Aiming at the problem that traditional yarn cylinder loading operation depends on manual operation, the industry is committed to achieving automatic grasping by robotic arms. To this end, the focus is on two key links of object enveloping and collision detection in automatic grasping of robotic arms. In order to solve the problem of insufficient envelope accuracy of the traditional hybrid hierarchical bounding box algorithm in complex scenarios, an improved hybrid hierarchical bounding box model based on convex hull structure was designed, which significantly improved the spatial fitness of the bounding box by constructing the convex hull constraints in the leaf nodes. Aiming at the problem of low computational inefficiency of the classical separating axis theorem in dealing with collision detection of complex convex polygons, a gradient descent-based separating axis optimization strategy was proposed. By establishing the functional relationship between projection length variations and separating axis rotation angle, the search direction and rotation step of separating axes were dynamically adjusted. Experimental results showed that compared with the traditional hybrid hierarchical bounding box model, the improved hybrid hierarchical bounding box model had obvious improvement in the envelope accuracy. Compared with the classical separating axis algorithm, the gradient descent separating axis algorithm reduced the average iteration time and the iteration count by 90.67% and 98.48%, respectively. The proposed method is suitable for complex working conditions in industrial scenarios where objects are densely arranged and require high-precision collision detection.