Becker, Aaron T.Schmidt, ArneManzoor, SherylHuang, LiFekete, Sándor P.2019-10-012019-10-017/9/2018Copyright 2018 IEEE Robotics and Automation Letters. This is a pre-print version of a published paper that is available at: https://ieeexplore.ieee.org/abstract/document/8408555 Recommended citation: Schmidt, Arne, Sheryl Manzoor, Li Huang, Aaron T. Becker, and Sándor P. Fekete. "Efficient parallel self-assembly under uniform control inputs." IEEE Robotics and Automation Letters 3, no. 4 (2018): 3521-3528. DOI: 10.1109/LRA.2018.2853758 This item has been deposited in accordance with publisher copyright and licensing terms with the author's permission.https://hdl.handle.net/10657/4908We prove that by successively combining subassemblies, we can achieve sublinear construction times for “staged” assembly of microscale objects from a large number of tiny particles, for vast classes of shapes; this is a significant advance in the context of programmable matter and self-assembly for building high-yield microfactories. The underlying model has particles moving under the influence of uniform external forces until they hit an obstacle; particles bond when forced together with a compatible particle. Previous work considered sequential composition of objects, resulting in construction time that is linear in the number N of particles, which is inefficient for large N. Our progress implies critical speedup for constructible shapes; for convex polyominoes, even a constant construction time is possible. We also show that our construction process can be used for pipelining, resulting in an amortized constant production time.en-USShapeSelf-assemblyProductionRobotsTilesContainersArticle