Interest in agricultural robotics has increased considerably in recent years due to benefits such as improvement in productivity and labor reduction. However, current problems associated with unstructured environments make the development of robotic harvesters challenging. Most research in agricultural robotics focuses on single arm manipulation. Here, we propose a dual-arm approach. We present a dual-arm fruit harvesting robot equipped with a RGB-D camera, cutting and collecting tools. We exploit the cooperative task description to maximize the capabilities of the dual-arm robot. We designed a Hierarchical Quadratic Programming based control strategy to fulfill the set of hard constrains related to the robot and environment: robot joint limits, robot self-collisions, robot-fruit and robot-tree collisions. We combine deep learning and standard image processing algorithms to detect and track fruits as well as the tree trunk in the scene. We validate our perception methods on real-world RGB-D images and our control method on simulated experiments.