Auction-Based Task Allocation with Energy-Conscientious Trajectory Optimization for AMR Fleets

This paper presents a hierarchical two-stage framework for multi-robot task allocation and trajectory optimization in asymmetric task spaces: (1) a sequential auction allocates tasks using closed-form bid functions, and (2) each robot independently solves an optimal control problem for energy-minimal trajectories with a physics-based battery model, followed by a collision avoidance refinement step using pairwise proximity penalties. Event-triggered warm-start rescheduling with bounded trigger frequency handles robot faults, priority arrivals, and energy deviations. Across 505 scenarios with 2-20 robots and up to 100 tasks on three factory layouts, both energy- and distance-based auction variants achieve 11.8% average energy savings over nearest-task allocation, with rescheduling latency under 10 ms. The central finding is that bid-metric performance is regime-dependent: in uniform workspaces, distance bids outperform energy bids by 3.5% (p < 0.05, Wilcoxon) because a 15.7% closed-form approximation error degrades bid ranking accuracy to 87%; however, when workspace friction heterogeneity is sufficient (r < 0.85 energy-distance correlation), a zone-aware energy bid outperforms distance bids by 2-2.4%. These results provide practitioner guidance: use distance bids in near-uniform terrain and energy-aware bids when friction variation is significant.