Error analysis of a stochastic immersed boundary method incorporating thermal fluctuations

A stochastic numerical scheme for an extended immersed boundary method which incorporates thermal fluctuations for the simulation of microscopic biological systems consisting of fluid and immersed elastica was introduced in reference [2]. The numerical scheme uses techniques from stochastic calculus to overcome stability and accuracy issues associated with standard finite difference methods. The numerical scheme handles a range of time steps in a unified manner, including time steps which are greater than the smallest time scales of the system. The time step regimes we shall investigate can be classified as small, intermediate, or large relative to the time scales of the fluid dynamics of the system. Small time steps resolve in a computationally explicit manner the dynamics of all the degrees of freedom of the system. Large time steps resolve in a computationally explicit manner only the degrees of freedom of the immersed elastica, with the contributions of the dynamics of the fluid degrees of freedom accounted for in only a statistical manner over a time step. Intermediate time steps resolve in a computationally explicit manner only some degrees of freedom of the fluid with the remaining degrees of freedom accounted for statistically over a time step. In this paper, uniform bounds are established for the strong error of the stochastic numerical method for each of the time step regimes. The scaling of the numerical errors with respect to the parameters of the method is then discussed.     

Improved component mode synthesis and variants

This survey focuses on the two known model order reduction schemes being widely integrated in various commercial finite element packages, namely, the static and dynamic condensation methods. The advantages as well as the corresponding drawbacks have been extensively analyzed in several papers throughout the last decades. Based on combining the beneficial properties of the aforementioned methods, several alternative reduction methodologies are outlined in this paper, i.e., the generalized improved reduction system method, the generalized component mode synthesis and the improved component mode synthesis with its generalized version, which incorporate in a more efficient way the system’s inertia terms. Therefore, the associated error regarding higher frequency ranges of interest is better controlled. Basis of these methodologies is the so-called master and slave degrees of freedom partitioning, the right selection of which highly influences the reduced order model’s dynamics. The methods are tested and verified on a rather small three-dimensional bar structure and on the lever part of a turbocharger’s variable turbine geometry. Several reduced order models are generated by varying both the number of Craig–Bampton modes and the selection of the required master degrees of freedom. A comparison is conducted based on the modal criterion of the corresponding eigenvectors and the associated computation time required.     

Forward dynamical analysis of flexible multibody systems using system-level model reduction

Fast simulation (e.g., real-time) of flexible multibody systems is typically restricted by the presence of both differential and algebraic equations in the model equations, and the number of degrees of freedom required to accurately model flexibility. Model reduction techniques can alleviate the problem, although the classically used body-level model reduction and general-purpose system-level techniques do not eliminate the algebraic equations and do not necessarily result in optimal dimension reduction. In this research, Global Modal Parametrization, a model reduction technique for flexible multibody systems is further developed to speed up simulation of flexible multibody systems. The reduction of the model is achieved by projection on a curvilinear subspace instead of the classically used fixed vector space, requiring significantly less degrees of freedom to represent the system dynamics with the same level of accuracy. The numerical experiment in this paper illustrates previously unexposed sources of approximation error: (1) the rigid body motion is computed in a forward dynamical analysis resulting in a small divergence of the rigid body motion, and (2) the errors resulting from the transformation from the modal degrees of freedom of the reduced model back to the original degrees of freedom. The effect of the configuration space discretization coarseness on the different approximation error sources is investigated. The trade-offs to be defined by the user to control these approximation errors are explained.     

A new marker design for a robust marker tracking system against occlusions

Marker systems are a widely used optical tracking method that does not support occlusions. Thus, this paper proposes a new marker design to overcome the problem of marker occlusions. It is highly adaptable, because it can be used by any marker tracking system that uses its central area to codify the digital identification. Our proposal takes advantage of an untapped frame to place some textures that will be tracked during marker occlusion. In addition, these textures are customizable, which lets users make their own designs. Two tracking methods are combined to offer a robust tracking, updating the six degrees of freedom of the camera in real time. The first one is a fast technique based on temporal coherence, whereas the second one is a robust technique based on appearance, which is used as a recovery mode. Copyright © 2012 John Wiley & Sons, Ltd.     

Model checking transactional memories

Model checking transactional memories (TMs) is difficult because of the unbounded number, length, and delay of concurrent transactions, as well as the unbounded size of the memory. We show that, under certain conditions satisfied by most TMs we know of, the model checking problem can be reduced to a finite-state problem, and we illustrate the use of the method by proving the correctness of several TMs, including two-phase locking, DSTM, and TL2. The safety properties we consider include strict serializability and opacity; the liveness properties include obstruction freedom, livelock freedom, and wait freedom. Our main contribution lies in the structure of the proofs, which are largely automated and not restricted to the TMs mentioned above. In a first step we show that every TM that enjoys certain structural properties either violates a requirement on some program with two threads and two shared variables, or satisfies the requirement on all programs. In the second step, we use a model checker to prove the requirement for the TM applied to a most general program with two threads and two variables. In the safety case, the model checker checks language inclusion between two finite-state transition systems, a nondeterministic transition system representing the given TM applied to a most general program, and a deterministic transition system representing a most liberal safe TM applied to the same program. The given TM transition system is nondeterministic because a TM can be used with different contention managers, which resolve conflicts differently. In the liveness case, the model checker analyzes fairness conditions on the given TM transition system.     

A new approach to improve absolute positioning accuracy of robot manipulators

This article describes a new calibration system for robot manipulators which improves their absolute positioning accuracy by using parameter-estimation algorithms based on the Newton method. When 3D position data of the specified points on a manipulator and the joint encoder values are input to the calibration system, the system estimates the offset values of joint encoders, link lengths, and position and orientation of the manipulator base coordinate system with respect to the world coordinate system which is difficult to obtain by conventional calibration methods. This calibration system can be applied to various manipulator types by just changing the basic kinematic equations. The system employs an algebraic programming system called REDUCE to automatically reduce the manipulator kinematic equation and partial differential calculus in the Newton method. For efficiency, first only the arm part with three degrees of freedom and then the hand part are calibrated. The experimental results demonstrate the effectiveness of this system by reducing the robot's absolute positioning errors to the order of repeatability errors.     

基于状态估计的摩擦模糊建模与鲁棒自适应控制

针对一类多自由度机械系统, 研究了基于状态估计的摩擦模糊建模与鲁棒自适应控制问题. 提出用模糊状态估计器估计摩擦模型中的不可测变量, 并用严格正实和李雅普诺夫稳定性理论证明了状态估计误差的一致最终有界性. 运用模糊状态估计结果设计了多变量鲁棒自适应控制器, 其中摩擦模糊模型中的自适应参数是基于李雅普诺夫稳定性理论设计的, 并证明了闭环系统跟踪误差的一致最终有界性. 本文对多自由度质量、弹簧和摩擦阻尼系统进行的仿真, 结果表明所提出的状态估计算法和自适应控制策略是有效的.     

SVD‐Based Accurate Identification and Compensation of the Coupling Hysteresis and Creep Dynamics in Piezoelectric Actuators

In this paper, the coupling hysteresis and creep in piezoelectric actuators are identified and compensated for accurate tracking. First, we present the coupling hysteresis and creep model in smart actuators. Next, a complete identification strategy is designed according to the properties of the Preisach model. Then, an approach for parameter updating of the coupling model is provided. With the identified hysteresis and creep, the model‐based inversion compensation is designed. Finally, we apply the model identification and compensation to a piezoelectric stage to demonstrate the effectiveness of the proposed approaches. Significant reduction of the tracking error is achieved with the model‐based inversion feedforward compensator in which the relative errors at 10 Hz and 50 Hz are reduced to 1.85% and 4.53%, respectively. In addition, the model‐based feedforward is augmented with an integral feedback controller. With the composite controller, the relative errors at 10 Hz and 50 Hz are reduced to 0.42% and 3.04%, respectively.     

Robust Path Planning for Non-Holonomic Robots

This paper deals with mobile robots path planning. We decompose the problem in three parts. In the first part, we describe a modeling method based on a configuration space discretization. Each model element is built following a particular structure which is easy to handle, as we will show. We describe the methodologies and the algorithms allowing to build the model. In the second part, we propose a path-planning application for a non-holonomic robot in configuration space. In the third part, we modify the path in order to be robust according to the control errors.     

信度网结构在线学习算法

提出一种新的信度网结构在线学习算法.其核心思想是,利用新样本对信度网结构和参数不断进行增量式修改,以逐步逼近真实模型.本算法分为两个步骤:首先分别利用参数增量修改律和添加边、删除边、边反向3种结构增量修改律,并结合新采集的样本,对当前信度网模型进行增量式修改;然后利用结果选择判定准则,从增量式修改所得的后代信度网集合中选择一个合适的信度网作为本次迭代结果.该结果在与当前样本的一致性和与上一代模型的距离之间达到一个合理的折衷.实验结果表明,本算法能有效地实现信度网结构的在线学习.由于在线学习不需要历史样本,     

Bionic Quadruped Robot Dynamic Gait Control Strategy Based on Twenty Degrees of Freedom

Quadruped robot dynamic gaits have much more advantages than static gaits on speed and efficiency, however high speed and efficiency calls for more complex mechanical structure and complicated control algorithm. It becomes even more challenging when the robot has more degrees of freedom. As a result, most of the present researches focused on simple robot, while the researches on dynamic gaits for complex robot with more degrees of freedom are relatively limited. The paper is focusing on the dynamic gaits control for complex robot with twenty degrees of freedom for the first time. Firstly, we build a relatively complete 3D model for quadruped robot based on spring loaded inverted pendulum (SLIP) model, analyze the inverse kinematics of the model, plan the trajectory of the swing foot and analyze the hydraulic drive. Secondly, we promote the control algorithm of one-legged to the quadruped robot based on the virtual leg and plan the state variables of pace gait and bound gait. Lastly, we realize the above two kinds of dynamic gaits in ADAMS-MATLAB joint simulation platform which testify the validity of above method.      

Interpolation-based parametric model order reduction for material removal in elastic multibody systems

One essential step in the simulation of elastic multibody systems is the model order reduction of the elastic degrees of freedom. For simulations of material removal, the system matrices can be described as parameter dependent. In this contribution, parametric model reduction methods based on interpolation are applied for this type of problem. Thereby, the interpolation of the reduced system matrices, interpolation of projection matrices, interpolation of subspaces and the interpolation of the transfer functions are investigated. The advantages and disadvantages of these techniques, especially for the application in elastic multibody systems are carved out and illustrated for the manufacturing of a T-shaped workpiece which varies in its thickness due to material removal. In this contribution, we focus on the investigation of the methods in the frequency domain.     

机器人减速器传动误差建模与优化

为提高工业机器人旋转矢量(RV)减速器的传动精度,合理分配各零件的加工和装配公差,本文提出一种基于等价模型的RV减速器传动误差建模与优化方法.该方法根据RV减速器的传动结构,构建17自由度的等价误差模型,利用传统经验参数进行求解,获得减速器仿真传动误差;同时,将仿真传动误差与实际测量传动误差进行对比,运用最小二乘法建立经验参数辨识模型;在此基础上通过粒子群算法优化辨识模型中的经验参数,将该参数运用到实际RV减速器生产中,结果显示:与传统经验参数建立的误差模型相比,本文提出的方法使得传动精度的仿真精度误差平均缩小9.99%,大幅度提高了等价误差模型的准确性.     

The role of abduction in database view updating

The problem of view updating in databases consists in modifying the extension of view relations (i.e., relations defined in terms of base ones) transforming only the content of the extensional database, i.e., the extensional representation of base relations. This task is non-deductive in nature and its relationships with non-monotonic reasoning, and specifically with abduction, have been recently pointed out.In the paper we investigate the role of abduction in view updating, singling out similarities and differences between view updating and abduction. View updating is regarded as a two-step process: first, view definitions (and constraints) are used to reduce a view update into updates on base relations; then, the content of the extensional database is taken into account to determine the actual transformations to be performed. The first step is abductive in nature; we apply to such a step a definition of abduction based on deduction, which characterizes by means of a unique logical formula the conditions on base predicates which accomplish an update request. We then show how, in the second step, the set of transactions to be performed can be obtained from the formula generated in the first step. We provide a formal result showing the correctness of the approach.     

A surface mesh deformation method near component intersections for high-fidelity design optimization

Aerodynamic shape optimization based on computational fluid dynamics (CFD) requires three steps: updating the geometry based on the design variables, updating the CFD surface mesh for the new geometry, and updating the CFD volume mesh based on the new surface mesh. While there are many tools available for the first and third steps, the methods available for the second step are insufficient for geometries that have intersecting components. For these geometries, the CFD surface mesh needs to be updated near component intersections to conform to the component geometries and the updated intersection curves. To address this need, we introduce a method that can deform the CFD surface mesh nodes near component intersections. The method can handle arbitrary design changes for each intersecting component as long as the geometric topology is unchanged. Furthermore, the method is suitable for gradient-based optimization because it smoothly deforms every CFD surface node without introducing topological changes in the CFD surface mesh. In this paper, we detail each step of the proposed method and visualize the range of design changes that can be achieved with this approach. Finally, we use the proposed method in an aerodynamic shape optimization problem to optimize the wing-body intersection of the DLR-F6 configuration. These results demonstrate the effectiveness of the proposed method in a high-fidelity design optimization framework. The method applies to both structured and unstructured CFD meshes and makes it possible to use computer-aided design and conceptual design geometry tools within high-fidelity design optimization.

     

Error estimators for the position of discontinuities in hyperbolic conservation laws with source terms which are solved using operator splitting

When computing numerical solutions of hyperbolic conservation laws with source terms, one may obtain spurious solutions — these are unphysical solutions that only occur in numerics such as shock waves moving with wrong speeds, cf. [9], [3], [1], [13], [4]. Therefore it is important to know how errors of the location of a discontinuity can be controlled. To derive appropriate error-estimates and to use them to control such errors, is the aim of our investigations in this paper. We restrict our considerations to numerical solutions which are computed by using a splitting method. In splitting methods, the homogeneous conservation law and an ordinary differential equation (modelling the source term) are solved separately in each time step. Firstly, we derive error-estimates for the scalar Riemann problem. The analysis shows that the local error of the location of a discontinuity mainly consists of two parts. The first part is introduced by the splitting and the second part is due to smearing of the discontinuity. Next, these error-estimates are used to construct an adaptation of the step size so that the error of the location of the discontinuity remains sufficiently small. The adaptation is applied to several examples, which are a scalar problem, a simplified combustion model, and the one-dimensional inviscid reacting compressible Euler equations. All the examples show that the adaptation based on the derived error-estimates works well. The theory can also be extended to planar two-dimensional problems. Received: 3 November 1997 / Accepted: 20 December 1998     

Maximal feedback linearization and its internal dynamics with applications to mechanical systems on

For systems that are not feedback linearizable, a natural question is: how to find the largest feedback linearizable subsystem and, if the partial linearization is not unique, what are the control‐theoretic properties of various partial linearizations. In this paper, we will consider the problem of how to choose a partially linearizing output that renders the zero dynamics asymptotically stable and when such an output exists. We will state general results solving completely the problem for systems whose linearizability defect is one by identifying and describing two classes of systems. For the first class, all maximal partial linearizations lead to the same zero dynamics. For the second class, any asymptotic behavior of the zero dynamics can be achieved by a suitable choice of a partially linearizing output. In the second part, we apply our results to mechanical systems with two‐degrees‐of‐freedom and provide a detailed study of their partial linearizations. We illustrate the obtained results by examples of Acrobot (which belongs to the second class) and Pendubot (which belongs to the first class).     

用有限元法计算特征值问题的一种新的动态凝聚方法

有限元法是常用的建模方法,由于所建模型具有较大的自由度,通常需要进行降阶处理.一般来讲,模型前几阶特征值和特征向量可以较精确地得到,利用所得到的特征值和主振型分量(在特征向量中与所给定的主自由度对应的振型分量),本文提出了一种新的动态凝聚方法,该方法是通过迭代方式,利用所得到的特征值和主振型分量对Guyan降阶法所得到的降阶模型进行修正.与同类方法相比,本文方法具有较高的计算精度和很小的计算量,且迭代收敛的稳定性很好.最后本文给出了一个计算实例.     

Multi-Level Shape Representation Using Global Deformations and Locally Adaptive Finite Elements

We present a model-based method for the multi-level shape, pose estimation and abstraction of an object's surface from range data. The surface shape is estimated based on the parameters of a superquadric that is subjected to global deformations (tapering and bending) and a varying number of levels of local deformations. Local deformations are implemented using locally adaptive finite elements whose shape functions are piecewise cubic functions with C ¹ continuity. The surface pose is estimated based on the model's translational and rotational degrees of freedom. The algorithm first does a coarse fit, solving for a first approximation to the translation, rotation and global deformation parameters and then does several passes of mesh refinement, by locally subdividing triangles based on the distance between the given datapoints and the model. The adaptive finite element algorithm ensures that during subdivision the desirable finite element mesh generation properties of conformity, non-degeneracy and smoothness are maintained. Each pass of the algorithm uses physics-based modeling techniques to iteratively adjust the global and local parameters of the model in response to forces that are computed from approximation errors between the model and the data. We present results demonstrating the multi-level shape representation for both sparse and dense range data.