Collaborative Planning for UAV-UGV Teams under Operational Constraints via Masked Error-bounded Neuro-Symbolic Diffusion

Collaborative planning under operational constraints is essential for heterogeneous robot teams in large-scale missions. Unmanned Aerial Vehicles (UAVs) provide rapid area coverage but are limited by onboard energy, while Unmanned Ground Vehicles (UGVs) can serve as mobile recharging stations yet are constrained by road-network traversability. Effective collaboration must enforce operational constraints during execution while enabling parallel, coordinated actions. Masked Diffusion Models (MDMs) have shown promise through token unmasking but have two key limitations: entropy-guided scheduling assumes distributional alignment and reliance on differentiable constraints for diffusion-time optimization. We propose Masked Error-bounded Neuro-Symbolic Diffusion (MEND), which formulates collaborative planning as a conditional masked generative process to generate context-aware action sequences for UAV-UGV teams. MEND introduces a neuro-symbolic diffusion paradigm that constrains conditional masked diffusion policies at execution by reweighting the learned action distribution with a logic-induced admissibility indicator, thereby enforcing compliance with operational constraints. MEND introduces an error-bounded inference scheduling at execution that constructs the unmasking schedule by selecting positions with minimal predictive entropy over the constraint-aware action distribution, enhancing collaborative planning optimality under operational constraints. Extensive experimental results in simulation, on real-world maps, and with physical robot teams demonstrate that MEND advances UAV-UGV collaborative planning under operational constraints.