Abstract
Tool path smoothness is critical for ensuring the dynamic performance of robotic machining systems, as it directly influences machining efficiency and quality. In recent years, spline-based methods (e.g., Bézier-spline, B-spline, NURB-spline, and PH-spline) have been widely employed to achieve tool path smoothing. However, most existing studies have focused on achieving only G2 or c2 continuity of tool paths, leading to discontinuous jerk behavior and resulting in high-order resonance frequencies within the machining system. Although some attention has been given to the need for C3 continuity in tool paths, synchronization between tool tip position and orientation remains suboptimal due to the complex, high-dimensional nonlinear kinematics of robotic machining systems. An analytical C3 continuous tool path smoothing method based on Catmull-Rom splines is developed in this study for robotic machining systems. The method smooths corners between adjacent discrete linear segments by inserting an adjustable Catmull-Rom (ACR) spline, with control points and adjustment parameters specifically designed to minimize deviation errors between the smoothed and original tool paths. Subsequently, the tool tip position and orientation are synchronized with the tool tip displacement, maintaining C3 continuity, by replacing the remaining linear segments with ACR splines. These splines' control points can be directly selected without requiring any iterative calculations, and synchronization error is guaranteed to be zero. The developed method involves a fully analytical calculation process, eliminating the need for iterative methods. Numerical simulations demonstrate that the tool paths generated by the developed method satisfy preset tolerances with smooth, continuous jerks in both workpiece and joint coordinate spaces, and that synchronization errors are indeed zero.