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

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.

Figures (11)

• Figure 1: Illustration of the piecewise linear segment trajectory and associated notations.
• Figure 2: Comparison of an ideal piecewise-constant command, a second-order velocity-loop response ($\omega=10~\mathrm{rad/s}$), and the proposed sigmoid-based approximation. The approximation captures both smooth transitions and tracking latency.
• Figure 3: Trajectories for the co-directional random crossing scenario. Agents traverse a central congested area toward opposing goals, with random perturbations added to waypoints for environmental stochasticity.
• Figure 4: Results for the co-directional scenario. (Top) Velocity profiles showing smooth adjustments for conflict resolution. (Bottom) Inter-agent distance trajectories maintaining the required safety boundary $d_{\rm safe}$.
• Figure 5: Example trajectories for the counter-directional random crossing scenario with $K \in \{3,7,11\}$. Each agent traverses 10 waypoints from its initial position to a goal located approximately opposite the workspace, with small random perturbations added to the goal and intermediate waypoints.