Dynamic modeling and design optimization of a 3-DOF spherical parallel manipulator

This paper deals with the dynamic modeling and design optimization of a three Degree-of-Freedom spherical parallel manipulator. Using the method of Lagrange multipliers, the equations of motion of the manipulator are derived by considering its motion characteristics, namely, all the components rotating about the center of rotation. Using the derived dynamic model, a multiobjective optimization problem is formulated to optimize the structural and geometric parameters of the spherical parallel manipulator. The proposed approach is illustrated with the design optimization of an unlimited-roll spherical parallel manipulator with a main objective to minimize the mechanism mass in order to enhance both kinematic and dynamic performances.     

含摩擦滑移铰及驱动约束多刚体系统数值算法

研究了具有驱动约束及非光滑滑移铰多体系统动力学方程的建模与数值计算方法．将驱动约束视为非定常约束，非光滑滑移铰视为双边定常约束，滑移铰的摩擦模型采用库仑摩擦模型；应用第一类Lagrange方程建立系统的动力学方程，应用距离函数建立滑移铰的约束方程；将线性互补方法和Baumgarte约束稳定化方法引入，以解决滑移铰法向约束力的计算以及约束方程违约问题．最后应用曲柄摇杆机构作为算例，说明该方法的有效性．     

An approach for dynamic analysis of planar multibody systems with revolute clearance joints

Engineering with Computers - Clearance is inevitable for manufacture and assembly in the revolute joints of multibody systems. Excessive value of joint clearance will lead to the poor dynamic...     

一类动态互联复杂系统的稳定性分析

通过引入动态图及动态邻接矩阵相关理论,对具有动态互联信息结构约束的复杂系统进行描述和建模,并引入ＬｏｔｋａＶｏｌｔｅｒｒａ方程作为该系统的动态互联信息结构模型．根据李雅普诺夫方法,对系统的动态互联模型进行了详细分析,研究了非负定限内联结平衡的设定及其渐近稳定条件,进而研究了整个系统的稳定条件．最后得到了该类动态互联复杂系统联结稳定及整个系统稳定的相关结论．     

Auto-regressive modeling with dynamic weighted canonical correlation analysis

Multivariate statistical analytical methods, such as principal component analysis (PCA) and canonical correlation analysis (CCA), are widely used to extract useful information from data collected in modern industrial processes. Their dynamic extensions are also designed intensively in the literature to exploit dynamic variations in the processes. However, none of these algorithms consider the inevitably strong dependence in adjacent samples caused by high sampling frequencies or relatively slow continuous process changes, and the dependence may lead to unnecessarily large time lags and sub-optimal prediction performance. In this paper, a dynamic weighted CCA (DWCCA) algorithm is proposed to address this issue with the aid of basis functions. DWCCA constructs its latent space by maximizing the correlation between current data and a weighted representation of past data. To remove the negative effect caused by strongly collinear successive samples, it is assumed that the weights of past data rely only on a limited number of basis functions, and in this work, polynomial basis, Fourier basis, and Gaussian basis functions are considered and compared. Comprehensive modeling scheme is also designed for DWCCA with subsequent PCA decomposition to exploit static and dynamic variations concurrently. Case studies on the Tennessee Eastman process and the boiler process are presented to illustrate the effectiveness of the proposed dynamic models over other existing dynamic methods.     

Physically based modeling and simulation with dynamic spherical volumetric simplex splines

In this paper, we present a novel computational modeling and simulation framework based on dynamic spherical volumetric simplex splines. The framework can handle the modeling and simulation of genus-zero objects with real physical properties. In this framework, we first develop an accurate and efficient algorithm to reconstruct the high-fidelity digital model of a real-world object with spherical volumetric simplex splines which can represent with accuracy geometric, material, and other properties of the object simultaneously. With the tight coupling of Lagrangian mechanics, the dynamic volumetric simplex splines representing the object can accurately simulate its physical behavior because it can unify the geometric and material properties in the simulation. The visualization can be directly computed from the object’s geometric or physical representation based on the dynamic spherical volumetric simplex splines during simulation without interpolation or resampling. We have applied the framework for biomechanic simulation of brain deformations, such as the brain shifting during surgery and brain injury under blunt impact. We have compared our simulation results with the ground truth obtained through intra-operative magnetic resonance imaging and real biomechanic experiments. The evaluations demonstrate the excellent performance of our new technique.     

Self-calibration of spherical rectification for a PTZ-stereo system

Since PTZ (pan–tilt–zoom) camera is able to obtain multi-view-angle and multi-resolution information, PTZ-stereo system using two PTZ cameras has much higher capability and flexibility compared with traditional stereo system. In this paper, we propose a self-calibration framework to deal with the calibration of spherical rectification, which can be deemed as a kind of relative pose estimation, for a PTZ-stereo system. The goal of this calibration is to guarantee high performance of stereo rectification, so that stereo matching can be achieved more efficiently and accurately. In this framework, we assume two PTZ cameras are fully calibrated, i.e., the focal length and the local camera orientation can be computed by given pan–tilt–zoom values. This approach, which is based on point matches, aims at finding uniformly distributed point matches in an iterative way. At each iteration, according to the distribution of previously used point matches, the system could automatically guide two cameras to move to collect a new match. Point matching is firstly performed for the lowest zoom setting (widest field of view). Once a candidate match is chosen, each camera is then controlled to zoom in on corresponding point to get a refined match with high spatial resolution. The final match will be added into the estimation to update the calibration parameters. Compared with previous researches, the proposed framework has the following advantages: (1) Neither manual interaction nor calibration object is needed. Calibration samples (point matches) will be added and removed in each stage automatically. (2) The distribution of calibration samples is as uniform as possible so that biased estimation could be avoided to some extent. (3) The accuracy of calibration can be controlled and improved when iteration goes on. These advantages make the proposed framework more practicable in applications. Experimental results illustrate its accuracy.     

An overview of dynamic parameter identification of robots

Due to the importance to model-based control, dynamic parameter identification has attracted much attention. However, until now, there is still much work for the identification of dynamic parameters to be done. In this paper, an overview is given of the existing work on dynamic parameter identification of serial and parallel robots. The methods for estimating the dynamic parameters are summarized, and the advantages and disadvantages of each method are discussed. The model to be identified and the trajectory optimization are reviewed. Further, the methods for validating the estimated model are summarized and the application of dynamic parameter identification is mentioned. The results of this review are useful for manufacturers of robots in selecting proper identification method and also for researchers in determining further research areas.     

Design, modeling and first experimentation of a two-degree-of-freedom spherical actuator

This paper deals with the design of a two-actuated-degree-of-freedom (DOF) spherical electrical actuator for mobile robotic applications. It presents the different steps involved in this design, namely the choice of the actuation principle (induction), its application to the case of a spherical geometry and two DOFs, the analytical and numerical modeling of the motor, and the sizing and the manufacture of a first one-actuated-DOF spherical prototype. The first experimental results, obtained thanks to our test bench and presenting the torque vs rotor angular speed characteristic of the actuator, are likewise compared with the model predictions.     

Auto-parametric semi-trivial and post-critical response of a spherical pendulum damper

The pendulum vibration damper modelled as a two degree of freedom strongly non-linear auto-parametric system is investigated. A kinematic external excitation in the suspension point is applied. The excitation is considered to be horizontal and harmonically variable in time. A semi-trivial solution and its stability are analyzed. Special attention is paid to the resonance domain. In certain domains of pendulum and excitation parameters the semi-trivial solution does not exist in this domain and various post-critical three-dimensional regimes occur. Some of them are non-stationary despite the harmonic excitation. Three different types of the resonance domain are investigated. Their main properties depend significantly on dynamic parameters of the pendulum and of the external excitation amplitude. An analytical and numerical study brings forth several recommendations for designers of these devices. Their aim is to avoid any post-critical response regimes endangering the pendulum functionality.     

基于UML的嵌入式建模方法改进策略研究

统一建模语言UML(unified modeling language)在嵌入式系统设计建模中已经获得了广泛的承认,有很多成功的应用.但UML在嵌入式建模中存在时间约束描述能力不强和所建模型形式化复杂、验证难及模型重用性不高等问题.针对这些问题提出了一种改进策略:定义实时语义和映射规则,建立实时描述模式模板,使用模板中实时描述模式描述时间约束信息.改进后的方法能可视化地分析模型、纠正错误和简单地进行形式化转换,能利用支撑工具对模型进行验证,较好地解决了UML在嵌入式系统建模中存在的问题.     

基于LuGre模型非光滑柱铰链平面多体系统动力学的建模和数值方法

以含非光滑柱铰链平面多刚体系统为研究对象,将间隙充分小的柱铰链视为双边约束,用LuGre摩擦模型描述柱铰链内的摩擦;由第一类Lagrange方程导出该系统的动力学方程(微分 代数方程).铰链处的摩擦使得其动力学方程是关于Lagrange乘子的非线性代数方程组,由于LuGre摩擦模型具有很好的连续性,可将非线性代数方程组与常微分方程组的数值算法(如拟牛顿法和龙格 库塔法)相结合求解其动力学方程.最后,通过数值仿真算例说明了该算法的可行性和有效性,既能很好地反映柱铰链摩擦对系统动力学特性的影响,又能避免Coulomb干摩擦给方程求解带来的困难.     

The angular capacity of spherical joints used in mechanisms with closed loops and multiple degrees of freedom

Typical kinematic and dynamic analysis of mechanisms considers the joints just as theoretical constraints. Nevertheless, for some particular kinematic joints (e.g. spherical joints) the physical realization takes the shape of distinct components that are attached to the adjacent bodies. While a spherical joint allows three theoretic relative rotations, except the self rotation of the shaft the other two rotations have a reduced range because of constructive limitations. In this paper we propose a function named angular capacity to represent the range of the physically permitted motion in a spherical joint. A graphical representation of the angular capacity is also proposed to intuitively illustrate the relative motion range and the constructive parameters that influence it are identified. Angular capacity of a spherical joint is defined as a constructive feature of the joint assembly—out of the mechanism context—but also as a motion range demanded by the mechanism from the spherical joint. For the first case general relations have been proposed for the constructive angular capacity calculation and useful consideration has been made for the embodiment design of the spherical joints. For the latter, a complete methodology and relationships for mechanisms with two degrees of mobility are proposed as well. Finally, the suspension-steering mechanism of the passenger cars is presented as a use case.     

主被动关节柔性树形机器人系统动力学建模与仿真

进一步完善空间算子代数理论体系,研究了带有主被动关节的树形柔性机器人系统符号动力学高效率建模的方法.利用拓扑结构和低序体阵列的方法描述了树型机器人系统.采用空间算子研究了欠驱动树型多体系统的描述方法.根据系统中铰的驱动情况分别对铰链定义为主动铰和被动铰,建立树形机器人系统的运动学,然后通过铰链的类型分别按照两次从系统的顶端到基座的顺序、一次从基座到顶端的顺序进行了系统铰接体惯量的递推、系统冗余力的递推、广义加速度和广义主动力的递推,最后将分叉处的广义力和广义加速度矢量相加得到树形机器人系统的广义动力学模型.通过上述递推过程建立动力学模型,实现了高效率O(N)(N为系统自由度)次的计算效率.最后以加拿大树形空间机械臂为例做仿真验证了本研究内容的正确性和高效性.     

非线性动态系统建模方法研究

讨论了一类非线性动态系统建模的新方法。首先,假设原非线性动态系统可以用Hammerstein模型来表示。然后,将Hammerstein模型的非线性传递函数转换为等价的线性形式,从而建立起中间模型。接下来,利用粒子群优化（Particle Swarm Optimization,PSO）算法辨识出中间模型参数。最后,通过中间模型参数与Hammerstein模型参数之间的关系,推出非线性静态环节和线性动态环节的参数,从而实现原非线性动态系统建模。为了进一步增强建模的性能,提出了利用一种改进的粒子群优化（Improved Particle Swarm Optimization,IPSO）算法。仿真结果说明了该方法的合理性和有效性。     

Formulation and analysis of dynamic supply chain of backfill in construction waste management using agent-based modeling

Backfill is the excavated material from earthworks, which constitutes over 50% of the construction wastes in Hong Kong. This paper considers a supply chain that consists of construction sites, landfills and commercial sources in which operators seek cooperation to maximize backfill reuse and improve waste recovery efficiency. Unlike the ordinary material supply chain in manufacturing industries, the supply chain for backfill involves many dynamic processes, which increases the complexity of analyzing and solving the logistic issue. Therefore, this study attempts to identify an appropriate methodology to analyze the dynamic supply chain, for facilitating the backfill reuse. A centralized optimization model and a distributed agent-based model are proposed and implemented in comparing their performances. The centralized optimization model can obtain a global optimum but requires sharing of complete information from all supply chain entities, resulting in barriers for implementation. In addition, whenever the backfill supply chain changes, the centralized optimization model needs to reconfigure the network structure and recompute the optimum. The distributed agent-based model focuses on task distribution and cooperation between business entities in the backfill supply chain. In the agent-based model, decision making and communication between construction sites, landfills, and commercial sources are emulated by a number of autonomous agents. They perform together through a negotiation algorithm for optimizing the supply chain configuration that reduces the backfill shipment cost. A comparative study indicates that the agent-based model is more capable of studying the dynamic backfill supply chain due to its decentralization of optimization and fast reaction to unexpected disturbances.     

PWM DC-DC 变换器的一种改进的采样数据建模和分析方法

以连续导通电压型DC-DC变换器为例,分别给出了PWM变换器的闭环及其功率级的一种非线性和线性化的采样-数据模型,并推导了其中各种传递函数.仿真实例表明了该方法的精确性.     

Behavioral interpretation of the object-oriented paradigm for interconnected dynamic system modeling

This article presents a mathematical interpretation of the object-oriented modeling paradigm inspired from the Willems' behavioral approach of systems theory. The object modeling of interconnected dynamic systems is introduced independently from any computer language and expressed as a set computation problem. Two behavioral representations (complete and partial) of an object are defined. Three object relationships, i.e. instantiation, composition and generalization are examined in the behavioral framework. Each definition is illustrated by basic examples, e.g. a storage tank, a resistor, a control valve and an electrical circuit. The implementation of the behavioral representations into the object-oriented language Modelica is finally presented.     

Optimal production planning for a multi-product closed loop system with uncertain demand and return

We study the production planning problem for a multi-product closed loop system, in which the manufacturer has two channels for supplying products: producing brand-new products and remanufacturing returns into as-new ones. In the remanufacturing process, used products are bought back and remanufactured into as-new products which are sold together with the brand-new ones. The demands for all the products are uncertain, and their returns are uncertain and price-sensitive. The problem is to maximize the manufacturer's expected profit by jointly determining the production quantities of brand-new products, the quantities of remanufactured products and the acquisition prices of the used products, subject to a capacity constraint. A mathematical model is presented to formulate the problem and a Lagrangian relaxation based approach is developed to solve the problem. Numerical examples are presented to illustrate the model and test the solution approach. Computational results show that the proposed approach is highly promising for solving the problems. The sensitivity analysis is also conducted to generate managerial insights.     

Geometric modeling and local controllability of a spherical mobile robot actuated by an internal pendulum

In this paper, we present the modeling and local equilibrium controllability analysis of a spherical robot. The robot consists of a spherical shell that is internally actuated by a pendulum mechanism. The rolling motion of the sphere manifests itself as a nonholonomic constraint in the modeling. We derive the dynamic model of the system using Lagrangian reduction and the variational principle. We first compute the Lagrangian and identify the symmetry with respect to a group action. The system Lagrangian and the rolling constraint are invariant with respect to the group isotropy and hence permit a reduced dynamic formulation termed as the nonholonomic ‘Euler‐Poincaré’ equation with advected dynamics. Using Lie brackets and symmetric products of the potential and control vector fields, local configuration accessibility and local (fiber) equilibrium controllability are presented. Copyright © 2015 John Wiley & Sons, Ltd.