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This paper presents an autonomous robotic assembly system for Soma cube blocks, which, after observing the individual blocks and their assembled shape, quickly plans and executes the assembly motion sequence that picks up each block and incrementally build the target shape. A multi stage planner is used to find the suitable assembly solutions, assembly sequences and grip sequences considering various constraints, and re-grasping is used when the block target pose is not directly realizable or the block pose is ambiguous. The suggested system is implemented for a commercial UR5e robotic arm and a novel two degrees of freedom (DOF) gripper capable of in-hand manipulation, which further speeds up the manipulation speed. It was experimentally validated through a public competitive demonstration, where the suggested system completed all assembly tasks reliably with outstanding performance.