Near Time‐Optimal Trajectory Generation for Flexible Systems Utilizing Time‐Optimal Motion Primitives

ABSTRACT

This paper presents a trajectory generation method that unifies and effectively links key ideas from input shaping and optimal control for vibration‐sensitive motion systems. The method constructs trajectories directly from time‐optimal motion primitives, enabling fast transition times while maintaining insensitivity to parameter uncertainty. By explicitly incorporating system damping and stiffness into the motion‐primitive design, the resulting trajectories account for oscillatory dynamics, thereby reducing residual vibrations compared to approaches that neglect these effects. The approach avoids non‐linear optimization and instead relies on efficiently computed motion primitives, allowing real‐time execution on industrial hardware (PLC). An extensive measurement study on a laboratory system, together with comparisons to established and recently proposed methods, demonstrates the advantages of the approach in terms of transition time, residual oscillations, and parameter sensitivity. The results highlight the practical relevance of combining dynamic awareness, structural simplicity, and computational efficiency within a unified trajectory planning scheme.