Relative Robots: Scaling Automated Assembly of Discrete Cellular Lattices

We propose metrics for evaluating the performance of robotically assembled discrete cellular lattice structures (referred to as digital materials) by defining a set of tools used to evaluate how the assembly system impacts the achievable performance objective of relative stiffness. We show that mass-specific stiffness can be described by the dependencies E*(γ, D(n, f, RA)), where E* is specific modulus, γ is lattice topology, and the allowable acceptance of the joint interface, D, is defined by an error budget analysis that incorporates the scale of the structure, and/or number of discrete components assembled, n, the type of robotic assembler, RA, and the static error contributions due to tolerance stack-up in the specified assembler structural loop, and the dynamic error limitations of the assembler operating at specified assembly rates, f. We refer to three primary physical robotic construction system topologies defined by the relationship between their configuration workspace, and the global configuration space: global robotic assembler (GR), mobile robotic assembler (MR), and relative robotic assemblers (RR), each exhibiting varying sensitivity to static, and dynamic error accumulation. Results of this analysis inform an iterative machine design process where final desired material performance is used to define robotic assembly system design parameters.