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This paper addresses a Multi-Agent Collective Construction (MACC) problemthat aims to build a three-dimensional structure comprised of cubic blocks. Weuse cube-shaped robots that can carry one cubic block at a time, and moveforward, reverse, left, and right to an adjacent cell of the same height orclimb up and down one cube height. To construct structures taller than onecube, the robots must build supporting stairs made of blocks and remove thestairs once the structure is built. Conventional techniques solve for theentire structure at once and quickly become intractable for larger workspacesand complex structures, especially in a multi-agent setting. To this end, wepresent a decomposition algorithm that computes valid substructures based onintrinsic structural dependencies. We use Mixed Integer Linear Programming(MILP) to solve for each of these substructures and then aggregate thesolutions to construct the entire structure. Extensive testing on 200 randomlygenerated structures shows an order of magnitude improvement in the solutioncomputation time compared to an MILP approach without decomposition.Additionally, compared to Reinforcement Learning (RL) based andheuristics-based approaches drawn from the literature, our solution indicatesorders of magnitude improvement in the number of pick-up and drop-off actionsrequired to construct a structure. Furthermore, we leverage the independencebetween substructures to detect which sub-structures can be built in parallel.With this parallelization technique, we illustrate a further improvement in thenumber of time steps required to complete building the structure. This work isa step towards applying multi-agent collective construction for real-worldstructures by significantly reducing solution computation time with a boundedincrease in the number of time steps required to build the structure.

Multi-agent Collective Construction using 3D Decomposition