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The apple target recognition algorithm is one of the core technologies of the apple picking robot. However, most of the existing apple detection algorithms cannot distinguish between the apples that are occluded by tree branches and occluded by other apples. The apples, grasping end-effector and mechanical picking arm of the robot are very likely to be damaged if the algorithm is directly applied to the picking robot. Based on this practical problem, in order to automatically recognize the graspable and ungraspable apples in an apple tree image, a light-weight apple targets detection method was proposed for picking robot using improved YOLOv5s. Firstly, BottleneckCSP module was improved designed to BottleneckCSP-2 module which was used to replace the BottleneckCSP module in backbone architecture of original YOLOv5s network. Secondly, SE module, which belonged to the visual attention mechanism network, was inserted to the proposed improved backbone network. Thirdly, the bonding fusion mode of feature maps, which were inputs to the target detection layer of medium size in the original YOLOv5s network, were improved. Finally, the initial anchor box size of the original network was improved. The experimental results indicated that the graspable apples, which were unoccluded or only occluded by tree leaves, and the ungraspable apples, which were occluded by tree branches or occluded by other fruits, could be identified effectively using the proposed improved network model in this study. Specifically, the recognition recall, precision, mAP and F1 were 91.48%, 83.83%, 86.75% and 87.49%, respectively. The average recognition time was 0.015 s per image. Contrasted with original YOLOv5s, YOLOv3, YOLOv4 and EfficientDet-D0 model, the mAP of the proposed improved YOLOv5s model increased by 5.05%, 14.95%, 4.74% and 6.75% respectively, the size of the model compressed by 9.29%, 94.6%, 94.8% and 15.3% respectively. The average recognition speeds per image of the proposed improved YOLOv5s model were 2.53, 1.13 and 3.53 times of EfficientDet-D0, YOLOv4 and YOLOv3 and model, respectively. The proposed method can provide technical support for the real-time accurate detection of multiple fruit targets for the apple picking robot.