Enhancing Smoothness via Redundancy in 3D Laser Cutting Manufacturing: A Collision-Free, Minimized Jerk Trajectory Optimization Approach ^†

In modern manufacturing, achieving high-speed laser cutting requires advanced robotic trajectory planning for smoothness and collision avoidance. Poorly optimized motion can cause frequent velocity changes, leading to mechanical vibrations that shorten machine service life. This study presents an innovative trajectory optimization approach for laser cutting machines equipped with a redundant standoff axis. A B-spline-based analytical model formulates rotational axes trajectories as quadratic programming problems to minimize jerk (the rate of acceleration change) under machining accuracy and kinematic constraints. Additionally, an M path, represented by the wrist center’s trajectory, refines translational axes by adjusting the standoff axis through a similar optimization model, thereby reducing mechanical stress. Collision avoidance is ensured through a concurrent iterative optimization process, considering the feasible domains of representative 3D geometric tool orientations. Simulation experiments on a complex B-pillar workpiece demonstrate the framework’s effectiveness, clearly indicating significant reductions in jerk and improved trajectory smoothness for both rotational and translational axes compared with conventional methods and a prior approach. This work advances high-speed machining capabilities by offering a novel, robust solution that leverages redundant structures to further improve trajectory smoothness and reliability in demanding industrial applications.