison of simulation techniques and algebraic techniques for verifying concurrent systems

Simulation-based assertional techniques and process algebraic techniques are two of the major methods that have been proposed for the verification of concurrent and distributed systems. It is shown how each of these techniques can be applied to the task of verifying systems described as input/output automata; both safety and liveness properties are considered. A small but typical circuit is verified in both of these ways, first using forward simulations, an execution correspondence lemma, and a simple fairness argument, and second using deductions within the process algebra DIOA for I/O automata. An extended evaluation and comparison of the two methods is given.Supported by NSF grant CCR-89-15206, by DARPA contracts N00014-89-J-1988 and N00014-92J-4033, and by ONR contract N00014-91-J-1046.     

Variable stability simulation techniques for nonlinear rate-dependent systems

This paper deals with the development of variable stability simulation techniques for nonlinear rate-dependent systems. In particular, the model-following and response-feedback modes of dynamic simulation are considered for these systems. The paper begins with a development of variable stability simulation theory for nonlinear rate-dependent systems. Simple examples are given to demonstrate the application of the theory. A model-following flight control system, in which the inertial coupling nonlinearities of the plant and model are taken into account, is then developed. Time histories are included to demonstrate the quality of model following that can be achieved. Finally, linear systems are considered as a special case of the general theory.     

The application of simulation techniques to information systems analysis

This paper describes the application of a computer simulation model as a tool to aid in the analysis and design of an information system. Unique to the study is the adaptation of an existing production control simulation model for the purpose of analyzing flows in a hierarchical computer network.The existing simulation model and its method of adaptation are presented. The results of the simulation analysis are utilized by a newly developed file allocation algorithm in the design of a hierarchical information system. The study was performed under close cooperation with several steel manufacturers and initiated under NSF grant ATA 73-07822 AO1.