In recent years, with the deepening integration of digital twins (DT) and the Industrial Internet of Things (IIoT), solutions based on digital twins have been widely applied in IIoT scenarios. However, most existing solutions tend to overlook the latency issue during the interaction between mobile devices, such as industrial mobile robots (IMR), and their DTs while in motion. Excessive interaction latency can directly impair the real-time response capability and decision accuracy of industrial mobile robots, and in severe cases, it may lead to the failure of intricate industrial tasks. In order to solve the above problems, we propose a digital twin dynamic migration method for industrial mobile robots. Firstly, we design and implement a STGCNTransformer-based movement trajectory prediction method for IMR to predict the future movement trajectory of IMR and pre-migrate the DT of IMR to all intelligent gateways (IG) within the prediction range. Then, we design and implement a Proximal Policy Optimization-based DT migration time determination method for IMR and obtain the migration timing of DT under the premise of balancing the DT migration overhead, the load of the IG where the DT is deployed, the load of the IG where the DT is connected, and the communication delay between the IMR and the IG where the DT is deployed. Next, the DT of the IMR is migrated based on the IMR's anticipated trajectory and optimal times for migration, with the objective of minimizing the interaction latency between the IMR and its DT. Finally, we conduct simulation experiments on the proposed method. Through theoretical and simulation experiments, it has been proven that the proposed method can effectively ensure the dynamic interaction delay between the IMR and its DT during the moving process, thereby enhancing the real-time responsiveness and decision precision of the IMR.