Robotic harvesters have the potential to substantially reduce the physical workload of agricultural laborers. However, in complex agricultural environments, traditional single-arm robot path planning methods often struggle to accomplish fruit harvesting tasks due to the presence of collision avoidance requirements and orientation constraints during grasping. In this work, we design a dual-arm tomato harvesting robot and propose a reinforcement learning-based cooperative control algorithm tailored to the dual-arm system. First, a deep learning-based semantic segmentation network is employed to extract the spatial locations of tomatoes and branches from sensory data. Building upon this perception module, we develop a reinforcement learning-based cooperative path planning approach to address inter-arm collision avoidance and end-effector orientation constraints during the harvesting process. Furthermore, a task-driven policy network architecture is introduced to decouple the complex harvesting task into structured subproblems, thereby enabling more efficient learning and improved performance. Simulation and experimental results demonstrate that the proposed method can generate collision-free harvesting trajectories that satisfy dual-arm orientation constraints, significantly improving the tomato harvesting success rate.