The motion planning problem and exponential stabilisation of a heavy chain. Part I†

A model of a heavy chain system with a punctual load (tip mass) in the form of a system of partial differential equations is interpreted as an abstract semigroup system on a Hilbert state space. Our aim is to solve the output motion planning problem of the same nature as in the case of an unloaded heavy chain (Grabowski, P. (2003 Grabowski, P. 2003. Abstract Semigroup Model of Heavy Chain System with Application to a Motion Planning Problem. Proceedings of 9th IEEE International Conference: Methods and Models in Automation and Robotics. 25–28 August2003, Mi?dzyzdroje, Poland. pp.77–86. (IS1-2-3.PDF) [Google Scholar]), ‘Abstract Semigroup Model of Heavy Chain System with Application to a Motion Planning Problem’, in Proceedings of 9th IEEE International Conference: Methods and Models in Automation and Robotics, 25–28 August, Mi?dzyzdroje, Poland, pp. 77–86 (IS1-2-3.PDF)). In order to solve this problem we first analyse its well-posedness and some basic properties. Next, we solve the output motion planning problem using a substitute of the inverse of the input–output operator represented in terms of the Laplace transforms. A problem of exponential stabilisation is also formulated and solved using a stabiliser of the colocated type. The exponential stabilisation is proved using the method of Lyapunov functionals combined with some frequency-domain tools. The method of Lyapunov functionals can be replaced by the spectral or exact controllability approach as shown in the second part (Grabowski, P. (2008 Grabowski, P. 2008. ‘The Motion Planning Problem and Exponential Stabilisation of a Heavy Chain. Part II’. Opuscula Mathematica, 28: 481–505. (2008) (Special issue dedicated to the memory of Professor Andrzej Lasota) [Google Scholar]), ‘The Motion Planning Problem and Exponential Stabilisation of a Heavy Chain. Part II’, Opuscula Mathematica, 28 (2008 Grabowski, P. 2008. ‘The Motion Planning Problem and Exponential Stabilisation of a Heavy Chain. Part II’. Opuscula Mathematica, 28: 481–505. (2008) (Special issue dedicated to the memory of Professor Andrzej Lasota) [Google Scholar]) (Special issue dedicated to the memory of Professor Andrzej Lasota), 481–505) of the present article. A laboratory setup which allows verification of the results in practice is described in detail. Its dynamical model is used as an example to illustrate the theoretical results.     

Product-forms in batch networks: Approximation and asymptotics

It is shown that a Markovian queue, with bulk arrivals and departures having any probability mass functions for their batch sizes, has geometrically distributed queue length at equilibrium (when this exists) provided there is an additional special bulk arrival stream, with particular rate and batch size distribution, when the server is idle. It is shown that the time-averaged input rate of the special arrivals tends to zero as the queue becomes saturated, and a heavy-traffic limit for the queue without special arrivals is derived by martingale methods. This is shown to give the same asymptotic queue length probabilities as the geometric model. The product form is then extended to tandem networks of batch queues using the reversed compound agent theorem (RCAT). In order to obtain the product form in this case, it is required that, in addition to special arrival streams, so-called ‘partial batches’ are discarded immediately from the network when there are not enough customers in the queue to fill an entire departing batch. Somewhat surprisingly it turns out that, in heavy traffic, the product-form network does not always agree with the regulated Brownian motion (RBM) diffusion limit for the standard network without special arrivals and where partial batches are not discarded, but forwarded to the next node. Indeed, we show that the two models agree in heavy traffic if and only if the skew-symmetry condition for the RBM to have a product form is satisfied. When the condition does hold, our theoretical and numerical results thus validate the use of the product-form batch networks as moderate-traffic approximations to the analogous standard queueing network model without special arrivals and where partial batches may be forwarded to the next node instead of being lost. In the case that the condition does not hold, we obtain a new product-form stationary distribution for the associated non-RBM diffusion limit.     

Motion planning in velocity affine mechanical systems

We address the motion planning problem in specific mechanical systems whose linear and angular velocities depend affinely on control. The configuration space of these systems encompasses the rotation group, and the motion planning involves the system orientation. Derivation of the motion planning algorithm for velocity affine systems has been inspired by the continuation method. Performance of this algorithm is illustrated with examples of the kinematics of a serial nonholonomic manipulator, the plate-ball kinematics and the attitude control of a rigid body.     

Robust model-following controller design for LTI systems affected by parametric uncertainties: a design example for aircraft motion

This article addresses the design problem of a robust model-following controller (MFC) which minimises the error between plant controlled output and model output for a linear time-invariant (LTI) plant system affected by parametric uncertainties and an LTI target model. To design such an MFC, a previously proposed MFC scheme, whose applicability has already been demonstrated with flight controller design, is adopted in this article. Our design procedure is as follows: first, a basic MFC is designed using the nominal LTI plant model and the LTI target model while a structured free matrix in the MFC is not assigned; second, model-following performance of the MFC for appropriately defined disturbance input and model input for the parametric uncertain plant model and the LTI target model is minimised using the structured free matrix; and finally, a robust MFC is obtained using the basic MFC and the optimal structured matrix. In the second step, an iterative design method for robust H ₂ controllers for LTI parameter-dependent (LTIPD) systems using parameter-dependent Lyapunov functions (PDLFs), which is also proposed in this article, is applied. Two MFCs for the lateral-directional (L/D) motions of a research aircraft, which has been developed for an in-flight simulator, for two different real aircraft models, i.e. a Boeing 747 model and a Lockheed Jetstar model, are designed and their performance is confirmed via numerical simulations and flight tests.     

基于PCI总线的开放式运动控制系统设计及应用

针对PC机性能的不断发展以及PCI总线的性能特点,设计了一种基于PCI总线的开放式运动控制系统,可嵌入不同的机械传动设备以实现数字化控制。系统采用主从式多CPU并行工作模式,实现高速稳定运行。通过扩展PCI运动控制卡可实现32轴的运动控制。本系统在激光快速成型机上进行了大量的应用,实验结果验证了本系统的可行性与稳定性。     

基于OpenGL的三维虚拟人手语动画的研究与实现

研究了一种基于OpenGL实现三维虚拟人手语动画的方法.首先构造了三维虚拟人的最小骨骼模型;其次研究分析了手部的关键动作,提出了手部动厕的关键帧手势;又考虑到手部的运动干涉和运动约束,给出了手语动画中的不可能手势,接着基于关键帧手势以及不可能的手势,利用手部各关节之间的联动关系,给出了手部各节点位置的计算方法;最后基于OpenGL实现了三维虚拟人的手语动画.实验结果表明,基于关键帧手势以及不可能的手势的三维虚拟人的手语动画方法不仅解决了真实人手部动作的复杂性问题,又没有裁剪必要的手部动作,获得了理想的手语动画效果.     

软件测试研究

软件测试是保证软件质量和提高软件可靠性的重要手段.随着软件程序量和复杂度不断地增加,人们对软件质量的要求也在不断提高,软件测试在软件开发过程中占据的位置也变的越来越重要了,同时软件测试的工作量也显得越加艰巨.系统介绍了软件测试的概述包括软件测试的定义、阶段、过程模型和目的,并分析总结了软件测试的策略、方法和自动化.     

运动估计算法预测搜索起始点

高精度的预测搜索起始点方法可以减少运动估计算法的搜索点数,提高搜索速度和精度.对中值,均值,左块,SAD比较等方法进行了理论介绍和实验分析,提出一种新的预测搜索起始点方法.该方法足利用相邻块运动矢量的相关性和运动矢最的偏向分布特征给相邻块分配不同的权重来预测搜索起始点.实验结果表明对不同种类的标准测试序列新方法比其它方...     

一种自适应的基于中心偏置特性的矩形搜索方法

H.264编码标准中为了得到更高的压缩比,针对计算量比较大的运动估计部分,采用了六边形运动估计算法。与全搜索算法相比,六边形算法减少了搜索时间,但是,六边形算法采用了固定的模板及固定的搜素步骤,没有充分的利用到视频图像的中心偏置特性。充分利用视频图像的中心偏置特性,提出了一种新的矩形搜索算法,使搜索具有自适应特性,试验表明,在图像质量保持不变的条件下,该算法的搜索速度大幅提高。     

基于局部先验模型的单目视频人体运动跟踪

在基于模型的单目视频人体运动跟踪中,视频图像信息往往不足以恢复人体姿态,通常需要加入对姿态的先验约束才能得到合理的解.为了有效地刻画人体运动过程的时变动态特征,提出局部先验模型,其中包括局部动态过程和局部姿态分布密度,通过在样本空间中检索出相似姿态的集合,并利用该集合学习模型参数来比较精确地刻画人体的运动规律.实验结果表明,与全局动态模型相比,局部先验模型有效地克服了肢体自遮挡和肢体混淆等问题,取得了更好的跟踪结果.