## 1 Introduction  
With the continuous development of the manufacturing industry, the demand for grinding tasks for specific workpieces is increasing. Not only has the quantity of grinding developed rapidly, but the requirements for the quality of grinding have also increased significantly. Nowadays, although a considerable part of such grinding tasks is completed by humans, more and more grinding tasks are performed by robots. In the field of grinding and polishing processing, compared with manual operation, the grinding quality of robots is more stable and can work continuously for a long time, which can obtain better economic and social benefits. Thus, research on robot grinding and polishing has drawn increasing attention and been a popular research field during the past decades. In recent years, the rapid development of intelligent technologies has led to remarkable advancements in the field of intelligent manufacturing [1, 2]. A number of new technologies have been proposed for robot grinding and polishing, particularly with regards to trajectory planning and force controlling. A novel selected force controlling method (SFC) with consideration of regional division (RD) based on the machining allowance is proposed by [PERSON] et al. [3] for improving the robotic grinding accuracy of complex curved blades, on the basis of the self-developed adaptive impedance controller. [PERSON] et al. [4] presented an adaptive intelligent human-robot collaborative approach to facilitate trajectory planning for robotic belt grinding of complex parts, which bridges the experience of skilled operators through an immersive virtual reality. [PERSON] et al. [5] proposed a mobile robotic grinding system for large-scale workpieces and a vision-based grinding strategy for the mobile robot. [PERSON] et al. [6] proposed a novel path accuracy enhancement strategy and different evaluation methods for a six-degree-of-freedom industrial robot used for grinding an aero-engine blade. In order to improve robot grinding performance, there have been cases where two robots have been used to work together for grinding tasks in recent years, usually with one manipulator clamping the workpiece to be polished, and the other installing a grinding tool for grinding, which has the advantages of more flexibility, high efficiency, and good performance. However, this scheme brings challenges for both planning the movement path of the manipulators and the contact problem handling in grinding, which have drawn increasing attention and been a popular research field over the years. [PERSON] and [PERSON] et al. [7] proposed an \"IK switch\" multi-arm trajectory planning method, which can solve complex closed-chain operation tasks. [PERSON] et al. [8] used the potential function method to make the system avoid collisions in the whole motion by taking advantage of the redundancy of the degrees of freedom of the dual robotic arms. Due to the complexity of the dual-arm systems and particularity of scenarios, most of the existing research is too complicated to be practically applied to robotic grinding tasks. Therefore, in order to accomplish the goals in a more concise and feasible way, it is necessary to simplify the task planning and control process of collaborative robotic grinding in practice. In this paper, we develop a dual-arm collaborative system for robotic grinding tasks, where the motion trajectory of the dual arms is planned based on the kinematic constraint and an impedance control scheme is designed. To be specific, the dual-arm system is first modeled according to the kinematic constraints. In order to reduce the complexity of the movement of the two robotic arms, we decompose the trajectory of the workpiece surface to different directions orthogonally, so that the two robots can track the decomposed trajectory separately. Meanwhile, an impedance controller is designed to keep two manipulators tracking the desired trajectory in the interaction.