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.
Figures & tables
Fig. 1: Overview of the proposed two-stage auction-plus-OCP framework with collision avoidance refinement and event-triggered rescheduling.
Fig. 2: Bicycle Model for AMR.
Event
Trigger
Action
Robot fault
Robot i unavailable
Re-auction σi unstarted
Priority task
New task tnew
Auction tnew
Energy dev.
∣Eact−Epred∣/Epred>δ
Re-auction deviant robot
TABLE I: Rescheduling Event Types
Fig. 3: Fleet trajectory for 4 AMRs and 50 tasks on a clustered layout.
Fleet
Energy
vs. B1
vs. B2
vs. B3
Size
(kJ)
Nearest
Short-path
Dist. Auc.
2
1.18
−3.3±1.8
+17.9±2.4
−4.1±1.2
5
2.45
+2.7±2.1
+10.3±1.9
−4.0±1.4
10
3.82
+10.3±2.6
+9.2±2.2
−3.9±1.1
15
4.96
+23.7±3.1
+11.6±2.5
−2.7±0.9
20
5.71
+25.4±3.4
+9.2±2.0
−2.6±0.8
TABLE II: Fleet Energy Savings (%)
Friction Range
r
Gap (%)
Bid Acc.
Winner
Uniform ( μ=0.02 )
0.98
+3.7±3.2
89%
Distance
μ∈[0.015,0.03]
0.93
+2.5±2.9
87%
Distance
μ∈[0.01,0.04]
0.84
+0.7±4.4
88%
Tie
μ∈[0.005,0.06]
0.75
−2.1±6.3
91%
Energy
μ∈[0.005,0.08]
0.74
−2.4±6.6
92%
Energy
TABLE III: Energy vs. Distance Bids Under Friction Heterogeneity
Tasks ( m )
Auction (ms)
OCP (ms)
Total (ms)
10
1.7
48.3
52.1
20
6.3
124.7
136.8
50
43.3
387.2
448.9
100
405.2
1241.6
1699.1
TABLE IV: Computation Time Breakdown ( n=10 )
Disruption
Mean
Max
Tasks
Overhead
Type
(ms)
(ms)
Reassgn.
vs. Cold (%)
Robot fault
4.2
7.8
6.3
+8.2
Priority task
7.1
9.0
1.0
+3.1
Energy deviation
3.5
6.2
3.8
+5.7
Combined
6.7
7.3
5.1
+6.9
Overall
5.6
9.0
4.1
+6.0
TABLE V: Rescheduling Performance by Disruption Type