Extracting Initial Iterative Control Signal Based on Trajectory Primitives Matching and Combining
Jianming Xu, Lingxin Kong, and Yaodong Wang
College of Information Engineering, Zhejiang University of Technology
Hangzhou, Zhejiang, China
The initial iterative control signal is often adopted a zero or a certain value in the conventional iterative learning control (ILC) system, and an ILC process needs to renew again as long as the desired trajectory is changed. In this paper, the NURBS (Non-Uniform Rational B-Splines) model is used for describing all trajectory primitives and the desired trajectory. It is studied that the problem of the initial iterative control signal is extracted in ILC, which presents a method of extracting the initial iterative control signal based on the trajectory primitive optimal matching and combining algorithm. Firstly, the definition of the similarity index between the two different spacial trajectories is introduced. Secondly, an optimal matching and combining algorithm is designed under a certain similarity index, which is used to find two or more combined primitive sequences with space patterns similar to the desired trajectory. Thirdly, the initial iterative control signals of the desired trajectory are extracted by using the control information of the combined primitive sequences. Finally, the simulation is carried out to demonstrate the effectiveness of the present method.
-  S. Arimoto, S. Kawamura and F. Miyazaki, “Bettering operation of robots by learning,” J. of Robot System, Vol.1, No.2, pp.123-140, 1984.
-  J. X. Xu and T. Zhu, “Dual-scale direct learning control of trajectory tracking for a class of nonlinear uncertain systems,” IEEE Trans. on Automatic Control, Vol.44, No.10, pp. 1884-1888, 1999.
-  J. X. Xu, “Direct learning of control efforts for trajectories with different time scales,” IEEE Trans. on Automatic Control, Vol.43, No.7, pp. 1027-1030, 1998.
-  J. X. Xu, “Direct learning of control efforts for trajectories with different magnitude scales,” Automatica, Vol.33, No.12, pp. 2191-2195, 1997.
-  J. X. Xu, S. K. Panda and T. H. Lee, “Introduction to ILC: concepts, schematics and implementation,” Real-time Iterative Learning Control: Design and Applications, pp. 7-28, 2009.
-  P. Janssens, G. Pipeleers and J. Swevers. “Initialization of ILC based on a previously learned trajectory,” American Control Conference (ACC) IEEE, pp. 610-614, 2012.
-  M. Arif, T. Ishihara, and H. Inooka, “Incorporation of experience in iterative learning controllers using locally weighted learning,” Automatic, Vol.37, No.6, pp. 881-888, 2001.
-  D. J. Hoelzle, A. G. Alleyne, and A. J. Wagoner Johnson.“Basis task approach to iterative learning control with applications to micro-robotic deposition,” IEEE Trans. on Control Systems Technology, Vol.19, No.5, pp. 1138-1148, 2011.
-  W. Kabsch,“A solution for the best rotation to relate two sets of vectors,” ActaCrystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography, Vol.32, No.5, pp. 922-923, 1976.
-  S. Umeyama, “Least-squares estimation of transformation parameters between two point patterns,” IEEE Trans. on Pattern Analysis & Machine Intelligence. Vol.13, No.4, pp. 376-380, 1991.
-  F. Z. Shi, “The CAGD & NURBS book,” Beijing: Beijing University of Aeronautics and Astronautics Press, pp. 275-277, 1994.
-  J.-X. Xu, and S. K. Panda, T. H. Lee, “Robust optimal ILC design for precision servo: application to an XY table,” Real-time Iterative Learning Control: Design and Application, pp. 29-44, 2009.