Low-harmonic rational Bézier curves for trajectory generation of high-speed machinery

Abstract For a given high-speed machinery, a significant source of the internally induced vibrational excitation is the presence of high frequency harmonics in the trajectories that the system is forced to follow. In this paper a special class of rational Bezier curves is presented that correspond to low-harmonic trajectory patterns. Harmonic Bernstein polynomials and harmonic deCasteljau algorithm are also introduced as two major tools for generating the harmonic rational Bezier curves. These curves can be used to synthesize trajectories within the dynamic response limitations of the actuators while avoiding the excitation of the natural modes of vibration of the system.

[1]  Matthew T. Mason,et al.  Robot Motion: Planning and Control , 1983 .

[2]  穂坂 衛,et al.  Modeling of curves and surfaces in CAD/CAM , 1992 .

[3]  J. Rastegar,et al.  Trajectory synthesis and inverse dynamics model formulation and control of tip motion of a high performance flexible positioning system , 1994 .

[4]  C. S. G. Lee,et al.  Robotics: Control, Sensing, Vision, and Intelligence , 1987 .

[5]  T. Lyche,et al.  A stable recurrence relation for trigonometric B-splines , 1979 .

[6]  Farshad Khorrami,et al.  Inversion of nonlinear systems via the trajectory pattern method , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[7]  Josef Hoschek,et al.  Fundamentals of computer aided geometric design , 1996 .

[8]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[9]  Javier Sánchez-Reyes.  Single-valued curves in polar coordinates , 1990, Comput. Aided Des..

[10]  K. Doty,et al.  On-Line Polynomial Trajectories for Robot Manipulators , 1985 .

[11]  G. Farin.  NURB curves and surfaces: from projective geometry to practical use , 1995 .

[12]  J. Rastegar,et al.  Trajectory Synthesis and Inverse Dynamics Formulation for Minimal Vibrational Excitation for Flexible Structures based on Trajectory Patterns , 1993, 1993 American Control Conference.

[13]  Jahangir Rastegar,et al.  A new model based tracking controller for robot manipulators using the trajectory pattern inverse dynamics , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[14]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

[15]  C. Lin,et al.  Formulation and optimization of cubic polynomial joint trajectories for industrial robots , 1983 .

[16]  John J. Craig Zhu,et al.  Introduction to robotics mechanics and control , 1991 .

[17]  J. Rastegar,et al.  MANIPULATOR TRAJECTORY SYNTHESIS FOR MINIMAL VIBRATIONAL EXCITATION DUE TO THE PAYLOAD , 1993 .

[18]  Rajnikant V. Patel,et al.  Formulation of Joint Trajectories for Industrial Robots Using B-Splines , 1987, IEEE Transactions on Industrial Electronics.

[19]  Javier Sánchez-Reyes.  Single-valued spline curves in polar coordinates , 1992, Comput. Aided Des..