A G2 continuous laser cutting strategy for corner smoothing via adaptive cubic Bezier curves

In laser cutting, corner machining efficiency is often limited by transition curves whose high-order formulations increase computational complexity and amplify curvature extrema under linear length constraints, thereby restricting achievable feed rates. To address this issue, this paper proposes a fast corner machining method based on G²-continuous Bézier smoothing. A pair of symmetric Bézier curves with monotonic curvature is constructed to minimize the curvature extremum at the corner. The smoothed path is then segmented into a hybrid trajectory of linear and Bézier segments at the curvature extremum, ensuring positive acceleration continuity. Finally, a look-ahead velocity feasibility strategy is introduced to guarantee stable machining of the hybrid trajectory. Experimental results show that the proposed method not only achieves smooth transitions for adjacent tool corners of any size, resulting in more stable curvature changes for the overall mixed path, but also significantly improves the processing efficiency and quality of the workpiece surface.