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

arXiv: https://arxiv.org/abs/2506.21982 · HTML: https://mlsanity.com/paper/2506.21982/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2025.

## Built on by (most cited first, 1 of 1)

- [Simulation-Informed Diffusion for Decentralized Multi-robot Motion Planning](https://mlsanity.com/paper/2605.27697/) (2026)

## Abstract (arXiv)

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.