多轨迹段平滑过渡的前瞻插补算法

针对轨迹规划时采用首尾速度为零的加减速控制方法中存在的频繁启停,以及末端执行器在插补过程中加速度过渡不平滑等问题,提出了一种基于非对称S形加减速控制的多轨迹段平滑过渡的前瞻插补算法.该算法在相邻轨迹段间采用圆弧模型对衔接拐角处平滑过渡,在给定轨迹衔接点坐标和过渡圆弧半径等参数的情况下,规划出衔接圆弧处的最优速度.对插补算法中归一化因子的求解,采用一种新型柔性加减速控制算法,该算法由余弦加减速曲线在直线形加减速曲线上拟合而成,减少了余弦加减速算法的运算量,保证了加速度控制的平稳性.试验结果表明,该算法可以实现多轨迹段衔接处的圆滑过渡,保证运动速度的平滑度与连续性,有效提升了末端执行器的运行效率.     

笛卡尔空间轨迹平滑过渡的前瞻插补算法

为了解决由于六轴串联工业机器人由于笛卡尔空间运动轨迹不平滑导致频繁启停的问题,提出了基于三次准均匀B样条曲线的前瞻插补算法实现轨迹平滑过渡和提高运行效率。该算法采用三次准均匀B样条曲线作为笛卡尔空间中相邻轨迹的过渡曲线,根据过渡曲线的曲率求出过渡曲线的速度约束,利用速度前瞻根据各轨迹段长度规划出合适的衔接速度,对各轨迹段分别采用非对称S曲线加减速控制,通过等时插补获得实际插补点。在六轴串联工业机器人的控制平台上进行实验验证,结果表明,相较于传统算法,该算法可以使六轴串联工业机器人在笛卡尔空间的运动轨迹更加连续与平滑,运行效率得到了有效提升。     

静脉采血机器人NURBS曲线轨迹规划研究北大核心CSCD

为研究静脉采血机器人在针体植入过程中的NURBS曲线轨迹规划问题,以提高NURBS曲线的插补精度、系统运行过程中的平稳性为优化指标,提出了基于Simpson法的NURBS插补算法求解预估插补参数,并改进预估插补参数校正法来简化计算。采用基于正弦加速度曲线的NURBS插补速度规划方法并在法向加速度和弓高误差的共同约束下,控制插补速度并保证加速度连续。最后在设计的静脉采血机器人上用MATLAB进行仿真分析。结果表明,该算法简化了插补计算,降低了弓高误差,提高了插补精度,并有效控制了速度波动率,使运行平稳、运行轨迹连续平滑。     

数控系统连续微段重构与插补算法

针对目前微段加工所采用的非重构微段加工方法中存在的因加工轨迹与设计曲线轮廓误差较大而产生的轮廓加工精度较低的问题,及因微段节点处速度方向不连续而导致的加工表面质量不高、加工过程机床振动较大的问题,在计算机数控(computerized numerical control,CNC)中采用实时曲线重构与插补算法进行连续微段加工以实现对复杂曲面的高速高精度加工.微段插补技术包括样条曲线的实时重构及递推插补算法,及建立满足插补过程中加减速要求的且可以直接递推的插补样条曲线的重构条件.应用微段曲线重构技术进行的样件数控加工实验中,在保证曲线轮廓加工精度达到微米级精度的同时,加工速度提高了2～2.4倍.实验结果表明,实时曲线重构微段加工不仅可以实现在重构曲线的范围内只进行一次整体加减速的速度规划,提高加工效率,而且加工轨迹的进给速率的衔接平滑、轨迹光滑、表面质量好,并且利用重构的可以直接递推插补的样条曲线,有效解决了复杂算法加工过程中精度与运算速度的矛盾,提高了加工精度.     

数控系统连续微段重构与插补算法研究

针对目前微段加工研究中采用的非重构微段加工方法存在的加工轨迹与设计曲线轮廓误差较大,轮廓加工精度较低,及微段节点处速度方向不连续,因此加工表面质量不高,加工过程机床振动较大的问题。在计算机数控（Computerized Numerical Control,CNC）中采用实时曲线重构与插补算法进行连续微段加工以实现对曲面的高速高精度加工。微段插补技术包括样条曲线的实时重构及递推插补算法,及建立满足加减速要求的可以直接递推的插补样条曲线的重构条件。应用微段曲线重构技术进行的样件数控加工实验中,在保证曲线轮廓加工精度达到um级精度的同时,加工速度提高了2~2.4倍。实验结果表明,实时曲线重构微段加工不仅可以实现在重构曲线的范围内进行整体加减速速度规划,提高加工效率,而且加工轨迹的进给速度的衔接平滑,轨迹光滑,表面质量好,并且利用重构的可以直接递推插补的样条曲线,有效解决了平衡了复杂算法加工过程中精度与运算速度的矛盾,提高了加工精度。     

基于NURBS曲线直接插补算法的嵌入式数控系统设计与实现

提出了一种结合486SX级别的X86微处理器和可编程逻辑器件CPLD两级控制的嵌入式数控系统设计方案,阐述了该系统的硬件接口电路设计;提出了基于改进S形加减速的NURBS曲线直接插补算法,在满足最大弦高误差、最大法向加速度以及最大进给速度要求的情况下,对插补曲线的加速段和减速段进行速度规划;最后采用基于该插补算法的嵌入式数控系统,在半圆形毛坯上进行了五角星NURBS曲线的实际加工,验证了所设计嵌入式数控系统的可行性和有效性,具有一定的工程应用价值。     

基于多项式加减速控制的轨迹规划的研究

轨迹规划是机器人控制系统研究的重要内容之一,它对机器人性能的提高起着关键性的作用。为解决机器人在笛卡尔空间直线和圆弧拟合自由曲线时存在的误差较大的问题,提出机器人冲击最优的轨迹规划算法。通过多项式速度控制曲线和阿当姆斯微分方程,并以最大弓高误差、最大加速度为约束条件,对机器人轨迹进行插补。同时使用四元数来对机器人姿态进行描述,并使用球形线性插值法对其进行插补。最后以IRB2600工业机器人为仿真本体,使用Matlab对所提出的算法进行仿真,可以得到误差允许范围内的工业机器人运行轨迹,证明了此算法理论上的有效性。     

基于曲率约束和位移补偿的NURBS曲线柔性高精插补方法

针对NURBS曲线插补过程中曲率极大值点附近进给速度容易超限和分段插补末端位移损失的问题,提出一种基于曲率约束和位移补偿的NURBS曲线柔性高精插补方法.首先根据NURBS曲线曲率极大值对曲线进行分段并计算每段弧长,结合曲线曲率变化和机床动力学性能得到进给速度约束;然后以加加速度渐变的柔性加减速方法进行速度控制,根据曲线分段长度和曲率采取对应的速度规划策略;在实时插补中,根据实际位移计算各插补周期的平均速度并对末端位移损失进行补偿,将连续的速度曲线离散为各周期的阶跃速度变化;最后以改进的牛顿迭代方法计算插补参数,输出插补点坐标.仿真实验结果表明,该方法可以有效地提高插补精度,降低速度波动.     

基于弧长的渐开线插补新算法

现有的圆的渐开线插补方法没有利用弧长作为计量方式的算法,基于该情况,提出一种新的渐开线插补算法.分析曲线曲率与插补误差的关系,确定使用直线加减速算法控制插补速度.依据数字增量插补算法原理,根据进给速度和插补周期,确定每步的进给弧长.利用弧长公式求出渐开线的弧长表达式,根据前一个插补点的滚动角确定相邻插补点的滚动角及坐标,计算出各个坐标轴的进给量.该方法既保证加工质量又保证加工速度,即为高精高速的渐开线插补新算法.     

数控系统新参数域样条曲线加工算法

针对样条曲线参数域与时间域不一致,导致在数控系统的连续微段加工中,重构样条曲线无法快速递推插补,计算效率低;而直接等参数增量递推,又会带来节点速度突变、位置精度差的问题.故提出了实现参数域和插补周期数统一的域变换算法,建立了新参数域下的五次样条曲线,并且给出了基于该曲线的柔性加减速条件下节点切矢量及二阶导矢预计算,及曲线快速递推的算法.应用新算法的微段加工实验表明,加工效率提高了约3.3倍,而递推插补运算时间的减少到直接利用曲线公式插补的1/3.因此算法通过新型样条重构及快速递推提高了插补计算的速度,同时,在保证精度的条件下,基于新样条的速度规划减少了微段加工频繁加减速,提高了加工效率,提升了数控系统的性能.     

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.     

An accurate adaptive NURBS curve interpolator with real-time flexible acceleration/deceleration control

Parametric interpolation has been widely used in CNC machining because of its advantages over the traditional linear or circular interpolation. Many researchers focused on this field and have made great progress in the specific one, NURBS curve interpolation. These works greatly improved the CNC machining with constant feedrate, confined chord error and limited acceleration/deceleration. However, during CNC machining process, mechanical shocks to machine tool caused by the undesired acceleration/deceleration profile will dramatically deteriorate the surface accuracy and quality of the machined parts. This is, in most occasions, very harmful to machine tools. In this paper, an accurate adaptive NURBS curve interpolator is proposed with consideration of acceleration–deceleration control. The proposed design effectively reduces the machining shocks by constraining the machine tool jerk dynamically. Meanwhile, the constant feedrate is maintained during most time of machining process, and thus high accuracy is achieved while the feedrate profile is greatly smoothed. In order to deal with the sudden change of the acceleration/deceleration around the corner with large curvature, a real-time flexible acceleration/deceleration control scheme is introduced to adjust the feedrate correspondingly. Case study has been taken to verify the feasibility and advantages of the proposed design.     

An adaptive parametric interpolator for trajectory planning

A real-time interpolation algorithm for trajectory planning is studied in this paper. The NURBS interpolation algorithm is proposed to confine contour errors and feedrate fluctuations. The feedrate is adjusted adaptively according to the specified acceleration/deceleration values and jerk value. A direct digital convolution method is also introduced into velocity planning for NURBS interpolator, and it is more efficient than the traditional method of polynomial functions. The feedrate at the sharp corner is smoothed by imposing limitations on the acceleration and jerk values generated in the machining process. Since the computation of the total length of NURBS curve is required for the digital convolution method, a numerical adaptive quadrature algorithm is used to approximate the integrand. Simulation results demonstrate the effectiveness of the proposed interpolator for machining curved paths.     

数控机床上下料机器人运动控制轨迹优化研究

运动轨迹优化是工业机器人研究的一个重要领域.七段S型曲线是从传统的梯形加减速算法基础上发展而来的,尽管S型速度曲线控制算法提高了加减速过程中的稳定性,使运动过程中的速度变化连续,有较好的平滑性,但其加加速度仍存在阶跃变化问题,导致加速度存在明显的拐点,容易造成机器人在运动过程中发生冲击或振动.在上述研究的基础上,将多项式速度曲线控制算法与S型速度曲线控制算法相结合,提出了一种改进的S型速度曲线控制算法,通过优化加加速度,使其速度、加速度连续变化,曲线平滑性更好.在新代机械手臂控制系统下,对改进后S型速度曲线控制算法进行试验,证明所提出的算法在加减速过程中能够获得更加平滑的速度和加速度.     

一种改进的NURBS曲线插补算法

针对NURBS曲线曲率变化过快或出现曲率不连续点会导致插补进给速率变化过快,超出机床的加减速能力。提出一种利用NURBS曲线曲率特征的改进插补算法。该算法根据NURBS曲线曲率的变化情况将曲线分成曲率平缓段和曲率突变段,在前瞻过程中扫描出曲率突变段,获得该段的起始点、终止点及最低速率点等信息,采用梯形加减速方法对该段进行速度规划,以满足机床动态特性,实现在曲率平缓段以指令速度插补,在曲率突变段以规划速度平滑插补。仿真实验结果表明,在保证加工精度的前提下,该增强算法以较高效率实现了曲率突变段的平滑插补。     

基于STM32的点对点运动控制器设计

提出一种基于STM32的运动控制器,采用S形加减速控制脉冲频率变化,减小系统振动及提高定位精度,采用数据采样插补方法进行轨迹规划,实时迭代算法计算运行速度控制输出脉冲的频率,有效提高了脉冲输出效率;分析了该方法产生的误差,提出误差实时计算补偿策略;实验表明,控制器在点对点的运动中重复定位精度高,稳定性好;该控制器已经成功应用到两轴点对点的运动控制系统中。     

Development of an integrated look-ahead dynamics-based NURBS interpolator for high precision machinery

Methodologies for planning motion trajectory of parametric interpolation such as non-uniform rational B-spline (NURBS) curves have been proposed in the past. However, most of the algorithms were developed based on the constraints of feedrate, acceleration/deceleration (acc/dec), jerk, and chord errors. The errors caused by servo dynamics were rarely included in the design process. This paper proposes an integrated look-ahead dynamics-based (ILD) algorithm which considers geometric and servo errors simultaneously. The ILD consists of three different modules: a sharp corner detection module, a jerk-limited module, and a dynamics module. The sharp corner detection module identifies sharp corners of a curve and then divides the curve into small segments. The jerk-limited module plans the feedrate profile of each segment according to the constraints of feedrate, acc/dec, jerk, and chord errors. To ensure that the contour errors are bounded within the specified value, the dynamics module further modifies the feedrate profile based on the derived contour error equation. Simulations and experiments are performed to validate the ILD algorithm. It is shown that the ILD approach improves tracking and contour accuracies significantly compared to adaptive-feedrate and curvature-feedrate algorithms.     

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.     

The feedrate scheduling of NURBS interpolator for CNC machine tools

This paper proposes an off-line feedrate scheduling method of CNC machines constrained by chord tolerance, acceleration and jerk limitations. The off-line process for curve scanning and feedrate scheduling is realized as a pre-processor, which releases the computational burden in real-time task. The proposed method first scans a non-uniform rational B-spline (NURBS) curve and finds out the crucial points with large curvature (named as critical point) or G⁰ continuity (named as breakpoint). Then, the NURBS curve is divided into several NURBS sub-curves using curve splitting method which guarantees the convergence of predictor–corrector interpolation (PCI) algorithm. The suitable feedrate at critical point is adjusted according to the limits of chord error, centripetal acceleration and jerk, and at breakpoint is adjusted based on the formulation of velocity variation. The feedrate profile corresponding to each NURBS block is constructed according to the block length and the given limits of acceleration and jerk. In addition, feedrate compensation method for short NURBS blocks is performed to make the jerk-limited feedrate profile more continuous and precise. Because the feedrate profile is established in off-line, the calculation of NURBS interpolation is extremely efficient for CNC high-speed machining. Finally, simulations and experiments with two free-form NURBS curves are conducted to verify the feasibility and applicability of the proposed method.     

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。