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。     

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.     

反向插补的NURBS曲线前瞻插补算法

为了避免现有NURBS曲线前瞻插补算法在确定自适应减速起始点时不够准确而产生的减速距离大于实际需要距离的问题,防止插补出现低速运行区域,提出一种基于反向插补的减速点确定方法.在该方法中,前瞻算法从减速区域的终止点开始,采用S型加减速规划进行逆向插补,以确立逆向插补曲线与自适应插补曲线的交区间,将交区间的起始点作为自适应减速区间的起始点,并再次进行前瞻插补,得到理想的减速区域速度规划方案.仿真实验结果表明,文中算法有效地避免了插补过程中的低速运行现象,提高了插补效率.     

面向高质量加工的NURBS曲线插补算法

通过分析数控系统加工时常用的插补算法的特点,提出一种基于NURBS曲线的插补算法.该算法包括速度规划和实时插补两部分:速度规划部分考虑了工件加工时允许的最大轮廓误差,以保证高速运行过程中加速度的连续,使机床运行平稳,避免产生大的冲击;实时插补部分应用弦截法计算插补参数,能将实时插补产生的速度波动控制到理想水平,进一步减小了机床震颤.仿真实验结果表明,文中算法能够减小机床振动,实现高质量加工.     

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.     

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.     

实现速度平滑过渡的NURBS实时插补算法

在分析机床最大速度、加速度和速度不连续点对实际加工的影响的基础上,设计了一种能够实现速度平滑过渡的NURBS实时插补算法.算法首先进行一次预插补,求出减速过程中超出机床最大加速度以及速度不连续的点,并采用逆求的方法求出减速点.然后在实时插补时根据求出的减速点进行速度规划.仿真实验结果表明,该插补算法能够在保证加工精度的前提下,以较高效率实现速度的平滑过渡.     

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。     

步进电机三轴联动的快速加减速算法研究

加减速控制是数控系统的关键技术,对提高数控系统的精度及速度有重要的意义.提出了一种步进电机三轴联动的快速加减速算法--动态查表法,该算法结合DDA插补算法,可以用普通的单片机实现多种加减速曲线的运动控制,具有运算速度快、精度高等优点.     

NURBS曲线高速高精度加工的插补控制

针对复杂零件高速精密加工的需求,提出了一种NURBS曲线的实时插补算法,它基于NURBS曲线的矩阵表示,通过适当的插补预处理、运用参数预估计与校正的插实施以及合理的近似计算方法,简化了插补的实时计算,保证了算法的实时性,特别是引入了插补误差和进给加速度的实时监控,使进给速度能随曲线曲率自适应调整,实现了NURBS曲线高速高精度加工的插补控制。     

An adaptive real-time NURBS curve interpolation for 4-axis polishing machine tool

The non-uniform rational B-spine (NURBS) curve interpolation is a key technology of the advanced computer numerical control (CNC) system. NURBS curve interpolation can realize a high-speed and high-precision machining, and it can also avoid some inevitable deficiencies of the linear and circular interpolation functions which are generally used in traditional NC system. Before the interpolation, some calculation tasks are finished, which will decrease the amount of calculation during interpolation and increase the interpolation efficiency. Further, an adaptive NURBS curve interpolation with real-time and flexible S-shaped curve acceleration/deceleration (ACC/DEC) control method is added to the interpolation algorithms. The NC machining simulation conducted with the MATLAB software and the NURBS curve interpolation experiments performed on the 4-axis polishing machine tool demonstrate the validity and correctness of the adaptive real-time NURBS curve interpolation algorithm in the CNC system.     

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.     

NURBS曲线曲面插补算法基于S12的测试

传统的基于直线和圆弧的插补算法已经不能满足数控技术发展的需要,采用基于自由曲线的插补算法是大势所趋。目前关于NURBS曲线插补的研究大部分还停留在单段的研究上,没有突破传统数控技术的范围。在目前开放式数控技术日益重要的情况下,提出了基于整条曲线或者整个曲面的插补算法,并将该算法应用在S12单片机上进行测试,测试结果显示能够满足要求。     

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.     

基于Adams-Bashforth-Moulton预估校正法的NURBS插补算法研究

针对传统的基于连续微小线段的插补方法在复杂零件型面加工中具有插补误差大和速度波动大等不足,对NURBS曲线的插补原理、插补参数计算、速度波动等方面进行了研究,结合加工弓高误差、法向加速度、法向加加速度等约束条件进行了速度规划,提出了一种基于Adams-Bashforth-Moulton(ABM)预估校正法的NURBS曲...     

一种基于RTLinux 的五自由度开放式并联激光加工数控系统

研究了一种基于RTLinux 的五自由度开放式并联激光加工数控系统,系统中嵌入了三分支五自由度构 型的位置正反解模型,解决了特定位置多解的问题．插补过程应用了S 曲线加减速控制和小线段插补结合的算法． 同时,在数控系统中增加了工艺控制模块,实现了激光功率、离焦量等激光加工工艺参数的调整功能．     

Real-time NURBS interpolation using FPGA for high speed motion control

Modern motion control adopts NURBS (Non-Uniform Rational B-Spline) interpolation for the purpose of achieving high-speed and high-accuracy performance. However, in conventional control architectures, the computation of the basis functions of a NURBS curve is very time-consuming due to serial computing constraints. In this paper, a novel FPGA (Field Programmable Gate Array) based motion controller utilizing its high-speed parallel computing power is proposed to realize the Cox-de Boor algorithm for second and higher degrees NURBS interpolation. The motion control algorithm is also embedded in the FPGA chip to implement real-time control and NURBS interpolation simultaneously for multi-axis servo systems. The proposed FPGA-based motion controller is capable of performing the Cox-de Boor algorithm and the IIR (Infinite Impulse Response) control algorithm in about 46 clock cycles, as compared to the 1303 clock cycles by the traditional approach. Numerical simulations and experimental tests using an X-Y table verify the outstanding computation performance of the FPGA-based motion controller. The result indicates that shorter sampling time (10 μs) can be achieved for NURBS interpolation which is highly critical to the success of high-speed and high-accuracy motion control.