This paper addresses a Multi-Agent Collective Construction (MACC) problem
that aims to build a three-dimensional structure comprised of cubic blocks. We
use cube-shaped robots that can carry one cubic block at a time, and move
forward, reverse, left, and right to an adjacent cell of the same height or
climb up and down one cube height. To construct structures taller than one
cube, the robots must build supporting stairs made of blocks and remove the
stairs once the structure is built. Conventional techniques solve for the
entire structure at once and quickly become intractable for larger workspaces
and complex structures, especially in a multi-agent setting. To this end, we
present a decomposition algorithm that computes valid substructures based on
intrinsic structural dependencies. We use Mixed Integer Linear Programming
(MILP) to solve for each of these substructures and then aggregate the
solutions to construct the entire structure. Extensive testing on 200 randomly
generated structures shows an order of magnitude improvement in the solution
computation time compared to an MILP approach without decomposition.
Additionally, compared to Reinforcement Learning (RL) based and
heuristics-based approaches drawn from the literature, our solution indicates
orders of magnitude improvement in the number of pick-up and drop-off actions
required to construct a structure. Furthermore, we leverage the independence
between substructures to detect which sub-structures can be built in parallel.
With this parallelization technique, we illustrate a further improvement in the
number of time steps required to complete building the structure. This work is
a step towards applying multi-agent collective construction for real-world
structures by significantly reducing solution computation time with a bounded
increase in the number of time steps required to build the structure.Comment: Presented at the Multi-agent Path Finding Workshop at AAAI 202