三次均匀有理B样条曲线插补算法的研究

插补算法是机器人系统实现运动控制的核心模块,对三次均匀有理B样条曲线的插补算法进行了研究.基于三次非均匀有理B样条曲线(NURBS),得出三次均匀有理B样条曲线的表达式.反算B样务曲线的控制顶点中发现规律,采用一种简单快捷的方法求取控制顶点,这使插补算法计算简单,更易于计算机编程.并且在算法中考虑到运动控制加减速的问题,这使插补算法符合实际,实用性强.最后采用三次均匀有理B样条曲线对螺旋线进行插补,仿真结果良好.     

面向五轴加工的等距双NURBS刀具路径同步插补方法

针对由离散刀位点数据生成的五轴加工等距非均匀有理B样条曲线刀具路径中两条非均匀有理B样条曲线参数不同步的问题,建立了一种等距双非均匀有理B样条曲线参数的同步模型,实现等距双非均匀有理B样条曲线刀具路径插补过程中两条非均匀有理B样条曲线参数的同步运动。将三轴非均匀有理B样条曲线插补算法应用于五轴加工等距双非均匀有理B样条曲线刀具路径中的刀具中心点非均匀有理B样条曲线,根据参数同步模型将插补算法同步到刀轴点非均匀有理B样条曲线中。仿真表明,采用该算法能够使刀具始终沿着等距双非均匀有理B样条曲线刀路进行同步插补,参数同步插补精度主要集中在10-6 mm级数上,适用于复杂曲面的五轴加工。     

非均匀有理B样条曲线直接插补进给速度规划

在非均匀有理B样条直接插补算法中,为了提高插补实时性、克服前瞻规划算法的缺点,提出了基于进给速度预处理曲线的进给速度规划方法.该方法在插补前,通过建立进给速度预处理曲线来取代非均匀有理B样条曲线实时插补进给速度规划的前瞻算法.在速度规划过程中,为了防止进给加速度和加加速度超过机床性能要求,在曲线曲率变化较大的区域,采用基于逐点比较计算的方法规划每个参数点处的进给速度.通过MATLAB仿真表明所提方法具有较高的加工精度、良好的进给速度平滑效果和实时插补性能.     

一种优化的NURBS曲线插补算法

为弥补目前非均匀有理B样条插补算法的不足,提出一种优化的非均匀有理B样条曲线插补算法。算法采用插补前S曲线加减速方法,不仅优化了前瞻过程,而且在回溯过程中考虑了短样条的情况。算法对长样条和短样条非均匀有理B样条曲线能用统一的方法进行插补,通过引入环形缓冲区和预插补(非离线),提高了加工效率,同时合理地安排插补任务增强了系统的实时性。通过MATLAB仿真,验证了算法的有效性。     

一种实时快速NURBS插补算法研究与实现

非均匀有理B样条刀具轨迹参数u与弧长S之间没有精确解析表达式,且是非线性映射现象,为了减少速度波动,减轻在线插补计算量,提出了基于双圆弧引导曲线的快速非均匀有理B样条插补算法.利用步长参数和高斯积分对刀具轨迹进行采样,采样点是基于参数u与弧长S的坐标点,利用双圆弧拟合方法对采样点拟合成插补引导曲线,建立参数u和弧长S解析表达式.在插补时依靠建立的双圆弧引导曲线进行快速的非均匀有理B样条插补.仿真实验结果表明了所提方法的u可靠性和有效性.     

基于前瞻算法的高效非均匀有理B样条曲线插补器

根据计算机数字控制系统的实际性能和非均匀有理B样条曲线的几何特性,设计了一种能够实现加速度平滑过渡的高效非均匀有理B样条曲线插补器。首先,该插补器利用快速插补计算模拟实际加工过程,找到加速度不连续的点;然后,采用S曲线加减速方法向后逆求减速点,并通过约束速度和加速度的方法,预估S曲线加减速第三阶段起点,不仅提高了所求减速点位置的精度,还实现了减速点处加速度的连续性。仿真结果表明,该插补器能在保证加工精度的前提下,以较高效率实现加速度的平滑过渡。     

基于干涉预处理的NURBS曲线前瞻插补算法

鉴于直接自适应插补容易在加工过程中引起较大的速度波动,而按曲率极值点对NURBS曲线进行分段插补造成加减速过程中加速度和加加速度超限,提出一种基于干涉预处理的非均匀有理B样条曲线前瞻控制插补算法。首先对曲线进行自适应处理,得到各自适应插补点的运动参数;然后找出其中加速度或加加速度超限的点(即危险点),并对这些点的速度进行前瞻控制,根据前瞻控制信息对相邻危险点进行干涉处理,最终得到用来对曲线分段的危险点信息和相应的控制策略;最后根据各危险点之间的干涉类型对曲线进行实时插补。仿真实验表明,该算法能够在保证加工精度的前提下,实现进给速度的平滑过渡,并且能够保证加速度和加加速度不超限。     

基于S型加减速的自适应前瞻NURBS曲线插补算法

为实现加工过程中进给速度和加速度的平滑过渡,减小其突变时对机床的冲击,更好地保证加工精度,提出一种基于S型加减速的前瞻自适应非均匀有理B样条曲线插补算法.该算法根据弓高误差的要求,确定出各插补点的自适应进给速度及位置参数,然后找出速度改变点及其等速区间.为避免相邻速度改变点间加减速过程的互相影响,分别在插补前瞻距离和预前瞻距离内,根据设备允许的最大加速度、加加速度以及S型加减速算法对各速度改变点参数进行分析,筛选出决定加减速过程的关键点,再进行S型加减速控制,使进给速度和加速度得以平滑过渡,从而满足机床加减速能力的要求.仿真结果表明,该算法能够满足高速高精度的要求,验证了其可行性.     

基于曲率特性的柔性加减速NURBS插补器

为降低非均匀有理B样条段间转接时对机床的机械冲击,提出了一种基于曲率特性的柔性加减速控制方法。研究了满足插补误差要求的非均匀有理B样条梯形加减速的算法,推导了满足S型加减速要求的简化算法。用两种算法进行的基于弓高误差的非均匀有理B样条仿真加工实验表明,在曲率突变处加速度和加加速度均出现突变,对机床造成较大冲击。而基于曲率变化进行的柔性加减速的仿真试验表明,相关特性参数符合加减速的规划要求。将算法集成至自行开发的开放式控制器中,加工实验表明,该算法使数控机床的速度变化更加平稳,并具有良好的实时性。     

基于速度平滑控制的高效非均匀有理B样条曲线插补算法

为提高曲面加工的质量和效率,提出了一种基于冗余误差和速度平滑控制的非均匀有理B样条曲线插补算法.该算法先按照曲率大小将非均匀有理B样条曲线分段,再根据数控机床最大加速度调整分段.消除了曲率突变对加工的负面影响.同时为每个分段分别设置合适的编程进给速度,提高了加工效率.最后提出两段速度平滑控制方法,使速度过渡更为平滑.模拟试验证明了该算法的有效性.     

Real-time NURBS curve interpolator based on section

Parameter interpolation is more capable of modern computer numerical control (CNC) than traditional linear/circular interpolation with higher speed and higher precision. Most of non-uniform rational B-spline (NURBS) interpolation algorithms were developed based on the chord error and machines capability, where interpolation points are calculated beforehand to overcome acceleration/deceleration (acc/dec) and jerk problem, which needs large memory. In this paper, a NURBS interpolator based on feedrate section is proposed. Instead of a single interpolation point, this interpolator aims to feedrate section, which makes it possible to run on a digital signal processor or field programmable gate array (FPGA) whose memory is limited. Experiment on FPGA showed the performance of interpolation. A mould experiment verifies the feasibility of application.     

Electronic cam motion generation with special reference to constrained velocity, acceleration, and jerk

Electronic cam motion involves velocity tracking control of the master motor and trajectory generation of the slave motor. Special concerns such as the limits of the velocity, acceleration, and jerk are beyond the considerations in the conventional electronic cam motion control. This study proposes the curve-fitting of a Lagrange polynomial to the cam profile, based on trajectory optimization by cubic B-spline interpolation. The proposed algorithms may yield a higher tracking precision than the conventional master-slaves control method does, providing an optimization problem is concerned. The optimization problem contains three dynamic constraints including velocity, acceleration, and jerk of the motor system.     

Adaptive parametric interpolation scheme with limited acceleration and jerk values for NC machining

Parametric interpolation has many advantages over the traditional linear or circular interpolation in computer numerical control (CNC) machining. The existing work in this regard is reported to have achieved constant feedrate, confined chord error and limited acceleration/deceleration in one interpolator. However, the excessive jerk still exists due to abrupt change in acceleration profile, which will cause shock to the machine as well as deteriorate the surface accuracy. In this paper, an adaptive interpolation scheme incorporating machine’s dynamics capability consideration is proposed and illustrated in details. In the proposed algorithm, the commanded feedrate is maintained at most of the time and adaptively reduced in large curvature areas to meet the demand of the machining accuracy requirement, while at the same time, the acceleration and jerk values are limited within the machine’s capabilities during the whole interpolation process. It ensures a high machining accuracy, eliminates the phenomenon of overshoot/undershoot and reduces mechanical shock to the machine tools. The real-time performance of this interpolator is also measured to demonstrate its practical application. Two non-uniform rational B-spline (NURBS) curve interpolation experiments are provided to verify the feasibility and advantages of the proposed scheme.     

三自由度Delta并联机械手轨迹规划方法*

以三自由度Delta并联机械手为研究对象,针对其高速搬运作业下的操作空间和关节空间的轨迹规划策略进行研究。结合实际作业需求,对机械手末端运动轨迹的关键路径点进行设置,建立点到点的搬运作业轨迹。以机械手运动学逆解模型为基础,在操作空间利用3-4-5次多项式运动规律建立操作空间运动特征到关节空间运动特征的映射关系。以机械手运动学正解模型为基础,在关节空间利用五次非均匀有理B样条(NURBS)运动规律建立关节空间运动特征到操作空间运动特征的映射关系。在运动轨迹关键点位置及运动时间相同的条件下,对两种轨迹规划方法进行计算机仿真,对比分析机械手关节角度、角速度和角加速度等运动特征,并通过物理样机试验进行验证。结果表明关节空间内基于五次非均匀有理B样条运动规律的轨迹规划方法在减小运动过程中机械手振动和降低电动机功耗等方面优势明显。     

Development of integrated acceleration/deceleration look-ahead interpolation technique for multi-blocks NURBS curves

Modern motion control adopts acceleration/deceleration before interpolation (ADBI) motion planning to eliminate path command errors. However, the individual velocity profiles might not be continuous at the junction of the blocks. Acceleration/deceleration after interpolation (ADAI) method may provide an alternative for solving the discontinuous problems, but it causes path command errors. In this paper, an integrated acceleration/deceleration interpolation (IAD) scheme which integrates the ADBI and ADAI modules is proposed. The ADBI provides a look-ahead function which plans the feedrate profiles based on chord errors, command errors, curvatures, and acceleration limits. Within the look-ahead function, the command error equation is utilized to determine the feedrate at the junction of adjacent blocks. Then the ADBI performs non-uniform rational B-spline (NURBS) interpolation using the planned feedrate profile and outputs the position points to the ADAI module. The ADAI module processes the points by a digital convolution technique such that the continuity of the block junction velocity is ensured. Finally, the IAD is applied to the multi-block NURBS interpolation to validate its effectiveness. Simulations and experiments are conducted to demonstrate the IAD scheme. It is shown that the IAD scheme can reduce the acceleration significantly at the junctions of the blocks under the given tolerance of the command error. Furthermore, the proposed algorithm can improve tracking and contour accuracies as compared to the hybrid multi-blocks look-ahead approach.     

On the development of a parametric interpolator with confined chord error, feedrate, acceleration and jerk

A parametric interpolator for the trajectory planning of non-uniform rational basis spline (NURBS) curves is proposed in this study. The input constraints include the chord error, speed limit, acceleration limit and jerk limit. Since there is no unique representation to relate these constraints, appropriate models are developed to determine several feedrates in terms of different kinematic conditions, the minimum one of which is selected as the desired feedrate. A look-ahead stage is developed to plan a series of segment points from the curves, where a segment point represents the change in the acceleration across zero. The segment points, which enable the appropriate design of kinematic profiles, are used in real-time sampling for determining the sampling points. Several examples are presented to demonstrate the feasibility of the proposed algorithm.     

玻璃成形抛光相对线速度基本恒定控制算法研究

针对玻璃成形抛光中玻璃与抛光轮接触点相对线速度持续减小从而影响加工效率的问题,以控制相对线速度基本恒定、保证加工效率和精度为目标,提出基于三次NURBS曲线的速度控制算法。基于线性加减速方案,确定速度特性曲线控制点。结合Preston公式,以相对线速度基本恒定为约束条件,求解抛光轮中心末速度。以加加速度连续为约束条件,求取与控制点对应的权因子,确定抛光轮中心速度变化时的控制方程。采用四阶龙格-库塔数值方法确定插补初始点,再由米勒-汉明数值方法进行迭代校正,实现参数式曲线插补控制算法。试验结果表明,该速度控制方法能够有效保持玻璃与抛光轮接触点相对线速度基本恒定,加工效率较传统方法有较大提高。     

三次B样条曲线插补在多轴运动控制卡上的实现

为充分利用PC机资源,提高数控加工精度,介绍了基于TMS320F2812数字信号处理器（DSP）的多轴运动控制卡的设计方法以及三次B样条曲线恒速进给实时插补方案在控制卡上的应用。结果表明,该方法能有效地简化插补过程中的轨迹计算,显著缩短插补计算时间,使所有的插补点都在理论曲线上;只要合理决定曲线参变量,完全可以保证运动控制系统的高速高精度要求。     

An accurate NURBS curve interpolation algorithm with short spline interpolation capacity

In this paper, a novel and accurate real-time non-uniform rational B-spline curve interpolation algorithm is proposed. This algorithm not only considers chord errors, feedrate fluctuations, jerk-limited, and acceleration/deceleration (Acc/Dec) capabilities of the machine, but also optimizes the look-ahead process. In the meanwhile, it improves machining efficiency by adding the circular buffer and pre-interpolation (non-off-line) and enhances the real-time performance by removing the time-consuming calculation from the interrupt service routine. Furthermore, the proposed interpolation algorithm can interpolate both the long spline and the short spline with uniform method. The advantages of the proposed method were confirmed by the simulation results.     

改进鲸鱼优化算法在机械臂时间最优轨迹规划的应用

针对机械臂时间最优轨迹规划问题,提出一种改进鲸鱼优化算法的最优轨迹规划方法。首先把机械臂各个关节的角度、角速度、角加速度作为约束参数,在关节空间中采用五次多项式插值构造机械臂的轨迹,然后建立以机械臂运行时间最优为目标的目标函数,采用改进的鲸鱼优化算法（IWOA）来对时间进行优化,提高机械臂的运行效率。最后通过MATLAB进行仿真,结果表明,改进的鲸鱼优化算法相较于其它同类算法求解精度更高,收敛速度更快,并且经过IWOA和轨迹优化结合得到的机械臂的位移、速度和加速度曲线都是平滑的且没有明显的突变,验证了该轨迹规划方法的有效性。