When multi-arm space robots perform complex space tasks, how to achieve a balance between grasping accuracy and platform stability is the core issue of current research. With the continuous improvement of task requirements, the coordination and control accuracy of the robot system have become particularly important. This study proposes an enhanced visual servoing and zero reaction control joint algorithm, which aims to improve grasping accuracy while eliminating platform posture disturbances, thereby optimizing the overall performance of the multi-arm space robot system. The study is compared with traditional control algorithms. The experimental results show that E-VS-ZAC performs well in grasping accuracy, with an error of 3.5 mm, which is about 30% higher than VSC and IKC. In terms of platform posture disturbance, the disturbance value of E-VS-ZAC is 1.2°, which is significantly lower than 3.5° of IKC, and has obvious advantages in platform stability control. E-VS-ZAC has also achieved excellent performance in task execution efficiency, end-effector stability and trajectory accuracy. In summary, the E-VS-ZAC algorithm shows excellent grasping accuracy and platform stability in the task execution of the multi-arm space robot system, which can provide strong support for efficient collaborative control in complex environments in the future.