We present a material-robot system consisting of mobile robots which can assemble discrete cellular structures. We detail the manufacturing of cuboctahedral unit cells, termed voxels, which passively connect to neighboring voxels with magnets. We then describe "relative" robots which can locomote on, transport, and place voxels. These robots are designed relative to and in coordination with the cellular structure--the geometry of the voxel informs the robot's global geometric configuration, local mechanisms, and end effectors, and robotic assembly features are designed into the voxels. We describe control strategies for determining build sequence, robot path planning, discrete motion control, and feedback, integrated within a custom software environment for simulating and executing single or multi-robot construction. We use this material-robot system to build several types of structures, such as 1D beams, 2D plates, and 3D enclosures. The robots can navigate and assemble structures with minimal feedback, relying on voxelsized resolution to achieve successful global positioning. We show multi-robot assembly to increase throughput and expand system capability using a deterministic centralized control strategy.

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Assembly of large scale structural systems in space is understood as critical to serving applications that cannot be deployed from a single launch. Recent literature proposes the use of discrete modular structures for in-space assembly and relatively small scale robotics that are able to modify and traverse the structure. This paper addresses the algorithmic problems in scaling reconfigurable space structures built through robotic construction, where reconfiguration is defined as the problem of transforming an initial structure into a different goal configuration. We analyze different algorithmic paradigms and present corresponding abstractions and graph formulations, examining specialized algorithms that consider discretized space and time steps. We then discuss fundamental design trades for different computational architectures, such as centralized versus distributed, and present two representative algorithms as concrete examples for comparison. We analyze how those algorithms achieve different objective functions and goals, such as minimization of total distance traveled, maximization of faulttolerance, or minimization of total time spent in assembly. This is meant to offer an impression of algorithmic constraints on scalability of corresponding structural and robotic design. From this study, a set of recommendations is developed on where and when to use each paradigm, as well as implications for physical robotic and structural system design.