Multi-Agent Path Planning via Compatible Encounter-Space Allocation in Crowded Spaces Dynamically Occupied by Work Activities

Lifelong multiagent path planning on construction floors must accommodate continually changing goals and work occupancy. Existing planners can update paths and timing online, but work motion space coupling changes the spatial basis of unfinished encounters, while rerouting affects later encounters. Planning must therefore construct and maintain local encounter possibility. We propose Width based Planning with Compatible Encounter Space Allocation (WP), which constructs shared passage relationships from actual encounter demands and real time widths. Shared channels, ordered anchors, and urgency based updates coordinate successive encounters while retaining individual greedy motion between them. A necessary and sufficient width condition for fixed-point position exchange and a necessary directional condition for composite exchange provide geometric grounds for channel construction and encounter relocation. In crowded floor computational experiments, WP maintained route continuation after occupancy changes and enabled multi agent clearing, with infrequent, brief near stops. Complete run comparisons with four methods showed 25.2% to 52.2% more mean goal arrivals than the best baseline at each configuration of 5 to 10 agents, with lower mean computation time than the rolling horizon K_CBS adaptation. The contribution is a planning principle that constructs and continuously maintains local passage relationships from real time space, unifying shared spatial allocation and conditional local clearing to extend lifelong planning to work motion space coupling.