Real-time capable feedrate optimization for laser processes with redundant axes via two-stage regularized linear programming

Abstract

Galvanometer scanners offer high dynamics and precision for laser processes, but are limited in their workspace. To expand the workspace, the galvanometer scanner can be integrated into a larger mechanical motion system with redundant axes, including slow mechanical axes and fast scanner axes. While this configuration provides additional degrees of freedom in feedrate planning, conventional Computerized Numerical Control (CNC)-based laser machining systems cannot exploit them effectively, resulting in suboptimal finishing times. This paper introduces the first real-time capable, optimization-based approach to the minimum-time planning problem under motion redundancy, considering limits in redundant axes and toolpath dynamics up to the third order. This is achieved by decoupling the nonlinear problem into two linear problems and introducing a sequential windowing and adaptive scaling strategy, which allows the toolpath to be scaled to arbitrary lengths. Additionally, a new numerical approximation of the transformation between axis and Cartesian coordinates is introduced. This allows for optimization without arc-length parameterization and simplifies the previous toolpath geometry processing. The constraint feasibility and computational efficiency of the proposed optimization method are validated using spline toolpaths. On a desktop PC with single-core execution, the computation time remains well below the actual processing time at around 10 %, showing linear scalability with respect to toolpath length. Experiments on two different laser machines equipped with redundant axes further validate the planning performance and computational robustness when following freeform contours with up to $10000$ constraint checkpoints. Compared to an industrial CNC-guided solution based on S-curve motion profiles, the proposed optimization algorithm reduces the finishing time by around 30 % in experiments with and without jerk constraints.