双足机器人动态步态规划

针对目前仿人机器人动态步行在样机上实现较少的情况,将多项式插值方法运用于机器人踝关节轨迹规划,结合已知髋关节运动轨迹,利用几何约束的方法求取膝关节运动轨迹,得到完整步态周期内各关节运动规律,最终实现NAO机器人的动态步行。实验结果证实了基于多项式插值的几何约束规划方法是可行且有效的。     

基于近似弧长参数化的机器人轨迹规划

主要研究了采用近似弧长参数化的插值方法进行关节式工业机器人的轨迹规划.运用近似弧长参数化的插值方法将机器人末端轨迹参数曲线离散为等弧长的插值点序列,通过机器人逆向运动学求解各关节的位移点序列,采用极限的方法进行各关节速度和加速度规划.这种轨迹规划方法可以避免关节空间的插值计算和雅克比矩阵的计算.在 matlab7.8平台上,对近似弧长参数化的插值方法、轨迹规划及可行性验证进行了实例仿真,仿真结果表明该轨迹规划方法是可行的.     

Evaluation and design of filters using a Taylor series expansion

We describe a new method for analyzing, classifying, and evaluating filters that can be applied to interpolation filters as well as to arbitrary derivative filters of any order. Our analysis is based on the Taylor series expansion of the convolution sum. Our analysis shows the need and derives the method for the normalization of derivative filter weights. Under certain minimal restrictions of the underlying function, we are able to compute tight absolute error bounds of the reconstruction process. We demonstrate the utilization of our methods to the analysis of the class of cubic BC-spline filters. As our technique is not restricted to interpolation filters, we are able to show that the Catmull-Rom spline filter and its derivative are the most accurate reconstruction and derivative filters, respectively, among the class of BC-spline filters. We also present a new derivative filter which features better spatial accuracy than any derivative BC-spline filter, and is optimal within our framework. We conclude by demonstrating the use of these optimal filters for accurate interpolation and gradient estimation in volume rendering     

基于QPSO算法的机器人时间最优轨迹规划

在考虑关节约束的前提下,为得到工业机器人时间最优的关节运动轨迹,提出一种工业机器人时间最优轨迹规划新算法。采用五次非均匀B样条插值法构造各关节运动轨迹,得到的机器人各关节位置准确,各关节速度、加速度和加加速度曲线连续。利用量子行为粒子群优化算法(Quantum-behaved Particle Swarm Optimization,简称QPSO)进行时间最优的轨迹规划,该算法可以在整个可行域上搜索,具有较强的全局搜索能力。与标准粒子群算法(Particle Swarm Optimization,简称PSO)和差分进化算法(Differential Evolution Algorithm,简称DE)相比较,结果显示使用该算法进行时间最优的轨迹规划得到的数值结果更小。     

基于嵌入式系统的机器人关节空间轨迹规划

针对工业机器人运行过程经常出现的因速度或加速度不连续从而导致抖动等问题,提出了一种基于B样条曲线的轨迹规划算法,该算法使用三次B样条曲线来对六自由度机器人的关节空间进行插值,并根据实时性的要求运用一种控制点衔接插补算法进行分段插补,最终应用于基于ARM9的嵌入式系统中。实验证明:该算法不仅计算量小、处理时间短,而且能保证速度曲线的连续平滑,减少了机械抖动。     

基于粒子群优化的时间最优机械臂轨迹规划算法

根据机械臂运动学约束,提出了关节空间基于粒子群优化(PSO)的时间最优3-5-3多项式插值轨迹规划算法,解决了由于多项式插值轨迹规划具有阶次高、没有凸包性质等缺点,难以应用传统优化方法进行优化的问题.粒子群算法结构简单、参数易调整的特点弥补了多项式阶插值的缺点.直接在优化目标空间搜索,巧妙地避免了粒子群计算构造自变量和因变量的映射,降低了搜索维数,简化了计算.在优化过程中,采用两个适应度函数之间切换的开关控制,使各段插值尽快收敛于运动学约束内.通过与传统3-5-3多项式插值的运动位置、速度、加速度曲线对比,证明该方法运行时间更短,稳定性和流畅性更好.     

国产MCT8000运动控制器的轨迹规划系统

高速度、高精度、主同效率和高可靠性是现代数控高性能化的四项关键指标。针对国产MCT8000运动控制卡开发了一种集加减速控制、快速插补运算于一体的轨迹规划系统。本文介绍了该系统运动轨迹规划方案和实现方法,并提供了这种方案的应用实例。     

机器视觉电子白板系统的防抖与坐标插值技术

在基于机器视觉的电子白板系统应用中,为了消除各种因素导致的触控点抖动,提出了一种改进的均值滤波的防抖方法。为了突破硬件设备的限制提高系统工作的流畅性,采用了一种基于曲线拟合的坐标插值方法来提高系统实时性并平滑处理触控点的运动轨迹。实验结果表明：触控点的抖动情况得到了消除,在摄像头最高工作频率60fps的情况下,系统能以每秒输出180个触控点坐标的速度实时工作,在不增加硬件成本的情况下提高了系统实时性。     

利用切片法仿真模拟井眼轨迹的三维可视化

论述了基于井筒切片技术的三维井眼轨迹软件在WPF中的设计思路与实现过程。首先采用三次样条插值法模拟井筒轨迹曲线,然后构建井筒截面切片,最后依次连接各切片并对连接处作贴图渲染处理。可利用导入的参数绘出三维井眼轨迹图,还可利用鼠标操作来实现对三维图形的缩放和视角变换等功能。油气井井眼轨迹的三维可视化以一种直观、逼真的效果呈现给工程技术人员,使其摆脱了抽象和枯燥的井眼数据的束缚,可以更好地解决钻井过程中遇到的各种技术难题。现场数据的测试结果表明,软件能较为精确地反映井下状况,并且操作简便,符合钻井作业的实际需求。     

A look-ahead command generator with control over trajectory and chord error for NURBS curve with unknown arc length

There are currently no analytical methods available which determine the exact arc length for NURBS curves and for this reason, a smooth feedrate profile with desired trajectory cannot be achieved. Numerical methods used to calculate the arc length are time-consuming processes which make generating a feedrate profile with desired accelerations difficult in real-time. This paper introduces a look-ahead trajectory generation method which determines the deceleration stage according to the fast estimated arc length and the reverse interpolation of each curve at every sampling time. This results in a feedrate trajectory generation with jerk-limited acceleration profiles for the NURBS curves. The feedrate profile is adjusted dynamically according to the geometrical path constraint determined by chord error for the curved path. A NURBS curve by two different kinematics conditions was used as a means to test the feasibility of the developed interpolation scheme and command generator.     

State‐space approach to interpolation in MPC

Interpolation between unconstrained optimal input trajectories and feasible trajectories forms the basis for a computationally efficient predictive control algorithm but lacks robustness in that uncertainty can destroy the guarantee of feasibility. To overcome this problem it is possible to introduce into the interpolation process a further input trajectory which is referred as ‘mean level’. This has been accomplished in an input–output setting and the purpose of the present paper is to show that it is possible to get a considerably simpler algorithm by recasting the problem into state‐space form. Copyright © 2000 John Wiley & Sons, Ltd.     

基于焊接机器人的实时轨迹插补算法

提出了一种实现焊接机器人实时轨迹插补的规划算法。该算法既能满足时间上的实时性,又能够在完成机器人当前轨迹插补的同时,实现在线调整插补参数,改变机器人当前插补方程,从而改变机器人运动轨迹与状态。而对于不同插补类型,只要找准对应线长的表示,不需要对算法本身进行修改,就可以完成相应的轨迹插补。该算法应用于“昆山一号”焊接机器人中,表明其满足焊接实时性和可调速性要求。     

基于再生核理论实现多FFSR协调操作动力学控制

基于再生核理论提出了在空间微重力环境下实现多自由飞行空间机器人(FFSR)协调操作的动力学控制方法．针对多个FFSR操作同一目标的情况,对目标期望轨迹进行采样,利用多FFSR协调操作的动力学方程,基于再生核理论实现了多FFSR协调操作的动力学控制．与现有的其它方法相比,该方法不用运动方程描述目标的运动轨迹,而是按照人们的需要控制目标做任意的非线性曲线运动,没有局限性;与多项式插值、样条插值相比,每增加一个节点,逼近误差在索伯列夫范数意义下单调下降;对任意形式加密的节点系,迭代过程一致收敛;公式单一,便于计算机计算．在仿真试验中验证了该方法的有效性．     

Estimation and model predictive control of non-linear batch processes using linear parameter varying models

In this paper, feedback control is implemented for batch processes using linear models which describe the batch dynamics locally along its optimal trajectory. A Linear Parameter Varying (LPV) model obtained by interpolation between these multiple models is used to emulate the behaviour of the non-linear batch. The interpolation functions and state estimates are computed using a recursive Bayesian technique. The control technique is based on model predictive control (MPC) which is used for regulation and targeting the product specifications at the end of the batch.     

Stabilized finite elements with equal order of interpolation for soil dynamics problems

Summary The accurate prediction of the behaviour of geostructures is based on the strong coupling between the pore fluid and the solid skeleton. If the relative acceleration of the fluid phase to the skeleton is neglected, the equations describing the problem can be written in terms of skeleton displacements (or velocities) and pore pressures. This mixed problem is similar to others found in solid and fluid dynamics. In the limit case of zero permeability and incompressibility of the fluid phase, the restrictions on the shape functions used to approximate displacements and pressures imposed by Babuska-Brezzi conditions or the Zienkiewicz-Taylor patch test hold. As a consequence, it is not possible to use directly elements with the same order of interpolation for the field variables. This paper proposes two alternative methods allowing us to circumvent the BB restrictions in the incompressibility limit, making it possible to use elements with the same order of interpolation. The first consists on introducing the divergence of the momentum equation of the mixture as an stabilization term, the second is a generalization of the two step-projection method introduced by Chorin for fluid dynamics problems.     

运行时间周期化工业机器人模型迭代寻优NURBS轨迹插补

为满足工业机器人高精度复杂曲线运动的需求,本文提出运行时间周期化工业机器人模型迭代寻优NURBS轨迹插补算法.首先,根据轨迹最大轮廓误差和机器人动力学特性对曲线分段.随后,提出优化回溯算法,使各子曲线段均可用S曲线加减速规划.之后,为保证机器人在进给速度极小值处不超速,将各加减速阶段运行时间调整为插补周期的整数倍,并对子曲线段衔接处速度平滑处理.最后,提出模型迭代寻优曲线插补,大大降低了速度波动率.仿真试验表明,该方法插补轨迹的各项指标均满足要求且最大速度波动率仅为0.000099%.真机试验也验证了该方法可有效减小轨迹误差.     

一种基于测地线的机器人轨迹规划方法

提出了一种基于测地线的机器人轨迹规划方法.该方法克服了传统的轨迹规划方法的某些不足,其规划是在关节空间(黎曼空间)内进行的,规划目标是直角坐标空间内的直线,即两点之间的最短路径,也可以是系统动能最小,或某项综合指标最优.该规划方法直接得到机器人的各关节的转角和角速度,无需进行运动学反解和多项式插值.本文的基于测地线的轨迹规划是以轨迹弧长作为参考变量的,因此它还具有非时间参考的机器人轨迹规 划的优点.􀁱     

基于GA的时间最优机械臂轨迹规划算法

由于多项式插值轨迹规划具有阶次高、没有凸包性质等特点,传统优化方法难以应用的特点,根据机械臂运动学约束,提出了关节空间基于遗传算法(GA)的3-5-3多项式插值轨迹规划算法。利用运动学约束,以最优时间为目标,针对关节型机器人在静态环境下的点到点的轨迹规划问题,利用GA算法解算多项式插值的时间。通过与基于PSO的3-5-3多项式机械臂轨迹规划运动位置、速度、加速度曲线对比,证明该方法在运行时间和运行平稳度上都有突出优点。     

Constrained control of SISO bilinear systems

Relative degree and nonminimum phase difficulties limit the applicability of input-output feedback linearization; hence the need for approximations. Earlier work on predictive control of bilinear systems overcame these problems by means of interpolation between feedback linearization and state feedback, the former providing optimality and the latter guaranteeing feasibility and stability through the use of invariant/feasible polytopes. The current work also makes use of polytopes in preference to ellipsoids but achieves distinctly different objectives. First, it is shown that feedback linearization can be used over particular polytopes without needing to resort to either approximation or interpolation. Then, it is shown that invariant polytopes based on bilinear controllers can be much larger. These two approaches are combined in an algorithm that guarantees stability over much larger initial condition sets and gives much improved closed-loop performance.     

Fuzzy guidance of the shuttle orbiter during atmospheric reentry

The guidance law for the Space Shuttle Orbiter is required to track a reference state trajectory satisfying a given drag-acceleration versus velocity profile. Newly available nonlinear guidance laws will require complicated multi-dimensional interpolation. In this paper, Sugeno approximators (hybrid fuzzy-crisp inference systems) trained by example are used to conduct this interpolation. Moreover, the concept of surface-tracking guidance is introduced in which the reference trajectory itself is updated when severe disturbances warrants it. Surface tracking requires an “on-line optimizer” which is implemented using a constellation of a few blocks, two of which are multi-input/multi-output Sugeno approximators. The different approximators and guidance laws have been studied and simulated.