Robotic cloth manipulation faces challenges due to the fabric's complex dynamics and the high dimensionality of configuration spaces. Previous methods have largely focused on isolated smoothing or folding tasks and overly reliant on simulations, often failing to bridge the significant sim-to-real gap in deformable object manipulation. To overcome these challenges, we propose a two-stream architecture with sequential and spatial pathways, unifying smoothing and folding tasks into a single adaptable policy model that accommodates various cloth types and states. The sequential stream determines the pick and place positions for the cloth, while the spatial stream, using a connectivity dynamics model, constructs a visibility graph from partial point cloud data of the self-occluded cloth, allowing the robot to infer the cloth's full configuration from incomplete observations. To bridge the sim-to-real gap, we utilize a hand tracking detection algorithm to gather and integrate human demonstration data into our novel end-to-end neural network, improving real-world adaptability. Our method, validated on a UR5 robot across four distinct cloth folding tasks with different goal shapes, consistently achieves folded states from arbitrary crumpled initial configurations, with success rates of 99\%, 99\%, 83\%, and 67\%. It outperforms existing state-of-the-art cloth manipulation techniques and demonstrates strong generalization to unseen cloth with diverse colors, shapes, and stiffness in real-world experiments.Videos and source code are available at: https://zcswdt.github.io/SSFold/
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