Path deviations caused by geometrical errors in machining equipment significantly affect the machining quality of optical components. To enhance the quality and efficiency of optical component processing, this paper presents a Chebyshev interpolated Levenberg-Marquardt algorithm (CILM) aimed at compensating for path deviations in a robotic smoothing system utilized for optical component processing. First, the positioning accuracy of the robotic smoothing system is measured using a laser tracker. Subsequently, an objective function is constructed based on robot kinematics and error models to optimize the geometric errors in the system. Then, the proposed method is adopted to identify the geometric parameters of the robotic smoothing system to compensate for the smoothing path deviations. The compensation results confirm the effectiveness of the proposed method in enhancing the absolute positioning accuracy of the robotic smoothing system. Additionally, experimental verification is conducted to validate the effectiveness of the proposed method in improving the surface quality of optical components through smoothing path compensation. The results of the three experiments indicate that the proposed CILM achieves optical components with peak-to-valley values 15.70%, 28.7%, and 4.01% lower than those obtained before compensation, along with root mean square of 33.67%, 21.57%, and 10.23% lower than before compensation values, respectively. Moreover, the power spectral density curves of CILM exhibit smoother characteristics in comparison to the curves before compensation.