Rigid body constraints realized in massively-parallel molecular dynamics on graphics processing units

Molecular dynamics (MD) methods compute the trajectory of a system of point particles in response to a potential function by numerically integrating Newton?s equations of motion. Extending these basic methods with rigid body constraints enables composite particles with complex shapes such as anisotropic nanoparticles, grains, molecules, and rigid proteins to be modeled. Rigid body constraints are added to the GPU-accelerated MD package, HOOMD-blue, version 0.10.0. The software can now simulate systems of particles, rigid bodies, or mixed systems in microcanonical (NVE), canonical (NVT), and isothermal-isobaric (NPT) ensembles. It can also apply the FIRE energy minimization technique to these systems. In this paper, we detail the massively parallel scheme that implements these algorithms and discuss how our design is tuned for the maximum possible performance. Two different case studies are included to demonstrate the performance attained, patchy spheres and tethered nanorods. In typical cases, HOOMD-blue on a single GTX 480 executes 2.5–3.6 times faster than LAMMPS executing the same simulation on any number of CPU cores in parallel. Simulations with rigid bodies may now be run with larger systems and for longer time scales on a single workstation than was previously even possible on large clusters.     

Heterogeneous graph attention networks for scalable multi-robot scheduling with temporospatial constraints

Autonomous Robots - Robot teams are increasingly being deployed in environments, such as manufacturing facilities and warehouses, to save cost and improve productivity. To efficiently coordinate...     

Rigid multibody system dynamics with uncertain rigid bodies

This paper is devoted to the construction of a probabilistic model of uncertain rigid bodies for multibody system dynamics. We first construct a stochastic model of an uncertain rigid body by replacing the mass, the center of mass, and the tensor of inertia by random variables. The prior probability distributions of the stochastic model are constructed using the maximum entropy principle under the constraints defined by the available information. The generators of independent realizations corresponding to the prior probability distribution of these random quantities are further developed. Then several uncertain rigid bodies can be linked to each other in order to calculate the random response of a multibody dynamical system. An application is proposed to illustrate the theoretical development.     

Rigid body attitude control with inclinometer and low-cost gyro measurements

In our paper, we consider the state regulation problem for the nonlinear kinematic equations and Euler equations of a rigid body observed under low-pass sensors. This problem is motivated by the corresponding state estimation problem covered in recent literature on walking robots and virtual reality gadgets. We show the existence of an asymptotically stabilizing feedback controller for the dynamics that provides reliable performance.     

Consensus for double-integrator dynamics with velocity constraints

The problem of consensus for double-integrator dynamics with velocity constraints and a constant group reference velocity is addressed such that: (i) the control law of an agent does not depend on the local neighbors’ velocities or accelerations, but only on the neighbors’ positions and on the own agent velocity; (ii) the constraints are non-symmetric; (iii) the class of nonlinear functions used to account for the velocity constraints is more general than the ones that are normally considered in the literature. We propose a decentralized control strategy with the neighboring topology described by an undirected interaction graph that is connected. Mathematical guarantees of convergence without violating the constraints are given. A numerical experiment is provided to illustrate the effectiveness of our approach.     

Estimating joint kinematics of a whole body chain model with closed-loop constraints

Computer simulation and optimal control requiring actual joint kinematics and based on the definition of a chain model become more used in biomechanics for studying the musculo-skeletal coordination or optimizing the performance. For this purpose, numerical optimization methods using a chain model have been developed and showed promising results to estimate joint kinematics for open-loop movements. The aim of this study was to exhaustively compare the type of method and closed-loop constraint with four criteria: (i) reconstruction quality, (ii) loop closure respect, (iii) regularity of joint kinematics, and (iv) computational time. Five algorithms were tested to estimate the whole body joint kinematics of 10 elite athletes paddling an ergometer: global optimization (GO) without closed-loop constraints, with soft closed-loop constraints and with strict closed-loop constraints, and Kalman filter (KF) without closed-loop constraints and with soft closed-loop constraints. Each athlete was modelled using a personalized 17-segment 42-degree of freedom chain model. Input data were measured by a 10-camera motion capture system sampled at 250 Hz. ANOVAs were performed on the four criteria to identify differences between the five algorithms. Marker residuals were slightly increased by about 2–3 mm using GO under strict constraints and KF with soft constraints. Closed-loop errors were five times reduced when introducing constraints (10 to 2 mm). KF algorithms gave significantly smoother joint kinematics than the three GO algorithms. Computational time was largely increased by introducing closed-loop constraints in GO algorithm (from 21 to 200 ms per frame) while it remained unchanged in KF algorithm (about 60 ms per frame). To conclude, KF with soft constraints represents the best compromise between the four criteria.     

Univariate marginal distribution algorithm dynamics for a class of parametric functions with unitation constraints

In this paper, we introduce a mathematical model for analyzing the dynamics of the univariate marginal distribution algorithm (UMDA) for a class of parametric functions with isolated global optima. We prove a number of results that are used to model the evolution of UMDA probability distributions for this class of functions. We show that a theoretical analysis can assess the effect of the function parameters on the convergence and rate of convergence of UMDA. We also introduce for the first time a long string limit analysis of UMDA. Finally, we relate the results to ongoing research on the application of the estimation of distribution algorithms for problems with unitation constraints.     

Application of fractional order theory of magneto-thermoelasticity to an infinite perfect conducting body with a cylindrical cavity

A fractional model of the equations of generalized magneto-thermoelasticity for a perfect conducting isotropic thermoelastic media is given. This model is applied to solve a problem of an infinite body with a cylindrical cavity in the presence of an axial uniform magnetic field. The boundary of the cavity is subjected to a combination of thermal and mechanical shock acting for a finite period of time. The solution is obtained by a direct approach by using the thermoelastic potential function. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using a numerical method based on Fourier series expansions. Numerical computations for the temperature, the displacement and the stress distributions as well as for the induced magnetic and electric fields are carried out and represented graphically. Comparisons are made with the results predicted by the generalizations, Lord–Shulman theory, and Green–Lindsay theory as well as to the coupled theory.

     

TRUSS: a reliable, scalable server architecture

Traditional techniques that mainframes use to increase reliability -special hardware or custom software - are incompatible with commodity server requirements. The Total Reliability Using Scalable Servers (TRUSS) architecture, developed at Carnegie Mellon, aims to bring reliability to commodity servers. TRUSS features a distributed shared-memory (DSM) multiprocessor that incorporates computation and memory storage redundancy to detect and recover from any single point of transient or permanent failure. Because its underlying DSM architecture presents the familiar shared-memory programming model, TRUSS requires no changes to existing applications and only minor modifications to the operating system to support error recovery.     

具有未建模动态和输出约束的耦合系统的分散自适应控制

针对一类具有输入、状态未建模动态和非线性输入的耦合系统,提出一种自适应神经网络控制方案.利用径向基函数神经网络逼近未知非线性连续函数;引入动态信号和正则化信号处理状态及输入未建模动态;通过引入非线性映射,将具有时变输出约束的严格反馈系统化为不含约束的严格反馈系统.最后,通过理论分析验证闭环系统中所有信号是半全局一致最终有界的,仿真结果进一步验证了所提出控制方案的有效性.     

A Hamiltonian and multi-Hamiltonian formulation of a rod model using quaternions

The geometrically exact model of an elastic rod, formulated in [23] the Simo–Reissner rod model has been proposed and investigated. We present a constrained Hamiltonian formulation of the elastic rod model as well as a constrained multi-Hamiltonian formulation of the model. In both formulations, quaternions are used to represent the group of rotations. The resulting Hamiltonian PDE and multi-Hamiltonian formulation have simple looking formats involving constant structure matrices.     

Kinematics and dynamics of a rigid body in nonholonomic coordinates

In this paper we consider dynamic equations of nonholomic systes in terms of pseudo-coordinates which appear in the general theory of rigid body. Especially, the rotator kinematics and dynamics in nonholonomic coordinates is presented. Besides, using the appropriate methods of the differential geometry and theory of Lie groups and Lie algebras a simplification of motion equations in the tangent space is obtained.     

The design of a scalable, fixed-time computer benchmark

By using the principle of fixed-time benchmarking, it is possible to compare a wide range of computers, from a small personal computer to the most powerful parallel supercomputer, on a single scale. Fixed-time benchmarks promise greater longevity than those based on a particular problem size and are more appropriate for “grand challenge” capability comparison. We present the design of a benchmark, SLALOM, that adjusts automatically to the computing power available and corrects several deficiencies in various existing benchmarks: it is highly scalable, solves a real problem, includes input and output times, and can be run on parallel computers of all kinds, using any convenient language. The benchmark provides an estimate of the size of problem solvable on scientific computers. It also can be used to demonstrate a new source of superlinear speedup in parallel computers. Results that span six orders of magnitude for contemporary computers of various architectures are presented.     

On a game with perfect information and time-claiming alternatives

This paper considers a new model of multistage games with perfect information in which players can control decision-making time. At each stage of the game, players choose a certain alternative from a finite set of basic alternatives and also time necessary to realize this basic alternative. The payoffs of players depend on the game path defined by the chosen alternatives and also on the time to realize this path at each stage. We use the subgame-perfect ε-Nash equilibrium as the optimality principle of the model. This paper is a continuation of the earlier research [5].     

A parallel molecular dynamics simulation scheme for a molecular system with bond constraints in NPT ensemble

Equations of motion based on an atomic group scaling scheme are described for a molecular system with bond constraints. The NPT ensemble extended system method is employed along with a numerical integration scheme using an operator technique. For parallelization of the integration scheme, a domain decomposition scheme is employed based on a group of atoms which share common constraints. This decomposition scheme fits well into the integration scheme and involves no extra inter-processor communication during the SHAKE/RATTLE procedures. An example is given for a solvated protein system containing a total of 23 558 atoms on 64 processors.     

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.     

Multibody dynamics with redundant constraints and singular mass matrix: existence, uniqueness, and determination of solutions for accelerations and constraint forces

This paper addresses some important issues for multibody dynamics; issues that are basic and really not too difficult to solve, but rarely considered in the literature. The aim of this paper is to contribute to the resolution and clarification of these topics in multibody dynamics. There are many formulations for determining the equations of motion in constrained multibody systems. This paper will focus on three of the most important methods: the Lagrange equations of the first kind, the null space method and the Maggi equations. In all cases we consider singular inertia matrices and redundant constraint equations. We assume that the inertia matrix is positive-semidefinite (symmetric) and that the constraint equations may be redundant but always consistent. It is demonstrated that the aforementioned dynamic formulations lead to the same three mathematical conditions of existence and uniqueness of solutions, conditions that have at the same time a clear physical meaning. We conclude that the mathematical problem always has a solution if the physical problem is well conditioned. This paper also addresses the problem of determining the constraint forces in the case of redundant constraints. This problem is examined from a broad perspective. We will present several examples and a simple method to find practical solutions in cases where the forces of constraint are undetermined. The method is based on the weighted minimum norm condition. A physical interpretation of this minimum norm condition is provided in detail for all examples. In some cases a comparison with the results obtained by considering flexibility is included.     

Explicit and implicit animation with fuzzy constraints of a versatile multi‐body system for virtual hand surgery

This work is designed to control the movement of hand structural agents under external action, using the implicit animation driven by explicit animation technique (AI‐CAE technique). Starting from the configuration of a hand at rest obtained by a 3D scanner and after meshing of the structural agents, we seek the configuration of the rigid agents under orthopaedic surgeon external action and interacting reliance of deformable and rigid agents. We have developed a model and software tools to answer this interactive application with adaptive execution. The first contribution comes from notations and definition of a versatile multi‐body system dedicated to the explicit and implicit animation. The second contribution comes from the implicit animation driven by explicit animation itself, and from its ability to mimic the role of cartilages and ligaments. The resulting technique is applied to the bone structure consistency of a specific human hand in the context of virtual hand orthopaedic surgery. The versatile specific multi‐body is made up of hierarchical interacting agents conceivable as a construction set of rigid bones with cartilages–ligaments and underlying links. The explicit animation produces a desired configuration from geometric command parameters of torsion, flexion, pivot and axis shifting, given in a scenario subdivided into temporal sequences. The implicit animation controls the movement by implementing a physics‐based model and fuzzy constraints of position and orientation. It gives better configuration than the explicit animation because it takes into account the interactions between agents, and it gives a neat solution without the problems of complexity due to geometric modelling. A methodology based on the AI‐CAE technique is discussed, medical expertise and validation tests are presented. Copyright © 2011 John Wiley & Sons, Ltd.