Two robots must install 352 screws into a 2.4m × 6m timber slab. The adhesive curing time is fixed — if a screw isn't driven within the window, the bond fails. The robots share the same workspace. They cannot occupy the same space at the same time.
The scheduling framework (arXiv:2603.20577) solves this by organizing tasks into levels — spatiotemporally disjoint sets where no two tasks in the same level can produce a collision. Robots execute all tasks within a level in parallel, then synchronize at a barrier before advancing to the next level. Collision avoidance isn't computed during execution; it's guaranteed by construction of the level structure.
The result is 108 subroutines completed under tight adhesive deadlines. The computational scaling is steady with problem size, unlike monolithic scheduling approaches that grow combinatorially.
The key insight is the barrier mechanism. Rather than continuously monitoring both robots' positions and replanning when conflicts arise, the system pre-computes which tasks are safe to execute simultaneously. The barrier is a synchronization point — both robots must finish their current level before either enters the next. This trades real-time flexibility for construction-time safety.
It's the scheduling equivalent of traffic signals vs. roundabouts. Signals (barriers) introduce waiting time but guarantee no collisions by temporal separation. Roundabouts (continuous monitoring) are more efficient on average but require constant negotiation. When the cost of collision is a failed adhesive bond and a ruined structural element, the signal wins.
The construction industry needs this. Timber prefabrication is growing, adhesive windows are non-negotiable, and the robots are already faster than humans. The bottleneck isn't speed — it's coordination.