Hand layup is a commonly used process for making composite structures from several plies of carbon-fiber prepreg. The process involves multiple human operators manipulating and conforming layers of prepreg to a mold. The manual layup process is ergonomically challenging, tedious, and limits throughput. Moreover, different operators may perform the process differently and hence introduce inconsistency. We have developed a smart robotic cell to automate the prepreg sheet layup process. The cell uses multiple robots to manipulate and drape sheets over a tool. A human expert provides a sequence to conform the ply and types of end-effectors to be used as input to the system. The system automatically generates trajectories for the robots that can achieve the specified layup. This paper describes a systematic approach for selecting and placing robots in the cell and description of tools and end effectors needed for utilizing the cell. We also describe planning algorithms for (a) generating plans to grasp and manipulate the ply and (b) generating feasible robot trajectories. Our system can generate plans in a computationally efficient manner for complex parts. We demonstrate the automated layup by conducting physical experiments on an industry-inspired mold using the generated plans. Our system can perform sheet layup at speed comparable to human operators.