SHARP: A Risk-Constrained Transformer with Closed-Form CVaR Safety Masks for Multi-Robot Task Allocation in Human-Shared Warehouses

Modern fulfillment centers share floor space with human workers, making warehouse multi-robot task allocation a safety-critical problem. We propose SHARP (Safe Heterogeneous Allocation with Risk Prediction), a Transformer-based constrained reinforcement-learning framework with a closed-form deployment-time safety mask. Under a Gaussian pedestrian belief and fixed closest-approach directions, the mask uses Bonferroni-allocated per-pair CVaR scores; a nonnegative mask score implies a conservative trajectory-level chance constraint under the stated assumptions. We also present an idealized primal–dual surrogate analysis, without claiming global convergence for the nonconvex Transformer/PPO implementation. Expanded experiments use ten training seeds per learned method and deterministic final-checkpoint evaluation on twenty independently generated held-out instances. No statistically significant difference between SHARP and Lagrangian-PPO was detected in any of the four scenarios. The held-out analysis further reveals late-training instability and severe over-conservatism in the dense S40_high scenario. These findings position SHARP as an auditable geometric filtering mechanism, while identifying conservatism and training stability as important limitations for deployment.