## 4 Experimental Section
### Baseline Methods  
This study evaluated the proposed collaborative pushing and grasping method using deep reinforcement learning and image masking against several baseline methods in both simulated and real-world environments. We first utilized the CoppeliaSim simulation environment, employing a Hiwin Ra605_710_GC robotic arm ( HIWIN Technologies Corp, Taichung, Taiwan) and a Xeg_32 electric gripper (HIWIN Technologies Corp, Taichung, Taiwan) to perform pre-grasping tasks with dynamic and static objects. Following the methodology of [PERSON] et al. [13], we used five basic three-dimensional geometric figures to assess the performance of our deep reinforcement learning algorithm. Ten objects representing these geometric shapes were randomly placed in the simulation workspace, focusing on the number of pushes and grasps required to manipulate them successfully. These tests, illustrated in Figure 5, were designed to create diverse scenarios with varying levels of difficulty. After validating the model in the simulation environment, we conducted real-world experiments to further evaluate its effectiveness. The trained model was tested on a real robotic arm under conditions that mirrored the simulation, with both static and dynamic objects used to assess the model's adaptability and robustness. Objects were strategically positioned in the workspace, ranging from four to ten per test, to represent different difficulty levels based on the number of actions required for successful manipulation. The results, shown in Figure 6, demonstrated the model's ability to handle complex tasks, with higher numbers of required actions indicating greater difficulty. To provide a comprehensive analysis, we compared our proposed method to traditional pushing and grasping techniques that rely on predefined rules and control strategies, serving as a benchmark for improvement. The differences in performance were clearly captured through videos of both the simulation and real-world experiments, which have been provided to visually illustrate the effectiveness of our approach. These experiments demonstrate that the proposed method, trained using deep reinforcement learning and image-based object detection, significantly outperforms traditional methods in terms of adaptability and efficiency in various collaborative pushing and grasping tasks. Table 1 presents the performance metrics for the proposed deep reinforcement learning (DRL) method applied to collaborative pushing and grasping tasks with a robotic arm, across different scenarios characterized by varying numbers and types of objects (static  
Figure 5: Numbers of objects and pushes required for the six tests. Figure 6: Six scenarios used for tests. vs. dynamic). The success rate remains high in simpler scenarios; for instance, in the \"Static Objects (Easy)\" scenario with four objects, a 95% success rate was achieved. As the complexity of the environment increased, such as in the \"Static Objects (Medium)\" scenario with six objects, the success rate slightly decreased to 89%, and further dropped to 75% in the \"Static Objects (Hard)\" scenario with ten objects. A similar trend is observed with dynamic objects: the success rate starts at 90% in the \"Dynamic Objects (Easy)\" scenario with four objects, decreases to 82% in the \"Dynamic Objects (Medium)\" scenario with six objects, and further falls to 68% in the \"Dynamic Objects (Hard)\" scenario with ten objects. These results indicate that while the DRL method is highly effective in simpler tasks, its performance declines as task complexity increases. The average number of pushes and grasps required and the time taken to complete the tasks also reflect the increasing difficulty across scenarios. In the \"Static Objects (Easy)\" scenario, the robot required an average of 2 pushes and 1 grasp, taking about 12 s to complete the task.