×
Zhang, Qiang; Li, Shurong; Guo, Jianxin

Minimum time trajectory optimization of CNC machining with tracking error constraints. (English) Zbl 1406.93214

Abstr. Appl. Anal. 2014, Article ID 835098, 15 p. (2014).
Summary: An off-line optimization approach of high precision minimum time feedrate for CNC machining is proposed. Besides the ordinary considered velocity, acceleration, and jerk constraints, dynamic performance constraint of each servo drive is also considered in this optimization problem to improve the tracking precision along the optimized feedrate trajectory. Tracking error is applied to indicate the servo dynamic performance of each axis. By using variable substitution, the tracking error constrained minimum time trajectory planning problem is formulated as a nonlinear path constrained optimal control problem. Bang-bang constraints structure of the optimal trajectory is proved in this paper; then a novel constraint handling method is proposed to realize a convex optimization based solution of the nonlinear constrained optimal control problem. A simple ellipse feedrate planning test is presented to demonstrate the effectiveness of the approach. Then the practicability and robustness of the trajectory generated by the proposed approach are demonstrated by a butterfly contour machining example.

MSC:

93C83 Control/observation systems involving computers (process control, etc.)
93C15 Control/observation systems governed by ordinary differential equations
49N90 Applications of optimal control and differential games
49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)

Keywords:

minimum time trajectory optimization; CNC machining; bang-bang constraints structure
Cite Review PDF
Full Text: DOI
OA License

References:

[1] Smith, T. S.; Farouki, R. T.; Timar, S. D.; Boyadjieff, G. L., Algorithms for time-optimal control of CNC machines along curved tool paths, Robotics and Computer-Integrated Manufacturing, 21, 1, 37-53 (2005) · doi:10.1016/j.rcim.2004.05.004
[2] Timar, S. D.; Farouki, R. T., Time-optimal traversal of curved paths by Cartesian CNC machines under both constant and speed-dependent axis acceleration bounds, Robotics and Computer-Integrated Manufacturing, 23, 5, 563-579 (2007) · doi:10.1016/j.rcim.2006.07.002
[3] Yuan, C. M.; Zhang, K.; Fan, W.; Gao, X. S., Time-optimal interpolation for CNC machining along curved tool paths with confined chord error, Journal of Systems Science and Complexity, 26, 5, 836-870 (2013) · Zbl 1294.93031
[4] Zhou, J. F.; Sun, Y. W.; Guo, D. M., Adaptive feedrate interpolation with multi constraints for five-axis parametric tool path, The International Journal of Advanced Manufacturing Technology, 71, 9-12, 1873-1882 (2014)
[5] Chen, Y.; Desrochers, A. A., Proof of the structure of the minimum-time control law of robotic manipulators using a Hamiltonian formulation, IEEE Transactions on Robotics and Automation, 6, 3, 388-393 (1990) · doi:10.1109/70.56659
[6] McCarthy, J. M.; Bobrow, J. E., The number of saturated actuators and constraint forces during time-optimal movement of a general robotic system, IEEE Transactions on Robotics and Automation, 8, 3, 407-409 (1992) · doi:10.1109/70.143358
[7] Gourdeau, R.; Schwartz, H. M., Optimal control of a robot manipulator using a weighted time-energy cost function, IEEE Conference on Decision and Control
[8] Dong, J.-Y.; Ferreira, P. M.; Stori, J. A., Feed-rate optimization with jerk constraints for generating minimum-time trajectories, International Journal of Machine Tools and Manufacture, 47, 12-13, 1941-1955 (2007) · doi:10.1016/j.ijmachtools.2007.03.006
[9] Zhang, K.; Yuan, C.; Gao, X.; Li, H., A greedy algorithm for feedrate planning of CNC machines along curved tool paths with confined jerk, Robotics and Computer-Integrated Manufacturing, 28, 4, 472-483 (2012) · doi:10.1016/j.rcim.2012.02.006
[10] Zhang, K.; Yuan, C. M.; Gao, X. S., Efficient algorithm for time-optimal feedrate planning and smoothing with confined chord error and acceleration, The International Journal of Advanced Manufacturing Technology, 66, 9-12, 1685-1697 (2013) · doi:10.1007/s00170-012-4450-3
[11] Zhang, Q.; Li, S.-R., Efficient computation of smooth minimum time trajectory for CNC machining, The International Journal of Advanced Manufacturing Technology, 68, 1-4, 683-692 (2013) · doi:10.1007/s00170-013-4790-7
[12] Fan, W.; Gao, X.; Lee, C.; Zhang, K.; Zhang, Q., Time-optimal interpolation for five-axis CNC machining along parametric tool path based on linear programming, The International Journal of Advanced Manufacturing Technology, 69, 5-8, 1373-1388 (2013) · doi:10.1007/s00170-013-5083-x
[13] Tarn, T.; Bejczy, A. K.; Yun, X.; Li, Z., Effect of motor dynamics on nonlinear feedback robot arm control, IEEE Transactions on Robotics and Automation, 7, 1, 114-122 (1991) · doi:10.1109/70.68075
[14] Tarkiainen, M.; Shiller, Z., Time optimal motions of manipulators with actuator dynamics, Proceedings of the IEEE International Conference on Robotics and Automation
[15] Kwan, C. M., Robust adaptive force/motion control of constrained robots, IEE Proceedings on Control Theory and Applications, 143, 1, 103-109 (1996) · Zbl 0849.93049 · doi:10.1049/ip-cta:19960090
[16] Ardeshiri, T.; Norrlof, M.; Lofberg, J.; Hansson, A., Convex optimization approach for time-optimal path tracking of robots with speed dependent constraints, Proceedings of the 18th IFAC World Congress
[17] Srinivasan, K.; Kulkarni, P. K., Cross-coupled control of biaxial feed drive servomechanisms, Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, 112, 2, 225-232 (1990) · doi:10.1115/1.2896129
[18] Chuang, H. Y.; Liu, C. H., A model-referenced adaptive control strategy for improving contour accuracy of multiaxis machine tools, IEEE Transactions on Industry Applications, 28, 1, 221-227 (1992) · doi:10.1109/28.120234
[19] Takahashi, H.; Bickel, R. J., Developing a controller to reduce contour error, Proceedings of the IEEE International Workshop on Advanced Motion Control, ACM
[20] Dong, J.; Stori, J. A., Optimal feed-rate scheduling for high-speed contouring, Journal of Manufacturing Science and Engineering, 129, 1, 63-76 (2007) · doi:10.1115/1.2280549
[21] Ernesto, C. A.; Farouki, R. T., Solution of inverse dynamics problems for contour error minimization in CNC machines, International Journal of Advanced Manufacturing Technology, 49, 5-8, 589-604 (2010) · doi:10.1007/s00170-009-2407-y
[22] Guo, J. X.; Zhang, Q.; Gao, X. S., Tracking error reduction in CNC machining by reshaping the kinematic trajectory, Journal of Systems Science and Complexity, 26, 5, 817-835 (2013) · Zbl 1294.93037
[23] Tsai, M. S.; Nien, H. W.; Yau, H. T., Development of an integrated look-ahead dynamics-based NURBS interpolator for high precision machinery, CAD Computer Aided Design, 40, 5, 554-566 (2008) · doi:10.1016/j.cad.2008.01.015
[24] Guo, J.; Zhang, K.; Zhang, Q.; Gao, X., Efficient time-optimal feedrate planning under dynamic constraints for a high-order CNC servo system, CAD Computer Aided Design, 45, 12, 1538-1546 (2013) · doi:10.1016/j.cad.2013.07.002
[25] Zhang, K.; Guo, J. X.; Gao, X. S., Cubic spline trajectory generation with axis jerk and tracking error constraints, International Journal of Precision Engineering and Manufacturing, 14, 7, 1141-1146 (2013)
[26] Hartl, R. F.; Sethi, S. P.; Vickson, R., A survey of the maximum principles for optimal control problems with state constraints, SIAM Review, 37, 2, 181-218 (1995) · Zbl 0832.49013 · doi:10.1137/1037043
[27] Bobrow, J. E.; Dubowsky, S.; Gibson, J. S., Time-optimal control of robotic manipulators along specified paths, International Journal of Robotics Research, 4, 3, 3-17 (1985)
[28] Zhang, Q.; Li, S. R.; Gao, X. S., Practical smooth minimum time trajectory planning for path following robotic manipulators, Proceedings of the American Control Conference
[29] Chen, T. W. C.; Vassiliadis, V. S., Inequality path constraints in optimal control: a finite iteration \(\varepsilon \)-convergent scheme based on pointwise discretization, Journal of Process Control, 15, 3, 353-362 (2005) · doi:10.1016/j.jprocont.2004.04.002
[30] Verscheure, D.; Demeulenaere, B.; Swevers, J.; de Schutter, J.; Diehl, M., Time-optimal path tracking for robots: a convex optimization approach, IEEE Transactions on Automatic Control, 54, 10, 2318-2327 (2009) · Zbl 1367.90088 · doi:10.1109/TAC.2009.2028959
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.