TitleSmooth polynomial interpolation for point-to-point trajectories with vibration avoidance
Publication TypeJournal Article
Year of Publication2015
AuthorsSencer, B, Ishizaki, K, Society, IECON2015 -. 41

This paper presents a novel smooth polynomial trajectory generation technique for machine tools and high-speed motion systems. A major source of vibrations in fast moving high performance production machines are the inertial vibrations that are mainly excited due to frequency content of the reference command generator, so called the trajectory generator. In general practice, those inertial vibrations are avoided within the controller architecture through notch filtering. Or, input-shaping methods may be utilized to attenuate certain frequency components of interpolated reference trajectory and thus avoid exciting structural modes. Instead of employing those post-filtering techniques, this paper introduces a direct trajectory generation technique with a shaped frequency content to minimize residual vibrations. The time stamped displacement profile is defined as a 9th order polynomial. Profile parameters are determined through an optimization procedure where the objective function is defined as the total frequency energy of the reference acceleration profile measured in a predetermined frequency band. Given the position, velocity and acceleration boundary conditions of the desired motion profile, trajectory parameters are calculated analytically by solving the quadratic programming problem. Effectiveness of the proposed trajectory generation technique is evaluated through comparison against the well-know minimum jerk trajectories. Both, simulation studies and experimental tracking test are performed on a flexible X-Y motion drive system following point-to-point trajectories.