Time optimal feedrate generation with confined tracking error based on linear programming

In this paper, the problem of time optimal feedrate generation under confined feedrate, axis accelerations, and axis tracking errors is considered. The main contribution is to reduce the tracking error constraint to constraints about the axis velocities and accelerations, when the tracking error satisfies a second order linear ordinary differential equation. Based on this simplification on the tracking error, the original feedrate generation problem is reduced to a new form which can be efficiently solved with linear programming algorithms. Simulation results are used to validate the methods.

[1]  Alessandro Gasparetto,et al.  Experimental validation and comparative analysis of optimal time-jerk algorithms for trajectory planning , 2012 .

[2]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, STOC '84.

[3]  H. Chuang,et al.  A model-referenced adaptive control strategy for improving contour accuracy of multi-axis machine tools , 1990, Conference Record of the 1990 IEEE Industry Applications Society Annual Meeting.

[4]  A. Visioli.  Optimal tuning of PID controllers for integral and unstable processes , 2001 .

[5]  Rida T. Farouki,et al.  Solution of inverse dynamics problems for contour error minimization in CNC machines , 2010 .

[6]  Jiing-Yih Lai,et al.  On the development of a parametric interpolator with confined chord error, feedrate, acceleration and jerk , 2008 .

[7]  Jingyan Dong,et al.  A Generalized Time-Optimal Bidirectional Scan Algorithm for Constrained Feed-Rate Optimization , 2006 .

[8]  Jingyan Dong,et al.  Optimal Feed-Rate Scheduling for High-Speed Contouring , 2003 .

[9]  Qiang Zhang,et al.  Tracking error reduction in CNC machining by reshaping the kinematic trajectory , 2013, J. Syst. Sci. Complex..

[10]  K. Srinivasan,et al.  Optimal Contouring Control of Multi-Axial Feed Drive Servomechanisms , 1989 .

[11]  J. A. Stori,et al.  A Generalized Time-Optimal Bi-Directional Scan Algorithm for Constrained Feedrate Optimization , 2004 .

[12]  Ke Zhang,et al.  Time-optimal interpolation for CNC machining along curved tool pathes with confined chord error , 2013, J. Syst. Sci. Complex..

[13]  M. Tsai,et al.  Development of a dynamics-based NURBS interpolator with real-time look-ahead algorithm , 2007 .

[14]  X. Gao,et al.  Interpolation of Parametric CNC Machine Tool Path Under Confined Jounce 1 ) , 2011 .

[15]  Xiao-Shan Gao,et al.  A Greedy Algorithm for Feed-rate Planning of CNC Machines along Curved Tool Paths with Confined Jerk for Each Axis , 2010 .

[16]  J. Bobrow,et al.  Time-Optimal Control of Robotic Manipulators Along Specified Paths , 1985 .

[17]  Behrooz Arezoo,et al.  A look-ahead command generator with control over trajectory and chord error for NURBS curve with unknown arc length , 2010, Comput. Aided Des..

[18]  Yusuf Altintas,et al.  High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation , 2001 .

[19]  An-Chen Lee,et al.  The feedrate scheduling of NURBS interpolator for CNC machine tools , 2011, Comput. Aided Des..

[20]  Yi Huang,et al.  ADRC based input disturbance rejection for minimum-phase plants with unknown orders and/or uncertain relative degrees , 2012, J. Syst. Sci. Complex..

[21]  Elizabeth A. Croft,et al.  Feed optimization for five-axis CNC machine tools with drive constraints , 2008 .

[22]  Yoram Koren,et al.  Cross-Coupled Biaxial Computer Control for Manufacturing Systems , 1980 .

[23]  Rida T. Farouki,et al.  Time-optimal traversal of curved paths by Cartesian CNC machines under both constant and speed-dependent axis acceleration bounds , 2007 .

[24]  Meng-Shiun Tsai,et al.  Development of an integrated look-ahead dynamics-based NURBS interpolator for high precision machinery , 2008, Comput. Aided Des..

[25]  Xiao-Shan Gao,et al.  A greedy algorithm for feedrate planning of CNC machines along curved tool paths with confined jerk , 2012 .

[26]  Xiao-Shan Gao,et al.  Efficient algorithm for time-optimal feedrate planning and smoothing with confined chord error and acceleration , 2013 .

[27]  Wei Yan,et al.  Interpolation of parametric CNC machining path under confined jounce , 2012 .

[28]  Dongming Guo,et al.  Variable feedrate interpolation of NURBS Toolpath with geometric and kinematical constraints for five-axis CNC machining , 2013, J. Syst. Sci. Complex..

[29]  Zvi Shiller,et al.  On singular time-optimal control along specified paths , 1994, IEEE Trans. Robotics Autom..