多轴轮廓运动系统的轨迹生成与性能优化
|
摘要
多轴轮廓运动系统是运动控制技术的一个重要分支,其主要用途是实现高性能轮廓加工,高性能轮廓加工是现代制造业中的一项核心技术,广泛地应用于众多工业领域,具有重要的战略意义与研究价值。为改善多轴轮廓运动系统的加工质量与加工效率,需要采用先进的控制策略对运动轨迹的规划与控制进行性能优化。本论文结合一个典型的多轴轮廓运动系统—基于PC+运动控制卡的开放式三轴数控雕铣机控制系统的开发,围绕“多轴轮廓运动系统的轨迹生成与性能优化”这个主题,针对高性能轮廓加工与多轴轮廓控制中存在的一些关键问题,着重从轨迹逼近、实时插补、轨迹优化与协调控制等方面进行了系统深入的研究,主要研究内容可归纳如下:
(1)针对光滑曲线的逼近问题,采用直线/圆弧逼近方法进行了设计与对比的研究。以一个平面四分之一椭圆弧为例,根据期望的精度要求分别采用直线和圆弧来逼近该椭圆弧,其中直线逼近采用基于曲率圆模型的等误差法和等参数增量法;圆弧逼近采用基于minimax逼近的最优圆弧逼近和以多边形为中介的双圆弧逼近。通过不同逼近方法的逼近方式与误差控制模型,分别从逼近点数的多少及轨迹的连续性两方面来进行具体设计,并根据仿真实验结果来分析不同参数对逼近误差的影响,以及不同逼近方法对运动控制精度的影响。
(2)针对空间曲面加工中存在的进给速度波动问题,提出了基于时间分割法与数字积分法混合实现的空间直线插补方法及其连续进给运动的实现方法。该插补方法是采用时间分割法中的时间分割原理,对数字积分法中的累加溢出过程按照进给速度的要求采用可控的插补周期进行时间分割,以消除零头距离并实现平滑的进给速度。为配合上述插补方法实现连续进给运动,提出了一种离线分段速度规划方法对由大量微小直线段组成的加工代码进行前瞻预处理,确定每段直线段代码在梯形加减速方法下可以实现的终点速度,以提高加工效率,避免在转角处的冲击。然后,在插补过程中,提出了一种非对称梯形加减速控制方法,采用逐点判断的方式按照非对称梯形速度曲线进行加减速控制。最后,通过仿真实验与实际加工实验对该方法的有效性与优越性进行了研究,其中实际加工实验在三轴数控雕铣机上进行。
(3)针对空间曲面加工中可能出现表面凹坑、光洁度较差等问题,提出了一种基于网格均匀化的刀位轨迹优化方法。该方法在Cimatron软件生成的加工刀位轨迹基础上,分横向光顺与纵向平滑两步进行,首先进行横向光顺,通过建立主导轮廓线并对不规则的点进行修正,以降低相邻刀路倾斜度的变化程度,然后进行纵向平滑,对同一条刀路上的刀位点进行光滑连续直线段的识别,再采用分段三次样条进行拟合,以提高同一刀路上的曲线光滑程度。最后,通过仿真实验与实际加工实验对该方法的有效性与优越性进行了研究,其中实际加工实验在三轴数控雕铣机上进行。
(4)针对在多轴轮廓运动中轮廓误差难以直接计算与控制的问题,提出了一种基于工作坐标系的最优轮廓控制方法。该方法通过在期望轨迹上建立活动的Frenet坐标系作为工作坐标系,用跟踪误差在工作坐标系中的法向分量来近似轮廓误差,将系统动力学方程由全局坐标系变换到工作坐标系,采用最优线性二次型方法来设计最优轮廓控制器,通过提高法向误差分量的权值来改善轮廓精度。最后,通过仿真实验对该方法的效果进行了验证。
Multi-axis contouring motion system is an important branch of motion control technology. Its main use is to accomplish high performance contouring machining. High performance contouring machining is a core technology in modern manufacturing. It is widely applied in many industries and has important strategic sense and high research value. To improve machining quality and efficiency of multi-axis contouring motion system, it is necessary to adopt advanced control strategy to optimize the plan and control of motion trajectory. In this dissertation, a typical contouring motion system - open three-axis CNC milling and engraving control system was developed. The topic of the dissertation is trajectory generation and performance optimization of multi-axis contouring motion system. To solve some key problems in high performance contouring machining and multi-axis contouring control, research was developed systematically and deeply from four aspects, including trajectory approximation, real-time interpolation, trajectory optimization and coordinated control. The main work is as following.
Firstly, to approximate smooth curves, design and comparative research were developed with straight line/circular arc approximation methods. Taking a quarter of a planar ellipse for an example, straight line segments and circular arc segments were adopted respectively to approximate the planar ellipse according to the desired accuracy. In the process of straight line approximation, constant error approach and constant parameter increment approach, which are both based on the model of curvature circle, were applied. In the process of circular arc approximation, optimal circular arc approach, based on the principal of minimax approximation, and bi-arc approach with a polygon approximation were applied. Through the approximation manner and error control model of different approximation methods, detailed design was developed from two aspects including the number of approximation segments and the continuity of the trajectory. According to the result of simulation experiment, the effect of different parameters on approximation error and the effect of different methods on motion control accuracy were analyzed.
Secondly, to solve the feedrate fluctuation in machining three-dimension sculptured surface, a new hybrid space linear interpolation method, based on the principles of Time-division and Digital Differential Analyzer (DDA), and implementation method of continuous feed motion were proposed. This interpolation method applied the principle of time-division to the procedure of accumulation in DDA by means of controlling interpolation cycle time. Therefore, it could eliminate the odd distance and maintains smooth feedrate. To accomplish continuous feed motion in company with this interpolation method, an off-line segmented speed planning method was proposed to preprocess NC codes composed of a large number of short straight line segments in advance and determine a realizable end speed for each straight line segment by means of trapezoid speed curves. Therefore, machining efficiency was improved and jerk at corners was avoided. Then, a non-symmetrical trapezoid acceleration/deceleration control method in the process of interpolation was proposed, which adopted a point-by-point arbitration manner to control acceleration and deceleration according to non-symmetrical trapezoid speed curves. The validity and superiority of the proposed methods were studied through simulation and actual machining experiment implemented on a three-axis CNC milling and engraving machine.
Thirdly, to solve the disadvantages such as surface dents, poor roughness in machining three-dimension sculptured surface, a tool path optimization method based on mesh uniformization was proposed. Based on the original tool path generated by Cimatron software, this method was implemented with two steps including transverse fairing and longitudinal smoothing. In the process of transverse fairing, irregular points were modified by means of constructing the dominant contour to reduce the variety of the inclination degree between the succeeding paths. Then, in the process of longitudinal smoothing, smooth continuous line segments along the same path were identified and fitted by means of using piecewise 3-order spline curve to improve the smoothness of curve along the same path. The validity and superiority of the proposed method were studied through simulation and actual machining experiment implemented on a three-axis CNC milling and engraving machine.
Fourthly, to solve the difficult computation and control of contouring error in multi-axis contouring motion, an optimal contouring control method based on task coordinate frame was proposed. By establishing a movable Frenet coordinate frame on a desired trajectory as the task coordinate frame, contouring error was approximated by the normal component of tracking error in the task coordinate frame. Then by transforming the system dynamics from the world coordinate frame to the task coordinate frame, the optimal Linear Quadratic Regulator (LQR) approach was used to design the optimal contouring controller. To improve the contouring accuracy, the weight of normal error component was enhanced. The effect of the proposed method was validated through simulation experiment.
(1)针对光滑曲线的逼近问题,采用直线/圆弧逼近方法进行了设计与对比的研究。以一个平面四分之一椭圆弧为例,根据期望的精度要求分别采用直线和圆弧来逼近该椭圆弧,其中直线逼近采用基于曲率圆模型的等误差法和等参数增量法;圆弧逼近采用基于minimax逼近的最优圆弧逼近和以多边形为中介的双圆弧逼近。通过不同逼近方法的逼近方式与误差控制模型,分别从逼近点数的多少及轨迹的连续性两方面来进行具体设计,并根据仿真实验结果来分析不同参数对逼近误差的影响,以及不同逼近方法对运动控制精度的影响。
(2)针对空间曲面加工中存在的进给速度波动问题,提出了基于时间分割法与数字积分法混合实现的空间直线插补方法及其连续进给运动的实现方法。该插补方法是采用时间分割法中的时间分割原理,对数字积分法中的累加溢出过程按照进给速度的要求采用可控的插补周期进行时间分割,以消除零头距离并实现平滑的进给速度。为配合上述插补方法实现连续进给运动,提出了一种离线分段速度规划方法对由大量微小直线段组成的加工代码进行前瞻预处理,确定每段直线段代码在梯形加减速方法下可以实现的终点速度,以提高加工效率,避免在转角处的冲击。然后,在插补过程中,提出了一种非对称梯形加减速控制方法,采用逐点判断的方式按照非对称梯形速度曲线进行加减速控制。最后,通过仿真实验与实际加工实验对该方法的有效性与优越性进行了研究,其中实际加工实验在三轴数控雕铣机上进行。
(3)针对空间曲面加工中可能出现表面凹坑、光洁度较差等问题,提出了一种基于网格均匀化的刀位轨迹优化方法。该方法在Cimatron软件生成的加工刀位轨迹基础上,分横向光顺与纵向平滑两步进行,首先进行横向光顺,通过建立主导轮廓线并对不规则的点进行修正,以降低相邻刀路倾斜度的变化程度,然后进行纵向平滑,对同一条刀路上的刀位点进行光滑连续直线段的识别,再采用分段三次样条进行拟合,以提高同一刀路上的曲线光滑程度。最后,通过仿真实验与实际加工实验对该方法的有效性与优越性进行了研究,其中实际加工实验在三轴数控雕铣机上进行。
(4)针对在多轴轮廓运动中轮廓误差难以直接计算与控制的问题,提出了一种基于工作坐标系的最优轮廓控制方法。该方法通过在期望轨迹上建立活动的Frenet坐标系作为工作坐标系,用跟踪误差在工作坐标系中的法向分量来近似轮廓误差,将系统动力学方程由全局坐标系变换到工作坐标系,采用最优线性二次型方法来设计最优轮廓控制器,通过提高法向误差分量的权值来改善轮廓精度。最后,通过仿真实验对该方法的效果进行了验证。
Multi-axis contouring motion system is an important branch of motion control technology. Its main use is to accomplish high performance contouring machining. High performance contouring machining is a core technology in modern manufacturing. It is widely applied in many industries and has important strategic sense and high research value. To improve machining quality and efficiency of multi-axis contouring motion system, it is necessary to adopt advanced control strategy to optimize the plan and control of motion trajectory. In this dissertation, a typical contouring motion system - open three-axis CNC milling and engraving control system was developed. The topic of the dissertation is trajectory generation and performance optimization of multi-axis contouring motion system. To solve some key problems in high performance contouring machining and multi-axis contouring control, research was developed systematically and deeply from four aspects, including trajectory approximation, real-time interpolation, trajectory optimization and coordinated control. The main work is as following.
Firstly, to approximate smooth curves, design and comparative research were developed with straight line/circular arc approximation methods. Taking a quarter of a planar ellipse for an example, straight line segments and circular arc segments were adopted respectively to approximate the planar ellipse according to the desired accuracy. In the process of straight line approximation, constant error approach and constant parameter increment approach, which are both based on the model of curvature circle, were applied. In the process of circular arc approximation, optimal circular arc approach, based on the principal of minimax approximation, and bi-arc approach with a polygon approximation were applied. Through the approximation manner and error control model of different approximation methods, detailed design was developed from two aspects including the number of approximation segments and the continuity of the trajectory. According to the result of simulation experiment, the effect of different parameters on approximation error and the effect of different methods on motion control accuracy were analyzed.
Secondly, to solve the feedrate fluctuation in machining three-dimension sculptured surface, a new hybrid space linear interpolation method, based on the principles of Time-division and Digital Differential Analyzer (DDA), and implementation method of continuous feed motion were proposed. This interpolation method applied the principle of time-division to the procedure of accumulation in DDA by means of controlling interpolation cycle time. Therefore, it could eliminate the odd distance and maintains smooth feedrate. To accomplish continuous feed motion in company with this interpolation method, an off-line segmented speed planning method was proposed to preprocess NC codes composed of a large number of short straight line segments in advance and determine a realizable end speed for each straight line segment by means of trapezoid speed curves. Therefore, machining efficiency was improved and jerk at corners was avoided. Then, a non-symmetrical trapezoid acceleration/deceleration control method in the process of interpolation was proposed, which adopted a point-by-point arbitration manner to control acceleration and deceleration according to non-symmetrical trapezoid speed curves. The validity and superiority of the proposed methods were studied through simulation and actual machining experiment implemented on a three-axis CNC milling and engraving machine.
Thirdly, to solve the disadvantages such as surface dents, poor roughness in machining three-dimension sculptured surface, a tool path optimization method based on mesh uniformization was proposed. Based on the original tool path generated by Cimatron software, this method was implemented with two steps including transverse fairing and longitudinal smoothing. In the process of transverse fairing, irregular points were modified by means of constructing the dominant contour to reduce the variety of the inclination degree between the succeeding paths. Then, in the process of longitudinal smoothing, smooth continuous line segments along the same path were identified and fitted by means of using piecewise 3-order spline curve to improve the smoothness of curve along the same path. The validity and superiority of the proposed method were studied through simulation and actual machining experiment implemented on a three-axis CNC milling and engraving machine.
Fourthly, to solve the difficult computation and control of contouring error in multi-axis contouring motion, an optimal contouring control method based on task coordinate frame was proposed. By establishing a movable Frenet coordinate frame on a desired trajectory as the task coordinate frame, contouring error was approximated by the normal component of tracking error in the task coordinate frame. Then by transforming the system dynamics from the world coordinate frame to the task coordinate frame, the optimal Linear Quadratic Regulator (LQR) approach was used to design the optimal contouring controller. To improve the contouring accuracy, the weight of normal error component was enhanced. The effect of the proposed method was validated through simulation experiment.
引文
蔡耀志.1995.显参数曲线的实用圆弧逼近算法[J].浙江大学学报(自然科学版),29(5):576-581.
蔡永林,孙卫青.2002.一种新的平面曲线圆弧插补节点获取方法[J].工程图学学报,23(1):97-103.
曹亦明,徐华,杨泽红等.2005.基于RTLinux的模块化、网络化开放式控制器系统[J].高技术通讯,15(3):32-38.
陈金成.2001.多轴联动高性能数控加工的运动优化与复杂轨迹实时控制策略研究[D]:博士.上海:上海交通大学,43-51.
陈金成,徐志明,徐正飞等.2002.基于分段三次样条曲线的高速加工平滑运动轮廓自适应算法研究[J].机械工程学报,38(5):61-65.
陈金成,徐志明,钟廷修等.2002.机床沿曲线高速加工时的运动学与动力学特性分析[J].机械工程学报,38(1):31-35.
陈金成,钟廷修.2002.基于Gauss-Legendre求积的参数曲线实时插补[J].上海交通大学学报,36(8):1104-1108.
陈玮,周学才.2001.基于网络的开放式机器人通用控制系统的研究[J].华南理工大学学报(自然科学版),29(5):35-37.
丛爽,李泽湘.2006.实用运动控制技术[M].北京:电子工业出版社,1-25.
丛爽,刘宜.2006.多轴协调运动中的交叉耦合控制[J].机械设计与制造,10:166-168.
杜道山,燕存良,李从心.2006.一种实时前瞻的自适应NURBS插补算法[J].上海交通大学学报,40(5):843-847.
冯勇,霍勇进.1996.现代计算机数控系统[M].北京:机械工业出版社,114-117.
冯之敬.1999.机械制造工程原理[M].北京:清华大学出版社,1-7.
高有行.1998.对逐点比较法的改进算法[J].西安电子科技大学学报,25(3):299-303.
葛巧琴.1998.机械CAD/CAM[M].南京:东南大学出版社,127-139.
郭长旺,朱国力,龚时华等.2000.基于组件技术的开放式数控系统研究[J].华中理工大学学报,28(7):38-40.
韩庆瑶,贾桂红.2005.NURBS曲线的数控加工编程预处理[J].机械设计与制造,5):99-101.
胡自化,张平.2000.三次B样条曲线恒速进给实时插补算法的研究[J].制造技术与机床,8):31-33.
金树福.1998.逐点比较法进给速度的稳恒研究[J].上海交通大学学报,32(10):102-104.
康存锋,杨建武,费仁元等.2004.开放式PC型运动控制器的研究[J].中国机械工程15(9):800-802.
雷为民,乔建中,李本忍等.1999.关于软件数控的一些基本构想[J].小型微型计算机系统,20(2):81-87.
李宏胜.2006.T-S模糊交叉耦合协调运动控制研究[J].制造技术与机床3):45-48.
李圣怡,张云洲,张明亮等.2000.交叉耦合算法的超精密数控机床伺服控制[J].制造技术与机床,7):10-13.
李嗣福.2001.计算机控制基础[M].合肥:中国科学技术大学出版社,268-278.
理查德·摩雷,李泽湘,夏恩卡·萨思特里.1998.机器人操作的数学导论[M].北京:机械工业出版社,110-118.
刘宜,丛爽.2007.高性能直线/圆弧插补的设计与对比[C].第26届中国控制会议论文集.张家界:14-18.
刘宜,丛爽.2008.一种基于网格均匀化的刀位轨迹优化方法及其实现[J].中国科学院研究生院学报,25(4):569-578.
卢建彪,雍俊海.2006.二次Bezier曲线的双圆弧样条插值二分算法[J].计算机应用研究,23(8):166-167.
卢艳军,赵波,任立义.2004.基于PC的开放式数控系统控制器[J].机械工程师,8):6-8.
罗欣,李光斌,朱涵梁等.1994.时间分割法抛物线插补算法研究[J].华中理工大学学报,22(7):49-53.
马骋,冯之敬.2000.零幅相误差跟踪控制器[J].清华大学学报(自然科学版),40(5):44-46.
彭芳瑜,何莹,李斌.2006a.NURBS曲线高速插补中的前瞻控制[J].计算机辅助设计与图形学学报,18(5):625-629.
彭芳瑜,李黎,陈徐兵等.2006b.连续小直线段高速高精插补中的动力学约束条件[J].计算机辅助设计与图形学学报,18(12):1812-1816.
彭家贵,陈卿.2002.微分几何[M].北京:高等教育出版社,14-30.
曲永印,赵希梅,郭庆鼎.2006.基于零相位误差跟踪控制器的轮廓误差交叉耦合控制[J].中国机械工程,17(11):1135-1137.
任锟,傅建中,陈子辰.2006.高速加工中速度前瞻控制新算法研究[J].浙江大学学报(工学版),40(11):1985-1988.
沈纪桂.1997.数控加工圆弧拟合的优化方法[J].机械工程学报,33(6):64-69.
孙德茂.2005.数控系统轮廓圆弧插补算法研究[J].制造技术与机床7):121-123.
孙家昶.1977.局部坐标系下的样条函数与圆弧样条曲线[J].数学学报,20(1):28-40.
谈勇,王治森,闫晓婧.2004.基于累加弦长的三次参数样条曲线的插补控制[J].合肥工 业大学学报(自然科学版),27(6):619-622.
田锡天,杨海成,Fichtner.2002.五次插值样条在NC过程链中的应用研究[J].机械科学与技术,21(11):75-77.
屠晓明,刘雄伟.2001.直线Bresenham生成算法的三维推广[J].计算机辅助设计与图形学学报,13(9):779-782.
王爱玲.2002a.现代数控编程技术及应用[M].北京:国防工业出版社,69-73.
王爱玲.2002b.现代数控原理及控制系统[M].北京:国防工业出版社,68-132.
王广炎,张润孝,帅梅等.1999.数控机床的轮廓误差的控制[J].机床与液压,6):59-62.
王永章.1995.机床的数字控制技术[M].哈尔滨:哈尔滨工业大学出版社,78-88.
王宇晗,肖凌剑,曾水生等.2004.小线段高速加工速度衔接数学模型[J].上海交通大学学报,38(6):901-904.
王忠平,田作华.2007.基于矢量的DDA空间圆弧插补算法[J].机械设计与制造,9):164-165.
邬义杰,商允舜.2006.微小直线段插补终点控制算法研究[J].组合机床与自动化加工技术,2):1-2,5.
吴海,于锡纯,徐心和.1998.基于轮廓最优预见的机床进给伺服控制研究[J].中国机械工程,9(9):22-24.
吴宏,蒋仕龙,龚小云等.2004.运动控制器的现状与发展[J].制造技术与机床1):24-27.
吴辉,宁亭.1995.螺旋线及正弦曲线的一种快速插补算法[J].华中理工大学学报,23(5):57-59.
西门子股份公司.2005.Sinurnedk 840D/840Di/810D高级编程手册[EB/OL].联邦德国:西门子股份公司,[2005-01-06].http://www.ad.siemens.com.cn/download/down_file.asp?ClassM= 1&B3ID=00534.
肖本贤,陈荣保.1998.模糊控制用于高精度CNC系统多轴轨迹联动研究[J].合肥工业大学学报(自然科学版),21(4):55-60.
肖本贤,郭福权,邓红辉等.2004.基于干扰观测器的轮廓误差耦合控制研究[J].系统仿真学报,16(4):789-793.
徐志祥,赵国勇,赵福令等.2006.一种基于NURBS插补器的多轴交叉耦合控制方法[J].机械科学与技术,25(12):1451-1453.
杨旭静,钟志华,陈泽忠.2006.自由曲线轮廓加工的圆弧样条刀具路径研究[J].中国机械工程,17(12):1275-1282.
叶伯生,杨叔子.1996.CNC系统中三次参数样条曲线的插补算法[J].华中理工大学学报,24(9):9-11.
叶佩青,赵慎良.2004.微小直线段的连续插补控制算法研究[J].中国机械工程,15(15):1354-1356.
游华云,叶佩青.2002.机床工业亟需发展五轴数控技术[J].制造技术与机床,12):25-28.
游有鹏,王珉,缪群华.2000.样条曲线脉冲增量插补控制[J].制造技术与机床,17(3):40-43.
约翰·奥普里.2005.微分几何及其应用[M].英文第2版.北京:机械工业出版社,19-30.
张广立,谈世哲.2002.基于WindowsNT的开放式机器人控制系统[J].机器人,24(5):443-446.
赵国勇,徐志祥,赵福令.2006.高速高精度数控加工中NURBS曲线插补的研究[J].中国机械工程17(3):291-294.
郑金兴,张铭钧,孟庆鑫.2007.适于高速加工的五次参数样条曲线插补及其速度生成算法的研究[J].哈尔滨工程大学学报,28(7):795-801.
周济,周艳红.2002.数控加工技术[M].北京:国防工业出版社,6-28.
An C H,Atkeson C G,Griffiths J D,et al.1989.Experimental evaluation of feedforward and computed torque control[J].Robotics and Automation,IEEE Transactions on,5(3):368-373.
Babb M.1996.The foundation of open architecture control system[J].Control Engineering,43(1):75-76.
Bahr B,Xiao X,Krishnan K.2001.A real-time scheme of cubic parametric curve interpolations for CNC systems[J].Computers in Industry,45(3):309-317.
Beard T.1996.Machining in Circles[EB/OL].Cincinnati:Gardner Publications,[2008-03-05].http://www.mmsonline.com/articles/079601.html.
Bolton K M.1975.Biarc curves[J].Computer-Aided Design,7(2):89-92.
Bresenham J E.1965.Algorithm for Computer Control of a Digital Plotter[J].IBM Systems Journal,4(1):25-30.
Chai O H,Wong Y S,Poo A N.1994.A DDA parabolic interpolator for computer numerical control of machine tools[J].Mechatronics,4(7):673-692.
Chang Y F.2003.Buffered DDA command generation in a CNC[J].Control Engineering Practice,11(7):797-804.
Chang Y F.2005a.Design and implementation of a linear jerk filter for a computerized numerical controller[J].Control Engineering Practice,13(5):567-576.
Chang Y F.2005b.Generating Commands for Parametric Curve Motion Using Buffered DDA[J].JSME International Journal Series C,48(4):785-793.
Chang Y F,Hong R C.2005.Parametric curve machining of a CNC milling EDM[J].International Journal of Machine Tools and Manufacture,45(7-8):941-948.
Chen N. 2005. Contouring control in high performance motion systems[D]:Master.Hong Kong:Hong Kong University of Science and Technology,35～46.
Cheng H. 2001. Dynamics and control of parallel manipulators with actuation redundancy [D]:Master.Hong Kong:The Hong Kong University of science and Technology,27～36.
Cheng M Y, Tsai M C,Kuo J C. 2002. Real-time NURBS command generators for CNC servo controllers[J] .International Journal of Machine Tools and Manufacture, 42(7):801～813.
Chiang L E. 1994. 3-D CNC trajectory interpolation using Bresenham's algorithm[C]. IEEE International Symposium on Industrial Electronics. Santiago, Chile: IEEE,264～268.
Chiu G T C,Tomizuka M. 1998. Coordinated position control of multi-axis mechanical systems[J].Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, 120(3):389～393.
Chiu G T C,Tomizuka M. 2001. Contouring control of machine tool feed drive systems: A task coordinate frame approach[J].IEEE Transactions on Control Systems Technology, 9(1):130-139.
Chou J J,Yang D C H. 1991. Command generation for three-axis CNC machining[J]. Journal of engineering for industry, 113(3):305～310.
Chou J J,Yang D C H. 1992. On the generation of coordinated motion of five-axis CNC/CMM machines[J].Journal of Engineering for Industry, 114(1):15～22.
Chuang H Y,Chang Y C. 2000. Novel contour error compensator for 3-PRPS platform[J].Journal of Robotic Systems, 17(5):273～289.
Chuang H Y,Chang Y C. 2001. Evaluation of an adaptive weighting cross-coupled controller for a 3-PRPS platform[J].JSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing, 44(1):164-170.
De Souza A F,Coelho R T. 2007. Experimental investigation of feed rate limitations on high speed milling aimed at industrial applications[J].International Journal of Advanced Manufacturing Technology, 32(11-12): 1104-1114.
Devol J. 1954-12-10. Programmed Article Transfer. USA, 2988237[P].
Dong J,Stori J A. 2006. A Generalized Time-Optimal Bidirectional Scan Algorithm for Constrained Feed-Rate Optimization[J].Journal of Dynamic Systems, Measurement, and Control, 128(2):379～390.
Dong J,Stori J A. 2007. Optimal Feed-Rate Scheduling for High-Speed Contouring[J]. Journal of Manufacturing Science and Engineering, 129(1):63～76.
Dong J, Ferreira P M,Stori J A. 2007. Feed-rate optimization with jerk constraints for generating minimum-time trajectories[J].International Journal of Machine Tools and Manufacture, 47(12～13):1941～1955.
Erbatur K, Kaynak M O,Sabanovic A. 1999. A study on robustness property of sliding-mode controllers: a novel design and experimental investigations[J].Industrial Electronics, IEEE Transactions on 46(5):1012～1018.
Erdim H, Lazoglu I,Ozturk B. 2006. Feedrate scheduling strategies for free-form surfaces[J].International Journal of Machine Tools and Manufacture, 46(7～8):747～757.
Erdim H, Lazoglu I,Kaymakci M. 2007. Free-form surface machining and comparing feedrate scheduling strategies[J].Machining Science and Technology, 11(1): 117-133.
Erkorkmaz K,Altintas Y. 2001. High speed CNC system design. Part I: Jerk limited trajectory generation and quintic spline interpolation[J].International Journal of Machine Tools and Manufacture, 41(9):1323～1345.
Erkorkmaz K,Altintas Y. 2005. Quintic spline interpolation with minimal feed fluctuation[J].Journal of Manufacturing Science and Engineering, Transactions of the ASME, 127(2):339～349.
Fang R W,Chen J S. 2002a. A cross-coupling controller using an H∞ scheme and its application to a two-axis direct-drive robot[J]. Journal of Robotic Systems, 19(10):483～497.
Fang R W,Chen J S. 2002b. Cross-coupling control for a direct-drive robot[J].JSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing, 45(3):749～757.
Fang R W,Chen J S. 2004. The design and implementation of a cross-coupling controller for multi-link direct-drive robots[C]. 2004 5th Asian Control Conference. Melbourne,Australia: IEEE,335～342.
FANUC. 2005. 5-axis Machining Features of FANUC Series 30i-A/31i-A5[EB/OL]. Japan: FANUC LTD, [2005-03-05]. http://www.fanuc.co.jp/en/product/new_product/2005/0504/0504_5axismachining.html.
Farouki R T,Shah S. 1996. Real-time CNC interpolators for Pythagorean-hodograph curves[J].Computer Aided Geometric Design, 13(7):583～600.
Farouki R T, Tsai Y F.Yuan G F. 1999. Contour machining of free-form surfaces with real-time PH curve CNC interpolators[J].Computer Aided Geometric Design, 16(1):61～76.
Farouki R T, Manni C,Sestini A. 2001a. Real-time CNC interpolators for Bezier conics[J].Computer Aided Geometric Design, 18(7):639～655.
Farouki R T,Tsai Y F. 2001b. Exact Taylor series coefficients for variable-feedrate CNC curve interpolators[J].Computer-Aided Design, 33(2):155～165.
Fujita S,Yoshida T. 1996. OSEC:Open system environment for controller[C]. 7th International Machine Tool Engineers Conference. Tokyo: IMTEC,234-244.
Han G C, Kim D I, Kim H G, et al. 1999. A High speed machining algorithm for CNC machine tools[C]. The 25th Annual Conference of the IEEE Industrial Electronics Society (IECON'99). San Jose, CA, USA: IEEE,1493～1497.
Hemin G E. 1998. Architecture Who Defines It And Who Benefits[J].Manufacturing Engineering, 121(7):88～89.
Herrin G E. 1990. Next generation controller[J].Modern Machine Shop, 63(7):148～152.
Hoschek J. 1992. Circular splines[J].Computer-Aided Design, 24(11):611-618.
Hu J, Xiao L, Wang Y, et al. 2006. An optimal feedrate model and solution algorithm for a high-speed machine of small line blocks with look-ahead[J].International Journal of Advanced Manufacturing Technology, 28(9):930～935.
Ip R W L, Lau H C W,Chan F T S. 2003. An economical sculptured surface machining approach using fuzzy models and ball-nosed cutters[J] .Journal of Materials Processing Technology, 138(1～3):579～585.
Ko J H,Cho D W. 2004. Feed rate scheduling model considering transverse rupture strength of a tool for 3D ball-end milling[J].International Journal of Machine Tools and Manufacture, 44(10):1047～1059.
Ko J H, Yun W S,Cho D W. 2003. Off-line feed rate scheduling using virtual CNC based on an evaluation of cutting performance[J].Computer-Aided Design, 35(4):383～393.
Kokotovic P V. 1992. The joy of feedback: nonlinear and adaptive[J].Control Systems Magazine, IEEE, 12(3):7～17.
Koren Y. 1976. Interpolator For A Computer Numerical Control System[J].IEEE Transactions on Computers, C-25(1):32～37.
Koren Y. 1979. Design Of Computer Control For Manufacturing Systems[J]. Journal of engineering for industry, 101(3):326～332.
Koren Y. 1980. Cross-coupled Biaxial Computer Control for Manufacturing Systems[J].Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, 102(4):265～272.
Koren Y. 1997. Control of machine tools[J].Journal of Manufacturing Science and Engineering, Transactions of the ASME, 119(4(B)):749～755.
Koren Y,Lo C C. 1991. Variable-Gain Cross-Coupling Controller for Contouring[J].Annual oftheCIRP,40(1):371～374.
Koren Y,Lo C C. 1992. Advanced controllers for feed drives[J].CIRP Annals - Manufacturing Technology, 41(2):689～698
Koren Y, Lo C C,Shpitalni M. 1993. CNC interpolators: algorithms and analysis[C]. ASME PROD ENG DIV PUBL PED. New Orleans, LA, USA: ASME,83-92.
Koren Y,Masory O. 1981. Reference-Pulse Circular Interpolators For CNC Systems[J]. Journal of engineering for industry, 103(1):131-136.
Lei W T, Sung M P, Lin L Y, et al. 2007. Fast real-time NURBS path interpolation for CNC machine tools[J].International Journal of Machine Tools and Manufacture, 47(10):1530～1541.
Li Z Z, Zheng M, Zheng L, et al. 2003. A solid model-based milling process simulation and optimization system integrated with CAD/CAM[J].Journal of Materials Processing Technology, 138(1～3):513～517.
Lim F S, Wong Y S,Rahman M. 1992. Circular interpolators for numerical control. A comparison of the modified DDA techniques and an LSI interpolator[J].Computers in Industry, 18(1):41～52.
Lin M T, Tsai M S.Yau H T. 2007. Development of a dynamics-based NURBS interpolator with real-time look-ahead algorithm[J].International Journal of Machine Tools and Manufacture, 47(15):2246～2262.
Lin R S. 2000. Real-time surface interpolator for 3-D parametric surface machining on 3-axis machine tools[J].International Journal of Machine Tools and Manufacture, 40(10):1513～1526.
Lin R S,Koren Y. 1996. Real-time interpolators for multi-axis CNC machine tools[J].Jounal of Manufacturing Systems, 25(2): 145-149.
Liu X A, Ahmad F A, Yamazaki K A, et al. 2005. Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics[J].International Journal of Machine Tools and Manufacture, 45(4～5):433～444.
Liu X W,Cheng K. 2002. Three-dimensional extension of Bresenham's algorithm and its application in straight-line interpolation[J].Journal of Engineering Manufacture, 216(3):459～463
Lo C C. 1997. Feedback interpolators for CNC machine tools[J] Journal of Manufacturing Science and Engineering, Transactions of the ASME, 119(4(A)):587～592.
Lou Y J, Chen N,Li Z X. 2006. Task Space Based Contouring Control of Parallel Machining Systems[C]. Intelligent Robots and Systems, 2006 IEEE/RSJ International Conference on. Beijing,China: IEEE,2047-2052.
Lue C W, Cheng Y M,Chin J H. 2004. System structure and contour tracking for a hybrid motion platform[J].The International Journal of Advanced Manufacturing Technology 26(11～12):1388～1396.
Luo F Y,Zhou Y F,Yin J.2006.A universal velocity profile generation approach for high-speed machining of small line segments with look-ahead[J].The International Journal of Advanced Manufacturing Technology,35(5-6):505-518.
Marciniak K,Putz B.1984.Approximation of spirals by piecewise curves of fewest circular arc segments[J].Computer-Aided Design,16(2):87-90.
Masory O,Koren Y.1982.Reference-Word Circular Interpolators For CNC Systems[J].Journal of engineering for industry,104(4):400-405.
Mathews J H,Fink K D.2002.数值方法[M].北京:电子工业出版社,207-220.
Meek D S,Walton D J.1992.Approximation of dicrete data by G1 arc splines[J].Computer-Aided Design,24(6):301-306.
Meek D S,Walton D J.1993.Approximating quadratic NURBS curves by arc splines[J].Computer-Aided Design,25(6):371-376.
Meek D S,Walton D J.1995.Approximating smooth planar curves by arc splines[J].Journal of Computational and Applied Mathematics,59(2):221-231.
Nam S H,Yang M Y.2004.A study on a generalized parametric interpolator with real-time jerk-limited acceleration[J].Computer-Aided Design,36(1):27-36.
Neely E C.2000.Five-Axis Is Worth It[J].Manufacturing Engineering,125(5):38-42.
OSACA.2001.OSACA Handbook Version 2.0[EB/OL].Stuttgart:OSACA Association,[2005-02-16].http://www.osaca.org/documentation_and_software/handbook.htm.
Owen J V.1995.Opening up controls architecture[J].Manuufacturing Engineering,11):53-60.
Papaioannou S G,Omirou S L.1996.3-dimensional circular interpolation for CNC machines[J].Journal of Manufacturing Science and Engineering,Transactions of the ASME,118(2):274-277.
Park H.2004.Error-bounded biarc approximation of planar curves[J].Computer-Aided Design,36(12):1241-1251.
Park H,Lee J H.2007.B-spline curve fitting based on adaptive curve refinement using dominant points[J].Computer-Aided Design,39(6):439-451.
Park J,Nam S,Yang M.2005.Development of a real-time trajectory generator for NURBS interpolation based on the two-stage interpolation method[J].International Journal of Advanced Manufacturing Technology,26(4):359-365.
Parsons J.1952-08-14.Machine Tool Numerical Control System.USA,3431478[P].
Piegl L A,Tiller W.2000.Least-squares B-spline curve approximation with arbitrary end derivatives[J].Engineering with Computers,16(2):109-116.
Piegl L A,Tiller W. 2002. Biarc approximation of NURBS curves[J].Computer～Aided Design, 34(11):807～814.
Prischow G, Altintas Y,Jovane F. 2001. Open controller architecturepast,present and future[J].Annals of the CIRP, 50(2):463～470.
Prischow G, Junghans G,Sperling W. 1993. Open system controllers-a challenge for the future of the machine tool industry[J]. Annals of CIRP, 41(1):449～452.
Proctor F M,Albus J S. 1997. Open-architecture Controllers[J].IEEE Spectrum, 34(6):60～64.
Qiu H, Kai C.Yan L. 1997. Optimal circular arc interpolation for NC tool path generation in curve contour manufacturing[J].Computer-Aided Design, 29(11):751～760.
Schuett T. 1996. A Closer Look at Look-Ahead[EB/OL]. Cincinnati: Gardner Publications, [2008-02-28].http://www.mmsonline.com/articles/039603.html.
Shih Y T, Chen C S,Lee A C. 2002. A novel cross-coupling control design for Bi-axis motion[J].International Journal of Machine Tools and Manufacture 42(14):1539～1548.
Srinivasan K,Kulkarni P K. 1990. Cross-coupled control of biaxial feed drive servomechanisms[J].Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, 112(2):225～232.
Sun D, Feng G, Lam C M, et al. 2005. Orientation control of a differential mobile robot through wheel synchronization[J].IEEE/ASME Transactions on Mechatronics, 10(3):345～351.
Sun Y, Wang, J. , Guo, D. 2006. Guide curve based interpolation scheme of parametric curves for precision CNC machining[J].International Journal of Machine Tools and Manufacture, 46(3～4):235～242.
Tomizuka M. 1987. Zero phase error tracking algorithm for digital control [J]. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, 190(1):65～68.
Tounsi N,Elbestawi M A. 2003. Optimized feed scheduling in three axes machining. Part I: Fundamentals of the optimized feed scheduling strategy[J].International Journal of Machine Tools and Manufacture, 43(3):253～267.
Tsai M C, Cheng C W,Cheng M Y. 2003a. A real-time NURBS surface interpolator for precision three-axis CNC machining[J].International Journal of Machine Tools and Manufacture, 43(12):1217～1227.
Tsai M C,Chung C W. 2003b. A real-time predictor-corrector interpolator for CNC machining[J].Journal of Manufacturing Science and Engineering, Transactions of the ASME, 125(3):449～460.
Tsai M S, Nien H W,Yau H T. 2008. An integrated look-ahead dynamic interpolator for NURBS curve[C]. Proceedings of the IEEE Conference on Decision and Control. New Orleans, LA, United States: IEEE, 1868-1873.
Wang F C, Schofield S,Wright P K. 1996. Real time quintic spline interpolator for an open architecture machine tool[C]. Proc of the ASME Dyn Sys Con Div. Atlanta, GA, USA: ASME,291-297.
Wang F C,Wright P K. 1998. Open architecture controllers for machine tools, Part 2: a real time quintic spline interpolator[J].Journal of Manufacturing Science and Engineering, Transactions of the ASME, 120(2):425～432.
Wang F C,Yang D C H. 1993. Nearly arc-length parameterized quintic-spline interpolation for precision machining[J].Computer-Aided Design, 25(5):281-288.
Wang Y Z, Liu T, Fu H Y, et al. 2007. Open Architecture Cnc System Hitcnc And Key Technology[J].Chinese Journal Of Mechanical Engineering(English Edition), 20(2):13～16.
Xiu D X. 1998. Trajectory control of a new class of CNC machine tools[D]:Doctor.Boca Raton,USA:Florida Atlantic University,74～150.
Xu R Z, Xie L, Li C X, et al. 2006. Adaptive parametric interpolation scheme with limited acceleration and jerk values for NC machining[J].The International Journal of Advanced Manufacturing Technology, 36(3～4):343～354.
Xu Z M, Chen J C,Fang Z J. 2002. Performance evaluation of a real-time interpolation algorithm for NURBS curves[J].International Journal of Advanced Manufacturing Technology, 20(4):270～276.
Yang D C H.Chou J J. 1994a. Automatic generation of piecewise constant speed motion with smooth transition for multi-axis machines[J].Joumal of Mechanical Design, Transactions Of the ASME, 116(2):581～586.
Yang D C H,Golub A D. 1994b. Precision trajectory generation for CNC milling of arbitrary contours and surfaces[J].International Journal of Machine Tools and Manufacture, 34(7):1005-1018.
Yang D C H,Kong T. 1994c. Parametric interpolator versus linear interpolator for precision CNC machining[J].Computer-Aided Design, 26(3):225～234.
Yang D C H.Wang F C. 1992. Quintic spline interpolator for motion command generation of computer-controlled machines Scottsdale, AZ, USA: Publ by ASME, New York, NY, USA,537～544.
Yang M Y,Hong W P. 2001. A PC-NC milling machine with new simultaneous 3-axis control algorithm[J]. International Journal of Machine Tools and Manufacture, 41(4):555～566.
Yang M Y,Hong W P. 2002. Three-dimensional reference pulse linear and circular interpolators for CNC systems[J].International Journal of Production Research, 40(2):425～439.
Yang X. 2002. Efficient circular arc interpolation based on active tolerance control[J].Computer-Aided Design, 34(13):1037～1046.
Yang X.Chen Z C. 2005. A new high precision fitting approach for nurbs tool paths generation[C]. Proceedings of the 25 thCIE Conference. Long Beach, USA: ASME,255-262.
Yang X,Chen Z C. 2006. A practicable approach to G1 biarc approximations for making accurate, smooth and non-gouged profile features in CNC contouring[J] .Computer-Aided Design, 38(11):1205～1213.
Yau H T,Kuo M J. 2001. NURBS machining and feed rate adjustment for high-speed cutting of complex sculptured surfaces[J].International Journal of Production Research, 39(1):21～41.
Yau H T, Lin M T,Tsai M S. 2006. Real-time NURBS interpolation using FPGA for high speed motion control[J].CAD Computer Aided Design, 38(10):1123-1133.
Yau H T, Wang J B,Chen W C. 2005. Development and implementation for real-time lookahead interpolator by using Bezier curve to fit CNC continuous short blocks[C]. Proceedings of the 2005 IEEE International Conference on Mechatronics, ICM'05. Taipei: IEEE,78～83.
Yau H T,Wang J B. 2007a. Fast Bezier interpolator with real-time lookahead function for high-accuracy machining[J].International Journal of Machine Tools and Manufacture, 47(10):1518～1529.
Yau H T, Wang J B, Hsu C Y, et al. 2007b. PC-based controller with real-time look-ahead NURBS interpolator[J].Computer-Aided Design and Applications, 4(1～6):331-340.
Yeh S S,Hsu P L. 1997. Theory and applications of the robust cross-coupled control design[C]. Proceedings of the American Control Conference. Albuquerque, New Mexico: IEEE,791-795.
Yeh S S,Hsu P L. 1999a. Speed-controlled interpolator for machining parametric curves[J].Computer-Aided Design, 31(5):349～357.
Yeh S S,Hsu P L. 1999b. Analysis and design of the integrated controller for precise motion systems[J].IEEE Transactions on Control Systems Technology, 7(6):706～717
Yeh S S,Hsu P L. 2002. Estimation of the contouring error vector for the cross-coupledcontrol design[J].Mechatronics, IEEE/ASME Transactions on, 7(1):44～51.
Yeh S S,Hsu P L. 2003. Analysis and design of integrated control for multi-axis motion systems[J].Control Systems Technology, IEEE Transactions on, 11(3):375～382.
Yong T,Narayanaswami R. 2003. A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining[J].Computer Aided Design, 35(13):1249～1259.
Yue Y, Han Q,Wang Z. 2006. An Approximation Method of NURBS Curves in NC Machining[J].Journal of Wuhan University Of Technology(English Edition), 28(2):734～736.
Zhang D J, Lou Y J,Li Z X. 2006. Geometric Contouring Control on the Smooth Surface[C]. Intelligent Robots and Systems, 2006 IEEE/RSJ International Conference on. Beijing,China: IEEE,4496～4501.
Zhang H X, Yuan K,Mei S Q. 2006. Fuzzy logic cross-coupling control of wheeled mobile robots[C]. 2006 IEEE International Conference on Mechatronics and Automation, ICMA 2006. Luoyang. China: IEEE,740～744.
Zhang Q Y. 1996. Real-time NURBS curve trajectory generation for a robot using an open-architecture controller[D]:Doctor.Lawrence,USA:University of Kansas,65～80.
Zhang Q Y,Greenway R B. 1998. Development and implementation of a NURBS curve motion interpolator[J]. Robotics and Computer-Integrated Manufacturing, 14(1):27～36.
Zheng J X, Zhang M J,Meng Q X. 2006. Study of Quintic Spline Interpolation and Generated Velocity Profile for High Speed Machining[J]. Journal Of Wuhan University Of Technology(English Edition), 28(2):507～512.
蔡永林,孙卫青.2002.一种新的平面曲线圆弧插补节点获取方法[J].工程图学学报,23(1):97-103.
曹亦明,徐华,杨泽红等.2005.基于RTLinux的模块化、网络化开放式控制器系统[J].高技术通讯,15(3):32-38.
陈金成.2001.多轴联动高性能数控加工的运动优化与复杂轨迹实时控制策略研究[D]:博士.上海:上海交通大学,43-51.
陈金成,徐志明,徐正飞等.2002.基于分段三次样条曲线的高速加工平滑运动轮廓自适应算法研究[J].机械工程学报,38(5):61-65.
陈金成,徐志明,钟廷修等.2002.机床沿曲线高速加工时的运动学与动力学特性分析[J].机械工程学报,38(1):31-35.
陈金成,钟廷修.2002.基于Gauss-Legendre求积的参数曲线实时插补[J].上海交通大学学报,36(8):1104-1108.
陈玮,周学才.2001.基于网络的开放式机器人通用控制系统的研究[J].华南理工大学学报(自然科学版),29(5):35-37.
丛爽,李泽湘.2006.实用运动控制技术[M].北京:电子工业出版社,1-25.
丛爽,刘宜.2006.多轴协调运动中的交叉耦合控制[J].机械设计与制造,10:166-168.
杜道山,燕存良,李从心.2006.一种实时前瞻的自适应NURBS插补算法[J].上海交通大学学报,40(5):843-847.
冯勇,霍勇进.1996.现代计算机数控系统[M].北京:机械工业出版社,114-117.
冯之敬.1999.机械制造工程原理[M].北京:清华大学出版社,1-7.
高有行.1998.对逐点比较法的改进算法[J].西安电子科技大学学报,25(3):299-303.
葛巧琴.1998.机械CAD/CAM[M].南京:东南大学出版社,127-139.
郭长旺,朱国力,龚时华等.2000.基于组件技术的开放式数控系统研究[J].华中理工大学学报,28(7):38-40.
韩庆瑶,贾桂红.2005.NURBS曲线的数控加工编程预处理[J].机械设计与制造,5):99-101.
胡自化,张平.2000.三次B样条曲线恒速进给实时插补算法的研究[J].制造技术与机床,8):31-33.
金树福.1998.逐点比较法进给速度的稳恒研究[J].上海交通大学学报,32(10):102-104.
康存锋,杨建武,费仁元等.2004.开放式PC型运动控制器的研究[J].中国机械工程15(9):800-802.
雷为民,乔建中,李本忍等.1999.关于软件数控的一些基本构想[J].小型微型计算机系统,20(2):81-87.
李宏胜.2006.T-S模糊交叉耦合协调运动控制研究[J].制造技术与机床3):45-48.
李圣怡,张云洲,张明亮等.2000.交叉耦合算法的超精密数控机床伺服控制[J].制造技术与机床,7):10-13.
李嗣福.2001.计算机控制基础[M].合肥:中国科学技术大学出版社,268-278.
理查德·摩雷,李泽湘,夏恩卡·萨思特里.1998.机器人操作的数学导论[M].北京:机械工业出版社,110-118.
刘宜,丛爽.2007.高性能直线/圆弧插补的设计与对比[C].第26届中国控制会议论文集.张家界:14-18.
刘宜,丛爽.2008.一种基于网格均匀化的刀位轨迹优化方法及其实现[J].中国科学院研究生院学报,25(4):569-578.
卢建彪,雍俊海.2006.二次Bezier曲线的双圆弧样条插值二分算法[J].计算机应用研究,23(8):166-167.
卢艳军,赵波,任立义.2004.基于PC的开放式数控系统控制器[J].机械工程师,8):6-8.
罗欣,李光斌,朱涵梁等.1994.时间分割法抛物线插补算法研究[J].华中理工大学学报,22(7):49-53.
马骋,冯之敬.2000.零幅相误差跟踪控制器[J].清华大学学报(自然科学版),40(5):44-46.
彭芳瑜,何莹,李斌.2006a.NURBS曲线高速插补中的前瞻控制[J].计算机辅助设计与图形学学报,18(5):625-629.
彭芳瑜,李黎,陈徐兵等.2006b.连续小直线段高速高精插补中的动力学约束条件[J].计算机辅助设计与图形学学报,18(12):1812-1816.
彭家贵,陈卿.2002.微分几何[M].北京:高等教育出版社,14-30.
曲永印,赵希梅,郭庆鼎.2006.基于零相位误差跟踪控制器的轮廓误差交叉耦合控制[J].中国机械工程,17(11):1135-1137.
任锟,傅建中,陈子辰.2006.高速加工中速度前瞻控制新算法研究[J].浙江大学学报(工学版),40(11):1985-1988.
沈纪桂.1997.数控加工圆弧拟合的优化方法[J].机械工程学报,33(6):64-69.
孙德茂.2005.数控系统轮廓圆弧插补算法研究[J].制造技术与机床7):121-123.
孙家昶.1977.局部坐标系下的样条函数与圆弧样条曲线[J].数学学报,20(1):28-40.
谈勇,王治森,闫晓婧.2004.基于累加弦长的三次参数样条曲线的插补控制[J].合肥工 业大学学报(自然科学版),27(6):619-622.
田锡天,杨海成,Fichtner.2002.五次插值样条在NC过程链中的应用研究[J].机械科学与技术,21(11):75-77.
屠晓明,刘雄伟.2001.直线Bresenham生成算法的三维推广[J].计算机辅助设计与图形学学报,13(9):779-782.
王爱玲.2002a.现代数控编程技术及应用[M].北京:国防工业出版社,69-73.
王爱玲.2002b.现代数控原理及控制系统[M].北京:国防工业出版社,68-132.
王广炎,张润孝,帅梅等.1999.数控机床的轮廓误差的控制[J].机床与液压,6):59-62.
王永章.1995.机床的数字控制技术[M].哈尔滨:哈尔滨工业大学出版社,78-88.
王宇晗,肖凌剑,曾水生等.2004.小线段高速加工速度衔接数学模型[J].上海交通大学学报,38(6):901-904.
王忠平,田作华.2007.基于矢量的DDA空间圆弧插补算法[J].机械设计与制造,9):164-165.
邬义杰,商允舜.2006.微小直线段插补终点控制算法研究[J].组合机床与自动化加工技术,2):1-2,5.
吴海,于锡纯,徐心和.1998.基于轮廓最优预见的机床进给伺服控制研究[J].中国机械工程,9(9):22-24.
吴宏,蒋仕龙,龚小云等.2004.运动控制器的现状与发展[J].制造技术与机床1):24-27.
吴辉,宁亭.1995.螺旋线及正弦曲线的一种快速插补算法[J].华中理工大学学报,23(5):57-59.
西门子股份公司.2005.Sinurnedk 840D/840Di/810D高级编程手册[EB/OL].联邦德国:西门子股份公司,[2005-01-06].http://www.ad.siemens.com.cn/download/down_file.asp?ClassM= 1&B3ID=00534.
肖本贤,陈荣保.1998.模糊控制用于高精度CNC系统多轴轨迹联动研究[J].合肥工业大学学报(自然科学版),21(4):55-60.
肖本贤,郭福权,邓红辉等.2004.基于干扰观测器的轮廓误差耦合控制研究[J].系统仿真学报,16(4):789-793.
徐志祥,赵国勇,赵福令等.2006.一种基于NURBS插补器的多轴交叉耦合控制方法[J].机械科学与技术,25(12):1451-1453.
杨旭静,钟志华,陈泽忠.2006.自由曲线轮廓加工的圆弧样条刀具路径研究[J].中国机械工程,17(12):1275-1282.
叶伯生,杨叔子.1996.CNC系统中三次参数样条曲线的插补算法[J].华中理工大学学报,24(9):9-11.
叶佩青,赵慎良.2004.微小直线段的连续插补控制算法研究[J].中国机械工程,15(15):1354-1356.
游华云,叶佩青.2002.机床工业亟需发展五轴数控技术[J].制造技术与机床,12):25-28.
游有鹏,王珉,缪群华.2000.样条曲线脉冲增量插补控制[J].制造技术与机床,17(3):40-43.
约翰·奥普里.2005.微分几何及其应用[M].英文第2版.北京:机械工业出版社,19-30.
张广立,谈世哲.2002.基于WindowsNT的开放式机器人控制系统[J].机器人,24(5):443-446.
赵国勇,徐志祥,赵福令.2006.高速高精度数控加工中NURBS曲线插补的研究[J].中国机械工程17(3):291-294.
郑金兴,张铭钧,孟庆鑫.2007.适于高速加工的五次参数样条曲线插补及其速度生成算法的研究[J].哈尔滨工程大学学报,28(7):795-801.
周济,周艳红.2002.数控加工技术[M].北京:国防工业出版社,6-28.
An C H,Atkeson C G,Griffiths J D,et al.1989.Experimental evaluation of feedforward and computed torque control[J].Robotics and Automation,IEEE Transactions on,5(3):368-373.
Babb M.1996.The foundation of open architecture control system[J].Control Engineering,43(1):75-76.
Bahr B,Xiao X,Krishnan K.2001.A real-time scheme of cubic parametric curve interpolations for CNC systems[J].Computers in Industry,45(3):309-317.
Beard T.1996.Machining in Circles[EB/OL].Cincinnati:Gardner Publications,[2008-03-05].http://www.mmsonline.com/articles/079601.html.
Bolton K M.1975.Biarc curves[J].Computer-Aided Design,7(2):89-92.
Bresenham J E.1965.Algorithm for Computer Control of a Digital Plotter[J].IBM Systems Journal,4(1):25-30.
Chai O H,Wong Y S,Poo A N.1994.A DDA parabolic interpolator for computer numerical control of machine tools[J].Mechatronics,4(7):673-692.
Chang Y F.2003.Buffered DDA command generation in a CNC[J].Control Engineering Practice,11(7):797-804.
Chang Y F.2005a.Design and implementation of a linear jerk filter for a computerized numerical controller[J].Control Engineering Practice,13(5):567-576.
Chang Y F.2005b.Generating Commands for Parametric Curve Motion Using Buffered DDA[J].JSME International Journal Series C,48(4):785-793.
Chang Y F,Hong R C.2005.Parametric curve machining of a CNC milling EDM[J].International Journal of Machine Tools and Manufacture,45(7-8):941-948.
Chen N. 2005. Contouring control in high performance motion systems[D]:Master.Hong Kong:Hong Kong University of Science and Technology,35～46.
Cheng H. 2001. Dynamics and control of parallel manipulators with actuation redundancy [D]:Master.Hong Kong:The Hong Kong University of science and Technology,27～36.
Cheng M Y, Tsai M C,Kuo J C. 2002. Real-time NURBS command generators for CNC servo controllers[J] .International Journal of Machine Tools and Manufacture, 42(7):801～813.
Chiang L E. 1994. 3-D CNC trajectory interpolation using Bresenham's algorithm[C]. IEEE International Symposium on Industrial Electronics. Santiago, Chile: IEEE,264～268.
Chiu G T C,Tomizuka M. 1998. Coordinated position control of multi-axis mechanical systems[J].Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, 120(3):389～393.
Chiu G T C,Tomizuka M. 2001. Contouring control of machine tool feed drive systems: A task coordinate frame approach[J].IEEE Transactions on Control Systems Technology, 9(1):130-139.
Chou J J,Yang D C H. 1991. Command generation for three-axis CNC machining[J]. Journal of engineering for industry, 113(3):305～310.
Chou J J,Yang D C H. 1992. On the generation of coordinated motion of five-axis CNC/CMM machines[J].Journal of Engineering for Industry, 114(1):15～22.
Chuang H Y,Chang Y C. 2000. Novel contour error compensator for 3-PRPS platform[J].Journal of Robotic Systems, 17(5):273～289.
Chuang H Y,Chang Y C. 2001. Evaluation of an adaptive weighting cross-coupled controller for a 3-PRPS platform[J].JSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing, 44(1):164-170.
De Souza A F,Coelho R T. 2007. Experimental investigation of feed rate limitations on high speed milling aimed at industrial applications[J].International Journal of Advanced Manufacturing Technology, 32(11-12): 1104-1114.
Devol J. 1954-12-10. Programmed Article Transfer. USA, 2988237[P].
Dong J,Stori J A. 2006. A Generalized Time-Optimal Bidirectional Scan Algorithm for Constrained Feed-Rate Optimization[J].Journal of Dynamic Systems, Measurement, and Control, 128(2):379～390.
Dong J,Stori J A. 2007. Optimal Feed-Rate Scheduling for High-Speed Contouring[J]. Journal of Manufacturing Science and Engineering, 129(1):63～76.
Dong J, Ferreira P M,Stori J A. 2007. Feed-rate optimization with jerk constraints for generating minimum-time trajectories[J].International Journal of Machine Tools and Manufacture, 47(12～13):1941～1955.
Erbatur K, Kaynak M O,Sabanovic A. 1999. A study on robustness property of sliding-mode controllers: a novel design and experimental investigations[J].Industrial Electronics, IEEE Transactions on 46(5):1012～1018.
Erdim H, Lazoglu I,Ozturk B. 2006. Feedrate scheduling strategies for free-form surfaces[J].International Journal of Machine Tools and Manufacture, 46(7～8):747～757.
Erdim H, Lazoglu I,Kaymakci M. 2007. Free-form surface machining and comparing feedrate scheduling strategies[J].Machining Science and Technology, 11(1): 117-133.
Erkorkmaz K,Altintas Y. 2001. High speed CNC system design. Part I: Jerk limited trajectory generation and quintic spline interpolation[J].International Journal of Machine Tools and Manufacture, 41(9):1323～1345.
Erkorkmaz K,Altintas Y. 2005. Quintic spline interpolation with minimal feed fluctuation[J].Journal of Manufacturing Science and Engineering, Transactions of the ASME, 127(2):339～349.
Fang R W,Chen J S. 2002a. A cross-coupling controller using an H∞ scheme and its application to a two-axis direct-drive robot[J]. Journal of Robotic Systems, 19(10):483～497.
Fang R W,Chen J S. 2002b. Cross-coupling control for a direct-drive robot[J].JSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing, 45(3):749～757.
Fang R W,Chen J S. 2004. The design and implementation of a cross-coupling controller for multi-link direct-drive robots[C]. 2004 5th Asian Control Conference. Melbourne,Australia: IEEE,335～342.
FANUC. 2005. 5-axis Machining Features of FANUC Series 30i-A/31i-A5[EB/OL]. Japan: FANUC LTD, [2005-03-05]. http://www.fanuc.co.jp/en/product/new_product/2005/0504/0504_5axismachining.html.
Farouki R T,Shah S. 1996. Real-time CNC interpolators for Pythagorean-hodograph curves[J].Computer Aided Geometric Design, 13(7):583～600.
Farouki R T, Tsai Y F.Yuan G F. 1999. Contour machining of free-form surfaces with real-time PH curve CNC interpolators[J].Computer Aided Geometric Design, 16(1):61～76.
Farouki R T, Manni C,Sestini A. 2001a. Real-time CNC interpolators for Bezier conics[J].Computer Aided Geometric Design, 18(7):639～655.
Farouki R T,Tsai Y F. 2001b. Exact Taylor series coefficients for variable-feedrate CNC curve interpolators[J].Computer-Aided Design, 33(2):155～165.
Fujita S,Yoshida T. 1996. OSEC:Open system environment for controller[C]. 7th International Machine Tool Engineers Conference. Tokyo: IMTEC,234-244.
Han G C, Kim D I, Kim H G, et al. 1999. A High speed machining algorithm for CNC machine tools[C]. The 25th Annual Conference of the IEEE Industrial Electronics Society (IECON'99). San Jose, CA, USA: IEEE,1493～1497.
Hemin G E. 1998. Architecture Who Defines It And Who Benefits[J].Manufacturing Engineering, 121(7):88～89.
Herrin G E. 1990. Next generation controller[J].Modern Machine Shop, 63(7):148～152.
Hoschek J. 1992. Circular splines[J].Computer-Aided Design, 24(11):611-618.
Hu J, Xiao L, Wang Y, et al. 2006. An optimal feedrate model and solution algorithm for a high-speed machine of small line blocks with look-ahead[J].International Journal of Advanced Manufacturing Technology, 28(9):930～935.
Ip R W L, Lau H C W,Chan F T S. 2003. An economical sculptured surface machining approach using fuzzy models and ball-nosed cutters[J] .Journal of Materials Processing Technology, 138(1～3):579～585.
Ko J H,Cho D W. 2004. Feed rate scheduling model considering transverse rupture strength of a tool for 3D ball-end milling[J].International Journal of Machine Tools and Manufacture, 44(10):1047～1059.
Ko J H, Yun W S,Cho D W. 2003. Off-line feed rate scheduling using virtual CNC based on an evaluation of cutting performance[J].Computer-Aided Design, 35(4):383～393.
Kokotovic P V. 1992. The joy of feedback: nonlinear and adaptive[J].Control Systems Magazine, IEEE, 12(3):7～17.
Koren Y. 1976. Interpolator For A Computer Numerical Control System[J].IEEE Transactions on Computers, C-25(1):32～37.
Koren Y. 1979. Design Of Computer Control For Manufacturing Systems[J]. Journal of engineering for industry, 101(3):326～332.
Koren Y. 1980. Cross-coupled Biaxial Computer Control for Manufacturing Systems[J].Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, 102(4):265～272.
Koren Y. 1997. Control of machine tools[J].Journal of Manufacturing Science and Engineering, Transactions of the ASME, 119(4(B)):749～755.
Koren Y,Lo C C. 1991. Variable-Gain Cross-Coupling Controller for Contouring[J].Annual oftheCIRP,40(1):371～374.
Koren Y,Lo C C. 1992. Advanced controllers for feed drives[J].CIRP Annals - Manufacturing Technology, 41(2):689～698
Koren Y, Lo C C,Shpitalni M. 1993. CNC interpolators: algorithms and analysis[C]. ASME PROD ENG DIV PUBL PED. New Orleans, LA, USA: ASME,83-92.
Koren Y,Masory O. 1981. Reference-Pulse Circular Interpolators For CNC Systems[J]. Journal of engineering for industry, 103(1):131-136.
Lei W T, Sung M P, Lin L Y, et al. 2007. Fast real-time NURBS path interpolation for CNC machine tools[J].International Journal of Machine Tools and Manufacture, 47(10):1530～1541.
Li Z Z, Zheng M, Zheng L, et al. 2003. A solid model-based milling process simulation and optimization system integrated with CAD/CAM[J].Journal of Materials Processing Technology, 138(1～3):513～517.
Lim F S, Wong Y S,Rahman M. 1992. Circular interpolators for numerical control. A comparison of the modified DDA techniques and an LSI interpolator[J].Computers in Industry, 18(1):41～52.
Lin M T, Tsai M S.Yau H T. 2007. Development of a dynamics-based NURBS interpolator with real-time look-ahead algorithm[J].International Journal of Machine Tools and Manufacture, 47(15):2246～2262.
Lin R S. 2000. Real-time surface interpolator for 3-D parametric surface machining on 3-axis machine tools[J].International Journal of Machine Tools and Manufacture, 40(10):1513～1526.
Lin R S,Koren Y. 1996. Real-time interpolators for multi-axis CNC machine tools[J].Jounal of Manufacturing Systems, 25(2): 145-149.
Liu X A, Ahmad F A, Yamazaki K A, et al. 2005. Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics[J].International Journal of Machine Tools and Manufacture, 45(4～5):433～444.
Liu X W,Cheng K. 2002. Three-dimensional extension of Bresenham's algorithm and its application in straight-line interpolation[J].Journal of Engineering Manufacture, 216(3):459～463
Lo C C. 1997. Feedback interpolators for CNC machine tools[J] Journal of Manufacturing Science and Engineering, Transactions of the ASME, 119(4(A)):587～592.
Lou Y J, Chen N,Li Z X. 2006. Task Space Based Contouring Control of Parallel Machining Systems[C]. Intelligent Robots and Systems, 2006 IEEE/RSJ International Conference on. Beijing,China: IEEE,2047-2052.
Lue C W, Cheng Y M,Chin J H. 2004. System structure and contour tracking for a hybrid motion platform[J].The International Journal of Advanced Manufacturing Technology 26(11～12):1388～1396.
Luo F Y,Zhou Y F,Yin J.2006.A universal velocity profile generation approach for high-speed machining of small line segments with look-ahead[J].The International Journal of Advanced Manufacturing Technology,35(5-6):505-518.
Marciniak K,Putz B.1984.Approximation of spirals by piecewise curves of fewest circular arc segments[J].Computer-Aided Design,16(2):87-90.
Masory O,Koren Y.1982.Reference-Word Circular Interpolators For CNC Systems[J].Journal of engineering for industry,104(4):400-405.
Mathews J H,Fink K D.2002.数值方法[M].北京:电子工业出版社,207-220.
Meek D S,Walton D J.1992.Approximation of dicrete data by G1 arc splines[J].Computer-Aided Design,24(6):301-306.
Meek D S,Walton D J.1993.Approximating quadratic NURBS curves by arc splines[J].Computer-Aided Design,25(6):371-376.
Meek D S,Walton D J.1995.Approximating smooth planar curves by arc splines[J].Journal of Computational and Applied Mathematics,59(2):221-231.
Nam S H,Yang M Y.2004.A study on a generalized parametric interpolator with real-time jerk-limited acceleration[J].Computer-Aided Design,36(1):27-36.
Neely E C.2000.Five-Axis Is Worth It[J].Manufacturing Engineering,125(5):38-42.
OSACA.2001.OSACA Handbook Version 2.0[EB/OL].Stuttgart:OSACA Association,[2005-02-16].http://www.osaca.org/documentation_and_software/handbook.htm.
Owen J V.1995.Opening up controls architecture[J].Manuufacturing Engineering,11):53-60.
Papaioannou S G,Omirou S L.1996.3-dimensional circular interpolation for CNC machines[J].Journal of Manufacturing Science and Engineering,Transactions of the ASME,118(2):274-277.
Park H.2004.Error-bounded biarc approximation of planar curves[J].Computer-Aided Design,36(12):1241-1251.
Park H,Lee J H.2007.B-spline curve fitting based on adaptive curve refinement using dominant points[J].Computer-Aided Design,39(6):439-451.
Park J,Nam S,Yang M.2005.Development of a real-time trajectory generator for NURBS interpolation based on the two-stage interpolation method[J].International Journal of Advanced Manufacturing Technology,26(4):359-365.
Parsons J.1952-08-14.Machine Tool Numerical Control System.USA,3431478[P].
Piegl L A,Tiller W.2000.Least-squares B-spline curve approximation with arbitrary end derivatives[J].Engineering with Computers,16(2):109-116.
Piegl L A,Tiller W. 2002. Biarc approximation of NURBS curves[J].Computer～Aided Design, 34(11):807～814.
Prischow G, Altintas Y,Jovane F. 2001. Open controller architecturepast,present and future[J].Annals of the CIRP, 50(2):463～470.
Prischow G, Junghans G,Sperling W. 1993. Open system controllers-a challenge for the future of the machine tool industry[J]. Annals of CIRP, 41(1):449～452.
Proctor F M,Albus J S. 1997. Open-architecture Controllers[J].IEEE Spectrum, 34(6):60～64.
Qiu H, Kai C.Yan L. 1997. Optimal circular arc interpolation for NC tool path generation in curve contour manufacturing[J].Computer-Aided Design, 29(11):751～760.
Schuett T. 1996. A Closer Look at Look-Ahead[EB/OL]. Cincinnati: Gardner Publications, [2008-02-28].http://www.mmsonline.com/articles/039603.html.
Shih Y T, Chen C S,Lee A C. 2002. A novel cross-coupling control design for Bi-axis motion[J].International Journal of Machine Tools and Manufacture 42(14):1539～1548.
Srinivasan K,Kulkarni P K. 1990. Cross-coupled control of biaxial feed drive servomechanisms[J].Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, 112(2):225～232.
Sun D, Feng G, Lam C M, et al. 2005. Orientation control of a differential mobile robot through wheel synchronization[J].IEEE/ASME Transactions on Mechatronics, 10(3):345～351.
Sun Y, Wang, J. , Guo, D. 2006. Guide curve based interpolation scheme of parametric curves for precision CNC machining[J].International Journal of Machine Tools and Manufacture, 46(3～4):235～242.
Tomizuka M. 1987. Zero phase error tracking algorithm for digital control [J]. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, 190(1):65～68.
Tounsi N,Elbestawi M A. 2003. Optimized feed scheduling in three axes machining. Part I: Fundamentals of the optimized feed scheduling strategy[J].International Journal of Machine Tools and Manufacture, 43(3):253～267.
Tsai M C, Cheng C W,Cheng M Y. 2003a. A real-time NURBS surface interpolator for precision three-axis CNC machining[J].International Journal of Machine Tools and Manufacture, 43(12):1217～1227.
Tsai M C,Chung C W. 2003b. A real-time predictor-corrector interpolator for CNC machining[J].Journal of Manufacturing Science and Engineering, Transactions of the ASME, 125(3):449～460.
Tsai M S, Nien H W,Yau H T. 2008. An integrated look-ahead dynamic interpolator for NURBS curve[C]. Proceedings of the IEEE Conference on Decision and Control. New Orleans, LA, United States: IEEE, 1868-1873.
Wang F C, Schofield S,Wright P K. 1996. Real time quintic spline interpolator for an open architecture machine tool[C]. Proc of the ASME Dyn Sys Con Div. Atlanta, GA, USA: ASME,291-297.
Wang F C,Wright P K. 1998. Open architecture controllers for machine tools, Part 2: a real time quintic spline interpolator[J].Journal of Manufacturing Science and Engineering, Transactions of the ASME, 120(2):425～432.
Wang F C,Yang D C H. 1993. Nearly arc-length parameterized quintic-spline interpolation for precision machining[J].Computer-Aided Design, 25(5):281-288.
Wang Y Z, Liu T, Fu H Y, et al. 2007. Open Architecture Cnc System Hitcnc And Key Technology[J].Chinese Journal Of Mechanical Engineering(English Edition), 20(2):13～16.
Xiu D X. 1998. Trajectory control of a new class of CNC machine tools[D]:Doctor.Boca Raton,USA:Florida Atlantic University,74～150.
Xu R Z, Xie L, Li C X, et al. 2006. Adaptive parametric interpolation scheme with limited acceleration and jerk values for NC machining[J].The International Journal of Advanced Manufacturing Technology, 36(3～4):343～354.
Xu Z M, Chen J C,Fang Z J. 2002. Performance evaluation of a real-time interpolation algorithm for NURBS curves[J].International Journal of Advanced Manufacturing Technology, 20(4):270～276.
Yang D C H.Chou J J. 1994a. Automatic generation of piecewise constant speed motion with smooth transition for multi-axis machines[J].Joumal of Mechanical Design, Transactions Of the ASME, 116(2):581～586.
Yang D C H,Golub A D. 1994b. Precision trajectory generation for CNC milling of arbitrary contours and surfaces[J].International Journal of Machine Tools and Manufacture, 34(7):1005-1018.
Yang D C H,Kong T. 1994c. Parametric interpolator versus linear interpolator for precision CNC machining[J].Computer-Aided Design, 26(3):225～234.
Yang D C H.Wang F C. 1992. Quintic spline interpolator for motion command generation of computer-controlled machines Scottsdale, AZ, USA: Publ by ASME, New York, NY, USA,537～544.
Yang M Y,Hong W P. 2001. A PC-NC milling machine with new simultaneous 3-axis control algorithm[J]. International Journal of Machine Tools and Manufacture, 41(4):555～566.
Yang M Y,Hong W P. 2002. Three-dimensional reference pulse linear and circular interpolators for CNC systems[J].International Journal of Production Research, 40(2):425～439.
Yang X. 2002. Efficient circular arc interpolation based on active tolerance control[J].Computer-Aided Design, 34(13):1037～1046.
Yang X.Chen Z C. 2005. A new high precision fitting approach for nurbs tool paths generation[C]. Proceedings of the 25 thCIE Conference. Long Beach, USA: ASME,255-262.
Yang X,Chen Z C. 2006. A practicable approach to G1 biarc approximations for making accurate, smooth and non-gouged profile features in CNC contouring[J] .Computer-Aided Design, 38(11):1205～1213.
Yau H T,Kuo M J. 2001. NURBS machining and feed rate adjustment for high-speed cutting of complex sculptured surfaces[J].International Journal of Production Research, 39(1):21～41.
Yau H T, Lin M T,Tsai M S. 2006. Real-time NURBS interpolation using FPGA for high speed motion control[J].CAD Computer Aided Design, 38(10):1123-1133.
Yau H T, Wang J B,Chen W C. 2005. Development and implementation for real-time lookahead interpolator by using Bezier curve to fit CNC continuous short blocks[C]. Proceedings of the 2005 IEEE International Conference on Mechatronics, ICM'05. Taipei: IEEE,78～83.
Yau H T,Wang J B. 2007a. Fast Bezier interpolator with real-time lookahead function for high-accuracy machining[J].International Journal of Machine Tools and Manufacture, 47(10):1518～1529.
Yau H T, Wang J B, Hsu C Y, et al. 2007b. PC-based controller with real-time look-ahead NURBS interpolator[J].Computer-Aided Design and Applications, 4(1～6):331-340.
Yeh S S,Hsu P L. 1997. Theory and applications of the robust cross-coupled control design[C]. Proceedings of the American Control Conference. Albuquerque, New Mexico: IEEE,791-795.
Yeh S S,Hsu P L. 1999a. Speed-controlled interpolator for machining parametric curves[J].Computer-Aided Design, 31(5):349～357.
Yeh S S,Hsu P L. 1999b. Analysis and design of the integrated controller for precise motion systems[J].IEEE Transactions on Control Systems Technology, 7(6):706～717
Yeh S S,Hsu P L. 2002. Estimation of the contouring error vector for the cross-coupledcontrol design[J].Mechatronics, IEEE/ASME Transactions on, 7(1):44～51.
Yeh S S,Hsu P L. 2003. Analysis and design of integrated control for multi-axis motion systems[J].Control Systems Technology, IEEE Transactions on, 11(3):375～382.
Yong T,Narayanaswami R. 2003. A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining[J].Computer Aided Design, 35(13):1249～1259.
Yue Y, Han Q,Wang Z. 2006. An Approximation Method of NURBS Curves in NC Machining[J].Journal of Wuhan University Of Technology(English Edition), 28(2):734～736.
Zhang D J, Lou Y J,Li Z X. 2006. Geometric Contouring Control on the Smooth Surface[C]. Intelligent Robots and Systems, 2006 IEEE/RSJ International Conference on. Beijing,China: IEEE,4496～4501.
Zhang H X, Yuan K,Mei S Q. 2006. Fuzzy logic cross-coupling control of wheeled mobile robots[C]. 2006 IEEE International Conference on Mechatronics and Automation, ICMA 2006. Luoyang. China: IEEE,740～744.
Zhang Q Y. 1996. Real-time NURBS curve trajectory generation for a robot using an open-architecture controller[D]:Doctor.Lawrence,USA:University of Kansas,65～80.
Zhang Q Y,Greenway R B. 1998. Development and implementation of a NURBS curve motion interpolator[J]. Robotics and Computer-Integrated Manufacturing, 14(1):27～36.
Zheng J X, Zhang M J,Meng Q X. 2006. Study of Quintic Spline Interpolation and Generated Velocity Profile for High Speed Machining[J]. Journal Of Wuhan University Of Technology(English Edition), 28(2):507～512.