Collision-Free Velocity Scheduling for Multi-Agent Systems on Predefined Routes via Inexact-Projection ADMM

TL;DR

This paper presents a novel inexact-projection ADMM algorithm for collision-free velocity scheduling in multi-agent systems constrained to predefined routes, optimizing waypoint timings while ensuring safety and efficiency.

Contribution

It introduces a differentiable surrogate trajectory model and an ADMM-based optimization method that avoids explicit sequencing, improving scheduling feasibility and efficiency in complex scenarios.

Findings

Computes feasible, collision-free schedules across various congestion levels.

Achieves shorter mission times than hierarchical baselines in bottleneck scenarios.

Demonstrates effectiveness on random-crossing, bottleneck, and graph-based networks.

Abstract

In structured multi-agent transportation systems, agents often must follow predefined routes, making spatial rerouting undesirable or impossible. This paper addresses route-constrained multi-agent coordination by optimizing waypoint passage times while preserving each agent's assigned waypoint order and nominal route assignment. A differentiable surrogate trajectory model maps waypoint timings to smooth position profiles and captures first-order tracking lag, enabling pairwise safety to be encoded through distance-based penalties evaluated on a dense temporal grid spanning the mission horizon. The resulting nonlinear and nonconvex velocity-scheduling problem is solved using an inexact-projection Alternating Direction Method of Multipliers (ADMM) algorithm that combines structured timing updates with gradient-based collision-correction steps and avoids explicit integer sequencing variables. Numerical experiments on random-crossing, bottleneck, and graph-based network scenarios show that the proposed method computes feasible and time-efficient schedules across a range of congestion levels and yields shorter mission completion times than a representative hierarchical baseline in the tested bottleneck cases.