To address the issue of traditional control methods being inadequate for achieving high-precision grinding of complex surfaces, this study proposes an improved impedance control method designed for grinding robots. The proposed method operates within the Cartesian coordinate system and incorporates an exponential reaching law to enhance the machining quality of freeform surface workpieces. The method begins by calculating the executable impedance trajectory of the robot based on the impedance parameter model of the system and the obtained contact resistance. This trajectory serves as a reference for precise motion. Subsequently, a control method based on integral sliding mode impedance has been proposed to enable precise tracking of the calculated impedance trajectory. To resolve the widely recognized issue of chattering in sliding mode control, the exponential reaching law has been employed to effectively suppress the chattering effect, thereby enhancing the smoothness and stability of the control process. Additionally, the stability of the system has been thoroughly analyzed and validated using Lyapunov theory, guaranteeing its theoretical soundness and dependability. Finally, comprehensive simulations and experiments have been performed to evaluate the proposed approach under various operational conditions. The results thus obtained confirm that the method achieves a superior performance under dynamic as well as static conditions, offering improved precision and stability for grinding tasks on complex surfaces.

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