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We have developed, prototyped, and demonstrated the feasibility of a novel robotic technique for rapid fabrication of composite structures. Its chief innovation is that, unlike all other available fabrication methods, it does not require a mold. Instead, the structure is built patch by patch, using a rapidly reconfigurable forming surface, and a robot to position the evolving part. Both of these components are programmable, so only the control software needs to be changed to produce a new shape. Hence it should be possible to automatically program the system to produce a shape directly from an electronic model of it. It is therefore likely that the method will enable faster and less expensive fabrication of composites.