The emerging field of passive macro-scale tile-based self-assembly (TBSA) shows promise in enabling effective manufacturing processes by harnessing TBSA's intrinsic parallelism. However, current TBSA methodologies still do not fulfill their potentials, largely because such assemblies are often prone to errors, and the size of an individual assembly is limited due to insufficient mechanical stability. Moreover, the instability issue worsens as assemblies grow in size. Using a novel type of magnetically-bonded tiles carried by bristle-bot drives, we propose here a framework that reverses this tendency; i.e., as an assembly grows, it becomes more stable. Stability is achieved by introducing two sets of tiles that move in opposite directions, thus zeroing the assembly net force. Using physics-based computational experiments, we compare the performance of the proposed approach with the common orbital shaking method, proving that the proposed system of tiles indeed possesses self-stabilizing characteristics. Our approach enables assemblies containing hundreds of tiles to be built, while the shaking approach is inherently limited to a few tens of tiles. Our results indicate that one of the primary limitations of mechanical, agitation-based TBSA approaches, instability, might be overcome by employing a swarm of free-running, sensorless mobile robots, herein represented by passive tiles at the macroscopic scale.
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