The efficiency of robot control methods and the accuracy of their movements are often hindered by the complexity of defining motion paths. Commonly, these paths are represented by numerous linear segments, resulting in redundant motion commands, reduced smoothness, and velocity. To address these issues, this study investigates the application of mathematical algorithms, specifically the Ramer-Douglas-Peucker (RDP) method and higher-order polynomial interpolation, to optimize robot toolpaths. The RDP algorithm minimizes redundant points while retaining the trajectory’s overall shape, enhancing process speed and reducing energy costs. In addition, arc recognition is implemented to replace multiple linear operations with circular or arc-based motions, improving efficiency and reducing code complexity. The research employs RoboDK and Python API for offline programming, with experimental validation conducted on the Yaskawa Motoman HC10DTP robot. Results demonstrate that these methods can significantly reduce toolpath execution times – up to 3.7 times in certain cases – without significantly compromising trajectory accuracy. These approaches are applicable across various industries, including milling, painting, welding, and grinding, where smooth and precise motion is critical.