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.

翻译：在结构化多智能体运输系统中，智能体通常必须遵循预定路径，使得空间重新规划不可取或不可能。本文通过优化路径点通过时间来解决路径约束下的多智能体协调问题，同时保持每个智能体分配的路径点顺序和标称路径分配。一个可微的替代轨迹模型将路径点时间映射为平滑位置曲线，并捕获一阶跟踪延迟，通过在任务时域稠密时间网格上评估基于距离的惩罚项来实现成对安全性编码。由此产生的非线性和非凸速度调度问题使用不精确投影交替方向乘子法（ADMM）求解，该算法结合了结构化时间更新与基于梯度的碰撞校正步骤，并避免了显式的整数排序变量。在随机交叉、瓶颈和基于图的网络场景上的数值实验表明，所提方法能够在多种拥堵程度下计算出可行且时间高效的调度方案，并在测试的瓶颈案例中实现了比代表性分层基准方法更短的任务完成时间。