A MILP-Based Solution to Multi-Agent Motion Planning and Collision Avoidance in Constrained Environments

We propose a mixed-integer linear program (MILP) for multi-agent motion planning that embeds Polytopic Action-based Motion Planning (PAAMP) into a sequence-then-solve pipeline. Region sequences confine each agent to adjacent convex polytopes, while a big-M hyperplane model enforces inter-agent separation. Collision constraints are applied only to agents sharing or neighboring a region, which reduces binary variables exponentially compared with naive formulations. An L1 path-length-plus-acceleration cost yields smooth trajectories. We prove finite-time convergence and demonstrate on representative multi-agent scenarios with obstacles that our formulation produces collision-free trajectories an order of magnitude faster than an unstructured MILP baseline.